A composite ply failure model based on continuum damage mechanics
Composite Structures
65
3-4
347-355
2004
10.1016/j.compstruct.2003.11.010
A material model including the failure behaviour is derived for a thin unidirectional (UD) composite ply. The model is derived within a thermodynamic framework and the failure behaviour is modelled using continuum damage mechanics. The following features describe the model: (i) The ply is assumed to be in a plane state of stress. (ii) Three damage variables associated with the stress in the fibre-, transverse and shear directions, respectively, are used. (iii) The plastic behaviour of the matrix material is modelled. (iv) The difference in the material response in tensile and compressive loading is modelled. (v) Rate dependent behavior of plasticity and damage (i.e. strength) is modelled. ?? 2003 Elsevier Ltd. All rights reserved.
Composite materials; Continuum damage mechanics
Notched response of non-crimp fabric thin-ply laminates
Composites Science and Technology
79
97-114
2013
10.1016/j.compscitech.2013.02.001
Analysis methods to predict the open-hole tensile and compressive response of thin-ply non-crimp fabric laminates are investigated in this paper. The point- and average-stress models and the Finite Fracture Mechanics model are used. It is shown that all models predict with reasonable accuracy the observed size effects in both tension and compression. The Finite Fracture Mechanics model, which requires two material properties (the unnotched strength and the fracture toughness) and does not need calibration from a baseline specimen, is used to predict the notched response of thin-ply non-crimp fabric laminates and of typical aerospace grade laminates based on unidirectional pre-impregnated plies. No substantial differences in notch sensitivity and inherent material/geometry brittleness is predicted. © 2013 Elsevier Ltd.
Damage-mechanics analysis of matrix cracking in cross-ply CFRP laminates under thermal fatigue
Composites Science and Technology
61
12
1735-1742
2001
10.1016/S0266-3538(01)00077-X
Microscopic damage development in high-temperature CFRP, AS4/PEEK cross-ply laminates under thermal cycling has been investigated. Two types of laminate configurations were tested to discuss the effect of ply thickness. Matrix cracks initiated in both 0 and 90?? plies and the number of cracks increased as the number of cycles increased. The number of cracks in the stable growth region were twice as great as in a 90?? ply. To discuss these experimental results, a damage-mechanics analysis was used to evaluate the energy-release rate associated with cracking and thermal residual stress in cracked ply. It was clear that a modified Paris law approach is effective for thin plies and an average-stress approach is effective for thick plies. ?? 2001 Published by Elsevier Science Ltd. All rights reserved.
Average stress; B. Matrix cracking; C. Damage mechanics; Energy release rate; Thermal fatigue
Large damage capability of non-crimp fabric thin-ply laminates
Composites Part A: Applied Science and Manufacturing
63
110-122
2014
10.1016/j.compositesa.2014.04.002
The residual strength of thin-ply non-crimp fabric laminates with large through-the-thickness cracks is investigated in this paper. Analysis methods such as the linear elastic fracture mechanics, inherent flaw, point-stress, average-stress and Finite Fracture Mechanics are used to predict large damage capability. Experiments show that thin-ply non-crimp fabric laminates exhibit high resistance to propagation of large cracks and a remarked crack-bridging effect. Due to the unsuitability of existing models to capture such bridging processes, large damage capability is systematically underestimated by the traditional analysis methods. By taking into account the R-curve of the material in the Finite Fracture Mechanics analysis good predictions of the notched response of laminated plates with large through-penetration damage are obtained using only independently measured material properties; in addition, the Finite Fracture Mechanics model does not require fitting parameters or complex finite element analyses. © 2014 Elsevier Ltd. All rights reserved.
A. Laminates; B. Stress concentrations; C. Analytical modelling; D. Mechanical testing
Pseudo-ductility and damage suppression in thin ply {CFRP} angle-ply laminates
Composites Part A: Applied Science and Manufacturing
69
64-71
2015
http://dx.doi.org/10.1016/j.compositesa.2014.11.004
Abstract Composite materials usage is limited by linear elasticity and the sudden, brittle failure they often exhibit. It is possible to mitigate this inherent limitation and enlarge the design space by using thin plies. This paper presents an experimental study, using a spread tow thin ply carbon–epoxy prepreg material with a cured ply thickness of 0.03 mm, which shows that highly non-linear stress–strain behaviour can be achieved with angle-ply laminates, whilst suppressing the damage mechanisms that normally cause their premature failure. Several angles between 15° and 45° are investigated in a [ ± θ 5 ] s layup. It is shown that for all angles delaminations are suppressed, allowing considerable pseudo-ductile strains to develop. Significant fibre rotations take place, permitted by matrix plasticity, leading to a post-yield stiffening of the laminate, as the fibres reorient towards the direction of loading.
A. Laminates; B. Delamination; C. Laminate mechanics; D. Mechanical testing
Experimental studies of thin-ply laminated composites
Composites Science and Technology
67
996-1008
2007
10.1016/j.compscitech.2006.06.008
A new processing method was developed for spreading fiber tows to make thin-ply laminated composites. The present method with a constant airflow through sagged fiber filaments can efficiently spread the thick tows without damaging any fibers. This method is robust and easy compared with other available thin-ply methods. The thin plies of thickness less than one-third of the conventional plies can easily be made with the tow-spreading technology. Experiments were performed to evaluate the performance of tow-spread, thin-ply laminated composites. To study the thickness effect of the laminated composites, the test specimens were made with the same material and the same spread tows, but with dispersed and grouped laminations of the plies. Uniaxial tension static and fatigue loadings were applied on both unnotched and open-hole specimens. Impact and compression-after-impact tests were also conducted. From stress-strain curves, acoustic emission counts, X-ray photos, c-scan images and observation of damage modes of failed specimens, it was observed that the thin-ply laminated composites can suppress the microcracking, delamination and splitting damage for static, fatigue and impact loadings without special resin and/or 3-D reinforcements. Therefore, the laminate design can be simplified by using higher strain allowable without a progressive failure analysis. ?? 2006 Elsevier Ltd. All rights reserved.
B. Impact behavior; B. Static and fatigue; C. Notch; C. Transverse cracking and delamination; Tow-spreading technology
Experimental characterization of strength and damage resistance properties of thin-ply carbon fiber/toughened epoxy laminates
Composite Structures
82
3
382-389
2008
10.1016/j.compstruct.2007.01.015
Composite laminates manufactured from thin-ply prepregs are expected to have superior damage resistance properties compared to those from standard prepregs. Although the use of thin-ply prepregs leads to increase in manufacturing cost, the damage resistance properties against matrix cracking and delamination increase. This study investigates several strength properties as well as the damage resistance properties of carbon fiber/toughened epoxy composite laminates for the applicability of thin-ply prepregs to aircraft structures. Specifically, compressive strengths of open hole laminates (OHC strength) and laminates after impact loadings (CAI strength) are investigated by the comparison of results between laminates manufactured from the thin-ply prepregs and the standard prepregs. It is shown that laminates using thin-ply prepregs have superior strength compared to those using standard prepregs. It is expected that the design limit of composite aircraft structures increase by using thin-ply prepregs.
compression; laminates; strength; thin-ply prepreg
Damage characterization in thin-ply composite laminates under out-of-plane transverse loadings
Composite Structures
93
1
49-57
2010
10.1016/j.compstruct.2010.06.016
Composite laminates with thin-ply layers are expected to exhibit superior damage resistance to the standard composite laminates. This study investigated the damage characteristics of carbon fiber/toughened epoxy thin-ply laminates subjected to transverse loadings. Quasi-isotropic laminates were prepared using both standard prepregs and thin-ply prepregs in order to examine the effect of ply thickness on the damage accumulation processes. Clear difference on damage accumulation process between standard laminates and thin-ply laminates was identified; fiber fractures were susceptible to formation in thin-ply laminates. Finally, the reason of the difference on damage process was investigated using finite element analyses, and it was clarified that the accumulated delamination position has a significant effect on the fiber fractures during the indentation.
Delamination; Fiber failure; Laminates; Thin-ply prepreg; Transverse loading
Demonstration of pseudo-ductility in high performance glass/epoxy composites by hybridisation with thin-ply carbon prepreg
Composites Part A: Applied Science and Manufacturing
52
23-30
2013
10.1016/j.compositesa.2013.04.006
A new approach and material architecture is presented in order to overcome the inherent brittleness and unstable failure characteristic of conventional high performance composites. The concept is the use of thin-ply hybrid laminates. Fracture mechanics calculations were carried out to determine the critical carbon layer thickness for stable pull-out in a three layer unidirectional hybrid laminate, which can provide a pseudo-ductile failure. Unidirectional hybrid composites were fabricated by sandwiching various numbers of thin carbon prepreg plies between standard thickness glass prepreg plies and tested in tension. Specimens with one and two plies of thin carbon prepreg produced pseudo-ductile failure, whereas ones with three and four plies failed with unstable delamination. An explanation of the different failure modes is given in terms of the different energy release rates for delamination in various specimens. The observed damage characteristics agreed well with the expectations according to the estimated critical carbon layer thickness.
A. Carbon fibre; A. Glass fibres; B. Delamination; Hybrid
Thin ply composites: Experimental characterization and modeling of size-effects
Composites Science and Technology
101
121-132
2014
10.1016/j.compscitech.2014.06.027
Thin-ply composites are rapidly gaining interest in the composite industry, not only because of the larger design possibilities that they offer, but also because of positive size effects that have been shown to improve performance in various loading conditions [1]. In this work, carbon fiber-epoxy composites of different ply thicknesses (30-300g/m2 fiber areal weight) were produced from the same batch of Toray M40JB fiber and NorthTPT TP80ep matrix to study the influence of ply thickness on the ultimate strength and on the onset of damage in lamina, laminates and components. Uniaxial tension, open-hole compression and open-hole tensile fatigue tests on quasi isotropic [45°/90°/-45°/0°]ns laminates showed very significant improvements regarding the on-set of damage, and in some cases ultimate strength, when decreasing the ply thickness. These performance improvements are the result of major changes in the damage progression and failure modes of the laminates caused by a systematic delay or near suppression of transverse cracking and delamination growth in thin-ply composites. On the component level, thin-ply laminates enabled a marked improvement for bolted-joint bearing, especially in hot-wet conditions. Under impact, the 30μm thin ply laminate exhibited a quasi-brittle failure with extensive translaminar cracking while a ply thickness of 100μm was found as optimum to minimize the projected damage area. Ply thickness scaling of transverse and in-plane shear strength was identified based on classical laminate theory and unnotched tensile tests on quasi-isotropic specimens. The empirical scaling was found to follow a linear trend over a range of ply thicknesses from 30 to 250μm. Due to the near suppression of delamination, the strength of thin-ply composites could then be modeled more effectively than thick ply composites using classical laminate theory or standard multilayer shell modeling. © 2014 Elsevier Ltd.
A. Laminate; B. Fatigue; B. Impact behavior; B. Strength; Size-effects
Influence of woven ply degradation on fatigue crack growth in thin notched composites under tensile loading
International Journal of Fatigue
32
1
60-65
2010
10.1016/j.ijfatigue.2009.01.010
This paper deals with the fatigue of the through-the-thickness crack propagation in thin notched composite laminates made of two glass woven plies. It highlights the different crack growths between warp and weft directions of the woven ply. Experimental results show a decrease of the crack growth rate per cycle with the increase of the crack initiation time. Moreover, it has been shown that it is necessary to take into account the fatigue damage of the woven plies in term of loss of rigidity in the initiation phase. The fatigue crack growth rates are then quantified using Paris law type equations and linear elastic fracture mechanics (LEFM). © 2009 Elsevier Ltd. All rights reserved.
Crack propagation; Fatigue; Linear elastic fracture mechanics; Woven fabric composite
Experimental Evaluation of the Damage Growth Restraining in 90.DEG. Layer of Thin-ply CFRP Cross-ply Laminates
Journal of the Japan Society for Composite Materials
37
4
121-129
2011
10.6089/jscm.37.121
Abstract In this paper, a systematic and detailed observation was made of the crack extension behavior of thin 90° layers of cross-ply carbon fiber reinforced plastics (CFRP) laminates. The effect of ply thickness on the crack propagation mechanism was discussed with respect to the energy release rate of the intralaminar transverse crack, calculated using finite element analysis. In a laminate with a 40 ?m-thick-ply, the crack gradually extended with increasing strain. Conversely, extreme crack extension was found at around 1.0% strain in a laminate with a standard thick ply. Based on the numerical analysis, the crack suppression effect is verified using a thin ply; the effect is apparently caused by a decrease in the energy release rate at the crack tip in the thin layer.\nAbstract In this paper, a systematic and detailed observation was made of the crack extension behavior of thin 90° layers of cross-ply carbon fiber reinforced plastics (CFRP) laminates. The effect of ply thickness on the crack propagation mechanism was discussed with respect to the energy release rate of the intralaminar transverse crack, calculated using finite element analysis. In a laminate with a 40 ?m-thick-ply, the crack gradually extended with increasing strain. Conversely, extreme crack extension was found at around 1.0% strain in a laminate with a standard thick ply. Based on the numerical analysis, the crack suppression effect is verified using a thin ply; the effect is apparently caused by a decrease in the energy release rate at the crack tip in the thin layer.
Thin Ply Composites
Structures, Structural Dynamics & Materials Conference
April
1-5
2005
Large tows of carbon fiber can be spread by a simple, non-intrusive process from which plies down to 1/6 of the conventional 5-mil thickness can be obtained. Laminates made from such plies showed remarkable resistance to micro cracking, delamination and splitting under both static and fatigue loading. With thick-thin ply hybrids, superior performance, lower cost and lower minimum gage can all lead to applications not feasible with 5-mil thick plies. I.
Damage occurrence at edges of non-crimp-fabric thin-ply laminates under off-axis uniaxial loading
Composites Science and Technology
98
44-50
2014
10.1016/j.compscitech.2014.04.014
Thin-ply based laminates are a promising development in composite materials and are expected in the near future to outperform conventional laminates in mechanical performance. A rational design with thin plies requires understanding the effect of ply thickness on each damage mechanism. This paper presents an experimental investigation into damage occurrence in a quasi-isotropic laminate made from thin-ply, bi-axial, Non-Crimp-Fabric (NCF), under different off-axis uniaxial loadings. The NCF layers are positioned through the laminate thickness creating two regions, namely THICK and THIN (with and without ply clustering). Then, the onset and progress of three damage mechanisms (transverse matrix cracking, matrix crack induced delamination and free-edge delamination) for both regions are analyzed by monitoring the specimen’s free-edge. The results show that the critical region where damage occurs is that with ply clustering (THICK), whereas delamination originating from matrix cracks or free edge effects are delayed or even suppressed in the THIN region.
A. Carbon fibres; A. Thin-ply laminates; B. Delamination; B. Matrix cracking
On the Mechanics of Thin-Walled Laminated Composite Beams
Journal of Composite Materials
27
8
806-829
1993
10.1177/002199839302700804
A formal engineering approach of the mechanics of thin-walled laminated beanls based on kinenlatic assumptions consistent with Timoshenko beam theory is pre- sented. Thin-walled composite beams with open or closed cross section subjected to bend- ing and axial load are considered. A variational formulation is employed to obtain a com- prehensive description of the structural response. Beam stiffness coefficients.. which account for the cross section geometry and for the material anisotropy. are obtained. An explicit expression for the static shear correction factor of thin-walled composite beanls is derived from energy equivalence. A numerical example involving a laminated I-beam is used to demonstrate the capability of the nlodel for predicting displacements and ply stresses.
Restraining Effects of Transverse Cracking in 90 Layer of Thin-ply CFRP Cross-ply Laminates
Proc of 7th AsianAustralasian Conference on Composite MaterialACCM7
WED-SE25-06 (CD-ROM)
2010
It is generally known that the crack initiation strain is increased with decreasing of ply thickness of 90olayer. However, the mechanism has not been well clarified in the case of very thin thickness as thin as 40μm. A systematic detailed experimental observation was made on the damage growth behavior in 90olayer of cross-ply CFRP laminates. As a result of observation, the damage mode and the damage growth behavior were different depending on the ply thickness of 90olayer. It was clarified that crack extension was restrained and its speed became slower as ply thickness thinner. Moreover, it was shown that crack opening displacement became smaller as ply thickness became thinner, and the energy release rate at the crack tip became smaller based on FEM calculations.
cross ply laminates; damage growth; energy release rate; thin ply; transverse crack
Thin Film Mechanics
Harvard University
2004
1. Origin of residual stresses in thin films Epitaxial stresses Thermal stresses Intrinsic or growth stresses - surface stress effects - crystallite coalescence - grain growth - vacancy annihilation - effect of impurities - effect of phase transformations - stresses in sputtered films 2. Deformation processes in thin films Grain boundary diffusion controlled creep Dislocation mechanisms
Improvement of tensile properties of CFRP composites under LEO space environment by applying MWNTs and thin-ply
Composites Part A: Applied Science and Manufacturing
42
6
694-701
2011
10.1016/j.compositesa.2011.02.011
Multi-wall carbon nanotube (MWNT) added carbon fiber reinforced plastics (CFRP) and thin-ply composites are suggested as solutions to improve resistance against low earth orbit (LEO) environment and mechanical properties. Accelerated ground simulation experiments were performed for CFRP, MWNT reinforced CFRP, thin-ply CFRP and MWNT reinforced thin-ply CFRP. The used ground simulation facility can simulate high vacuum, atomic oxygen, ultraviolet (UV) light and thermal cycling simultaneously. The aging experiment was performed for 20 h. After the aging experiment, total mass loss (TML) and tensile properties were measured. As a result, by applying thin-ply thickness and MWNT fillers, the tensile strength was improved at ground conditions. Under an LEO space environment, while thin-ply composites cannot relieve the degradation rate, the composites with MWNT can do so. Highly improved tensile strength was observed by simultaneously applying the thin-ply techniques and MWNT under both LEO aged and LEO non-aged conditions. © 2011 Elsevier Ltd. All rights reserved.
A. Particle-reinforcement; A. Polymer-matrix composites (PMCs); B. Mechanical properties; D. Mechanical testing
An exact solution for the bending of thin and thick cross-ply laminated beams
Composite Structures
37
2
195-203
1997
10.1016/S0263-8223(97)80012-8
The state-space concept in conjunction with the Jordan canonical form is presented to solve the governing equations for the bending of cross-ply laminated composite beams. The classical, first-order, second-order and third-order theories have been used in the analysis. Exact solutions have been developed for symmetric and antisymmetric cross-ply beams with arbitrary boundary conditions subjected to arbitrary loadings. Several sets of numerical results are presented to show the deflected curve of the beam, the effect of shear deformation, the number of layers and the orthotropicity ratio on the static response of composite beams. Â 1997 Elsevier Science Ltd.
Effect of ply-thickness on impact damage morphology in CFRP laminates
Journal of Reinforced Plastics and Composites
30
13
1097-1106
2011
10.1177/0731684411416532
In this article, the effects of ply thickness on the impact damage mechanisms in CFRP laminates are discussed based on the experimental observations. Quasi-isotropic CFRP laminates were manufactured using 38 μm thick thin-ply prepregs. Impact damage inside the laminates was evaluated by using ultrasonic scanning and sectional fractography. Compression after impact strength was also evaluated. Thin-ply laminates showed 23% higher strength than standard-ply laminates. Transverse cracks decreased drastically in thin-ply laminates, and localized delamination was largely extended. Based on the discussions in our previous study and the literature, the specific ply thickness without drastic crack propagation appears to be less than or equal to 40 μm. Therefore, the thin laminates showed few and localized transverse cracks and delamination was largely propagated in the midplane. © The Author(s) 2011.
On the relation between the mode I fracture toughness of a composite laminate and that of a 0?? ply: Analytical model and experimental validation
Engineering Fracture Mechanics
78
13
2535-2546
2011
10.1016/j.engfracmech.2011.06.013
This paper proposes a simple model to predict the fracture toughness of multidirectional carbon-epoxy composite laminates using the fracture toughness of the 0?? ply. The model is based on a combination of Linear-Elastic Fracture Mechanics and lamination theory, and uses as material properties the ply elastic properties and the fracture toughness of the 0?? ply measured in compact tension test specimens. A good correlation is obtained by comparing the model predictions and experimental data obtained in center-cracked specimens manufactured using different lay-ups and materials. ?? 2011 Elsevier Ltd.
Fracture Mechanics; Polymer-matrix composites; Toughness testing
Analysis of Progressive Matrix Cracking In Composite Laminates II. First Ply Failure
Journal of Composite Materials
21
4
309-329
1987
10.1177/002199838702100402
The mechanics of transverse cracking in an elastic fibrous composite ply is explored for the case of low crack density. Cracks are assumed to initiate from a nucleus created by localized fiber debonding and matrix cracking.
A ply scale non-local fibre rupture criterion for CFRP woven ply laminated structures
Composite Structures
80
3
321-326
2007
10.1016/j.compstruct.2006.05.021
We propose here a model to describe the rupture of woven ply laminated structures. The validity scope of this model depends on the 'diffused damage' phase up to the first intra-laminar macro-crack only (first ply failure model). The model is based on a previous continuum damage approach [Hochard C, Aubourg PA, Charles JP. Modelling of the mechanical behaviour of woven fabric CFRP laminates up to failure. Compos Sci Technol 2001;61:221-30] and a new non-local fibre rupture criterion. This non-local criterion uses a ply scale characteristic volume of ply thickness and in plane area depending on the meso-structure of the ply. In the case of the balanced woven ply studied here, a simple circular area is chosen and identified on a test showing a stress gradient. The local shear damage and inelastic strain evolution laws and the non-local fibre rupture criterion have been integrated in Abaqus. Numerical results compared to tests for woven ply laminated structures show the efficiency of the proposed approach. © 2006 Elsevier Ltd. All rights reserved.
Damage mechanics; Non-local criterion; Size effect; Structural computation; Woven laminate
PREDICTIONS OF DEFLECTION AND FIRST-PLY FAILURE LOAD OF THIN LAMINATED COMPOSITE PLATES VIA THE FINITE ELEMENT APPROACH
International Journal of Solids and Structures
33
3
375-398
1996
10.1016/0020-7683(95)00042-9
A nonlinear finite element method, which is based on the von Karman-Mindlin plate theory and the principle of minimum total potential energy, is used to study the deformation and first-ply failure of thin laminated composite plates. The load displacement curves of a number of laminated composite plates are determined using the proposed finite element method. Stresses obtained fr'om the linear and nonlinear finite element analyses are used to determine, respectively, the linear and nonlinear first-ply failure loads of the laminated plates based on several phenomenological failure criteria. The accuracy of the finite element results is then verified by comparison with the available experimental data. It has been found that good agreement between the finite element and experimental load strain curves before first-ply failure is observed. If the reduction in plate stiffness induced by failure of plies is taken into account in the finite element model, close agreement between finite element and experimental load displacement curves from first-ply failure up to total failure may be obtained. Regarding the prediction of the first-ply failure load, it has been found that some of the phenomenological failure criteria may yield results of consistent accuracy for the laminated composite plates under consideration. Nevertheless, accurate prediction of the failure process after first-ply failure is still intractable. Hence, for reliability assurance further research on failure analysis of laminated composite plates subject to transverse loading is needed.
Evolution of ply cracks in multidirectional composite laminates
International Journal of Solids and Structures
47
10
1338-1349
2010
10.1016/j.ijsolstr.2010.01.016
This paper treats evolution of ply cracks in multidirectional composite laminates subjected to a quasi-static tensile load in the longitudinal direction. Starting with pre-existing ply cracks in off-axis plies, the formation of additional cracks is analyzed by an energy-based approach. A critical laminate energy parameter associated with formation of these cracks is defined and is evaluated using experimental data for a reference cross-ply laminate. The modeling approach requires crack surface displacements, which are calculated by a three-dimensional finite element (3-D FE) analysis performed on a suitable representative volume of the given cracked laminate. The model predictions agree well with experimental data for [0 / ± θ4 / 01 / 2]s and [0 / 90 / ∓ 45]s laminates. A parametric study is conducted to evaluate effects of ply thickness and ply stacking sequence on damage evolution in [0m / 90n / ∓ θp]s laminates. © 2010 Elsevier Ltd. All rights reserved.
Computational simulation; Damage evolution; Damage mechanics; Multidirectional composites; Ply cracking
Cured Shape of Cross-Ply Composite Thin Shells
Journal of Composite Materials
37
20
1801-1820
2003
10.1177/002199803035184
For a composite laminated plate, it has been found that classical laminate theory (CLT) can not always predict the final cured shape correctly and geometric nonlinearity must be considered. For composite laminated shells, experiments show that the cured shape depends on stacking sequence, radius, thickness, and size. This paper investigates the cured shape of several cross-ply composite shells. The cured shape of a cross-ply shell is generally cylindrical. A model is established to predict the cured shape. The model is based on the Rayleigh-Ritz energy method and considers geometric nonlinearity. Modeling and experiment show that, for certain stacking sequences, the generator of the cured shape may be orthogonal to the original generator, while other stacking sequences can lead to deeper or shallower cured shapes. The predictions of the model are very close to the results of FEM analysis and experiment. This model can be used as a guide in the manufacture of unsymmetric cross-ply laminates.
cross-ply composite shell; cured shape; fem analysis; rayleigh-ritz method
First ply failure study of thin composite conoidal shells subjected to uniformly distributed load
Thin-Walled Structures
76
1-7
2014
10.1016/j.tws.2013.10.021
The civil engineers often need to cover large column free open spaces with thin shell structures. The doubly curved shells are characteristically stiff and the ruled surfaces are easy to fabricate. The aesthetically pleasing conoidal shells satisfy both these criteria and are preferred by structural engineers. The engineers now look out for strong but lightweight materials and as a result the laminated composites have evolved. The first ply failure is very important issue for laminated composites. Such studies for plates are reported but similar work on thin shells is very scanty. This paper is aimed to fulfill this lacuna. © 2013 Published by Elsevier Ltd.
Fiber failure; Finite element method; First ply failure; Graphite epoxy; Matrix failure; Thin conoidal shells
A criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates
Composites Science and Technology
64
13-14
2239-2250
2004
10.1016/j.compscitech.2004.03.008
A variational approach is used to model the behaviour of composite cross-ply laminates damaged by transverse, longitudinal cracking and delamination. An energetic criterion is proposed. It is based on the strain energy release rate associated with each of the three damage modes. The first part of this paper is concerned with the modelling of the transverse and longitudinal cracking. In the second part, a model for studying delamination damage is presented. The numerical results show that these models provide a consistent level of accuracy for a variety of thin laminate material systems and configurations, with various combinations of delaminations and matrix cracks. In this paper several numerical simulations meant to describe initiation for each damage mode are proposed. The estimation of damage modes contributions is achieved for two thin laminates in order to predict the evolution of damage mode transition. © 2004 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites; B. Matrix cracking; C. Delamination; Damage mechanics; D. Life prediction
Intra/inter-ply shear behaviors of continuous fiber reinforced thermoplastic composites in thermoforming processes
Composite Structures
93
7
1692-1703
2011
10.1016/j.compstruct.2011.01.002
The thermoforming of continuous fiber reinforced thermoplastic (CFRTP) composite panels generally involves significant in-plane shear deformation. In the present work, the in-plane shear behavior of woven thermoplastic composites (Carbon/Polyphenylene Sulfide) over a range of processing temperatures is studied by bias-test experiments at different velocities. The experimental data of force versus displacement and force versus shear strain are presented for different extension velocities and temperatures. A thermo-visco-elastic model for numerical simulations of woven thermoplastic composite forming is proposed considering the influences of temperature and of strain rate. We applied a large displacement three-dimensional cohesive element with eight nodes which has been used for crack analysis in fracture mechanics by other authors, to investigate the inter-ply shear mechanism of woven thermoplastic composites. Applying three-dimensional cohesive elements, multi-plies forming simulations are performed to show inter-ply slip behaviors at different temperatures. The proposed models can be useful to predict from the properties of reinforcement and resin the intra/inter-ply shear behaviors of woven thermoplastic composites at high temperatures if experimental characterization of composite laminate behaviors is difficult to conduct.
Cohesive element; Continuous fiber reinforced thermoplastic composit; In-plane shear; Inter-ply slip; Thermoforming process
Analysis of stiffness reduction of cracked cross-ply laminates
Engineering Fracture Mechanics
25
5-6
771-778
1986
10.1016/0013-7944(86)90040-8
Stiffness reduction of cracked $[$0\^o"m90\^o"n$]$"s laminates is analyzed by variational methods on the basis of the principle of minimum complementary energy. For this purpose admissible stress systems are constructed which satisfy equilibrium...
Formation and growth of 90° ply fatigue cracks in carbon/epoxy laminates
Composites Science and Technology
40
3
307-324
1991
10.1016/0266-3538(91)90087-6
This study focuses on fatigue mechanisms of matrix cracking in carbon/epoxy cross-ply laminates. Tension-tension fatigue tests were conducted on two equivalent lay-ups, whose only difference consists in the stacking sequence and in the resulting 90° ply thickness. Transverse ply crack onset, accumulation and growth were measured. The 90° ply thickness was shown to have a considerable influence on the crack distribution in the transverse ply and on the fatigue crack growth rates. A fracture mechanics analysis for the strain energy release rate associated with 90° ply matrix crack formation and growth has been developed and compared with experimental results.
Clarification of Impact Damage Morphology in Thin-Ply CFRP Laminate
Proc of 11th Japan International SAMPE Symposium November 2527
AM-1-2
2009
When impact from dropping tools or hail is applied to CFRP laminates, internal damage such as delamination or transverse cracks, which is difficult to confirm from outside of structure, easily occurs. Because these internal damages decrease compressive strength drastically, compressive strength after impact (CAI strength) is one of the critical properties in aerospace structures. On the other hand, it is reported that transverse cracks is suppressed in thin-ply composite laminate which is composed of thin prepreg of dozens micrometer in thickness. Additionally, it is suggested that static tensile, static compressive and CAI strengths are improved in thin-ply composite laminate. Especially in CAI test, it is reported that impact damage morphology in thin-ply laminate is different from normal thickness laminate. However, damage morphology of thin-ply laminate was observed mainly by non-destructive methods, and the effect of ply thickness on internal damage morphology of impacted laminate has not been conducted. In this study, three-dimensional damage distribution model is constructed by both non-destructive inspection and optical observation in multiple cross-sections. Based on the precise observations, the effect of thinning of ply thickness on the internal damage morphology is clarified.
cfrp; internal damage; thin ply
Effects of layup angle and ply thickness on matrix crack interaction in contiguous plies of composite laminates
Composites Part A: Applied Science and Manufacturing
36
9
1229-1235
2005
10.1016/j.compositesa.2005.02.002
Matrix microcracking behaviors in constrained plies adjacent to a cracked ply are highlighted. Quasi-static tension tests of 0/θ/90s and 0/θ2/90s laminates with θ=30, 45 and 60 were conducted in order to investigate effects of the ply thickness and the intersecting angle of the cracked plies on the crack development in the adjacent plies. Matrix cracks developed along the fiber direction were the dominant damages observed in 30 plies of 0/θ2/90s laminates, whereas a high density form of matrix microcracking was mainly observed in θ plies of the other laminates. The difference of the matrix cracking behaviors in the adjacent plies among laminate configuration is characterized by calculating energy release rates associated with θ ply crack growth in the presence of 90 ply cracks using finite element analysis. It is clarified that microcracking in plies adjacent to a cracked ply is susceptible to formation in the cases of thin θ ply thickness and small intersecting angles of the cracked plies.
a; b; c; d; fea; finite element analysis; pmcs; polymer matrix composites; radiography; transverse cracking
Advanced Mechanics of Composite Materials
Advanced Mechanics of Composite Materials
57
57-132
2007
10.1016/B978-008045372-9/50003-8
The aim of this chapter is to describe the mechanics of a unidirectional ply. A ply or lamina is the most basic element of a composite material, a basic layer of unidirectional fibers in a matrix, produced when a unidirectional tape impregnated with resin is placed onto the surface of the tool, thus providing the shape of a composite part. In an actual ply, the fibers are arbitrarily distributed. The most important property of advanced composite materials is associated with the very high strength of a unidirectional ply, accompanied with relatively low density. This advantage of the material is provided mainly by the fibers. A ply can experience five types of elementary loading: tension along the fibers, tension across the fibers, in-plane shear, compression along the fibers, and compression across the fibers. Mechanical properties of composite materials depend on the processing method and parameters. To obtain the adequate material characteristics that can be used for analysis of structural elements, the specimens should be fabricated by the same processes that are used to manufacture the structural elements. This chapter also discusses the properties of unidirectional plies reinforced with fibers of a certain type–glass, carbon, and aramid. In hybrid composites, the plies can include fibers of two or may be more types. Hybrid composites provide wider opportunities to control material stiffness, strength, and cost. A promising application of these materials is associated with the thermostable structures, which do not change their dimensions under heating or cooling.
A synergistic damage mechanics approach to mechanical response of composite laminates with ply cracks
Journal of Composite Materials
47
20-21
2475-2501
2012
10.1177/0021998312466121
We treat selected test cases in the third world wide failure exercise by the approach described as synergistic damage mechanics. This approach utilizes micromechanics and continuum damage mechanics to predict the overall mechanical response of composite laminates with ply cracking in multiple orientations. The material constants needed in the continuum damage mechanic formulation are calculated from stiffness property changes incurred in a reference laminate. For other laminate configurations, the stiffness changes are derived using a relative constraint parameter which is calculated from the constraint on the opening displacement of ply cracks within the given cracked laminate evaluated numerically by a finite element analysis of appropriately constructed representative unit cell. The number density of ply cracks (cracks per unit length normal to the crack planes) under quasi-static loading is calculated by an energy-based approach. Finally, the stress-strain response of a laminate is determined by combining stiffness property changes and evolution of crack number density.
Damage modelling of the elementary ply for laminated composites
Composites Science and Technology
43
3
257-267
1992
10.1016/0266-3538(92)90097-M
In this paper, fibrous composite laminate damage is modelled at the elementary-ply scale. Damage mechanics is used to describe the matrix microcracking and fibre/matrix debonding. Damage variables are defined and associated with the material stiffness reduction. In order to take anelastic strains induced by damage into account, a plasticity model is built up. The behaviour differences between tension and compression in the fiber direction are treated. The model leads to a laminate failure criterion. The model-identification procedure is precisely detailed. It consists in performing three tension tests and one compression test on a laminate whose reinforcement directions are conveniently chosen. Some examples are developed in order to show the ability of such a model to describe ply behaviour effects on the mechanical and rupture behaviour of laminates.
Evaluation of a damage-mechanics approach to the modelling of notched strength in KFRP and GRP cross-ply laminates
Composites Science and Technology
62
2
255-263
2002
10.1016/S0266-3538(01)00201-9
quasi-isotropic layups [4], of a matrix, of The picture resembles the static observed in split length (normalised by the width, 2a
A non-local criterion for modelling unbalanced woven ply laminates with stress concentrations
Composite Structures
92
7
1574-1580
2010
10.1016/j.compstruct.2009.11.019
A non-local ply scale criterion [Hochard C, Lahellec N. Bordreuil C. A ply scale non-local fibre rupture criterion for CFRP woven ply laminated structures. Compos Struct 2007;80:321-26] was previously developed for predicting the failure of balanced woven ply structures with stress concentrations. This nonlocal criterion was based on the mean values determined over a Fracture Characteristic Volume (FCV) corresponding to a cylinder with a circular area and the same thickness as the ply. This non-local approach along with a ply scale continuum damage behavioural model was implemented in the ABAQUS Finite Element Code. The behavioural model was developed from a classical Continuum Damage Mechanics (CDM) model [Ladeveze P. A damage computational method for composite structures. Comput Struct 1992;44:79-87]. In the present study, this approach was extended to the case of unbalanced woven ply. The FCV approach and the CDM behavioural model are presented and comparisons are made between the experimental data and the modelling predictions obtained on plates with open holes, notches and saw cuts. (C) 2009 Elsevier Ltd. All rights reserved.
behavior; composite structures; damage mechanics; failure; finite element analysis; laminate; rupture; stress concentrations
Exploration of the potential for pseudo-ductility in thin ply {CFRP} angle-ply laminates via an analytical method
Composites Science and Technology
112
8-15
2015
http://dx.doi.org/10.1016/j.compscitech.2015.02.019
Abstract Thin ply laminates have shown much promise in recent times in terms of their exciting damage suppression characteristics. Utilisation of this damage suppression in carbon–epoxy angle-ply laminates has been shown experimentally to yield a highly non-linear stress–strain response. This paper presents an analytical modelling method that incorporates matrix plasticity and reorientation of the fibres into a classical laminate analysis for the prediction of the in-plane response of thin ply angle-ply laminates. It is shown that the method can successfully predict the non-linear behaviour of [ ± θ 5 ] s laminates with values of θ between 15° and 45°. The main characteristics of the stress–strain curve, such as the initial largely linear region, yield point and stiffening before final failure, are all well captured. The modelling has allowed straightforward identification of a particular fibre angle that exhibits strength in excess of 900 MPa, strain to failure of more than 3.5% and a promising pseudo-ductile strain of 1.2%.
A. Laminate; B. Non-linear behaviour; B. Plastic deformation; C. Laminate theory; C. Modelling
Damage analysis of pseudo-ductile thin-ply UD hybrid composites – A new analytical method
Composites Part A: Applied Science and Manufacturing
69
83-93
2015
10.1016/j.compositesa.2014.11.006
A new simple analytical approach for predicting all possible damage modes of Uni-Directional (UD) hybrid composites and their stress–strain response in tensile loading is proposed. To do so, the required stress level for the damage modes (fragmentation, delamination and final failure) are assessed separately. The damage process of the UD hybrid can then be predicted based on the order of the required stress for each damage mode. Using the developed analytical method, a new series of standard-thickness glass/thin-ply carbon hybrid composites was tested and a very good pseudo-ductile tensile response with 1.0% pseudo-ductile strain and no load drop until final failure was achieved. The yield stress value for the best tested layup was more than 1130MPa. The proposed analytical method is simple, very fast to run and it gives accurate results that can be used for designing thin-ply UD hybrid laminates with the desired tensile response and for conducting further parametric studies.
A. Hybrid; B. Delamination; B. Fragmentation; C. Analytical modelling
Analysis of first ply failure in composite laminates
Engineering Fracture Mechanics
25
5-6
763-770
1986
10.1016/0013-7944(86)90039-1
The mechanics of transverse cracking in an elastic fibrous composite ply is explored for the case of low crack density. Cracks are assumed to initiate from a nucleus created by localized fiber debonding and matrix cracking. It is found that...
Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria
Engineering Fracture Mechanics
75
9
2651-2665
2008
10.1016/j.engfracmech.2007.03.007
Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [02/902]s, [0/902]s, and [0/904]s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions. © 2007 Elsevier Ltd. All rights reserved.
Cracking; Cross-ply laminate; Polymer-matrix composites; Stiffness reduction
The formation and effect of outer-ply microcracks in cross-ply laminates: A variational approach
Engineering Fracture Mechanics
41
2
203-221
1992
10.1016/0013-7944(92)90181-D
The microcracking process in laminates which have outer-ply 90° plies (e.g.[90m/0n]s) has some important differences from the microcracking process in laminates which lack outer-ply 90° plies (e.g.[0n/90m]s). Foremost among the differences is the characteristic damage state. [90m/0n]s laminates form antisymmetric or staggered microcracks while [0n/90m]s laminates form symmetric microcracks. To explain observed differences, this paper presents a variational mechanics analysis of the stresses and the energy release rate in a [[90m/0n]s laminate having staggered microcracks. The new analysis and a previous analysis of [0m/90n]s laminates are used to assess the effect of laminate structure on the mechanical properties and failure properties of cross-ply laminates. The findings are as follows. (1) A given level of microcracking damage causes a greater amount of degradation in mechanical properties in [[90m/0n]s laminates than in the corresponding [0n/90m]s laminates. (2) Although [[90m/0n]s laminates will initiate microcracks at lower loads, the corresponding [0n/90m]s laminates will develop more microcracks after continued loading. (3) A bending effect present in [90m/0n]s laminates but not in [0n/90m]s laminates promotes mode I delamination in [90m/0n]s laminates.
Residual Stress Assessment in Thin Angle Ply Tubes
Applied Composite Materials
10
3
169-188
2003
10.1023/A:1023990507666
This preliminary study aims to investigate the residual stresses developed in hot cured thin-walled angle-ply filament wound tubes made of E-glass/epoxy, Kevlar/epoxy and carbon/epoxy materials. The residual stresses were estimated from change in geometry of these tubes when axially slitted at ambient temperature. Three basic deformation modes; namely opening up, closing-in and twisting, were observed and these depended on the winding angle, material and wall thickness. The residual stresses were also determined from hoop and axial strain gauges mounted on both the inner and outer surfaces at various locations around the tube. The stresses were compared with theoretical prediction based upon a linear thermo-elastic analysis. Both the predicted and measured values were found to increase with increasing hoop stiffness but there was a large discrepancy between the predicted and measured data, reaching a factor of 5 for the thinnest case. When compared with predicted failure stresses, the experimentally determined stresses were some 15% of the computed compressive strength.
angle ply; carbon; glass composite rings; kevlar; residual thermal stress release; slitting; twisting.
Finite deformation mechanics in buckled thin films on compliant supports.
Proceedings of the National Academy of Sciences of the United States of America
104
40
15607-15612
2007
10.1073/pnas.0702927104
We present detailed experimental and theoretical studies of the mechanics of thin buckled films on compliant substrates. In particular, accurate measurements of the wavelengths and amplitudes in structures that consist of thin, single-crystal ribbons of silicon covalently bonded to elastomeric substrates of poly(dimethylsiloxane) reveal responses that include wavelengths that change in an approximately linear fashion with strain in the substrate, for all values of strain above the critical strain for buckling. Theoretical reexamination of this system yields analytical models that can explain these and other experimental observations at a quantitative level. We show that the resulting mechanics has many features in common with that of a simple accordion bellows. These results have relevance to the many emerging applications of controlled buckling structures in stretchable electronics, microelectromechanical systems, thin-film metrology, optical devices, and others.
Damage mechanics of composite materials: II— a damaged-based notched strength model
Composites Science and Technology
39
4
303-326
1990
10.1016/0266-3538(90)90078-J
A new model of the notched strength of graphite-epoxy composites has been developed. In this second paper of a four-part series, a finite element model has been used to simulate observed subcritical notch tip cracking patterns in cross-ply laminates. The model produced maps displaying tensile stress contours in the 0° ply, and it was found that all specimens failed when the maximum tensile stress in the 0° ply exceeded the strength of that ply. The strength of the 0° ply in the vicinity of the notch tip was determined independently using a Weibull statistical strength model.
Thin Film Mechanics Bulging and Stretching
Mechanical Engineering
October
1999
Page 1. THIN FILM MECHANICS – BULGING AND STRETCHING Ph.D Dissertation Mechanical Engineering University of Vermont Wolfgang Sauter October 2000 Page 2. ii Abstract Thin films have experienced revolutionary development in recent years. ...
A synergistic damage-mechanics analysis of transverse cracking [????/904]s laminates
Composites Science and Technology
61
5
657-665
2001
10.1016/S0266-3538(01)00005-7
The deformational response of [????/904]s laminates under longitudinal tensile loading is treated by a synergistic approach that combines continuum damage mechanics (CDM) and micromechanics. The constraint of ???? plies on transverse cracks in 90?? plies is represented by a crack-opening displacement (COD) parameter in the CDM model and is expressed in terms of the ply properties and ply thickness ratios on the basis of a finite-element calculation. A methodology is proposed for predicting the laminate stiffness variations with crack density and applied strain (or stress) for various values of ply orientation ?? and is found to give good results. ?? 2001 Elsevier Science Ltd. All rights reserved.
Composite materials; Damage evolution; Damage mechanics; Stiffness degradation; Transverse cracking
Predicting the effect of non-uniform ply cracking on the thermoelastic properties of cross-ply laminates
Composites Science and Technology
62
14
1841-1856
2002
10.1016/S0266-3538(02)00091-X
When damage in the form of ply cracks in laminated composites arises during loading, the cracks are in general non-uniformly spaced due to property and geometrical inhomogeneities in the laminate. The objective of this paper is to establish the validity of an approximation that can be made when analysing the stress and displacement distributions in multiple-ply cross-ply laminates having arrays of non-uniformly spaced ply cracks. The approximation assumes that the stress and displacement distributions in the region between the planes containing neighbouring ply cracks are the same as those arising in an identical laminate having uniformly spaced ply cracks of the same separation. The validity of this approach is established by comparing predictions of the thermo-elastic constants of the cracked laminates generated by two distinct stress-transfer models. The first model, that generates the approximations for non-uniform ply crack spacings, is based on a stress-transfer analysis that was specifically developed for uniformly spaced ply cracks while the second model accurately takes account of the effects of the non-uniformity of ply crack spacing on the stress distribution. It is shown, following a comprehensive analysis of various laminate types and crack patterns for both carbon fibre and glass fibre systems, that the approximation suggested provides highly accurate predictions of effective thermo-elastic constants over a wide range of laminate parameter variations.
C. Anisotropy; C. Damage mechanics; C. Elastic properties; C. Laminates; C. Transverse cracking
Analysis of coupled ply damage and delamination failure processes in ceramic matrix composites
Acta Materialia
61
10
3535-3548
2013
10.1016/j.actamat.2013.02.027
Damage and failure processes in two relatively complex ceramic matrix composite sub-elements are studied using both experiments and computational modeling. The sub-elements, representative of turbine blade-to-disk attachment region, are analyzed and tested under uniaxial loading at room temperature. The computational models consider-in a coupled way-both the nonlinear behavior of plies due to intra-laminar ply damage mechanism as well as the interlaminar delamination mechanism at the ply interfaces. Analyses and experiments indicate that delamination is the dominant failure mode and ply damage processes have a little effect on delamination initiation and growth. However, the ultimate failure of the sub-elements is due to ply damage mechanism, the evolution of which is strongly affected by the delamination process. The spatial locations of major delamination cracks and ply failure regions, as predicted by the models, are in good agreement with the experiments. In addition, a reasonable quantitative agreement between analyses results and experimental data is observed. ?? 2013 United Technologies Corporation. Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved.
Ceramic matrix composites; Cohesive zone finite elements; Continuum damage mechanics; Delamination; Ply damage
Application of a phenomenological viscoplasticity model to the stress relaxation behavior of unidirectional and angle-ply CFRP laminates at high temperature
Composites Part A: Applied Science and Manufacturing
35
817-826
2004
10.1016/j.compositesa.2004.01.010
High-temperature stress relaxation behavior of symmetric angle-ply laminates made of unidirectional T800H/3631 carbon/epoxy composite is examined at relatively high strain levels. Stress relaxation tests are performed at 100 ??C for 5 h on plain coupon specimens of three types of angle-ply laminates [??30]3S, [??45]3S and [??60] 3S under displacement controlled conditions. For each ply orientation, the stress relaxation tests are carried out at three different strain levels. Stress relaxation phenomena clearly appear in all kinds of angle-ply laminate. The average stress in the angle-ply laminates rapidly relaxes to approach a steady-state value associated with the strain sustained. The rate of stress relaxation in the angle-ply laminates substantially diminishes in the tested time range. Stress relaxation simulation of the angle-ply laminates is performed using the classical laminated plate theory and a phenomenological viscoplasticity model for individual plies. Material constants involved in the ply viscoplasticity model are identified on the basis of the off-axis creep behavior for a unidirectional laminate based on the same kind of carbon/epoxy prepregs. Excellent agreements between the predicted and observed results are obtained by taking into account a local recovery of total strain in the gauge-length part of specimens as well as a fiber rotation induced by deformation. The successful application of the ply viscoplasticity model confirms that the stress relaxation behavior is consistent with the creep behavior in the same composite system. ?? 2004 Elsevier Ltd. All rights reserved.
Angle-ply laminates; A. Polymer-matrix composites (PMCs); B. High-temperature properties; B. Stress relaxation; C. Laminate mechanics
On the Transverse Cracking and Longitudinal Splitting Behaviour of Glass and Carbon Fibre Reinforced Epoxy Cross Ply Laminates and the Effect of Poisson and Thermally Generated Strain
Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences
366
1727
599-623
1979
10.2307/79822
90 degrees cross ply epoxy resin laminates reinforced with either glass or carbon fibres were tested in tension as a function of ply thickness. Transverse cracking of the 90 degrees plies and longitudinal splitting of the 0 degrees plies has been observed and the experimental strains recorded. Energetics arguments have been presented which explain this behaviour and permit experimental ply cracking strains to be estimated. The effects of thermal strains generated during fabrication and Poisson generated strains have been assessed and included in the energetics calculations. The thermal strains were determined and found to be large in carbon fibre/epoxy laminates compared with glass fibre/epoxy laminates. Poisson effects are significant in the glass fibre/epoxy laminates due to the higher failure strain of these composites. The micro mechanics of failure were also studied and fibre debonding identified as a source of 90 degrees ply failure.
Effect of transverse cracks on the mechanical properties of angle-ply composites laminates
Theoretical and Applied Fracture Mechanics
45
1
72-78
2006
10.1016/j.tafmec.2005.11.003
A modified shear lag analysis, taking into account the notion of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in [????n/90m]S angle-ply laminated composites. Effects of number of 90?? layers and number of ???? layers on the laminate stiffness have also been studied. The present results represent well the dependence of the degradation of mechanical properties on the fibre orientation angle of the outer layers, the number of cracked cross-ply layers and the number of uncracked outer ???? layers in the laminate. ?? 2005 Elsevier Ltd. All rights reserved.
Angle-ply laminates; Fibre angle; Stiffness reduction; Stress perturbation function; Transverse cracks
Transverse cracking of cross-ply laminates: A computational micromechanics perspective
Composites Science and Technology
110
196-204
2015
10.1016/j.compscitech.2015.02.008
Transverse cracking in cross-ply carbon/epoxy and glass/epoxy laminates in tension is analyzed by means of computational micromechanics. Longitudinal plies were modeled as homogenized, anisotropic elastic solids while the actual fiber distribution was included in the transverse plies. The mechanical response was obtained by the finite element analysis of a long representative volume element of the laminate. Damage in the transverse plies was triggered by interface decohesion and matrix cracking. The simulation strategy was applied to study the influence of ply thickness on the critical stress for the cracking of the transverse plies and on the evolution of crack density in 02/90n/2s laminates, with n=1, 2, 4 and 8. It was found that the transverse ply strength corresponding to the initiation and propagation of a through-thickness crack was independent of the ply thickness and that the transverse strength of carbon/epoxy laminates was 35% higher than that of the glass fiber counterparts. In addition, the mechanisms of crack initiation and propagation through the thickness as well as of multiple matrix cracking were ascertained and the stiffness reduction in the 90° ply as a function of crack density was computed as a function of the ply thickness.
A. polymer-matrix composites (PMC’s); C. Computational mechanics; C. Finite element analysis; C. Transverse cracking
Mechanics of precisely controlled thin film buckling on elastomeric substrate
Applied Physics Letters
90
13
174-176
2007
10.1063/1.2719027
Stretchable electronics has many important and emerging applications. Sun et al. [Nature Nanotech.1, 201 (2006)] recently demonstrated stretchable electronics based on precisely controlled buckle geometries in GaAs and Si nanoribbons on elastomeric substrates. A nonlinear buckling model is presented in this letter to study the mechanics of this type of thin film/substrate system. An analytical solution is obtained for the buckling geometry (wavelength and amplitude) and the maximum strain in buckled thin film. This solution agrees very well with the experiments, and shows explicitly how buckling can significantly reduce the thin film strain to achieve the system stretchability.
Biaxial mechanics and inter-lamellar shearing of stem-cell seeded electrospun angle-ply laminates for annulus fibrosus tissue engineering
Journal of Orthopaedic Research
31
6
864-870
2013
10.1002/jor.22312
The annulus fibrosus (AF) of the intervertebral disk plays a critical role in vertebral load transmission that is heavily dependent on the microscale structure and composition of the tissue. With degeneration, both structure and composition are compromised, resulting in a loss of AF mechanical function. Numerous tissue engineering strategies have addressed the issue of AF degeneration, but few have focused on recapitulation of AF microstructure and function. One approach that allows for generation of engineered AF with appropriate (+/-)30° lamellar microstructure is the use of aligned electrospun scaffolds seeded with mesenchymal stem cells (MSCs) and assembled into angle-ply laminates (APL). Previous work indicates that opposing lamellar orientation is necessary for development of near native uniaxial tensile properties. However, most native AF tensile loads are applied biaxially, as the disk is subjected to multi-axial loads and is constrained by its attachments to the vertebral bodies. Thus, the objective of this study was to evaluate the biaxial mechanical response of engineered AF bilayers, and to determine the importance of opposing lamellar structure under this loading regime. Opposing bilayers, which replicate native AF structure, showed a significantly higher modulus in both testing directions compared to parallel bilayers, and reached ∼60% of native AF biaxial properties. Associated with this increase in biaxial properties, significantly less shear, and significantly higher stretch in the fiber direction, was observed. These results provide additional insight into native tissue structure-function relationships, as well as new benchmarks for engineering functional AF tissue constructs.
annulus fibrosus; electrospinning; fibrocartilage; mesenchymal stem cells; tissue engineering
Mechanics of Fracture in Two-Ply Laminates
Rubber chemistry and technology
52
1
96-109
1979
This paper describes a study of fracture in two-ply rubber—cord composites subjected to repeated tensile deformations. Under the conditions used, failure occurs predominantly because of the growth of cracks between the plies. A fracture mechanics approach enables the rate of crack growth to be predicted in terms of the elastic properties and dimensions of the laminate, the magnitude of the deformations and the basic crack growth characteristics of the ply rubber. The theory indicates the growth rate to be determined by the strain energy released from the central region of the laminate and to be independent of crack length once this exceeds a small value. The latter feature has been verified experimentally and the magnitudes of the observed crack growth rates are in reasonable agreement with those predicted for various deformation cycles.
Tapered hygro-thermally curvature-stable laminates with non-standard ply orientations
Composites Part A: Applied Science and Manufacturing
44
140-148
2013
10.1016/j.compositesa.2012.08.023
Stacking sequence configurations for hygro-thermally curvature-stable (HTCS) laminates have recently been identified in nine unique classes of coupled laminate with standard ply angle orientations +45??, -45??, 0?? and 90??. All arise from the judicious re-alignment of the principal material axis of laminate classes with Bending-Twisting and/or Bending-Extension and Twisting-Shearing coupling; where off-axis material alignment of these parent classes gives rise to distinctly different mechanical coupling behaviour. However, for standard ply angle orientations, HTCS solutions were found in only 8-, 12-, 16- and 20-ply laminates. This article considers non-standard ply angle orientations +60??, -60??, 0?? and 90??, which lead to solutions in all ply number groupings for 10 plies and above, thus offering a possibility for ply terminations and hence tapered HTCS laminate designs. ?? 2012 Elsevier Ltd. All rights reserved.
A. Laminates; B. Thermomechanical; C. Laminate mechanics
Theoretical study on shape control of thin cross-ply laminates using piezoelectric actuators
Composite Structures
80
3
451-460
2007
10.1016/j.compstruct.2006.06.031
This paper investigates the application of a piezoelectric actuator to control deformation of thin unsymmetric cross-ply composite laminates. A theoretical model based on Rayleigh–Ritz principle is developed to predict laminate deformation and the effect of the piezoelectric actuator layer. Several stacking sequences are studied using the model. It is found that two stable shapes still exist for laminates with larger dimensions but the two shapes are not symmetric as in traditional cross-ply laminates. The bifurcation dimension increases when the thickness of piezoelectric layer increases. Laminate curvatures are in a perfectly linear relationship with an electric field applied to the piezoelectric actuator layer. Snap-through from one stable shape to the other can occur by applying an electric field. FEA results match model prediction fairly well. This model can be used as a guide to design piezocomposite laminates.
Cross-ply composite laminates; Cured shape; FEA; Piezoelectric actuator; Rayleigh–Ritz principle
Prospects in fracture mechanics of "engineering" laminates
Engineering Fracture Mechanics
72
899-908
2005
10.1016/j.engfracmech.2004.08.002
The test method development for inter-laminar fracture toughness testing of fibre-reinforced composites has yielded one international standard for Mode I opening loading of unidirectionally fibre-reinforced laminates so far. However, the bulk of composite materials in technical applications, summarily labelled "engineering laminates", mostly consists of laminates with optimised fibre-orientations, frequently varying from ply to ply, i.e., so-called multi-directional laminates. Increasingly, so-called "three-dimensional" laminates are also being developed and being put to use in engineering applications. The present paper explores some of the problems that arise when the standard Mode I test method is applied to engineering laminates in the form of cross-ply (0°/90°) lay-up or z-pin reinforced, three-dimensional composites. © 2004 Elsevier Ltd. All rights reserved.
Biaxial bending failure locus for woven-thin-ply carbon fibre reinforced plastic structures
Proc. 46th AIAA/ASME/ASCE/AHS/ASC Struct., …
April
1-8
2005
10.2514/6.2005-1811
This paper presents a study of the maximum biaxial curvatures that can be applied to woven-thin-ply carbon fibre reinforced plastic (CFRP) structures. A new test has been devised to impose biaxial curvatures; the test relies on the use of cylindrically curved specimens. Finite element analysis is used to show that the test is insensitive to the dimensions of the specimen and the boundary conditions.
Transverse cracking and delamination in cross-ply glass-fiber and carbon-fiber reinforced plastic laminates: Static and fatigue loading
Applied Mechanics Reviews
56
1
111-147
2003
10.1115/1.1519557
A review of developments and understanding of transverse cracking and delamination in cross-ply laminates is presented. First, experimental investigations reported in the literature for analyzing the development of transverse cracking are considered. Next, characteristics of different models for evaluating the stress distribution in the damaged laminates are developed. It is shown how these models associated with the statistical description of strength or energy released in the 90° plies make it possible to describe the development of transverse cracking in monotonic or fatigue loading. According to the nature of cross-ply laminates, transverse cracking is not, however, sufficient for describing the development of transverse cracks in 90° plies in the case of monotonic loading. In this case, the delamination process induced at transverse crack tips is to be considered for describing the experimental results. There are 108 references in this review article.
Modelling of splitting and delamination in notched cross-ply laminates
Composites Science and Technology
60
15
2849-2856
2000
10.1016/S0266-3538(00)00170-6
A finite-element approach has been developed for modelling the detailed damage development in notched composites. Separate elements are used for each ply, connected together with interface elements to allow delamination between the plies. Interface elements are also used to model splitting at the notch. The approach is applied to a cross-ply laminate with a centre crack loaded in tension, and the results compared with experimental measurements. The model accurately predicts the development of a narrow triangular delamination zone, and the extent of splitting as a function of applied tensile stress. The approach offers scope for improved simulation and understanding of the complex failure processes in notched composites. (C) 2000 Elsevier Science Ltd. All rights reserved.
composite-materials; damage mechanics; delamination; fatigue damage mechanics; finite-element analysis; fracture-mechanics; growth; hole; interface elements; modelling; notch; prediction; strength
Matrix cracking and delamination in laminated composites. Part I: Ply constitutive law, first ply failure and onset of delamination
Mechanics of Materials
43
169-185
2011
10.1016/j.mechmat.2010.12.003
Matrix cracking and delamination are the main initial forms of damage in advanced laminated composites manufactured by stacking unidirectional plies of fiber reinforced polymers. In this paper, the onset of matrix cracking is determined for in-plane stress states; in addition, delamination promoted by matrix cracks is analyzed. Taking into account that under in-plane shear stresses composite laminates show a non-linear response prior to the formation of a macro-crack, a plastic-damage model is proposed and implemented. The models predictions correlate well with published experimental data. © 2011 Elsevier Ltd. All rights reserved.
Constitutive behaviour; Energy release rate; Fiber-reinforced composite material; Fracture; Layered material
Mechanisms of internal damage and their effect on the behavior and properties of cross-ply composite laminates
International Applied Mechanics
38
6
641-657
2002
10.1023/A:1020456726805
This paper is a review of experimental and theoretical studies into the damage mechanisms in glass/epoxy and carbon/epoxy cross-ply composite laminates subjected to static or cyclic loading and their influence on the behavior and stiffness properties of such laminates. How the equivalent-constraint model is applied to the analysis of cross-ply laminates with transverse and longitudinal matrix cracks and crack-tip delaminations is shown and discussed.
Anticlastic Stability Modeling for Cross-ply Composites
Journal of Composite Materials
41
11
1325-1338
2006
10.1177/0021998306068073
A viable aspect of fiber-reinforced composites is their elastic tailoring ability. Anticlastic curvature is one example of elastic tailoring that occurs with an unsymmetric cross-ply layup. Residual stresses resulting from differences in coefficients of thermal expansion and elastic properties in each lamina can cause large out-of-plane deformations. In the case of thin unsymmetric cross-ply laminates under thermal curing load, a cylindrical shape is observed because of this inherent geometrical nonlinearity as opposed to the saddle shape that classical lamination theory predicts. In this article, a finite element approach, using ABAQUSTM, is implemented in order to predict the unsymmetric cross-ply laminate shapes under thermal curing stresses and understand the underlying limit point instability. Numerical results for curvatures of the predicted shapes are in agreement with published experimental and analytical data. The stability of the cylindrical laminates is also investigated. Depending on the aspect ratio of the rectangular laminate, a cylindrical shape may snap-through from its current stable configuration to another stable cylindrical shape with a different curvature. In particular, both the critical aspect ratio where snap-through will cease to occur and the buckling load are reported.
cross-ply; elastically tailored composites; finite elements; laminates; snap-through; stability
Steady-state cracking and edge effects in thermo-mechanical transverse cracking of cross-ply laminates
Composites Science and Technology
58
98
1811-1825
1998
10.1016/S0266-3538(98)00047-5
Composites for space applications such as advanced satellites will require the use of new and/or improved materials so that more stringent dimensional stability requirements can be met. In this work, we study the effect of ply-level initiation of damage under loading and processing stresses and imposed thermal loading. In particular, included in the study is the prediction and demonstration of a condition of steady-state cracking and the temperature change and loading level necessary to create this damage state, thus leading to the possibility of a predetermined loading range over which layer cracking will not propagate. We also consider the influence of the free-edges on the initiation of layer transverse cracking and potential microcracking that may develop at the fiber/matrix interface. The condition of constrained edge cracking is demonstrated where cracks develop but do not propagate across the laminate. To accomplish these studies unidirectional composites and various cross-ply laminates of IM7/5250-4 (graphite/bismaleimide) were produced and characterized.
composites; free-edge; mechanics; steady-state cracking; transverse cracks
Fluid Mechanics
Image Rochester NY
6
1
539
1987
10.1007/b138775
Mjog god kennslubok. Agaet fyrir byrjendur sem og lengra komna
A micromechanical study on the effect of intra-ply properties on transverse shear fracture in fibre reinforced composites
Composites Part A: Applied Science and Manufacturing
42
9
1217-1228
2011
10.1016/j.compositesa.2011.05.004
A micromechanics damage model is presented which examines the influence of intra-ply properties on the transverse shear deformation of a carbon fibre/epoxy composite. It was found that while thermal residual stress influenced the initial location of damage in the microstructure, its influence on the overall shear response was less pronounced. The fibre-matrix interface strength was found to control transverse shear strength, while the interface fracture energy had marked effect on the strain to failure and the interaction of damage mechanisms during fracture. It was also found that regions of low fibre volume fraction, such as areas near the ply boundary, were more susceptible to yielding due to the lack of reinforcement in these regions. The micromechanical model developed shows similar behaviour to in situ experimental observations and could thus prove useful in determining optimum constituent properties allowing for increased interlaminar shear strength of fibre reinforced composite laminates. ?? 2011 Elsevier Ltd. All rights reserved.
A. Polymer matrix composite; B. Debonding; B. Residual/internal stress; C. Micro-mechanics
Analysis of multiple off-axis ply cracks in composite laminates
International Journal of Solids and Structures
45
16
4574-4589
2008
10.1016/j.ijsolstr.2008.04.004
This paper presents a synergistic methodology to analyze damage behavior in composite laminates with transverse matrix cracks in plies of multiple orientations. The approach combines the strengths of micro-damage mechanics (MDM) and continuum damage mechanics (CDM) in predicting the stiffness degradation due to presence of transverse cracks. The micromechanics is performed on a representative unit cell using a three-dimensional finite element analysis to calculate the crack opening displacement (COD) accounting for the influence of the surrounding plies, the so-called constraint effect. This information is then incorporated in the CDM formulation dealing with laminates containing cracks in different ply orientations through a 'constraint parameter'. In CDM, a separate damage mode is defined for each type of crack and the expressions for engineering moduli of the damaged laminate are derived in terms of crack density and the constraint parameter. The COD and stiffness degradation predictions agree well with published experimental data for [0 / ± θ4 / 01 / 2]s laminate configuration. To enable damage analysis of other configurations of [0m / ± θn / 0m / 2]s laminate, a parametric study of the CODs is performed and using the computations a master equation is developed. © 2008 Elsevier Ltd. All rights reserved.
Composite materials; Damage mechanics; Modeling; Multiple damage modes; Transverse cracking
Beam analysis of angle-ply laminate end-notched flexure specimens
Composites Science and Technology
58
12
1929-1938
1998
10.1016/S0266-3538(98)00018-9
Analysis and experiments on quasi-unidirectional and angle-ply laminate end-notched flexure specimens are presented. The analysis is based on laminated beam theory incorporating first-order shear deformation theory. Compliance and strain-energy release rate determined for relatively thin unidirectional and angle-ply laminate ENF specimens were in good agreement with a previous classical plate theory formulation. For thicker laminates, however, effects of shear deformation on the compliance of the ENF specimen become significant. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminate ENF specimens was conducted. Specifically, [0]6, [??30]5 and [??45]5 laminates with mid-plane delaminations were considered. Experimental compliance data agreed well with analytical predictions. The fracture toughness increased with increased angle ?? at the ???? interface. This is attributed to the fracture work associated with the debonding of transversely oriented fiber bundles in the quasi-unidirectional plies. The angle-ply laminates displayed more yarn debonding than the quasi-unidirectional laminate. For all laminates it was observed that the crack propagated in a non-uniform manner which is correlated with elastic coupling effects with cracked regions of the laminate beams.
Analysis; End-notched flexure specimen; Fracture; Glass/polyester laminates; Strain energy release rate; Test methods
Viscoelastic micromechanical modeling of free edge and time effects in glass fiber/epoxy cross-ply laminates
Composites Part A: Applied Science and …
33
399-409
2002
http://dx.doi.org/10.1016/S1359-835X(01)00112-9
A viscoelastic finite element analysis has been carried out to investigate the free edge and time effects in a [0/90]ns glass fiber/epoxy cross-ply laminate, subjected to mechanical loads. The analysis is based on a three-dimensional micromechanical model that predicts the stress/strain field at the fiber and matrix levels near the free edge surface of the cross-ply laminate. The epoxy matrix is represented by a nonlinear viscoelastic constitutive model. In addition, two different damage criteria for the matrix cracking and interface debonding have been introduced into the model, which were incorporated into the finite element analysis program, adina, through the user-defined subroutine. Damage initiation as well as damage growth in the cross-ply laminate is predicted by the present model. It is found that the edge effect is more dominant in the damage initiation process and its influence on the global properties of cross-ply laminate, is not significant. Under a constant load, it is possible for the damage to grow further due to the viscosity of the matrix and the stress/strain redistribution in the cross-ply laminate.
finite element analysis (FEA); micro-mechanics; polymer-matrix composites; viscoelastic behaviour
Analysis of thick isotropic and cross-ply laminated plates by radial basis functions and a Unified Formulation
Journal of Sound and Vibration
330
4
771-787
2011
10.1016/j.jsv.2010.08.037
In this paper, we combine Carrera's Unified Formulation and a radial basis function collocation technique for predicting the static deformations and free vibration behavior of thin and thick isotropic and cross-ply laminated plates. Through numerical experiments, the capability and efficiency of this collocation technique for static and vibration problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.
Mechanics of thin-film transistors and solar cells on flexible substrates
Solar Energy
80
6
687-693
2006
10.1016/j.solener.2005.10.010
When devices are fabricated on thin foil substrates, any mismatch strain in the device structure makes the work piece curve. Any change of the radius of curvature produces a change in the size of the work piece, and thereby misalignment between individual device layers. To achieve tight tolerances, changes of curvature must be minimized throughout the fabrication process. Amorphous silicon thin-film transistors and solar cells respond differently to externally applied tensile strain. The elastic deformation of the transistor is correlated with small increase in the electron mobility. When the tensile strain reaches ???0.34%, crack formation starts and causes an abrupt change in the transistor performance. The performance of solar cells, on the other hand, does not change for tensile strain up to ???0.7%. At larger strain the short-circuit current, open-circuit voltage, fill factor, and the efficiency gradually decrease. ?? 2005 Elsevier Ltd. All rights reserved.
Amorphous silicon; Flexible electronics; Solar cell; Thin-film transistor
Contact mechanics of a thin-walled capsule adhered onto a rigid planar substrate.
Medical & biological engineering & computing
39
5
605-608
2001
10.1007/BF02345154
A thin-walled capsule, modelled as an incompressible liquid droplet contained in a thin flexible membrane, was allowed to adhere onto a rigid substrate. The contact mechanics were formulated, based on linear elasticity, to portray quantitatively the relationships between osmotic inflation, contact area and angle, membrane stretching and adhesion strength. The predicted results shed light on fundamental adhesive contact mechanics in a cell-substrate system.
--adhesion; contact mechanics; osmosis
Energy criterion for modelling damage evolution in cross-ply composite laminates
Composites Science and Technology
68
12
2318-2324
2008
10.1016/j.compscitech.2007.09.014
The energy dissipated in cross-ply laminates during loading–unloading loops is obtained from stress–strain curves for cross-ply laminates and used in an energy based approach to predict the development of matrix cracking. The dissipated energy is correlated to the crack density growth data recorded for a reference laminate. The critical strain energy release rate, Gc obtained in this way is increasing with the applied strain. This phenomenon reflects the statistical nature of Gc distribution in the 90-layer: the first cracks (lower strain) develop in positions with lower fracture toughness. The obtained Gc data are in a good agreement with fracture toughness data obtained using LEFM based “compliance calibration” model in which the stiffness change with increasing strain is used. Finally, the matrix cracking development is successfully simulated using in the LEFM model, the data for critical strain energy release rate and an earlier derived stiffness–crack density relationship. It has been demonstrated that knowing the laminates geometry and measuring the laminate stiffness reduction with strain or (alternatively measuring the dissipated energy) the damage evolution may be simulated, thus reducing the necessity for optical observations to validation only.
A. Polymer–matrix composites (PMCs); B. Matrix cracking; C. Damage mechanics; C. Fracture mechanics; D. Raman spectroscopy
Fracture and damage mechanics modelling of thin-walled structures - An overview
Engineering Fracture Mechanics
76
1
5-43
2009
10.1016/j.engfracmech.2007.10.005
This paper reviews the most important current approaches for residual strength prediction of thin-walled structures. Crack driving force parameters such the linear elastic stress intensity factor and its plastic zone corrected extension for contained yielding conditions, the crack tip opening displacement ??\n 5, the crack tip opening angle CTOA, the cohesive zone model parameters, separation energy, critical tensile stress and critical separation and the parameters of the damage models of Gurson-Tvergaard-Needleman type are introduced and discussed with respect to their benefits and limitations for the simulation of plane and stiffened panels. In addition, specific aspects of modern non-integral and integral structures which pose a challenge are addressed. These comprise multi-site damage, crack deviation and branching, welding residual stresses, strength mismatch in material compounds and problems in bonded structures, such as delamination. A number of examples are provided to illustrate the potential of the various approaches. ?? 2007 Elsevier Ltd. All rights reserved.
Damage mechanics; Fracture mechanics; Residual strength; Stable crack extension; Thin-walled structures
Accurate free vibration analysis of completely free symmetric cross-ply rectangular laminated plates
Composite Structures
60
3
359-365
2003
10.1016/S0263-8223(02)00337-9
The method of superposition is exploited to obtain accurate analytical type solutions for resonant frequencies and mode shapes of completely free symmetric cross-ply laminated rectangular plates. Verification tests are performed by comparing computed eigenvalues with known eigenvalues for the special case of thin orthotropic plates. Results of an analytical study of the free vibration behaviour of a typical symmetric cross-ply laminated completely free plate are tabulated. These results provide valuable checkpoints against which future researchers can compare their findings. This appears to be the first analytical type free vibration solution made available for the completely free laminated plate of this type. ?? 2003 Elsevier Science Ltd. All rights reserved.
Cross-ply; Eigenvalues; Free edges; Laminae; Laminated; Mode shapes; Plate; Superposition; Vibration
Damage modeling of the elementary ply for laminated composites
Composites Science and Technology
43
3
257-267
1992
In this paper, fibrous composite laminate damage is modelled at the elementary-ply scale. Damage mechanics is used to describe the matrix microcracking and fibre/matrix debonding. Damage variables are defined and associated with the material stiffness reduction. In order to take anelastic strains induced by damage into account, a plasticity model is built up. The behaviour differences between tension and compression in the fiber direction are treated. The model leads to a laminate failure criterion. The model-identification procedure is precisely detailed. It consists in performing three tension tests and one compression test on a laminate whose reinforcement directions are conveniently chosen. Some examples are developed in order to show the ability of such a model to describe ply behaviour effects on the mechanical and rupture behaviour of laminates.
damage; laminates; material behavior; structural mechanics
Energy-based prediction of progressive ply cracking and strength of general symmetric laminates using an homogenisation method
Composites Part A: Applied Science and Manufacturing
36
119-128
2005
10.1016/j.compositesa.2004.06.003
This article describes the application to a range of laminates of a recently developed homogenisation technique for general symmetric laminates that enables progressive ply cracking to be predicted in a laminate containing any number of plies having a variety of orientations. The energy-based methodology may be applied in conjunction with a strain-based fibre failure criterion to predict progressive ply crack formation and the strength of the laminate for situations where the laminate is subject to general in-plane loading and thermal residual stresses. The comparison of model performance with some experimental results for uniaxial loading described in the literature, for a range of laminate geometries without 0?? plies, indicates that the model correctly takes account of the effects of varying ply thicknesses. The predicted maximum stress applied during a ply cracking simulation can be a very good estimate of the laminate strength when ply cracking is the principal mode of damage, i.e. delamination is minimal. The comparison of model performance with experimental results in the literature, for quasi-isotropic laminates with 0?? plies having four different lay-ups, shows there is good agreement. The model indicates that there is a ply lay-up effect, and that fibre fracture occurs at the point of laminate failure. It is shown that by placing 90?? plies adjacent to the mid-plane of the laminate, the strength of the laminate is slightly reduced. Crown Copyright ?? 2004 Published by Elsevier Ltd. All rights reserved.
A. Polymer matrix composites; B. Transverse cracking; C. Damage mechanics; Strength
A continuum damage model for fiber reinforced laminates based on ply failure mechanisms
Composite Structures
76
1-2
162-173
2006
10.1016/j.compstruct.2006.06.023
A ply-level damage model for simulation of stiffness degradation due to progression of damage in fiber reinforced laminates is presented. The proposed damage model is based on damage mechanisms observed at the ply level and hypotheses regarding their effect on material stiffness. Focusing on matrix dominated failure modes, the damage behavior is split into two contributions, damage evolution and damage effect. The prior describes the progression of damage as a function of load, while the latter predicts the effect of this damage by a fourth order tensor relation as function of the current failure mode and stress state. The model relies on six material parameters, whose identification by standard tests is addressed. By combining the damage model with classical lamination theory, the behavior of laminates under plane stress loading is predicted. The capabilities of the proposed damage model are assessed based on comparison to experimental data from the literature. ?? 2006 Elsevier Ltd. All rights reserved.
Composite; Computational simulation; Continuum damage model; Fiber reinforced laminates; Non-linear constitutive behavior; Progressive damage; Puck failure criterion
Crashworthiness analysis of glass fibre/epoxy laminated thin walled composite conical frusta under axial compression
Composite Structures
108
1
584-599
2014
10.1016/j.compstruct.2013.09.060
The quasi-static axial compression of thin-walled E-glass fibre/epoxy resin reinforced (GFRP) composite conical frusta was carried out to study the crashworthiness of conical shells. The hollow frustrated E-glass fibre reinforced polymer (GFRP) conical specimens having semi-apical angle ranging from 15?? to 27?? were fabricated using random ply chopped, plain woven roving cross ply [0/90], and uni-directional angle ply [??60??] oriented mats to the required dimensions by hand layup process. Quasi-static axial compression load was applied over the small end of the conical specimen with a crosshead speed of 2. mm/min using Universal Testing Machine (UTM). From the experiment results, the load deformation characteristics of thin GFRP composite conical shells were analyzed and the results were validated through finite element analysis package ABAQUS??. Further, the influence of ply orientation and the laminate wall thickness towards the energy absorbing capability of each GFRP conical specimen was studied. The buckling mode of collapse and the crushed zones of GFRP composite conical shells were also investigated to identify the collapse mechanisms involved in thin fibre/resin composite laminated conical specimens under quasi-static axial compression. ?? 2013 Elsevier Ltd.
Buckling; Conical frusta; Crashworthiness; FEA; Thin composite shells
Behaviour up to rupture of woven ply laminate structures under static loading conditions
Composites Part A: Applied Science and Manufacturing
40
8
1017-1023
2009
10.1016/j.compositesa.2008.02.018
A general model based on continuum damage mechanics (CDM) and a non-local ply scale criterion were developed to describe the failure of carbon woven ply laminated structures. This non-local criterion is based on mean quantities over a fracture characteristic volume (FCV) corresponding to a cylinder with a circular area and a given ply thickness. The nonlinear behaviour and the non-local criterion were implemented in the finite element code ABAQUS. This paper presents new comparisons between the results of experimental data and simulations performed on plates with notches and saw cuts. The results show the efficiency of this approach, even for structures with very high stress gradients. A simplified approach based on the FCV and the Tsai criterion is also presented here and the results obtained with this method are then compared with the experimental data. © 2008 Elsevier Ltd. All rights reserved.
A. Laminate; B. Stress concentrations; C. Damage mechanics; C. Finite element analysis
Surface mechanics of functional thin films on glass surfaces
Surface and Coatings Technology
200
22-23 SPEC. ISS.
6181-6184
2006
10.1016/j.surfcoat.2005.11.008
High end glass products are imparted new functionalities through coatings. We show that scratch resistance is one of the main mechanical requirements placed upon such functionalizing thin films. We outline the approach that we develop toward a better understanding of thin film mechanics. Examples of recent results are presented relevant to the measurement of the adhesion of thin films and to the control over substrate effects in the elastic response of coated substrates. ?? 2005 Elsevier B.V. All rights reserved.
Adhesion; Multilayers; Silver; Thin films; Tin oxide; Zinc oxide
Fracture mechanics for thin-film adhesion
IBM Journal of Research and Development
38
4
367-377
1994
10.1147/rd.384.0367
The essential elements of the mechanics of delamination are reviewed\nand their implications for design are discussed. Two important conceptsfor\nthe prediction of the reliability of thin-film systems are emphasized:\n1) limiting solutions for the crack-driving force that are independent\nof flaw size, and2) “mixed-mode fracture.” Consideration of the first\nconcept highlights the possibility of flaw- tolerant design in which\nthe statistical effects associated with flaw distributions can be\neliminated. The significance ofmode- mixedness includesits effect\non crack trajectories andon the interface toughness, two key variablesin\ndetermining failure mechanisms. Theoretical predictions are given\nfor some cases of delamination otfhin films under compressive stresses,\nand the results are comparedwith experimental observations to illustrate\nappropriate designcriteria for the model systems studied.
Stitch Cracks in Constraint Plies Adjacent to a Cracked Ply
Journal of Composite Materials
35
23
2077-2097
2001
10.1177/002199801772661362
A high density form of matrixmicrocracking in constraint plies adjacent to a cracked ply, and here called stitch cracking, was found to form readily in awide variety of [+. n/-. n/902n] s laminates. Stitch cracks appear to form instead of interply delamination at the tip of the crack in the constrained ply, more typical of cross ply laminates, when the included angle is greater than 50{degrees}. Stitch cracks do not require fatigue loading to form, but appear due to thermal residual stress and monotonic loading. Stitch cracks were observed to instantly form in -. {degrees} constraint plies next to a cracked 90{degrees} ply, apparently when the included angle of the plies was less than about 50{degrees}. In addition, they formed in -15{degrees} and -60{degrees} plies next to corresponding cracked +. {degrees} surface plies. Data on stitch crack length and spacing is included. This paper seeks to raise awareness of stitch cracks by systematically demonstrating that they not only exist, but occur in awide variety of laminates. The data suggest that stitch cracks should not be overlooked during development of composite damage mechanics models.
Delamination of multidirectional composite laminates at 0°/θ° ply interfaces
Engineering Fracture Mechanics
73
16
2427-2442
2006
10.1016/j.engfracmech.2006.05.013
The main objective of this study is to develop a methodology for establishing mixed-mode delamination propagation criteria of non-unidirectional laminates. The crack interface was chosen to be 0°/45° and the effort was mainly focused on obtaining the mode I fracture toughness (GIC). The widely used DCB test was avoided due to anticipated problems with intralaminar damage developing at the ply interface of interest. The ADCB and AMMF methods were used to determine the mixed-mode fracture toughness with the largest amount of mode I. The selected stacking sequence resulted in desirable crack propagation behavior; there was no change of delamination plane, an acceptable crack front profile, no initial specimen curvature, and no energy dissipation through global specimen damage. Finite element simulation was found to be the only tool capable of analyzing the experimental data. © 2006 Elsevier Ltd. All rights reserved.
Damage mechanics; Delamination; Mixed-mode; Multidirectional
Interlaminar and intralaminar fracture modes in 0/90 cross-ply glass/epoxy laminate
Composites
26
2
125-133
1995
10.1016/0010-4361(95)90412-S
Delamination of a cross-ply 0/90 glass fibre-reinforced composite laminate with an epoxy-phenol matrix was studied using a double cantilever beam test. Fracture toughness was determined by measurement of bend angle of the cantilever beams. Results obtained with this method were in agreement with those from conventional compliance and area methods. Two different fracture modes were observed: interlaminar and intralaminar. In the interlaminar fracture mode, crack jumps in the space between two neighbouring 0° and 90° plies were observed. With the interlaminar fracture mode, during crack initiation G<sub>Ic</sub> decreased with crack length. Intralaminar fracture mode consisted of the gradual growth of a crack through a 0° ply. Fibres bridging the opposite sides of the crack were observed in this case, and fracture toughness G<sub>Ic</sub> did not change with crack length. G<sub>Ic</sub> (420 J m<sup>-2</sup>) at intralaminar fracture mode was approximately twice that at interlaminar fracture mode (220 J m<sup>-2</sup>). The difference in fracture toughness was explained by the dissipation of energy by fibres bridging the opposite sides of the crack at intralaminar fracture mode
Crack initiation; Crack propagation; Delamination; Dissipation; Energy; Energy dissipation; Epoxy resins; fracture; FRACTURE MECHANICS; fracture toughness; GLASS; Glass fiber reinforced plastics; Laminated composites; Toughness
A study of crack suppression mechanism of thin-ply carbon-fiber-reinforced polymer laminate with mesoscopic numerical simulation
Journal of Composite Materials
0021998313494430-
2013
10.1177/0021998313494430
In order to examine the effect of ply thickness on the crack initiation and propagation in the 90{degrees} layer in [0{degrees}/90{degrees}n/0{degrees}] laminates, we conducted numerical simulations using two-dimensional mesoscopic numerical models. We found that the stress increase in the thin layer with 40 {micro}m thickness was restricted in the vicinity of the adjacent layers, leading to restriction of crack penetration through the 90{degrees} layer. In addition, we confirmed the effect of stiffness of adjacent layers. In the case where the 90{degrees} layer was sandwiched between 45{degrees} layers, which had lower stiffness than the 0{degrees} layers, crack propagation in the 90{degrees} layer was faster than that observed with the 0{degrees} adjacent layers. Thus, the crack propagation behavior in the 90{degrees} layer was significantly influenced by the change in the stiffness caused by the orientation angle of the adjacent layers.
finite element analysis; interfacial strength; layered structures; thin-ply; transverse cracking
On transverse matrix cracking in cross-ply laminates loaded in simple bending
Composites Part A: Applied Science and Manufacturing
30
1003-1008
1999
10.1016/S1359-835X(99)00006-8
A one-dimensional analysis of a cross-ply laminate, containing cracked transverse plies, loaded in flexure is presented. Simple bending theory is used in conjunction with a shear-lag analysis, to calculate the degraded longitudinal modulus of a cracked transverse ply, enabling the flexural modulus of the laminate to be determined. The solution is shown to agree well with a more sophisticated stress transfer model in the literature. The analysis is then extended to calculate the applied bending moment at transverse crack onset under flexural loading using a fracture mechanics approach. The results suggest that the in situ transverse ply stress at which matrix cracking commences for the beam loaded in flexure is very close to the stress level at which the same ply would crack if the laminate were loaded in tension.
cross-ply laminates
Development of novel single-wall carbon nanotube-epoxy composite ply actuators
Smart Materials & Structures
14
6
1526-1532
2005
10.1088/0964-1726/14/6/045
This paper describes a carbon nanotube epoxy ply material that has electrochemical actuation properties. The material was formed by dispersing single-wall carbon nanotubes in a solvent and then solution casting a thin paper using a mold and vacuum oven. In order to take advantage of the high elastic modulus of carbon nanotubes for actuation, epoxy as a chemically inert polymer is considered. An epoxy layer was cast on the surface of the nanotube paper to make a two-layer ply. A wet electrochemical actuator was formed by placing the nanotube epoxy ply in a 2 M NaCl electrolyte solution. Electrochemical impedance spectroscopy and cyclic voltammetry were carried out to characterize the electrochemical properties of the actuator. The voltage-current relationship and power to drive the actuator material were also determined. Compared to previous single-wall carbon nanotube buckypaper tape actuators, which had poor adhesion between the nanotubes and tape, and other nanotube-thermal plastic polymer actuators, which could not provide high strength, the epoxy based actuator has a higher elastic modulus and strength, which will be useful for future structural applications. This demonstrates that a polymer layer can reinforce nanotube paper, which is an important step in building a new structural material that actuates. Further work is under way to develop a solid electrolyte to allow dry actuation. Finally, these actuator plies will be laminated to build a carbon nanocomposite material. This smart structural material will have potential applications that range from use in robotic surgical tools to use as structures that change shape.
Effect of residual shear strain on the cured shape of unsymmetric cross-ply thin laminates
Composites Science and Technology
38
1
55-67
1990
10.1016/0266-3538(90)90071-C
The warping of unsymmetrically laminated composites is induced by the thermal residual curing stress generated during the fabrication process. Most papers which have dealt with the warping of unsymmetric thin laminated composites assumed the in-plane shear strain to be negligible. However, inplane shear strain exists in certain cases for orthotropic laminates. This paper presents a new formulation including in-plane shear strain. Present results indicate that thermal residual shear strain is negligible in cases where width-to-thickness is very large or small. However, a significant amount of shear strain exists in the range of medium width-to-thickness ratio where a bifurcation point occurs. This paper investigates the effects of width-to-thickness, aspect ratio, number of layers, and stacking sequence on the shapes of the unsymmetric cross-play [0n/90n]T (n = 1,2…) family of laminates. Curvatures are calculated for square and rectangular laminates as using the nonlinear Newton-Raphson iteration method numerically. In some cases, numerical results are compared with experiments.
On the 'ply discount method' for determining effective thermo-elastic constants of laminates containing transverse cracks
Composites Part A: Applied Science and Manufacturing
36
1347-1354
2005
10.1016/j.compositesa.2004.11.012
Elastic constants and thermal expansion coefficients of a laminate containing transverse ply cracks are often calculated by reducing selected elastic moduli of the damaged plies. This approach is often referred to as the 'ply discount method'. In the present paper, specific ply moduli required for reduction are identified by enforcing compatibility with inter-relationships that exist between the thermo-elastic properties of cracked and uncracked laminates. The effect of laminate geometry is investigated by comparing ply reduction factors as a function of crack density for a number of different stacking sequences. Reduction factors are obtained from higher order laminated plate models of composites containing transverse cracks. A simplified approach for determining inplane modulus reduction factors is also investigated. ?? 2005 Elsevier Ltd. All rights reserved.
Damage mechanics; Laminate mechanics; Laminates; Transverse cracking
Model to predict effects of triaxial loading on ply cracking in general symmetric laminates
Composites Science and Technology
60
12-13
2255-2279
2000
10.1016/s0266-3538(00)00086-5
This paper first considers the mechanics for predicting stress transfer in a general symmetric laminate, having a uniform distribution of ply cracks in a single orientation, subject to combined general in-plane and through-thickness loading. The effects of residual stresses arising from thermal expansion mismatch are taken into account. The paper extends an existing stress transfer model so that the effect of through-thickness loading can be considered. The second step is the extension of an existing framework for the formulation of criteria that can be used to predict the progressive formation of ply cracks during complex loading. The effective stress/strain relations for a damaged laminate are shown to be identical in form to those of an undamaged laminate. By considering ply crack closure conditions, a series of very useful inter-relationships between thermo-elastic constants for damaged and corresponding undamaged laminates are derived. In particular, it is shown that a single damage dependent function controls the dependence of all thermo-elastic constants on the state of ply cracking. This function has been determined from stress transfer analysis for the special case of uniform ply crack distributions having a single orientation. The inter-relationships between thermoelastic constants enable the derivation of crack formation criteria that are relatively simple in form.
Crack initiation; Laminated composites; Loads (forces); Mathematical models; Residual stresses; Strain; Stress analysis; Thermal expansion; Thermoelasticity
Micromechanisms and mechanics of damage and fracture in thin film/substrate systems
International Applied Mechanics
40
2
140-155
2004
10.1023/B:INAM.0000028592.55112.b9
The purpose of this paper is to review the mechanisms and available theoretical methods for modeling the strength and failure of thin film/substrate systems.
Cracking; Decohesion; Delamination; Dislocation; Fragmentation of films; Mechanisms of strength and failure; Nanoindentation; Thin film/substrate system
A Study of the Opening Displacement of Transverse Cracks in Cross-Ply Laminates
International Journal of Damage Mechanics
2
3
272-289
1993
10.1177/105678959300200306
Transverse cracks in cross-ply laminates are investigated experimentally to reveal the essential characteristics of their opening displacement under tensile loads. The average crack opening displacement is studied as a function of the longitudinal overall strain and the effects of matrix toughness and transverse ply thickness on this parameter are examined. The interactive effects between closely spaced transverse cracks are also examined and found to be significant. Implications of the experimentally observed features on the micromechanics and continuum damage type models are discussed.
On the Crushing Mechanics of Thin-Walled Structures
Journal of Applied Mechanics
50
4a
727
1983
10.1115/1.3167137
A self-consistent theory is presented which describes the crushing behavior of a class of thin-walled structures. Assuming a rigid-plastic material and using the condition of kinematic continuity on the boundaries between rigid and deformable zones, a basic folding mechanism is constructed. This mechanism closely reproduces all the main features of folds and wrinkles actually observed on typical crumpled sheet metal structures. Calculations based on the energy balance postulate show that two- thirds of the plastic energy is always dissipated through inextensional deformations at stationary and moving plastic hinge lines. The extensional deformations are confined to relatively small sections of the shell surface but they account for the remaining one-third of the dissipated energy. The theory is illustrated by ap- plication to the problem of progressive folding of thin-walled rectangular columns. A good correlation is obtained with existing experimental data as far as the mean crushing force and the geometry of the local collapse mode is concern
Mechanics and dynamics of actin-driven thin membrane protrusions.
Biophysical journal
90
January
65-76
2006
10.1529/biophysj.105.071480
Motile cells explore their surrounding milieu by extending thin dynamic protrusions, or filopodia. The growth of filopodia is driven by actin filament bundles that polymerize underneath the cell membrane. We compute the mechanical and dynamical features of the protrusion growth process by explicitly incorporating the flexible plasma membrane. We find that a critical number of filaments are needed to generate net filopodial growth. Without external influences, the filopodium can extend indefinitely up to the buckling length of the F-actin bundle. Dynamical calculations show that the protrusion speed is enhanced by the thermal fluctuations of the membrane; a filament bundle encased in a flexible membrane grows much faster. The protrusion speed depends directly on the number and spatial arrangement of the filaments in the bundle and whether the filaments are tethered to the membrane. Filopodia also attract each other through distortions of the membrane. Spatially close filopodia will merge to form a larger one. Force-velocity relationships mimicking micromanipulation experiments testing our predictions are computed.
Size effects in thin CFRP panels subjected to impact
Science
35
l
599-607
1997
10.1016/S0263-8223(97)00098-6
The static indentation and impact behaviour of three- and nine-ply CFRP panels circularly clamped with rings of 100 and 300 mm diameter have been evaluated. The maximum static force is similar for small and large panels for both three- and nine-ply laminates. Increasing the panel size of the three-ply laminates subjected to impact only appears to affect the threshold of perforation. For the nine-ply laminates an increase in panel size produced a reduction in delamination area and backface cracking. Interpretation of energy maps is suggested as a means of identifying when the peak impact force has occurred and the threshold of perforation. © 1997 Elsevier Science Ltd.
Sculptured thin films and glancing angle deposition: Growth mechanics and applications
Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films
15
3
1460
1997
10.1116/1.580562
Sculptured thin films with three dimensional microstructure controlled on the 10 nm scale were fabricated with an evaporation technique. Glancing angle deposition (GLAD) and substrate motion were employed to “sculpt” columnar thin film microstructure into desired forms ranging from zigzag shaped to helical to four-sided “square” helical. Computer control of substrate motion was used to accurately position the substrate and to achieve the desired film structures. The growth mechanics of this novel thin film deposition technique are investigated with density measurements, scanning electron microscopy analysis, and measurements of effective refractive index. Adatom diffusion and atomic shadowing are the dominant growth mechanisms with glancing angle deposition conditions creating extreme shadowing. With controlled rotation of the substrate about two axes during deposition, a dense capping layer can be produced on top of the porous sculptured films. The success of the capping process was found to be strongly dependent on the technique used, with an exponential decrease (θ∝[1-A∙eB∙t]) with time of incident flux angle found to be the best to reduce filling of the porous film and fracturing of the capping film. The GLAD technique was found to have potentially promising application in optical, biological, and chemical devices and materials. © 1997 American Vacuum Society.
Constitutive Relationships for Laminates with Ply Cracks in In-plane Loading
International Journal of Damage Mechanics
14
3
235-259
2005
10.1177/1056789505050355
A theoretical framework which allows determining the whole set of 2-D thermomechanical constants of a damaged laminate as a function of crack density in different layers is presented. In this approach, closed-form expressions, which contain thermoelastic ply properties, laminate layup, and crack density as the input information are obtained. It is shown that the crack opening displacement (COD) and crack face sliding displacement, normalized with respect to a load variable, are important parameters in these expressions influencing the level of the properties degradation. They are determined in this paper using generalized plain strain FEM analysis results for noninteractive cracks. The strong dependence of the COD on the relative stiffness and thickness of the surrounding layers, found in this study, is described by a power law. The methodology is validated and the possible error introduced by the noninteractive crack assumption is estimated by comparing with the 3-D FEM solution for a cross-ply laminate with two orthogonal systems of ply cracks. Experimental data and comparison with other models are used for further verification.
Structural rigidity optimization of thin laminated shells
Composite Structures
95
35-43
2013
10.1016/j.compstruct.2012.07.014
In this work, we present an optimization methodology used in order to optimize laminated composite shell structures with variable stiffness. Considering the maximization of the structural global rigidity measured by the compliance, a topology optimization problem of the anisotropy fields for thin laminated plates as well as the associated optimization algorithm are extended to thin laminated shells. Numerical examples with quasi-homogeneous angle-ply stacking sequences showing the optimization methodology feasibility are presented.
Angle ply; Compliance; Laminate; Shell
Prediction of plastic strain accumulation in continuous fiber reinforced laminates by a constitutive ply model
International Journal of Fracture
158
145-156
2009
10.1007/s10704-009-9345-4
The present paper is concerned with the prediction of plastic ply\nstrains which accumulate in continuous fiber reinforced laminates\nwith polymeric matrix materials. The study is based on a constitutive\nmodel which is implemented within the Finite Element Method. Plastic\nstrains are expected to evolve when the ply is subjected to a pronounced\nshear load and/or to pronounced transverse compression. Two plasticity\nmechanisms are modeled at ply level under plane stress assumption\n(i.e. for thin shells and plates). They either concern the evolution\nof plastic shear strains or the evolution of plastic normal strains.\nThe proposed plasticity model is combined with an existing ply level\ncontinuum damage model. The capabilities of the proposed model are\nassessed by comparing its predictions to experimental data from literature.\nEmphasis is placed on loading conditions which drive the evolution\nof plastic strains. Excellent correlation with experimental results\nis shown for proportional as well as for non-proportional ply loadings.
Global and local behaviour based composite damping studies on thin-walled box structure
European Journal of Mechanics - A/Solids
29
2
253-265
2010
10.1016/j.euromechsol.2009.09.003
The local (plate)/global (beam) vibration and damping behavior of composite thin-walled box member subjected to vibratory environment are studied and presented in this paper. This investigation is carried out by the use of 3D beam and thin plate finite elements and the corresponding modal frequencies/damping values of composite box beam are predicted by modal strain energy method. Application examples illustrate the ability of the 3D beam and thin plate element to predict both local and global modal frequencies/damping of hollow box sections. The influence of L/h ratio, b/h ratio and ply angle on the frequency and loss factor of composite box beam is investigated. In addition, an attempt has also been made to investigate the effect of temperature on the composite damping characteristics of rectangular box type section.
Box structure; Composite damping; Finite element; Modal strain energy method
Instrumented drop weight impact testing of cross-ply and fabric composites
Composites
16
4
268-278
1985
10.1016/0010-4361(85)90279-4
A state-of-the-art instrumented drop weight impact test system developed at the University of Wyoming was used to investigate the impact performance of thin, simply-supported composite laminates. System calibration, data acquisition and data reduction techniques developed for this impact test svstem, which makes use of a piezqelectric force transducer, are presented, along with insights into system resonance characteristics. Composite material plates were tested to identify performance differences between cross-ply and fabric material forms. The six composite material systems investigated included cross-ply and fabric laminates of Hercules AS4 graphite, DuPont Kevlar 49 and Owens-Corning E·glass fibres impregnated with a Hercules 3501-6 epoxy resin. Test results are presented along with results of a literature review in this area.
ar fibres; composite materials; composite materials have; decades; drop weight impact e-glass; during the past two; epoxy resins; fabric; fibres; graphite fibres; instrumented impact; kev; laminates
Fracture behavior of cross-ply graphite/ epoxy laminates
Engineering Fracture Mechanics
22
6
1035-1048
1985
Fracture behavior of cross-ply and (04/908/04)T laminates of T300/934 graphite/epoxy material was studied using compact tension specimens of several widths and thicknesses, center notched tension and three point bend specimens. The process of damage initiation and propagation was studied and is discussed in detail. The critical stress intensity factor was evaluated and its variation with specimen size and type is shown. On the basis of these investigations, a suitable specimen for the evaluation of meaningful fracture toughness is suggested.
The use of a characteristic damage variable in the study of transverse cracking development under fatigue loading in cross-ply laminates
International Journal of Fatigue
24
389-395
2002
10.1016/S0142-1123(01)00094-9
A two dimensional shear lag analysis of a cracked cross-ply composite laminate subjected to uniaxial loading, taking into account residual thermal stresses, has been developed. This analysis has led us to introduce a characteristic non-dimensional damage variable ??, which is a function of the crack density, material properties, and lamina stacking sequence. This analysis has been applied to a CFRP composite material (T300/914). The use of the characteristic damage variable has led to phenomenological laws that allow accurate prediction of the number of fatigue cycles necessary for the initiation of the first matrix cracks, and the kinetics of this damage, up to the "saturation" stage, in any cross-ply laminate subjected to a uniaxial fatigue loading. ?? 2002 Elsevier Science Ltd. All rights reserved.
Fatigue damage accumulation; Fracture mechanics; Matrix cracking; Polymer matrix composites
Prediction of low-velocity impact damage in thin circular laminates
AIAA Journal
23
3
442-449
1985
10.2514/3.8933
Clamped circular composite plates made of quasi-isotropic graphite/epoxy laminate were analyzed for static equivalent impact loads. The analysis was based on the minimum total potential energy method and used the von Karman strain-displacement equations. A step-by-step incremental transverse displacement procedure was used to calculate plate load and ply stresses. The ply failure region and modes (splitting and fiber break) were calculated using the Tsai-Wu and the maximum stress criteria, respectively. Reduced moduli were then used in the failed region in subsequent increments of analyses. The analysis predicted that the failure would initiate as splitting in the bottom-most ply and then progress to other plies.
Thin film composite nanofiltration membranes fabricated from polymeric amine polyethylenimine imbedded with monomeric amine piperazine for enhanced salt separations
Reactive and Functional Polymers
86
168-183
2015
10.1016/j.reactfunctpolym.2014.08.009
Thin film composite (TFC) nanofiltration membranes were fabricated by interfacial polymerization using polymeric amine polyethylenimine (PEI) and monomeric amine piperazine (PIP) as the amine reactant. Membranes with a single-ply polyamide layer were produced by reacting trimesoyl chloride (TMC) with mixed amines of PEI and PIP, and incorporation of a small amount of PIP in PEI was found to increase the permeation flux effectively while still maintaining a good solute rejection. For instance, adding 10wt% PIP in the amine reactant solution resulted in a 6-fold increase in permeation flux, while a 91.6% MgCl2 rejection was maintained. In addition, 2-ply polyamide membranes were also prepared by two cycles of PEI–TMC and PIP–TMC interfacial reactions separately, and they showed a higher rejection than the single-ply polyamide membrane. At a low PIP/PEI concentration ratio, the single-ply polyamide membranes formed with mixed amines of PIP and PEI tended to be more permeable than the 2-ply polyamide membranes. However, it was demonstrated that by properly controlling the PIP/PEI concentration ratio, the 2-ply polyamide membranes with both a higher permeation flux and salt rejection than conventional single-ply polyamide membranes could be produced. The resulting membranes were characterized for chemical composition, surface hydrophilicity, surface charge and morphology of the polyamide skin layer.
Interfacial polymerization; Membrane; Nanofiltration; Piperazine; Polyethylenimine; Thin film composite
Progressive damage analyses of angle-ply laminates exhibiting free edge effects using continuum damage mechanics with layer-wise finite element method
Fatigue & Fracture of Engineering Materials & Structures
31
549-568
2008
10.1111/j.1460-2695.2008.01242.x
Capability of continuum damage mechanics (CDM) to predict the damage\nmechanism evolution of composite laminates has rarely been carried\nout, and most of the previous CDM works mainly focused on the overall\nresponse of the laminates. In this paper, progressive damage and\noverall response of the composite laminates under quasi-static, monotonic\nincreasing loading are investigated using three-dimensional (3D)\nCDM implementation in a finite element method that is based on the\nlayer-wise laminate plate theory. In the damage formulation, each\ncomposite ply is treated as a homogeneous orthotropic material exhibiting\northotropic damage in the form of distributed microscopic cracks\nthat are normal to the three principal material directions. The progressive\ndamage of different angle-ply composite laminates under quasi-static\nloading that exhibit free edge effects is investigated. It is shown\nthat using CDM global behaviour and various damage mechanisms affected\nby the complex nature of free edges can be qualitatively well predicted.
Simulating progressive failure of composite laminates including in-ply and delamination damage effects
Composites Part A: Applied Science and Manufacturing
61
185-200
2014
10.1016/j.compositesa.2014.02.013
A finite element (FE) model, which includes in-ply and delamination damage effects, is developed for the progressive failure analysis of composite laminates. A combined elastoplastic damage model which accounts for both plasticity and damage effects is used to represent the mechanical response of composite layers and is implemented in the FE code Abaqus using user-defined material subroutine UMAT. A cohesive zone model based on cohesive elements available in Abaqus is employed to simulate delamination behaviour in the adhesive interfaces. Continuum shell elements and cohesive elements are stacked together to simulate composite and adhesive layers, respectively. The model is applied to the progressive failure analysis of AS4/PEEK composite laminates subjected to in-plane tensile and out-of-plane transverse low-velocity impact loadings. It is shown that the model can be successfully applied to the simulations of composite laminates susceptible to delamination failure. © 2014 Elsevier Ltd. All rights reserved.
A. Laminates; B. Delamination; B. Plastic deformation; C. Damage mechanics
Constitutive ply damage modeling, FEM implementation, and analyses of laminated structures
Computers & Structures
86
9
908-918
2008
10.1016/j.compstruc.2007.04.021
The present work is concerned with the modeling of progressive damage in fiber reinforced polymer laminates and its implementation into a finite element code as constitutive material law. The objective is to predict damage evolution and material degradation due to matrix dominated failure modes (“matrix cracking”). In a previous work, a ply-level continuum damage model based on ply failure mechanisms postulated by Puck has been presented. This model predicts the evolution of the complete tensor of elasticity for the damaged material and is able to capture the effects of stiffness recovery and slanted cracking under transverse compression. In the current work, this damage model is adapted for arbitrary loading paths and implemented within the finite element method in order to analyze complex structures and study their damage behavior including load redistribution due to damage. To demonstrate some key features and the application of the damage model in structural analysis, it is applied in a single element analysis as well as in the simulation of Open Hole Compression tests for which results are compared to experimental data from the literature.
Constitutive model; Continuum damage mechanics; Fiber reinforced laminates; Finite element method; Polymer matrix composites; Progressive damage; Puck failure criterion
Micromechanics based ply level material degradation model for unidirectional composites
Composite Structures
94
2
671-680
2012
10.1016/j.compstruct.2011.09.001
The damaged response of a composite lamina depends on various mechanisms that take place at the microlevel, i.e., at the level of the fiber and matrix. The present work focuses on developing a ply level continuum damage model for point-wise stiffness degradation through simplified representation of the microlevel damage. A three dimensional micromechanical analysis of a single cell representative volume element is carried out for various volume fraction, and levels of damage. The model brings out the coupled effect of damage on the effective point-wise ply level stiffness. Further, the numerical results are employed to develop a functional continuum representation of stiffness degradation as a function of the damage parameters and fiber volume fraction perturbations. The micromechanics model is consistent with experimentally observed stiffness degradation, i.e., a strong influence of fiber breakage and fiber matrix debond, and a weak influence of normal cracking of matrix. The proposed model can be considered as an improved version of the widely accepted diffused (meso) damage models, i.e., DML. The study also gives a generalized and consistent definition for the free energy, which can be used for modeling growth of damage. ?? 2011 Elsevier Ltd.
Composites; Damage mechanics; Degradation models; Free energy; Micromechanics
Micro-Mechanics of Failure (MMF) for Continuous Fiber Reinforced Composites
Journal of Composite Materials
42
18
1873-1895
2008
10.1177/0021998308093911
The micromechanics of failure was developed to predict the failure of continuous fiber reinforced composites. A micromechanical approach using unit cells of square and hexagonal arrays was employed to compute the micro stresses of constituents and at the fiber--matrix interface, which were used to determine the failure initiation of a unidirectional ply. The constituent properties include two tensile and compressive strengths of fiber and matrix, plus normal and shear strengths at the interface. The matrix and interfacial dominated strength properties are determined by matching the micro stresses at the constituent levels with the observed transverse tensile and compressive strengths on the macro ply level. The longitudinal shear failure is then expected to be a result of damage progression after initial failure. Based on the current MMF, in the graphite/epoxy considered in this study both transverse tensile and compressive failure are expected to occur via matrix failure. However, in the glass/epoxy the transverse tensile and compressive failures are respectively caused by matrix failure and interfacial tensile failure. These predictions are compared with predictions from other widely used failure criteria as well as experimental data. Lastly, we predicted the failure of laminates. Instead of using a unidirectional ply-based failure theory, starting with the fiber, matrix, and their interface will lead to a much simpler, more generic theory.
constituent; failure; failure criterion; failure envelope; micromechanics; unidirectional composites
Damage mechanics characterization of transverse cracking behavior in high-temperature CFRP laminates
Composites Science and Technology
61
1049-1055
2001
10.1016/S0266-3538(00)00236-0
Transverse cracking under tensile loading in high-temperature CFRP, carbon/BMI (bismaleimide), G40-800/5260, has been investigated experimentally. Carbon/epoxy, T800H/3900-2, composite laminates are also examined for comparison. Both material systems have toughened-interlaminar layers. Laminate configurations are [0/90]s, [0/902]s, [±45/90]s, and [±45/902]s for G40-800/5260, while [0/90]s and [±45/90]s for T800H/3900-2. In all laminates, the first microscopic damage observed is a 90° ply transverse crack. In [±45/90n]s type laminates, cracking in 45°ply and delaminations are also observed. The cracking behavior is quantified by measuring crack densities as a function of the laminate strain. The difference between the damage progress near the 90° ply transverse crack tips between the material systems are observed. Damage mechanics analysis is used to predict 90° ply transverse cracking based on both the energy and stress criteria. The present analysis can be used as a means of characterization of the transverse cracking resistance of a material, which will be helpful in ranking materials. © 2001 Elsevier Science Ltd. All rights reserved.
C. Damage mechanics; C. Transverse cracking; High temperature CFRP; Microscopic damage; Toughened-interlaminar layer
Fracture Mechanics for Delamination Problems in Composite Materials
Journal of Composite Materials
17
3
210-223
1983
10.1177/002199838301700302
A fracture mechanics approach to the well-known delamination problem in com posite materials is presented. Based on the theory of anisotropic laminate elasticity and interlaminar fracture mechanics concepts, the composite delamination problem is for mulated and solved. The exact order of the delamination crack-tip stress singularity is determined. Asymptotic stress and displacement fields for an interlaminar crack are obtained. Fracture mechanics parameters such as mixed-mode stress intensity factors, KI, KII, KIII, and the energy release rate, G, for composite delamination problems are defined. To illustrate the fundamental nature of the delamination crack behavior, solu tions for edge-delaminated graphite-epoxy composites under uniform axial extension are presented. Effects of fiber orientation, ply thickness, and delamination length on the interlaminar fracture are examined.
Mechanics of thin-skinned fold-and-thrust belts
Bulletin of the Geological Society of America
89
1189-1198
1978
10.1130/0016-7606(1978)89<1189:MOTFB>2.0.CO;2
The essential characteristics of thin-skinned fold-and-thrust belts include the following: a wedge-shaped deforming region, thicker at the back end from which the thrusts come; a weak layer at the base of the wedge; and large amounts of shortening and thickening within the wedge. All these characteristics are incorporated into an analytical model of a perfectly plastic wedge, underlain by a weak basal layer and yielding in compressive flow. The model is sufficiently flexible to be applied to a variety of tectonic situations. In each situation the model shows that shortening of the wedge and sliding over its base can occur for reasonable values of the yield stress of the wedge and of the weak basal layer, of the surface topographic slope, of the back slope of the basal layer, and of the thickness of the wedge. The present model differs markedly from the conventional concept of gravity gliding in that it shows that horizontal compressive stresses can play a major role in overcoming the resistance to basal sliding. In addition, the model suggests that the topographic slope, when necessary, can be a result of the compression within the wedge itself; no additional outside agency for producing the topographic slope need be postulated. Thus, the model suggests that a surface topographic slope is in general neither a necessary nor a sufficient condition for the formation of a thin-skinned fold-and-thrust belt.
GBT formulation to analyse the buckling behaviour of FRP composite open-section thin-walled columns
Composite Structures
93
1
79-92
2010
10.1016/j.compstruct.2010.06.013
This paper presents a Generalised Beam Theory (GBT) formulation to analyse the local and global buckling behaviour of FRP (fibre-reinforced polymer) composite thin-walled columns with arbitrary open cross-sections, which takes into account both shear deformation and cross-section deformation effects. After describing the steps and procedures involved in performing the GBT cross-section analysis of an arbitrarily branched composite (laminate plate) thin-walled member, the paper addresses the numerical implementation of the proposed GBT formulation, carried out by means of the finite element method (GBT-based beam element) – particular attention is devoted to the derivation of the element linear and geometric stiffness matrices, which incorporate all the material coupling effects. In order to illustrate the application and capabilities of the proposed formulation and implementation, several numerical results are presented and discussed, dealing with the local and global buckling behaviour of FRP composite I-section columns with different ply orientations and stacking sequences. Taking advantage of the GBT modal features, deep insight is acquired on the complex composite member buckling mechanics, namely those involving bending–torsion or global–local coupling effects. In particular, one investigates the influence of (i) the constitutive assumption regarding the transverse extension occurring in the cross-section composite walls and (ii) the distribution of pre-buckling normal stresses (due to axial compression) on the buckling behaviour of I-section columns. For validation purposes, the above results are compared with values recently reported in the literature and estimates obtained from shell finite element analyses.
FRP composites; Generalised Beam Theory (GBT); I-section columns; Local/global buckling; Open-section thin-walled members; Shear deformation
Nonlinear delamination mechanics for thin films
Journal of the Mechanics and Physics of Solids
45
7
1137-1159
1997
Doi 10.1016/S0022-5096(96)00122-6
Delamination of prestressed thin films on thick substrates is analysed accounting for plastic dissipation in either the substrate or film. Emphasis is on large scale yielding wherein the height of the plastic zone at the propagating interface crack tip is comparable to the film thickness. Such conditions are common for both metal and polymer thin films on elastic substrates or for ceramic coatings on metal substrates when the interface between the film and substrate is reasonably strong. Under large scale yielding, the notion of a thickness-independent interface toughness no longer pertains, and a nonlinear fracture mechanics is required to quantify delamination. Two such approaches are pursued in this paper using models based on the attainment of critical conditions at the interface crack tip within the plastic zone. Steady-stale film delamination is analysed for conditions where yielding occurs either in the film or in the substrate, and critical combinations of prestress and thickness are predicted. The theory is applied to a recent set of experiments on copper films delaminating from silica substrates. (C) 1997 Elsevier Science Ltd.
crack tip plasticity; fracture toughness; interface; solids; toughness
On the mechanics of growing thin biological membranes
Journal of the Mechanics and Physics of Solids
63
1
128-140
2014
10.1016/j.jmps.2013.09.015
Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression. ?? 2013 Elsevier Ltd.
Finite elements; Growth; Membrane; Mitral valve; Shell
Microwedge indentation of the thin film fine line—I. Mechanics
Acta Materialia
44
8
3169-3175
1996
10.1016/1359-6454(95)00426-2
Analytical calculations of mechanics for strain energy release rate, bending strain and phase angle are reported for a new procedure to test thin film mechanical properties. In the Microwedge Indentation Test (MWIT), a symmetric wedge-shaped probe extends fully across a wide thin film interconnect line, so that analysis under the assumption of plane strain is appropriate. As the indentation proceeds, an interfacial crack between the interconnect line and the substrate develops if the interface is weak. From this, adhesion can be calculated. Eventually, the interfacial crack becomes long enough that buckling ensues, giving rise to large thin film bending strains. Consequently the phase angle changes continuously from 53 to −37°. Depending on whether spallation occurs by fracture in the center of the beam or at the end of the beam at the interfacial crack tip, a thin film critical bending strain or grain boundary fracture toughness may be determined.
Effect of ply orientation on the in-plane vibration of single-layer composite plates
Journal of Sound and Vibration
312
94-108
2008
10.1016/j.jsv.2007.10.028
Composite laminate structures can be designed for specific purposes by optimizing the number of plies and the ply orientations. Previous studies established the behavior of the first natural frequencies of the bending motion of a thin composite plate in the framework of classical plate theory for different boundary conditions. Since plates can also undergo in-plane vibration, the present study is aimed at investigating the effect of the ply orientation on such in-plane vibration. This is made possible through theoretical simulation with a model based on the Rayleigh-Ritz formulation in conjunction with Hamilton principle. The total matrices deduced by minimizing the Hamilton function exhibit a decoupling of bending and membrane motions, which are in plane. The natural frequencies of the membrane motion can therefore be calculated and the ply orientations are investigated for free-free boundary conditions for a square plate. The present model is first validated by comparing the natural frequencies of the bending and in-plane motions of isotropic plates with available data in the literature and the agreement is found to be excellent with the maximum discrepancy being only 0.25%. The validation is then extended to orthotropic plates for the first two bending natural frequencies under simply supported boundary conditions for different ply orientations. The present study establishes that for free-free boundary conditions the first natural frequency of the in-plane vibration of a composite square plate is symmetrical with respect to 45{ring operator} ply orientation and is maximum for this value. This study suggests that it is possible to use this analysis to design composite plates by properly tailoring ply orientations. © 2007 Elsevier Ltd. All rights reserved.
Indentation mechanics and its application to thin film characterization
Vacuum
82
1353-1359
2008
10.1016/j.vacuum.2008.03.077
Instrumented indentation mechanics and its applications to thin film characterization are described and discussed. Instrumented nanoindentation has become an outstanding tool for characterizing coatings and treated surfaces. It is routinely used in industry and university allowing for determining the mechanical performance of coated and treated pieces, that is of primary importance for keeping new surface functionality in time. The paper reviews important procedures and concepts that have proved to be very useful to analyse the contact response (elastic unloading, indentation strains and stresses, composite response of coated pieces). Examples are used to illustrate the very wide range of studies that can be carried out. ?? 2008 Elsevier Ltd. All rights reserved.
Elastic modulus; Hardness; Nanoindentation; Strain; Stress; Thin Film
Mechanics of thin-skinned fold-and-thrust belts : Insights from numerical models
Sears, J.W., Harms, T.A., and Evenchick, C.A., eds., Whence the Mountains? Inquiries into the Evolution of Orogenic Systems: A Volume in Honor of Raymond A. Price: Geological Society of America Special Paper
433
63-98
2007
10.1130/2007.2433(04).
In order to investigate the development of structures at scales smaller than that of an entire belt, we examined aspects of the mechanics of thin-skinned fold-and-thrust belts in cross section using an arbitrary Lagrangian-Eulerian frictional-plastic fi nite- element model. A series of models, beginning with the deformation of a thick uniform layer above a thin weak layer on a fi xed base, sequentially illustrates the effects of including fl exural isostatic subsidence, strain-softening, multiple layers of strong and very weak materials, and fi nally erosion and sedimentation. These continuum models develop thin shear zones containing highly sheared material that approximate fault zones. The corresponding structures are similar to those in fold-and-thrust belts and include: far-traveled thrust sheets, irregular-roof and smooth-roof duplexes, back thrusts, pop-ups, detachment folds, fault-bend folds, break thrusts, and piggyback basins. These structures can develop in-sequence or out-of-sequence, remain active for extended periods, or be reactivated. At the largest scale, the scale of the wedge, the fi nite-element model results agree with critical wedge solutions, but geometries differ at the sub-wedge scale because the models contain internal structures not predicted by the critical wedge stress analy- sis. These structures are a consequence of: (1) the complete solution of the govern- ing equations (as opposed to a solution assuming a stress state that is everywhere at yield), (2) the initial fi nite-thickness layers, (3) the spatial and temporal variations of internal and basal strength, and (4) the coupling between surface processes and deformation of the wedge. The structural styles produced in models involving feed- back with surface processes (erosion and sedimentation) are very similar to those mapped in the foothills of the southern Canadian Rockies and elsewhere. Although syndeformational sediments have been removed by postorogenic erosion across the foothills belt, evidence of the interaction between surface processes and deformation is preserved in the structural style.
fold-and-thrust belts; mechanics; numerical; surface processes; thin-skinned
The Formation and Propagation of Matrix Microcracks in Cross-Ply Laminates during Static Loading
Journal of reinforced plastics and composites
11
2
158-178
1992
10.1177/073168449201100204
Recently, a variational mechanics analysis approach has been used to de termine the thermoelastic stress state in cracked, cross-ply laminates (Nairn, J. A. 1989. J. Comp. Mat. , 23:1106). The analysis included a calculation of the energy release rate due to the formation of a microcrack in the 90° plies. This paper describes a series of ex perimental results on a wide variety of composite material systems and of cross-ply layups of generic type [0m,/90n]s. The variational mechanics energy release rate analysis can be used to predict all features of the experimental results and to draw some new conclusions about the progression of damage in cross-ply laminates. The recommended experiments are to measure the density of microcracks as a function of applied stress. Such results can be fit with the energy release rate expression and used to measure the microcracking or intralaminar fracture toughness. The measured microcracking fracture toughnesses are: Hercules AS4/3501-6-240 J/m2, Fiberite 934/T300—690 J/m2, DuPont Avimid® K Polymer/IM6-960 J/m2, Fiberite 977-2/T300-1800 to 2400 J/m2, and ICI PEEK/AS4- 3000 J/m2. Experiments that measure only the stress to initiate microcracking are specifically not recommended because they do not give an accurate measure of the micro cracking fracture toughness.
Ordered Three- and Five-ply Nanocomposites from ABC Block Terpolymer Microphase Separation with Niobia and Aluminosilicate Sols
Chemistry of Materials
21
22
5466-5473
2009
10.1021/cm902626z
We report the first use of a nonfrustrated block terpolymer for the synthesis of highly ordered oxide nanocomposites containing multiple plies. The morphological behavior of 15 ISO-oxide nanocomposites was investigated spanning a large range of compositions along the f(I) = f(S) isopleth using aluminosilicate and niobia sols. Morphologies were determined by transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) measurements. Four morphologies were identified, including core-shell hexagonal, core-shell double gyroid, three-domain lamellae, and core-shell inverse-hexagonal, in order of increasing O + oxide volume fraction. All of the resulting nanocomposites had three- or five-ply morphologies containing domains that were continuous in one, two, or three dimensions. The five-ply core-shell double gyroid phase was only found to be stable when the 0 + oxide domain was a minority. Removal of the polymer enabled simple and direct synthesis of mesoporous oxide materials while retaining the ordered network structure. We believe that advances in the synthesis of multiply nanocomposites will lead to advanced materials and devices containing multiple plies of functional materials.
diblock copolymers; direct access; metal-oxides; network phases; oxide) triblock copolymers; phase-behavior; plumbers nightmare; poly(isoprene-b-styrene-b-ethylene oxide); silica hybrids; thin-films
On Multiple Transverse Cracking in Glass Fibre Epoxy Cross-Ply Laminates
Journal of Materials Science
13
2131-2136
1978
10.1007/BF00739291
An investigation has been made of multiple transverse cracking in glass fibre epoxv cross-ply laminates. Four laminates of differing transverse ply thicknesses were investi gated. Transverse crack spacing was found to decrease with increasing applied stress and decreasing transverse ply thickness. Very close agreement has been found between the experimental results and a multiple cracking theory based on shear lag anaiysis in which the plies remain essentially elastically bonded. In these composites a small modulus change is observed at a strain lower than that at which cracking initiated. This phenomenon is associated with a visual, under some circumstances reversible, whitening effect.
Buckling analysis of cross-ply laminated conical panels using GDQ method
Composites Part B: Engineering
55
440-446
2013
10.1016/j.compositesb.2013.07.003
The buckling analysis of cross-ply laminated conical shell panels with simply supported boundary conditions at all edges and subjected to axial compression is studied. The conical shell panel is a very interesting problem as it can be considered as the general case for conical shells when the subtended angle is set to 2π and also cylindrical panels and shells when the semi-vertex angle is equal to zero. Equations were derived using classical shell theory of Donnell type and solved using generalized differential quadrature method. The results are compared and validated with the known results in the literature. The effects of subtended angle, semi-vertex angle, length, thickness and radius of the panel on the buckling load and mode are investigated.
A. Laminates; B. Buckling; C. Laminate mechanics; Generalized Differential Quadrature (GDQ) method
Postbuckling of angle-ply laminated cylindrical shells with meridional curvature
Thin-Walled Structures
47
3
359-364
2009
10.1016/j.tws.2008.07.002
The influence of meridional curvature on the postbuckling behaviour of angle-ply laminated cylindrical shells subjected to external pressure, torsional load, axial compression and uniform temperature rise is investigated using the semi-analytical finite element approach. The nonlinear governing equations are solved using Newton–Raphson iterative technique coupled with the adaptive displacement control method. The presence of asymmetric perturbation in the form of a small magnitude load spatially proportional to the linear buckling mode shape is considered to trace the postbuckling path. The variation of ply-angle and ply-thickness along the meridional direction is considered. The results presented reveal that the imperfection sensitivity of the cylindrical shells having negative Gaussian curvature decreases with the increase in the magnitude of H/r0 ratio for all the loading cases considered. The imperfection sensitivity of the positive Gaussian curvature shells increases for external pressure, torsional and thermal loading cases, whereas it decreases for axial loading case with the increase in H/r0 ratio.
Angle-ply; Cylindrical shell; Meridional curvature; Postbuckling; Semi-analytical finite element; Thermomechanical
Damage Mechanics and Fatigue Life Assessment of Composite Materials
International Journal of Damage Mechanics
8
339-354
1999
10.1177/105678959900800404
The present state of fatigue life assessment of composite materials is largely empirical. This paper discusses how the discipline of damage mechanics can elevate this status to a mechanisms-based methodology. Specific topics addressed are mechanisms of fatigue damage, characterization of damage and its evolution, criticality of damage and prediction of fatigue life. Data and analysis results for cross ply laminates are used to illustrate and discuss the topics.
Intra and damage analysis of laminated composites using coupled continuum damage mechanics with cohesive interface layer
Composite Structures
120
519-530
2015
10.1016/j.compstruct.2014.10.004
In the present article a model based on coupling of continuum damage mechanics with cohesive interface layer is proposed in order to predict the progressive damages including the large delamination growth in composite laminates. A new interface cohesive constitutive law is developed which is compatible with 3D continuum damage mechanics (CDM). To avoid the difficulties of 3D mesh generation and 3D interface modeling between the layers, the cohesive interface layer is implemented in the Reddy’s full layer-wise plate theory. An angle-ply laminate is analyzed to evaluate the developed CDM+cohesive layer in edge delamination initiation and evolution during uniaxial tension loading. The proposed approach is demonstrated to predict progressive damage and final failure load of angle-ply laminated composites both accurately and effectively.
Angle-ply laminate; Cohesive interface layer; Continuum damage mechanics; Edge delamination
Matrix cracking induced by cyclic ply stresses in composite laminates
Composites Science and Technology
61
15
2327-2336
2001
10.1016/S0266-3538(01)00125-7
The objective of this paper is to review the wealth of experimental results obtained in our laboratory during the last 10 years and the related analyses. The relevant studies essentially involve a brittle-matrix composite (carbon/epoxy T300/914), intended as a model material for characterization under various experimental conditions. The physical and geometrical parameters governing the initiation, accumulation, growth and saturation of matrix cracks under cyclic mechanical loading have been identified. A shear-lag analysis, associated with an energy release rate criterion, is used to predict cracking development in each cross-ply laminate subjected to any fatigue loading. More recently, an experimental program has been achieved to characterize the damage development due to thermal cyclic loading. This investigation brought out the limitations of a purely mechanical approach for the prediction of matrix cracking due to cyclic thermal exposure. © 2001 Published by Elsevier Science Ltd. All rights reserved.
A. polymer-matrix composites; A. Polymer-matrix composites; B. atrix cracking; B. Matrix cracking; Cyclic loading; Fracture mechanics
Responses of cross-ply laminates with viscous interfaces in cylindrical bending
Computer Methods in Applied Mechanics and Engineering
194
823-835
2005
10.1016/j.cma.2004.06.016
The responses of a simply supported cross-ply laminate in cylindrical bending with viscous interfaces are studied in this paper. Because of the introduction of viscous interfaces, the elastic fields in the laminate will depend on the time variable. The problem is solved exactly in the space domain, but approximately in the time domain. State-space method, which is very powerful for analyzing laminated structures, is employed. The variations of state variables with time are simulated using power series expansions. Numerical examples are considered and comparison with existent results validates the efficiency of the present method. ?? 2004 Elsevier B.V. All rights reserved.
Cross-ply laminates; Cylindrical bending; State-space approach; Viscous interface
Engineered disc-like angle-ply structures for intervertebral disc replacement.
Spine
35
8
867-73
2010
10.1097/BRS.0b013e3181d74414
STUDY DESIGN: To develop a construction algorithm in which electrospun nanofibrous scaffolds are coupled with a biocompatible hydrogel to engineer a mesenchymal stem cell (MSC)-based disc replacement.\n\nOBJECTIVE: To engineer a disc-like angle-ply structure (DAPS) that replicates the multiscale architecture of the intervertebral disc.\n\nSUMMARY OF BACKGROUND DATA: Successful engineering of a replacement for the intervertebral disc requires replication of its mechanical function and anatomic form. Despite many attempts to engineer a replacement for ailing and degenerated discs, no prior study has replicated the multiscale hierarchical architecture of the native disc, and very few have assessed the mechanical function of formed neo-tissues.\n\nMETHODS: A new algorithm for the construction of a disc analogue was developed, using agarose to form a central nucleus pulposus (NP) and oriented electrospun nanofibrous scaffolds to form the anulus fibrosus region (AF). Bovine MSCs were seeded into both regions and biochemical, histologic, and mechanical maturation were evaluated with in vitro culture.\n\nRESULTS: We show that mechanical testing in compression and torsion, loading methods commonly used to assess disc mechanics, reveal equilibrium and time-dependent behaviors that are qualitatively similar to native tissue, although lesser in magnitude. Further, we demonstrate that cells seeded into both AF and NP regions adopt distinct morphologies that mirror those seen in native tissue, and that, in the AF region, this ordered community of cells deposit matrix that is organized in an angle-ply configuration. Finally, constructs demonstrate functional development with long-term in vitro culture.\n\nCONCLUSION: These findings provide a new approach for disc tissue engineering that replicates multi-scale form and function of the intervertebral disc, providing a foundation from which to build a multi-scale, biologic, anatomically and hierarchically relevant composite disc analogue for eventual disc replacement.
Algorithms; Animals; Biomechanical Phenomena; Biomechanical Phenomena: physiology; Cattle; Cells, Cultured; Compressive Strength; Compressive Strength: physiology; Extracellular Matrix; Extracellular Matrix: physiology; Fibrocartilage; Fibrocartilage: cytology; Fibrocartilage: physiology; Humans; Hydrogels; Hydrogels: therapeutic use; Intervertebral Disc; Intervertebral Disc: cytology; Intervertebral Disc Displacement; Intervertebral Disc Displacement: surgery; Intervertebral Disc: physiology; Materials Testing; Materials Testing: methods; Mesenchymal Stem Cell Transplantation; Mesenchymal Stem Cell Transplantation: methods; Mesenchymal Stromal Cells; Mesenchymal Stromal Cells: cytology; Mesenchymal Stromal Cells: physiology; Nanofibers; Nanofibers: therapeutic use; Prosthesis Design; Prosthesis Design: methods; Sepharose; Sepharose: therapeutic use; Tissue Engineering; Tissue Engineering: methods; Tissue Scaffolds; Tissue Scaffolds: standards; Tissue Scaffolds: trends; Weight-Bearing; Weight-Bearing: physiology
Discrete ply model of circular pull-through test of fasteners in laminates
Composite Structures
94
10
3082-3091
2012
10.1016/j.compstruct.2012.05.008
In aeronautical structures, assemblies with thin laminates are becoming increasingly usual, especially for fuselage design. In these structures, out-of-plane loads can appear in bolted joints and can lead to progressive punching of the fastener's head in the laminate resulting, in some cases, in a failure mode called pull-through . [1]. This complex phenomenon, which occurs in assemblies, was studied firstly by using a simplified " circular" pull-through test method. Qualitative micrographic examinations showed damage very similar to that observed in impacted specimens. The research presented here extends the Discrete Ply Model Method (DPM) developed by Bouvet et al. . [2] to this case. The finite elements model is based on a particular mesh taking ply orientations into account. Cohesive elements are placed at the interfaces between solid elements to represent matrix cracks and delamination, thus allowing the natural coupling between these two damage modes to be represented. The model shows good correlation with test results, in terms of load/displacement curve, and correct prediction of the damage map until failure, including the splitting phenomenon. © 2012 Elsevier Ltd.
Cohesive element; Composite joints; Experiment; FE modelling; Pull-through
Composites : Part A Experimental and numerical studies of initial cracking in CFRP cross-ply laminates
Composites Part a
68
81-89
2015
10.1016/j.compositesa.2014.09.020
This work is concerned with the conditions for formation of the first (initial) cracks in composite laminates with cutouts or ply drop-offs subjected to in-plane loading. We study here the crack formation on the free edge of CFRP cross-ply laminates experimentally and by numerical stress and failure analysis. The free-edge surface strains are measured by the digital image correlation (DIC) technique. The numerical analysis consists of a two-scale approach, where the macro-level analysis is performed with a three-dimensional finite-element method (3D FEM) and the micro-level analysis uses a periodic unit-cell (PUC) in the transverse plies. The constitutive assumption made for the macro-level analysis is an orthotropic linear thermo-elastic solid for the unidirectional plies with a thin isotropic viscoplastic layer between the longitudinal and transverse plies. In the PUC, the fibers are assumed linear elastic, while the matrix is modeled as an elastic–viscoplastic solid. Crack formation is assumed to occur in the matrix by the dilatation induced brittle failure mechanism for which the dilatation energy density criterion is used.
Analysis of the transverse cracking in hybrid cross-ply composite laminates
Computational Materials Science
46
4
1102-1108
2009
10.1016/j.commatsci.2009.05.019
A modified shear-lag analysis, taking into account the concept of interlaminar shear stress, is employed to evaluate the effect of transverse cracks on the stiffness reductions in different glass/epoxy and graphite/epoxy hybrid cross-ply laminates. The modified shear-lag model is proposed that assumes interlaminar adhesive layer between two neighbouring layers transferring not only interlaminar shear stress but also normal stress. The stress distribution is solved by the used model which rigorously satisfies the stress equilibrium equations, boundary conditions and the traction continuity at interfaces between layers.
Continuum damage mechanics; Crack density; Hybrid cross-ply laminates; Stiffness reduction
Quantized fracture mechanics
Philosophical Magazine
84
2829-2845
2004
10.1080/14786430412331280382
A new energy-based theory, quantized fracture mechanics (QFM), is presented that modifies continuum-based fracture mechanics; stress- and strain-based QFM analogs are also proposed. The differentials in Griffith's criterion are substituted with finite differences; the implications are remarkable. Fracture of tiny systems with a given geometry and type of loading occurs at 'quantized' stresses that are well predicted by QFM: strengths predicted by QFM are compared with experimental results on carbon nanotubes, beta-SiC nanorods, alpha-Si3N4 whiskers, and polysilicon thin films; and also with molecular mechanics/dynamics simulation of fracture of carbon nanotubes and graphene with cracks and holes, and statistical mechanics-based simulations on fracture of two-dimensional spring networks. QFM is self-consistent, agreeing to first-order with linear elastic fracture mechanics (LEFM), and to second-order with non-linear fracture mechanics (NLFM). For vanishing crack length QFM predicts a finite ideal strength in agreement with Orowan's prediction. In contrast to LEFM, QFM has no restrictions on treating defect size and shape. The different fracture Modes (opening I, sliding II and tearing III), and the stability of the fracture propagations, are treated in a simple way.
Static and dynamic FE analysis of piezoelectric integrated thin-walled composite structures with large rotations
Composite Structures
112
345-357
2014
10.1016/j.compstruct.2014.02.029
A geometrically nonlinear finite element (FE) model based on large rotation shell theory is developed for static and dynamic analysis of piezoelectric integrated thin-walled structures with cross-ply or angle-ply laminates. The implemented large rotation theory has six kinematic parameters expressed by five nodal degrees of freedom (DOFs) based on first-order shear deformation (FOSD) hypothesis. An eight-node shell element with five mechanical DOFs and one electrical DOF is employed. Due to the assumption of small strains and weak electric potential, linear constitutive equations and constant electric field through the thickness are considered. The large rotation piezoelectric coupled FE model is validated by one static benchmark problem and afterwards applied to the static and dynamic analysis of piezoelectric integrated smart plates and shells composed of cross-ply or angle-ply laminates.
Composite structures; Finite element; Large rotations; Piezoelectric; Smart structures
Stability analysis of cross-ply laminated shells of revolution using a curved axisymmetric shell finite element
Thin-Walled Structures
49
6
732-742
2011
10.1016/j.tws.2011.01.005
A curved axisymmetric shell finite element based on a consistent first-order shear deformable shell theory is developed for the linear stability analysis of cross-ply laminated shells of revolution under compressive loads. Finite element analysis results are presented for isotropic, orthotropic and cross-ply laminated shells of revolution in comparison with the analytical and numerical results found in the literature. These comparisons demonstrate the applicability and the high performance of the element in stability analysis of thin and moderately thick cross-ply laminated composite shells of revolution under compressive loads. © 2011 Elsevier Ltd. All rights reserved.
Buckling; Finite element analysis; Laminated composite; Shell
Tool-Ply Friction In Composite Forming
AIP Conference Proceedings
907
1
1080-1085
2007
10.1063/1.2729658
Friction between fibre composite laminates and rigid tool materials is an important phenomenon in composite forming processes and the resulting product geometry, fibre orientations and fibre stresses. Pull‐out experiments are presented and compared with a novel meso mechanical model based on Reynolds’ equation for thin film lubrication. The film thickness is derived from this analysis, rather than postulated as in earlier publications. Good agreement is found between the experiments, the meso mechanical model results and earlier empirically determined master curves.
Fracture mechanics of a shaft-loaded blister of thin flexible membrane on rigid substrate
International Journal of Fracture
74
2
181-197
1990
10.1007/BF00036264
A shaft-loaded blister test has been developed to measure the interfacial energy W of a thin flexible polymeric film adhered to a rigid substrate. A theoretical analysis is given of an axisymmetric debond ('blister') in terms of an external applied load P, tensile stretching modulus E and thickness h of the adhering layer. The fracture mechanics model presented considers both elastic and elastoplastic deformations in the thin film. The intrinsic stable interface debonding process provides an attractive alternative to the conventional adhesion measurement techniques.
Mechanics of thin films and microdevices
IEEE Transactions on Device and Materials Reliability
4
2
176-188
2004
10.1109/TDMR.2004.829901
This paper discusses the latest developments in nanomechanics of thin films with applications in microelectromechanical systems (MEMS) and microelectronics. A precise methodology that combines in situ atomic force microscopy (AFM) surface measurements of uniaxially tension-loaded MEMS specimens and strain analysis via digital image correlation (DIC) achieving 0.1 pixel spatial displacement resolution is presented. By this method, the mechanical deformation of thin films was obtained in areas as small as 4 × 4 μm and with 1-2 nm spatial displacement resolution supporting the derivation of interrelations between the material microstructure and the local mechanical properties. This methodology provided for the first time the values of Young's modulus and Poisson's ratio from specimens with cross-sections as small as 2 × 6 μm. The value of properties derived via AFM/DIC demonstrated very limited scatter compared to indirect mechanical property measurement methods. The application of this technique on nonuniform geometries resolved nanoscale displacement and strain fields in the vicinity of ultrasharp elliptical perforations achieving very good agreement with finite element models. Furthermore, the stochastic and deterministic material failure properties described via Weibull statistics and fracture toughness, respectively, are illustrated for brittle thin films. Failure initiated at notches was found to be influenced by the local radius of curvature and the stress concentration factor. Precise fracture toughness values for MEMS materials were obtained from MEMS specimens with atomically sharp cracks. These studies were supported by measurements of displacements/strains conducted for the first time in the vicinity of mathematically sharp cracks via the AFM/DIC method. The method can be applied to a variety of thermomechanical reliability problems in multilayered thin films and inhomogeneous/anisotropic materials.
Fracture toughness; Microelectromechanical systems (MEMS); Nanomechanical measurements; Poisson's ratio; Young's modulus
Mechanical performance of thin-walled tubular composite elements under uniaxial loading part 1: tensile behavior
Composite Structures
31
2
163-170
1995
10.1016/0263-8223(95)00013-5
Filament wound thin-wall CFRP and GFRP composite tubes were tested under uniaxial (longitudinal) tensile loading up to failure. Elastic and strength properties as well as failure mechanisms were evaluated as related to the wall lay-up configuration. Angle-ply lay-ups of different (± θ)n orientations were compared with tubes having the same thickness but where internal and external θ plies were replaced by hoop (90) layers. Results showed that this replacement improved axial ultimate tensile strength as compared with the angle-ply reference. The three directional specimens with the hoop layers failed gradually at stress levels beyond the predicted first ply failure (FPF) as compared with angle-ply references whose behavior was highly affected and became nonlinear above FPF. Analytical prediction for elastic behavior and strength as functions of fiber orientation agreed well with experimental trends and demonstrated the advantage of three directional configuration as compared with angle-ply tube. This was attributed to the transverse stabilizing effect of the hoop layers which was manifested by a significant reduction of the Poisson ratio.
Some mechanics for the adhesion of thin films
Thin Solid Films
181
397-406
1989
10.1016/0040-6090(89)90508-7
There has recently been an increased interest in the mechanical properties of thin films, owing to their importance in electronic packaging applications. A review of some of the failure mechanisms associated with these films are presented in this paper. Films may fail by a number of different mechanisms depending upon the geometry and the stresses in the film. These include buckling, "mud-cracking", and/or delamination. A complete understanding of film failure requires consideration of the forces that drive crack growth, those that resist it, and an appreciation of what determines the mode of failure. Some of these aspects are explored in this paper by a discussion of the decohesion of tensile films from a brittle substrate. Although failure may occur by delamination of the interface, often it is the substrate that cracks, rather than the interface: the stresses in the film tend to drive the crack into the substrate. This tendency may be counteracted, however, ifa weak interface makes it energetically favourable for failure to occur at the interface. As well as influencing the preferred crack trajectory, the stresses may also influence the apparent fracture toughness of the interface. This is considered in the last section of this paper and is illustrated by a discussion of some model experiments.
Kinetics of iodine doping and dedoping processes in thin layers of ply-p-phenylene azomethine
Sensors and Actuators
7
3
199-207
1985
10.1016/0250-6874(85)85021-6
A new method for preparing thin films of a nitrogen-containing aromatic polymer (polyparaphenylene azomethine) is reported. Electrical properties of these thin films are reviewed when they are doped with halogen acceptors such as iodine gas. The kinetics of conductivity is analyzed in terms of adsorption and desorption rates of the doping species. Thin layers of polyparaphenylene azomethin (PPCN) exhibit a good reversibility in the doping/dedoping process and their conductivity response is sensitive to the partial pressure of the doping gas. PPCN or electroactive polymers of this type may be used as vapour-sensitive materials in gas detectors.
Predicting transverse crack formation in cross-ply laminates
Composites Science and Technology
58
7
1069-1081
1998
10.1016/S0266-3538(96)00142-X
As a contribution to the exercise to compare methods of predicting damage in composites and subsequent failure, this paper describes a method of predicting the values of the applied stresses for which transverse cracks form in a cross-ply laminate subject to biaxial loading, taking full account of both anisotropy and thermal residual stresses. The analysis is based upon an accurate technique for determining the stress and diplacement distributions in multiple-ply cross-ply laminates having ply cracks in one orientation. The resulting relationships governing crack formation are exceedingly simple in form involving parameters that may be defined and measured at the macroscopic laminate level, thus offering engineering methods that have great potential for use in design. The methods are then applied to the prediction of transverse cracking in a specific glass-reinforced plastic system for the case of the uniaxial loading of a [0/90]s GRP laminate, and for the equi-biaxial loading of a [??45]s laminate.
crack closure; cross-ply laminates; ply cracking; stress transfer; thermoelastic constants
Simulations and experiments of open hole tension tests – Assessment of intra-ply plasticity, damage, and localization
Composites Science and Technology
72
10
1090-1095
2012
10.1016/j.compscitech.2011.07.021
Laminated composites with various layups of unidirectional carbon fiber reinforced epoxy are investigated by numerical modeling and experimental testing. Open hole tension configurations are studied with special considerations of the non-linear behavior of the plies. Computational predictions are based on an anisotropic constitutive material law which includes plasticity and damage, the latter comprise hardening as well as softening. Experimental evaluations include a 3D image correlation photogrammetry system for capturing the strain fields of the sample surfaces. The open hole tension configuration represents a structural problem, in which the stress distribution is highly non-uniform. The measured and the predicted strain fields as well as the localization zones show very good agreement which indicates that the governing intra-ply mechanisms are captured well by the constitutive law.
A. Laminate; C. Anisotropy; C. Damage mechanics; C. Finite element analysis (FEA); D. Testing
Transverse Ply Cracking in Toughened and Untoughened Graphite/Epoxy and Graphite/Polycyanate Crossply Laminates
Journal of composite materials
25
12
1653-1667
1991
10.1177/002199839102501206
Transverse ply cracking of five toughened and untoughened graphite/epoxy and graphite/polycyanate laminates was studied using crossply laminates. Two different theoretical approaches, variational mechanics and resistance curves based on shearlag approximation, were used to analyze the data. Resistance of the laminates to transverse ply cracking was determined. Both theories show the same ranking of the laminates with respect to their resistance to microcracking. These results were compared with the critical strain energy release rate data obtained on the resins and the laminates.
Damage response of stitched cross-ply laminates under impact loadings
Engineering Fracture Mechanics
74
4
500-514
2007
10.1016/j.engfracmech.2006.05.012
The impact response of stitched graphite/epoxy laminates was examined with the aim of evaluating the efficiency of stitching as a reinforcing mechanism able to improve the delamination resistance of laminates. The investigation, which focussed on two classes of cross-ply stacking sequences ([03/903]s and [0/90]3s), showed that the role of stitches in controlling damage progression of laminates and their capability to reduce the impact sensitivity of specimens are greatly dependent on the impact behaviour of base (unstitched) laminates. In [03/903]s laminates, in particular, stitching is able to reduce damage area, on condition that the impact energy is higher than a threshold level and delaminations are sufficiently developed. In [0/90]3s laminates, on the other hand, stress concentration regions generated by the stitching process appear to promote the initiation and propagation of fibre fractures, thereby inducing a decrease in the penetration resistance of the laminate. ?? 2006 Elsevier Ltd. All rights reserved.
Composites; Damage; Impact; Stitching
On the mechanics of distortion in thin-walled open sections
Thin-Walled Structures
48
7
469-481
2010
10.1016/j.tws.2010.02.001
This paper addresses the distortional kinematics and mechanics of thin-walled sections and provides clear definitions of cross-section properties that characterise the distortional deformation, as it is usually done for conventional modes (axial, bending and torsion). In particular, a procedure to build the distortional displacement field of a given thin-walled section is described. The first part of the paper describes the essentials of distortion in comparison with the conventional modes of classical beam theories. It is shown that primary warping is the key factor that controls the distortion of thin-walled sections. Then, an analytical procedure to determine the distortional warping displacement distribution of a given cross-section is described, on the basis of orthogonality conditions existing between the distortional and conventional modes. Next, an overview of the kinematical assumptions underlying the distortional deformation is presented and a simple procedure to build distortional displacement fields of thin-walled sections is provided. This procedure is then applied to obtain the distortional displacement field of C-sections and general expressions of distortional cross-section properties are given. Finally, a simple example is presented to illustrate how the distortional displacement field of a C-section is built, on the basis of simple kinematics principles. The distortional critical stress and half wavelength are determined and good agreement with exact numerical estimates is found.
Analytical formulae; C-sections; Distortional buckling; Distortional mechanics; Kinematical assumptions; Thin-walled columns; Warping
A Three-Dimensional Ply Failure Model for Composite Structures
International Journal of Aerospace Engineering
2009
1-22
2009
10.1155/2009/486063
A fully 3D failure model to predict damage in composite structures\nsubjected to multiaxial loading is presented in this paper. The formulation\nincorporates shear nonlinearities effects, irreversible strains,\ndamage and strain rate effects by using a viscoplastic damageable\nconstitutive law. The proposed formulation enables the prediction\nof failure initiation and failure propagation by combining stress-based,\ndamage mechanics and fracture mechanics approaches within an unified\nenergy based context. An objectivity algorithm has been embedded\ninto the formulation to avoid problems associated with strain localization\nand mesh dependence. The proposed model has been implemented into\nABAQUS/Explicit FE code within brick elements as a userdefined material\nmodel. Numerical predictions for standard uniaxial tests at element\nand coupon levels are<p>presented and discussed.
Continuum Damage Mechanics Models for the Analysis of Progressive Failure in Open-Hole Tension Laminates
AIAA
1-18
2011
10.2514/6.2011-1861
The performance of a state-of-the-art continuum damage mechanics model for interlaminar damage, coupled with a cohesive zone model for delamination is examined for failure prediction of quasi-isotropic open-hole tension laminates. Limitations of continuum representations of intra-ply damage and the effect of mesh orientation on the analysis predictions are discussed. It is shown that accurate prediction of matrix crack paths and stress redistribution after cracking requires a mesh aligned with the fiber orientation. Based on these results, an aligned mesh is proposed for analysis of the open-hole tension specimens consisting of different meshes within the individual plies, such that the element edges are aligned with the ply fiber direction. The modeling approach is assessed by comparison of analysis predictions to experimental data for specimen configurations in which failure is dominated by complex interactions between matrix cracks and delaminations. It is shown that the different failure mechanisms observed in the tests are well predicted. In addition, the modeling approach is demonstrated to predict proper trends in the effect of scaling on strength and failure mechanisms of quasi-isotropic open-hole tension laminates.
Vibration of cross-ply laminated composite plates subjected to initial in-plane stresses
Thin-Walled Structures
40
7-8
557-571
2002
10.1016/S0263-8231(02)00012-5
Natural frequencies, modal displacements and stresses of cross-ply laminated composite plates subjected to initial in-plane stresses are analyzed by taking into account the effects of higher-order deformations and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for rectangular laminates is derived through Hamilton's principle. Several sets of truncated approximate theories can be derived to solve the eigenvalue problems of a simply supported laminated plate. After examining the convergence properties of the lowest natural frequency, only the numerical results for M=5, which are considered to be sufficient with respect to the accuracy of solutions, are presented. Numerical results are compared with those of the published existing three-dimensional theory and FEM solutions. The modal displacement and stress distributions in the thickness direction are plotted in figures. The buckling stresses can be obtained in terms of the natural frequencies of the laminates without initial in-plane stresses. ?? 2002 Elsevier Science Ltd. All rights reserved.
Composite; Cross-ply; Higher-order theory; Laminated plate; Modal displacement and stress; Vibration
Effect of ply angle misalignment on out-of-plane deformation of symmetrical cross-ply CFRP laminates: Accuracy of the ply angle alignment
Composite Structures
93
4
1225-1230
2011
10.1016/j.compstruct.2010.10.019
This paper discusses the accuracy of ply angle alignment and how it relates to out-of-plane deformation in carbon fiber reinforced plastics (CFRP) laminates. We investigated the deformation of symmetrical cross-ply laminates under hot and humid conditions. In spite of the symmetrically stacked laminates, unpredictable out-of-plane deformation occurred over time due to ply angle misalignment. The deformation was unstable and disproportionate to the absorbed moisture. A Monte Carlo simulation based on laminate theory was performed to quantify the deformation induced by the ply angle misalignment. Symmetrical cross-ply laminates were found to twist as they absorbed water when they underwent ply angle misalignments. By comparing the analytical results with experimental results, we concluded that a standard deviation of approximately 0.4?? exists as ply angle misalignment in the laminates used in this study and that this slight ply angle misalignment can be a significant factor in out-of-plane deformation of cross-ply laminates. ?? 2010 Elsevier Ltd.
CFRP; Dimensional stability; Moisture absorption; Ply angle misalignment
Fracture Mechanics: An Introduction
Book
123
369
2005
New developments in the applications of fracture mechanics to engineering problems have taken place in the last years. Composite materials have extensively been used in engineering problems. Quasi-brittle materials including concrete, cement pastes, rock, soil, etc. all benefit from these developments. Layered materials and especially thin film/substrate systems are becoming important in small volume systems used in micro and nanoelectromechancial systems (MEMS and NEMS). Nanostructured materials are being introduced in our every day life. In all these problems fracture mechanics plays a major role for the prediction of failure and safe design of materials and structures. These new challenges motivated the author to proceed with the second edition of the book. The second edition of the book contains four new chapters in addition to the ten chapters of the first edition. The fourteen chapters of the book cover the basic principles and traditional applications, as well as the latest developmentsof fracture mechanics as applied to problems of composite materials, thin films, nanoindentation and cementitious materials. Thus the book provides an introductory coverage of the traditional and contemporary applications of fracture mechanics in problems of utmost technological importance. With the addition of the four new chapters the book presents a comprehensive treatment of fracture mechanics. It includes the basic principles and traditional applications as well as the new frontiers of research of fracture mechanics during the last three decades in topics of contemporary importance, like composites, thin films, nanoindentation and cementitious materials. The book contains fifty exampleproblems and more than two hundred unsolved problems. A "Solutions Manual" is available upon request for course instructors from the author.
Adhesion and debonding of multi-layer thin film structures
Engineering Fracture Mechanics
61
1
141-162
1998
10.1016/S0013-7944(98)00052-6
A fracture mechanics technique to quantitatively measure the adhesion or interfacial fracture resistance of interfaces in thin film structures is described. Adhesion values obtained for the technologically important SiO2/TiN interface in microelectronic interconnect structures are related to a range of material, mechanical and design parameters which include interface morphology and adjacent ductile layer thickness. In addition, the interface was shown to be susceptible to environmentally-assisted subcritical debonding similar to stress corrosion cracking of SiO2 glass in moist air environments. Subcritical debonding behavior was sensitive to a range of material and design parameters, and is expected to have important implications for long term device reliability.
Adhesion; Debonding; Interconnect; Stress-corrosion; Thin film
Derivations of energy-based modelling for ply cracking in general symmetric laminates
Journal of Composite Materials
47
20-21
2641-2673
2013
10.1177/0021998313492359
Recently, as a part of the third World-Wide Failure Exercise (WWFE-III), the author provided a modelling capability, entitled Energy methods for modelling damage in laminates', published in this special issue (2013, Vol 20-21, pages 2613-2640). This paper describes full details and the mathematical basis of the author's methods used to predict the properties of undamaged laminates and the development of damage in laminates, based on an energy balance methodology.
cracking; damage; energy-based; laminate; micro-mechanics; orthotropic; wwfe-iii
Fiber composite thin shells subjected to thermal buckling loads
Computers & Structures
53
6
1263-1274
1994
10.1016/0045-7949(94)90394-8
The results of parametric studies to assess the effects of various parameters on the buckling behavior of angle-ply, laminated thin shells in a hot environment are presented in this paper. These results were obtained by using a three-dimensional finite element analysis. An angle-ply, laminated thin shell with fiber orientation of [theta/-theta]2 was subjected to compressive mechanical loads. The laminated thin shell has a cylindrical geometry. The laminate contained T300 graphite fibers embedded in an intermediate-modulus, high-strength (IMHS) matrix. The fiber volume fraction was 55% and the moisture content was 2%. The residual stresses induced into the laminated structure during the curing were taken into account. Parametric studies were performed to examine the effect on the critical buckling load of the following parameters: cylinder length and thickness, internal hydrostatic pressure, different ply thicknesses, different temperature profiles through the thickness of the structure, and different layup configurations and fiber volume fractions. In conjunction with these parameters the ply orientation varied from 0-degree to 90-degrees. Seven ply angles were examined: 0-degree, 15-degrees, 30-degrees, 45-degrees, 60-degrees, 75-degrees, and 90-degrees. The results show that the ply angle theta and the laminate thickness had significant effects on the critical buckling load. The fiber volume fraction and the internal hydrostatic pressure had important effects on the critical buckling load. The cylinder length had a moderate influence on the buckling load. The thin shell with [theta/-theta]2 or [theta/-theta]s angle-ply laminate had better buckling-load performance than the thin shell with [theta]4 off-axis laminate. The temperature profiles through the laminate thickness and various laminates with the same thickness but with the different ply thickness had insignificant effects on the buckling behavior of the thin shells.
Characterization of R-curve behavior of translaminar crack growth in cross-ply composite laminates using digital image correlation
Engineering Fracture Mechanics
117
51-70
2014
http://dx.doi.org/10.1016/j.engfracmech.2014.01.010
Abstract This paper presents experimental methods to estimate crack-tip field parameters and characterize R-curve behaviors of translaminar fracture in cross-ply composite laminates using digital image correlation. The investigated crack-tip field parameters include stress intensity factor, energy release rate and effective crack length. The nonlinear least-squares method and conservation integrals are used to determine these parameters from elastic far-field displacements, based on the homogeneous approximation of anisotropic solids for composite laminates. The sources of error of the two parameter-estimation methods are investigated. The results of the two methods show good consistency. Finally, the two-stage rising R-curves are obtained with acceptable accuracy.
Cross-ply composite laminates; Digital image correlation; R-curve; Stress intensity factor; Translaminar fracture
Discrete Differential Geometry of Thin Materials for Computational Mechanics
ProQuest Dissertations and Theses
135
2013
Instead of applying numerical methods directly to governing equations, another approach to computation is to discretize the geometric structure specific to the problem first, and then compute with the discrete geometry. This structure-respecting discrete-differential-geometric (DDG) approach often leads to new algorithms that more accurately track the physically behavior of the system with less computational effort. Thin objects, such as pieces of cloth, paper, sheet metal, freeform masonry, and steel-glass structures are particularly rich in geometric structure and so are well-suited for DDG. I show how understanding the geometry of time integration and contact leads to new algorithms, with strong correctness guarantees, for simulating thin elastic objects in contact; how the performance of these algorithms can be dramatically improved without harming the geometric structure, and thus the guarantees, of the original formulation; how the geometry of static equilibrium can be used to efficiently solve design problems related to masonry or glass buildings; and how discrete developable surfaces can be used to model thin sheets undergoing isometric deformation.
0984:Computer science; Applied sciences; Computational mechanics; Computer science; Contact mechanics; Discrete differential geometry; Thin structures
Thermal conductivity and expansion of cross-ply composites with matrix cracks
Journal of the Mechanics and Physics of Solids
43
8
1175-1198
1995
10.1016/0022-5096(95)00033-F
Theoretical models are developed for heat conduction and thermal expansion in a fiber-reinforced ceramic cross-ply laminate containing an array of parallel transverse matrix cracks. Two stages of the transverse matrix cracks are considered: Stage-I with tunnel cracks in the 90 ° plies aligned parallel to the fibers, and Stage-II with cracks extended across both the 90 and 0 ° plies with intact fibers bridging the matrix in the 0 ° plies. The effect of debonded fiber-matrix interfaces in the 0 ° plies is also considered in Stage-II. Approximate closed form solutions for the overall in-plane thermal conductivities and coefficients of thermal expansion (CTEs) as functions of matrix crack spacing and constituent properties are obtained using an approach which combines an analysis akin to a shear-lag analysis with finite element results. Emphasis is placed on the important class of composites whose fiber expansivity is smaller than that of the matrix. For this class, matrix cracking and interfacial debonding results in reduced thermal expansivity. Interfacial debonding has a significant effect on both longitudinal conductivity and thermal expansivity, especially the latter. Comparisons between the present model predictions and numerical and experimental results are provided where these are available.
Micromechanisms of interlaminar fracture in carbon fibre reinforced plastics at multidirectional ply interfaces under static and cyclic loading
Plastics, Rubber and Composites Processing and Applications
27
5
220-226
1998
Delaminations have been grown at 0°/0° and 0°/90° ply interfaces under mixed mode static and cyclic loading, using the mixed mode bending test. Fractographic analysis of the failure surfaces by scanning electron microscopy gave insights into the micromechanisms of delamination growth. Improved delamination resistance with an increasing mode II component was attributed to an increase in the total surface area generated. There was a secondary cracking mechanism at 0°/90° ply interfaces which resulted in slightly higher mixed mode toughnesses. Fatigue in thermoset matrix composites is very similar to static failure since there is no mechanism comparable to dislocation movement in metals by which damage can migrate and accumulate under low cyclic stresses. The relatively high scatter in composite toughness was explained in terms of variations in the spatial arrangement of fibres. It was shown how the examination of shear cusps may be used to identify crack growth directions in post-mortem failure investigations
bending; Carbon; Carbon fiber reinforced plastics; carbon fibre reinforced plastics; Composite micromechanics; Crack initiation; Crack propagation; Damage; Delamination; electron microscopy; Failure; fatigue; Fatigue of materials; Fractography; fracture; FRACTURE MECHANICS; fracture toughness; Interfaces; Load testing; Metals; Microscopy; Plastics; Reinforced plastics; Resistance; Scanning; Scanning electron microscopy; Stress analysis; Stresses; Surfaces; Thermosets; Toughness
The mechanics and physics of thin film decohesion and its measurement
Interface Science
3
3
169-193
1996
10.1007/BF00191045
The intent of this review is to utilize the mechanics of thin films in order to define quantitative procedures for predicting interface decohesion motivated by residual stress. The emphasis is on the role of the interface debond energy, especially methods for measuring this parameter in an accurate and reliable manner. Experimental results for metal films on dielectric substrates are reviewed and possible mechanisms are discussed.
adhesion measurement; blister test; coatings; cracking; interface toughness; microscratch; peel; test
Actin cortex mechanics and cellular morphogenesis.
Trends in cell biology
22
10
536-45
2012
10.1016/j.tcb.2012.07.001
The cortex is a thin, crosslinked actin network lying immediately beneath the plasma membrane of animal cells. Myosin motors exert contractile forces in the meshwork. Because the cortex is attached to the cell membrane, it plays a central role in cell shape control. The proteic constituents of the cortex undergo rapid turnover, making the cortex both mechanically rigid and highly plastic, two properties essential to its function. The cortex has recently attracted increasing attention and its functions in cellular processes such as cytokinesis, cell migration, and embryogenesis are progressively being dissected. In this review, we summarize current knowledge on the structural organization, composition, and mechanics of the actin cortex, focusing on the link between molecular processes and macroscopic physical properties. We also highlight consequences of cortex dysfunction in disease.
Actins; Actins: metabolism; Actomyosin; Actomyosin: metabolism; Animals; Cell Shape; Humans; Muscle Tonus
Multi-scale modeling in damage mechanics of composite materials
Journal of Materials Science
41
20
6800-6812
2006
10.1007/s10853-006-0210-9
Abstract This paper addresses the multi-scale modeling aspects of damage in composite materials. The multiplicity of the scales of the operating mechanisms is discussed and clarified by taking examples of damage in a unidirectional ceramic matrix composite and in a cross ply polymer matrix composite laminate. Two multi-scale modeling strategies––the hierarchical and the synergistic––are reviewed in the context of deformational response. Finally, the “big picture” as it relates to the cost-effective manufacturing of composite structures intended for long-term performance is outlined and desired future direction in multi-scale modeling is discussed.
X-ray studies on optical and structural properties of ZnO nanostructured thin films
Superlattices and Microstructures
39
267-274
2006
10.1016/j.spmi.2005.08.048
X-ray absorption near-edge fine structure (XANES) studies have been carried out on nanostructured ZnO thin films prepared by atmospheric pressure chemical vapour deposition (APCVD). Films have been characterized by X-ray diffraction (XRD) and optical luminescence spectroscopy exciting with laser light (PL) or X-ray (XEOL). According to XRD measurements, all the APCVD samples reveal a highly (002) oriented crystalline structure. The samples have different thickness (less than 1 ??m) and show significant shifts of the PL and XEOL bands in the visible region. Zn K-edge XANES spectra were recorded using synchrotron radiation at BM08 of ESRF (France), by detecting photoluminescence yield (PLY) and X-ray fluorescence yield (FLY). The differences between the PLY- and FLY-XANES confirm the possibility of studying the local environment in the luminescence centres and to correlate the structural and optical properties of ZnO nanostructured samples. ?? 2005 Elsevier Ltd. All rights reserved.
A simple approach for the analysis of embedded ply drops in composite and sandwich laminates
Composites Science and Technology
59
1213-1226
1999
10.1016/S0266-3538(98)00160-2
This paper presents a newly developed unified approach for the analysis and design of embedded ply drops in composite and sandwich laminates. In the analysis, the sub-laminates are modelled as wide beams, where the laminate stiffnesses are obtained from the classical thin-laminate theory. The effect of having unsymmetric and unbalanced sub-laminates (e.g. coupling effects) are included in the analysis. The interface/'resin-rich' layers are modelled as continuously distributed linear tension/compression and shear springs, and the interaction between the core material and the face laminates is modelled by using a 'two-parameter' elastic foundation model. The governing equations are formulated in terms of sets of first-order ordinary differential equations. The multiple-point boundary value problem constituted by the differential equations together with the imposed boundary conditions is solved numerically by direct integration and use of the 'multi-segment method' of integration.
C. Finite element analysis; C. Laminates; Embedded ply drops; Interface/'resin-rich' behaviour; 'Multi-segment method' of integration
Buckling, strength and failure mechanics of thin-walled structures
Thin-Walled Structures
41
89-90
2003
10.1016/S0263-8231(02)00081-2
Editorial for special issue of Thin-Walled Structure journal containing conference and workshop papers from the Third International Conference on Thin-Walled Structures and the International Workshop on Finite Element Methods applied to the analysis of Thin-Walled Structures.
Mechanical buckling: Mechanics, metrology, and stretchable electronics
Advanced Functional Materials
19
10
1526-1536
2009
10.1002/adfm.200801065
Mechanical buckling usually means catastrophic failure in structural mechanics systems. However, controlled buckling of thin films on compliant substrates has been used to advantage in diverse fields such as micro-/nanofabrication, optics, bioengineering, and metrology as well as fundamental mechanics studies. In this Feature Article, a mechanical buckling model is presented, which sprang, in part, from the buckling study of high-quality, single-crystalline nanomaterials. To check the mechanical-buckling phenomenon down to the nano-/molecular scale, well-aligned single-walled carbon nanotube arrays and cross linked carbon-based monolayers are transferred from growth substrate onto elastomeric substrate and then they are buckled into well-defined shapes that are amenable to quantitative analysis. From this nano- or molecular-scale buckling, it is shown that the mechanical moduli of nanoscale materials can easily be determined, even using a model based on continuum mechanics. In addition, buckling phenomena can be utilized for the determination of mechanical moduli of organic functional materials such as poly(3-hexylthiophene) (P3HT) and P3HT/6,6-phenyl-C61-butyric acid methyl ester (PCBM) composite, which are widely used for organic transistors and organic photovoltaics. The results provide useful information for the realization of flexible and/or stretchable organic electronics. Finally, the fabrication and applications of “wavy, stretchable” single-crystal Si electronics on elastomeric substrates are demonstrated.
Mechanics of freely-suspended ultrathin layered materials
Annalen der Physik
527
1-2
27-44
2015
10.1002/andp.201400153
The study of atomically thin two-dimensional materials is a young and rapidly growing field. In the past years, a great advance in the study of the remarkable electrical and optical properties of 2D materials fabricated by exfoliation of bulk layered materials has been achieved. Due to the extraordinary mechanical properties of these atomically thin materials, they also hold a great promise for future applications such as flexible electronics. For example, this family of materials can sustain very large deformations without breaking. Due to the combination of small dimensions, high Young's modulus and high crystallinity of 2D materials, they have attracted the attention of the field of nanomechanical systems as high frequency and high quality factor resonators. In this article, we review experiments on static and dynamic response of 2D materials. We provide an overview and comparison of the mechanics of different materials, and highlight the unique properties of these thin crystalline layers. We conclude with an outlook of the mechanics of 2D materials and future research directions such as the coupling of the mechanical deformation to their electronic structure.
2D materials; atomically thin crystals; mechanical properties; nanomechanical resonators
Analysis of multiple matrix cracking in [±θm/90n]s composite laminates. Part 2: Development of transverse ply cracks
Composites
23
5
299-304
1992
10.1016/0010-4361(92)90328-R
In this paper the progressive transverse ply cracking in [±θm/90n]s composite laminates is investigated theoretically. A general and simple expression for the energy release rate due to transverse matrix cracking is obtained using the potential energy approach in classical fracture mechanics and the assumption of a through-the-thickness flaw; thermal residual stresses are taken into account. The laminate resistance to crack multiplication is examined for both uniform and nonuniform crack spacing by substituting the measured applied stress/crack density data into corresponding energy release rate expressions. The resistance curve concept is employed to predict crack growth with increasing applied load. The results indicate that the assumption of uniform cracking and a resistance curve concept is a convenient and acceptable method for modelling crack initiation and multiplication in composite laminates.
composite materials; crack density; crack spacing parameter; cross-ply laminates; energy release rate; modelling; resistance curve; transverse ply cracking
Mechanics of compressive stress evolution during thin film growth
J.Mech.Phys.Solids
15
1996
2127-2148
2003
10.1016/j.jmps.2003.09.013
Based on recent in situ measurements, Chason et al.(2002) proposed that the evolution of compressive stress during thin lm growth by vapor deposition is due to an increase in surface chemical potential in the presence of growth ux and the consequent exchange of adatoms between the free surface and the grain boundaries.Based on this hypothesis, we present a model for grain boundary stress evolution during thin lm growth.To illustrate the mechanics of the problem, rst it is assumed that the local normal stress on the grain boundary is proportional to the local grain boundary opening only.The resulting “linear spring” model captures all essential features of the experimental observations.A more accurate description of the grain boundary stress evolution is presented by modeling the stress eld due to the material inserted into the grain boundary as that resulting from a continuous distribution of dislocations along the grain boundary.The adatom flux between the grain boundary and the free surface is assumed to be proportional to the dierence in chemical potential between the two.This model successfully explains a wide range of experimental observations, including the development of compressive stress during room temperature growth, eect of growth rate on the kinetics of compressive stress evolution and the continued tensile stress generation during low-temperature growth.
adatom; Adatom; Grain boundary diffusion; grain boundary di usion; stress evolution; Stress evolution; Thin film; thin ÿlm
Constrained 90-deg ply cracking in 0/90/0 and+ or- 45/90/ or+ 45 CFRP laminates
Composite Materials: Fatigue and Fracture
84-99
1986
The strength distribution of 90-deg plies in the laminates (±6/90„), with 6 = 0 deg and 45 deg and n = 2, 3, and 6 is described in the form of a two-parameter Weibull distribution. A common feature for both orientations of surface layers is that at decreasing 90-deg ply thickness the characteristic strength and shape parameter increase. The reason is that the surface layers suppress a growth of the defects in the 90-deg ply which are lying close to the interface with the surface layers. This causes the apparent shape parameter to increase from a value a = 6.4 for a thick 90-deg ply (which is comparable to the shape parameter determined on a unidirectional laminate) to a shape parameter of a = 10.47 for a thin 90-deg ply (n = 2) in case of the (02/90,), laminate. Further, it is shown that crack formation in the 90-deg plies of the (±45/90,), laminates is strongly influenced by the severe edge stresses. This causes the applied one-dimensional fracture strain criterion to be inaccurate for the (±45/90,), laminates.
carbon fibre reinforced plastic (CFRP); composite materials; cross-ply cracking; edge effect; graphite composites; Weibull strength distribution
Analysis of laminates with ply drops
Composites Science and Technology
61
5
749-758
2001
10.1016/S0266-3538(01)00010-0
Thickness tapered laminates obtained by terminating a certain number of plies contain resin-rich areas called 'resin pockets' near ply drops, where high stress concentrations exist. Study of the effects of ply drops and resin pockets on the tensile behaviour of tapered laminates considering certain important parameters like taper angle, the number of plies dropped, and the fiber orientation is reported here. Estimation of the tensile strength of tapered laminates necessitates accurate determination of the state of stress near the ply-drop region, which is, in general, three-dimensional (3-D) in nature. Recognising the fact that full 3-D finite-element analysis becomes computationally exorbitant, special layered 3-D finite-element analysis is carried out. Laminates with ply drops along only one direction are analysed to elicit the nature of the local bending effects occuring near the ply drops. Complete 3-D Tsai-Wu criterion considering all the six stress components is used to obtain a quick and comparative assessment of the tensile strength of these laminates. High stress concentration zones are identified and the effects of number of plies dropped at a station and resin pocket geometry are illustrated. The mechanism of load transfer near ply drops and the local bending that occurs are described. Susceptibility of ply drop zones to the set and subsequent growth of delaminations is also brought out. ?? 2001 Elsevier Science Ltd. All rights reserved.
A.Polymer-matrix composites (PMCs); B.Strength; C.Finite element analysis (FEA); C.Laminates; C.Stress transfer
A synergistic damage mechanics approach for composite laminates with matrix cracks in multiple orientations
Mechanics of Materials
41
8
954-968
2009
10.1016/j.mechmat.2009.02.008
This paper treats the problem of elastic response of composite laminates containing matrix cracks in plies of multiple orientations. The approach taken has been described as synergistic damage mechanics (SDM) and has been previously illustrated for [0m / ± θn / 0m / 2]s laminates with cracks of equal density in + θ and - θ plies [Singh, C.V., Talreja, R., 2008. Int. J. Solids Struct. 45(16), 4574-4589]. The current work extends the approach to [0m / ± θn / 90r]s and [0m / 90r / ± θn]s laminates with cracks additionally in the 90°-plies. The interaction between the ± θ-cracks and the 90°-cracks is analyzed in terms of the crack surface displacements using a three-dimensional finite element (FE) model and found to be significant only for crack orientations close to 90°. The stiffness degradation of the laminate with all cracking modes simultaneously present is formulated by continuum damage mechanics using a second order tensor characterization of damage. The elastic moduli changes predicted by the SDM procedure are validated by independent three-dimensional FE calculations. For a particular case of quasi-isotropic [0 / 90 / ∓ 45]s laminate, the elastic moduli predictions are evaluated against experimental data. Finally, a parametric study is performed to examine the effects of ply thickness changes on stiffness properties.
Bending of Two-Ply Cord Composite Cylindrical Shells
Mechanics Based Design of Structures and Machines
37
3
283-298
2009
The load-displacement behavior of two-ply laminate cord composite cylindrical shells was quantitatively and qualitatively assessed with an emphasis on the effect of cord-ply angle. An equilibrium approach was used to develop the load-displacement model that took into account the mechanics of the matrix, the cords, and the shell. The load-displacement results for a two-ply laminate cord composite cylindrical shell typical of what can be found in steel-belted radial tires were presented. Those results illustrate that the shell behavior depends upon the loading and the unique combination of the cord-ply angle, cord extension-twist coupling and large axial stiffness, rubber's small elastic modulus and large Poisson's ratio, and small cord volume fraction.
analytical; bending; cable; composite structures; cords; cylinders; design; hoses; laminated composites; loads; mechanics; rubber; shells; strain; strands; stress analysis; tire; wire rope; wire rope mechanics
An investigation on the post-buckling behavior of symmetric cross-ply laminated plates using a semi-energy finite strip approach
Composite Structures
71
365-370
2005
10.1016/j.compstruct.2005.09.010
A geometrically non-linear finite strip for the post-buckling analysis of geometrically perfect thin symmetric cross-ply laminated plates under uniform end shortening is presented in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von K??rm??n's compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von K??rm??n's compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the Principle of Minimum Potential Energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyze the post-local-buckling behavior of thin flat laminates. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. It should be mentioned that the FEM analysis was carried out employing the general purpose ANSYS package. The study of the results has provided confidence in the validity and capability of the developed finite strip in handling the post-buckling problem of symmetric cross-ply laminated plates. ?? 2005 Elsevier Ltd. All rights reserved.
Finite strip method; Post-buckling; Semi-energy approach; Symmetric cross-ply laminate; Von-K??rm??n's compatibility equation
Differential quadrature-layerwise modeling technique for three-dimensional analysis of cross-ply laminated plates of various edge-supports
Computer Methods in Applied Mechanics and Engineering
191
35
3811-3832
2002
10.1016/S0045-7825(02)00309-2
In this paper, a differential quadrature model is proposed, which is established within a layerwise framework for the bending analysis of composite laminates. Three-dimensional theory of elasticity is implemented, and all physical governing equations are satisfied, including characteristics of the continuity and discontinuity of interfacial transverse and in-plane displacement, strains and stresses along interfaces of the composite laminates, thus delivering highly accurate numerical solutions. Variation in boundary conditions, plate aspect and thickness ratios, and loading conditions are examined, demonstrating the applicability, accuracy, and stability of the present methodology. Numerical examples for rectangular cross-ply laminated plates subjected to a uniform load, sinusoidal load or uniformly distributed moment are studied. Selected results from these examples are compared with those available in existing published literature. © 2002 Elsevier Science B.V. All rights reserved.
Bending (deformation); Boundary conditions; Composite materials; Cross-ply laminates; Differential quadrature method; Elasticity; Laminated plates; Laminates; Layerwise theory; plate; Plates (structural components); Strain; Stress analysis; Three-dimensional theory of elasticity
A physically based continuum damage mechanics model for thin laminated composite structures
International Journal of Solids and Structures
40
9
2267-2300
2003
10.1016/S0020-7683(03)00016-7
The present work focuses on the development, implementation, and verification of a plane-stress continuum damage mechanics (CDM) based model for composite materials. A physical treatment of damage growth based on the extensive body of experimental literature on the subject is combined with the mathematical rigour of a CDM description to form the foundation of the model. The model has been implemented in the commercial finite element code, LS-DYNA and the results of the application of the model to the prediction of impact damage growth and its effects on the impact force histories in carbon fibre reinforced plastic laminates are shown to be physically meaningful and accurate. Furthermore, it is demonstrated that the material characterization parameters can be extracted from the results of standard test methodologies for which a large body of published data already exists for many composite materials. ?? 2002 Elsevier Science Ltd. All rights reserved.
Composites; Constitutive model; Continuum damage mechanics; Damage growth; Energy absorption; Impact
Free and forced vibration of cross-ply laminated composite shallow arches
International Journal of Solids and Structures
34
10
1217-1234
1997
10.1016/S0020-7683(96)00095-9
A model for the dynamic behavior of a laminated composite shallow arch is developed from shallow shell theory. Linear equations of motion are derived for thin, moderately thick and thick arches. Free vibration of the arch is explored and exact natural frequencies of the third-order, second-order, first-order and classical arch theories are determined for various boundary conditions. A generalized modal approach is presented to solve the dynamic response of cross-ply laminated arches with arbitrary boundary conditions and for arbitrary loadings. The Poisson effect and rotary inertia are incorporated in the formulation of the arch constitutive equation, in the analytical approaches and in the numerical results.
Micro-mechanical analysis of the in situ effect in polymer composite laminates
Composite Structures
116
827-840
2014
10.1016/j.compstruct.2014.06.014
A micro-mechanical finite element model of a composite sublaminate is proposed to study the mechanical response of ultra-thin plies, consisting of a representative volume element of a 90° thin lamina in-between two homogenised ±θ° plies. Random fibre distributions, materially and statistically equivalent to real distributions, are analysed. A three-dimensional computational micro-mechanics framework, with a special focus on the elastic–plastic and damage constitutive behaviours of the matrix and on the response of the fibre–matrix interface, is used in the present analysis. Varying the 90° ply thickness, it is possible to assess its effect on the mechanical response of laminated composites — the in situ effect. The proposed framework is able to accurately represent the micro-mechanical response of ultra-low grades, including (i) the mechanics of transverse cracking onset and propagation, (ii) the constraining effect observed in the laminae embedded in multidirectional laminates, (iii) the gradual, slow stress relaxation and progressive transverse cracking observed in very thin plies, and consequent increase of the crack density, (iv) the reduction in crack-opening displacement of the transverse cracks with ply thinness, (v) the formation of thin necks of matrix material around the regions where interfacial damage is more pronounced, and (vi) the in situ strengths.
FEA; In situ effect; Laminates; Micro-mechanics
First-principles statistical mechanics study of the stability of a subnanometer thin surface oxide in reactive environments: CO oxidation at Pd(100)
Physical Review Letters
98
4
98-101
2007
10.1103/PhysRevLett.98.046101
We employ a multiscale modeling approach to study the surface structure and composition of a Pd(100) model catalyst in reactive environments. Under gas phase conditions representative of technological CO oxidation (approximately 1 atm, 300-600 K) we find the system on the verge of either stabilizing subnanometer thin oxide structures or CO adlayers at the surface. Under steady-state operation this suggests the presence or continuous formation and reduction of oxidic patches at the surface, which could be key to understand the observable catalytic function.
Introduction to the Mechanics of a Continuous Medium
Journal of Applied Mechanics
33
1
238
1966
10.1115/1.3625016
This textbook offers a unified presentation of the concepts and general principles common to all branches of solid and fluid mechanics. It deals with: vectors and tensors, stress, strain and deformation, general principles, constitutive equations, fluid mechanics and linearized theory of elasticity.
Effective interlaminar shear moduli in composites containing transverse ply cracks
Composites Science and Technology
66
2591-2598
2006
10.1016/j.compscitech.2006.01.005
The effective interlaminar shear modulus for [?? / 90m??]S and [?? ?? / 90m??]S laminates containing transverse cracks through the middle 90m?? layers are determined analytically. The cracks are assumed to be evenly spaced and to extend across the entire laminate width. The ?? ply and 90m?? ply cluster are treated as a single homogeneous plate, while the ???? plies are treated as a single laminated plate. The two plates are connected through continuity of displacements and tractions at the interface. In addition to determining the effective shear modulus, a singularity analysis is presented in conjunction with a [0??/90??]S bi-directional laminate. The singularity is then utilized in conjunction with the laminate model to look at the interlaminar shear stress near the crack tip along the 0??/90?? interface. Numerical results are compared to both a finite element analysis and to a previously developed self-consistent model. ?? 2006 Elsevier Ltd. All rights reserved.
A. Damage mechanics; B. Elastic properties; C. Laminates; D. Laminate theory; E. Transverse cracking
Damage mechanics of composite materials. III: Prediction of damage growth and notched strength
Composites Science and Technology
40
2
147-165
1991
10.1016/0266-3538(91)90094-6
A new model describing the notched strength of carbon fibre composites has been developed. In the third paper of a four-part series, subcritical damage growth in notched cross-ply carbon fibre reinforced epoxy specimens has been modelled with the aid of linear elastic fracture mechanics. A function relating split length to applied stress for (90/0)s laminates has been derived. The predictions of split growth were used in conjunction with the failure model presented in Part II of this series to predict notched strength from first principles. The dependence of notched strength on notch size has been modelled without the need for empirical parameters.
Fluid Mechanics S1.2
Refrigeration And Air Conditioning
6
3
e18068
2010
http://dx.doi.org/10.1016/j.rser.2004.09.010
Dental thermal pain is a significant health problem in daily life and dentistry. There is a long-standing question regarding the phenomenon that cold stimulation evokes sharper and more shooting pain sensations than hot stimulation. This phenomenon, however, outlives the well-known hydrodynamic theory used to explain dental thermal pain mechanism. Here, we present a mathematical model based on the hypothesis that hot or cold stimulation-induced different directions of dentinal fluid flow and the corresponding odontoblast movements in dentinal microtubules contribute to different dental pain responses. We coupled a computational fluid dynamics model, describing the fluid mechanics in dentinal microtubules, with a modified Hodgkin-Huxley model, describing the discharge behavior of intradental neuron. The simulated results agreed well with existing experimental measurements. We thence demonstrated theoretically that intradental mechano-sensitive nociceptors are not "equally sensitive" to inward (into the pulp) and outward (away from the pulp) fluid flows, providing mechanistic insights into the difference between hot and cold dental pain. The model developed here could enable better diagnosis in endodontics which requires an understanding of pulpal histology, neurology and physiology, as well as their dynamic response to the thermal stimulation used in dental practices.
Prediction of initiation of transverse cracks in cross-ply CFRP laminates under fatigue loading by fatigue properties of unidirectional CFRP in 90° direction
Composites Part A: Applied Science and Manufacturing
68
398-405
2015
10.1016/j.compositesa.2014.10.022
A fatigue life to the initiation of transverse cracks in cross-ply carbon fiber-reinforced plastic (CFRP) laminates has been predicted using properties of the fatigue strength of unidirectional CFRP in the 90° direction. In the experiments, unidirectional [90]12 laminates were used to obtain a plot of maximum stress versus number of cycles to breaking, and two types of cross-ply laminates of [0/904]S and [0/906]S were used to evaluate the initiation and multiplication of transverse cracks under fatigue loading. Transverse cracks were studied by optical microscopy and soft X-ray photography. Analytical and experimental results showed good agreement, and the fatigue life for transverse crack initiation in cross-ply laminates was predicted successfully from the fatigue strength properties of the unidirectional CFRP in the 90° direction. The prediction results showed a conservative fatigue life than the experimental results.
A. Polymer–matrix composites (PMCs); B. Fatigue; B. Transverse cracking; C. Laminate mechanics
Transverse Ply Cracking in Cross-Ply CFRP Laminates—Initiation or Propagation Controlled?
Journal of Composite Materials
31
11
1080-1112
1997
0803973233
The fastener design for the transfer of concentrated transverse (out of plane, pull-out) loads to random glass fiber reinforced thermoset polymers was investigated. The elastic material properties, void content,a nd glass content of the composite were determined and a finite element model was used to analyze and compare the performance of the various washer designs for reducing the stress and strain levels near the edge of the washer at a bolted joint. Experimental studies were conducted to verify the finite element model.
Molecular simulation and continuum mechanics investigation of viscoelastic properties of fluids confined to molecularly thin films
Journal of Chemical Physics
114
17
7593-7601
2001
10.1063/1.1361077
A combination of molecular dynamics simulations of oscillatory shear flow and continuum mechanics is used to investigate viscoelastic properties of materials confined to molecularly thin films. The atoms of the simple liquid interact via a repulsive Lennard-Jones potential. The chain molecules are modeled as strings of similar spheres connected via finite extensible nonlinear elastic springs. The fluid is confined between two surfaces composed of identical spheres that are moved to simulate oscillatory flow. In order to mimic experiments, the temperature is controlled by coupling the wall atoms to a heat bath, and the viscoelastic properties are obtained via an analysis using continuum mechanics. Both simple and polymeric fluids exhibit linear viscoelastic behavior under typical simulation conditions, although inertial effects play an important role in determining the flow behavior. Simple fluids display a smooth transition from liquidlike to solidlike behavior when confined to molecularly thin films, whereas linear chain polymers and gels display predominantly elastic shear response at all frequencies investigated. These results are in qualitative agreement with the surface forces apparatus experiments on similar systems. (C) 2001 American Institute of Physics.
Development of novel single-wall carbon nanotube{&}ndash;epoxy composite ply actuators
Smart Materials and Structures
14
6
1526-1532
2005
10.1088/0964-1726/14/6/045
This paper describes a carbon nanotube epoxy ply material that has electrochemical actuation properties. The material was formed by dispersing single-wall carbon nanotubes in a solvent and then solution casting a thin paper using a mold and vacuum oven. In order to take advantage of the high elastic modulus of carbon nanotubes for actuation, epoxy as a chemically inert polymer is considered. An epoxy layer was cast on the surface of the nanotube paper to make a two-layer ply. A wet electrochemical actuator was formed by placing the nanotube epoxy ply in a 2 M NaCl electrolyte solution. Electrochemical impedance spectroscopy and cyclic voltammetry were carried out to characterize the electrochemical properties of the actuator. The voltage-current relationship and power to drive the actuator material were also determined. Compared to previous single-wall carbon nanotube buckypaper tape actuators, which had poor adhesion between the nanotubes and tape, and other nanotube-thermal plastic polymer actuators, which could not provide high strength, the epoxy based actuator has a higher elastic modulus and strength, which will be useful for future structural applications. This demonstrates that a polymer layer can reinforce nanotube paper, which is an important step in building a new structural material that actuates. Further work is under way to develop a solid electrolyte to allow dry actuation. Finally, these actuator plies will be laminated to build a carbon nanocomposite material. This smart structural material will have potential applications that range from use in robotic surgical tools to use as structures that change shape.
The Physics of Thin Film Optical Spectra - An Introduction
Materials Science
285
2005
10.1007/s13398-014-0173-7.2
The present monograph represents itself as a tutorial to the field of optical properties of thin solid films. It is neither a handbook for the thin film practitioner, nor an introduction to interference coatings design, nor a review on the latest developments in the field. Instead, it is a textbook which shall bridge the gap between ground level knowledge on optics, electrodynamics, quantum mechanics, and solid state physics on one hand, and the more specialized level of knowledge presumed in typical thin film optical research papers on the other hand.
Fracture mechanics and its application to failure in rubber articles
Rubber Chemistry and Technology
76
3
567
2003
10.5254/1.3547761
The results in Figure 18 were obtained by using a standard test-piece thickness, ply separation and cord angle. The latter two variables both affect the test-piece stiffness-very strongly in the case of the cord angle-while according to Equation (5), the former should affect the tearing energy directly. Figure 19 shows results in which all three variables were altered; as can be seen, the use of the strain energy release rate superimposes all the results onto a single relation.
8640:Chemical industry; 9130:Experimental/theoretical; Experiments; Fractures; Rubber; Technology: Comprehensive Works
First-ply failure prediction of an unsymmetrical laminated ellipsoidal woven GFRP composite shell with incorporated surface-bounded sensors and internally pressurized
Composites Part B: Engineering
77
502-518
2015
10.1016/j.compositesb.2015.03.058
First-ply failure of an unsymmetrical laminated ellipsoidal woven Glass Fiber Reinforced Polymer (GFRP) composite shell internally pressurized was investigated analytically using the linear interpolation technique. The shell's boundary was fixed at its end. Tsai-Wu failure criterion was used as the composite failure design factor. The analytical results, including critical internal pressure and strains in global directions, were validated with the experimental results for some arbitrarily selected points on the shell surface along meridian axis. Manufacturing of laminated ellipsoidal composite shells was performed by using the Vacuum Infusion Process (VIP), a novel method commonly adopted for the fabrication of laminated composite shells. Surface-bounded sensors were installed on the shells' surface to measure the strain values after the internal pressure was applied. According to the analytical investigation findings, the failure factor was critical at the innermost ply. In addition, for each ply, the shell's edge was observed to be the region with the highest failure factor. The experimental findings confirmed that the failure occurred in the regions close to the shell's edge, as predicated by the analytical approach. The results from both approaches were in a close agreement. Subsequently, the effect of various parameters including thickness, aspect ratio, and stacking sequence on the first-ply failure of laminated ellipsoidal woven GFRP composite shell were investigated and the critical mechanical factors to avoid failure were determined.
B. Strength; C. Analytical modeling; C. Laminate mechanics; D. Mechanical testing; Unsymmetrical laminated ellipsoidal woven GFRP she
the Structure and Mechanics of Atomically-Thin Graphene Membranes
PhD Thesis
1-139
2011
Graphene is an exciting new atomically-thin two dimensional system with ap- plications ranging from next generation transistors, to transparent and flexible electrodes, to nanomechanical systems. We study the structure, electronic, and mechanical properties of suspended graphene membranes, and use them to pro- duce mechanical resonators. We first showed that it was possible to produce suspended graphene membranes even down to one atom thick using exfoliated graphene, and resonate the mem- branes using optical interferometry. The resonators had frequencies in the MHz and quality factors from 20-850, but showed no reproducibility. In order to produce predictable and reproducible graphene resonators we de- veloped methods for making large arrays of single-layer graphene membranes of controlled size, shape and tension using chemical vapor deposition (CVD) grown graphene. We used transmission electron microscopy to study the polycrystalline structure of the graphene, we found that the different grains stitched together by disordered lines of 5-7 defects. Using electron transport and scanned probe techniques, we found that the polycrystalline grain structure reduces the ultimate strength of the graphene, but did not as strongly affect the electrical properties. We systematically studied the mechanical resonance of the single-layer CVD graphene membranes as a function of the size, clamping geometry, temperature and electrostatic tensioning. We found that the CVD graphene produces ten- sioned, electrically conducting, highly-tunable resonators. In addition we found that clamping the graphene membrane on all sides reduces the variation in the resonance frequency, and makes the behavior more predictable.
Mechanics of fragmentation of crocodile skin and other thin films.
Scientific reports
4
4966
2014
10.1038/srep04966
Fragmentation of thin layers of materials is mediated by a network of cracks on its surface. It is commonly seen in dehydrated paintings or asphalt pavements and even in graphene or other two-dimensional materials, but is also observed in the characteristic polygonal pattern on a crocodile's head. Here, we build a simple mechanical model of a thin film and investigate the generation and development of fragmentation patterns as the material is exposed to various modes of deformation. We find that the characteristic size of fragmentation, defined by the mean diameter of polygons, is strictly governed by mechanical properties of the film material. Our result demonstrates that skin fragmentation on the head of crocodiles is dominated by that it features a small ratio between the fracture energy and Young's modulus, and the patterns agree well with experimental observations. Understanding this mechanics-driven process could be applied to improve the lifetime and reliability of thin film coatings by mimicking crocodile skin.
On the mechanics of thin films and growing surfaces
Mathematics and Mechanics of Solids
18
6
561-575
2013
10.1177/1081286513485776
Many living structures are coated by thin films, which have distinct mechanical properties from the bulk. In particular, these thin layers may grow faster or slower than the inner core. Differential growth creates a balanced interplay between tension and compression and plays a critical role in enhancing structural rigidity. Typical examples with a compressive outer surface and a tensile inner core are the petioles of celery, caladium, or rhubarb. While plant physiologists have studied the impact of tissue tension on plant rigidity for more than a century, the fundamental theory of growing surfaces remains poorly understood. Here, we establish a theoretical and computational framework for continua with growing surfaces and demonstrate its application to classical phenomena in plant growth. To allow the surface to grow independently of the bulk, we equip it with its own potential energy and its own surface stress. We derive the governing equations for growing surfaces of zero thickness and obtain their spatial discretization using the finite-element method. To illustrate the features of our new surface growth model we simulate the effects of growth-induced longitudinal tissue tension in a stalk of rhubarb. Our results demonstrate that different growth rates create a mechanical environment of axial tissue tension and residual stress, which can be released by peeling off the outer layer. Our novel framework for continua with growing surfaces has immediate biomedical applications beyond these classical model problems in botany: it can be easily extended to model and predict surface growth in asthma, gastritis, obstructive sleep apnoea, brain development, and tumor invasion. Beyond biology and medicine, surface growth models are valuable tools for material scientists when designing functionalized surfaces with distinct user-defined properties.
Boundary energy; finite elements; plant growth; surface growth; thin films
Delamination and matrix cracking of cross-ply laminates due to a spherical indenter
Composite Structures
25
1-4
257-265
1993
10.1016/0263-8223(93)90172-M
An investigation was performed to study delamination growth induced by matrix cracks in cross-ply composites resulting from a spherical indenter. The major focus of the study was to understand fundamentally the damage mechanics in terms of matrix cracking and delamination growth, and interaction between them. A nonlinear three-dimensional finite element model based on an updated Lagrange formulation was developed during the investigation. An augmented Lagrangian method was utilized to model the delamination interface condition. A general contact node search algorithm was proposed which can handle complex contact conditions, such as arbitrary slippage and discontinuous curvature. The indentation resulting from the spherical rigid indenter was also modeled. Fracture mechanics was applied to determine the delamination propagation in three dimensions. The strain energy release rates were calculated by a crack-closure technique. The model was verified analytically and experimentally. © 1993.
Pre-cracking technique for fracture mechanics experiments along interface between thin film and substrate
Engineering Fracture Mechanics
72
12
1892-1904
2005
10.1016/j.engfracmech.2004.08.010
Utilizing the difference in interface strength due to fabrication process, a technique for producing a sharp pre-crack between a thin film and a substrate is proposed. A cracked specimen for examining fracture toughness of interface between a sputtered copper (Cu) thin film and silicon (Si) is made by the method. A vacuum-evaporated Cu thin film, which has poor adhesion to Si, is inserted between the sputtered Cu thin film and the Si substrate as a release layer. The release layer debonds from the Si substrate at very low load, and the sharp pre-crack is successfully introduced along the interface. Using the pre-cracked specimen, the interface fracture toughness test is conducted and the critical J-integral, J(C), is evaluated as about 1 J/m(2) for the sputtered Cu/Si interface. (c) 2005 Elsevier Ltd. All rights reserved.
copper film; fracture mechanics; fracture toughness; interface; interface crack; material testing; pre-crack; thin film
Fatigue failure of angle ply laminates
AIAA Journal
14
7
868-872
1976
10.2514/3.7162
Experimental investigation of failure of balanced angle-ply laminates under symmetric uniaxial tension revealed three distinct failure modes. The three different modes were observed for reinforcement angles smaller than {+/-}45{degrees}, for the {+/-}45{degrees} angle ply and for angles larger than {+/-}45{degrees}. Comparison of experimental failure loads with theoretical failure loads based on first laminate failure criteria showed good agreement for certain ranges of reinforcement angle and disagreement for others.
A progressive first ply failure model for woven ply CFRP laminates under static and fatigue loads
International Journal of Fatigue
28
10 SPEC. ISS.
1270-1276
2006
10.1016/j.ijfatigue.2006.02.024
A non-linear cumulative damage model for woven ply laminates under static and fatigue loads is developed in this paper. The validity scope of this model depends on the 'diffuse damage' phase up to the first intra-laminar macro-crack only (first ply failure model). The model, which is based on a continuum damage approach (CDM) and a non-local fibre rupture criteria, was implemented in a FEM code. Finally, full field strain measurements are used to compare experiments and computations for a plate with an open hole submitted to a fatigue tensile load. ?? 2006 Elsevier Ltd. All rights reserved.
Damage; Failure; Fatigue; Laminate; Textile composite
Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
Computer Methods in Applied Mechanics and Engineering
191
3669-3750
2002
10.1016/S0045-7825(02)00286-4
A new finite element method for fourth-order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem. The method combines concepts from the continuous Galerkin (CG) method, the discontinuous Galerkin (DG) method and stabilization techniques. A brief review of the CG method, the DG method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth-order elliptic problems. A continuous/discontinuous Galerkin (C/DG) method is proposed which uses Co-continuous interpolation functions and is formulated in the primary variable only. The advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided. In the context of thin bending theory, the C/DG method leads to a formulation where displacements are the only degrees of freedom, and no rotational degrees of freedom need to be considered. The main feature of the C/DG method is the weak enforcement of continuity of first and higher-order derivatives through stabilizing terms on interior boundaries. Consistency, stability and convergence of the method are shown analytically. Numerical experiments verify the theoretical results, and applications are presented for Bernoulli Euler beam bending, Poisson-Kirchhoff plate bending and a shear layer problem using Toupin-Mindlin strain gradient theory. © 2002 Elsevier Science B.V. All rights reserved.
Prediction of the postbuckling response of composite airframe panels including ply failure
Engineering Fracture Mechanics
77
18
3648-3657
2010
10.1016/j.engfracmech.2010.05.009
Future design scenarios aim to allow buckling in composite airframe panels. Reliable simulation procedures should be able to capture the postbuckling elastic as well as the inelastic response associated with damage. Damage in composite laminates in terms of ply failure may primarily occur as fiber fracture or matrix cracking. This paper presents a model which is able to capture both geometrical and material nonlinearity. It bases on the finite element formulation of a layered, iso-parametric, quadrilateral shell element which allows for an arbitrary reference surface as well as an arbitrary stacking sequence. Geometrical nonlinearity is accounted for by utilizing Green strains and second Piola–Kirchhoff stresses. Material nonlinearity is considered via a layerwise ideally brittle damage model. The model is applied to a buckling test of a stringer-stiffened composite airframe panel. The numerical results are compared with an experiment proving the applicability of the proposed concept.
Effect of lamina thickness on first ply failure in multidirectionally laminated composites
Journal of the Japan Society for Composite Materials
30
4
142--148
2004
10.1024/0301-1526.32.1.54
Carbon fiber tows are generally used for the reinforcement of plastics. Recently, we have developed a method in which tow can be efficiently spread without causing any fiber damage (FUKUI method). By using this method, we prepared thin laminas about 0.05 mm in thickness, and produced quasi-isotropic laminates by stacking these laminas. Furthermore, we obtained the laminas having an arbitrary thickness by stacking the laminas with the same unidirectional prepregs. In this work, the effects of the lamina thickness on the first ply failure occurred in multidirectionally laminated composites have been studied. Tensile tests were performed on the samples and also acoustic emission was monitored during the tests. It is found that the initial failure stress increases with decreasing lamina thickness. This result can be predicted by Kageyama's study.
Stress analysis in thin coatings and substrate subjected to point contact loading (mechanics of scratch test)
Journal of Materials Processing Technology
205
1-3
89-98
2008
10.1016/j.jmatprotec.2007.11.098
In this article, a model is developed to predict the stresses in thin coatings induced by a point concentrated load in continuation of articles in describing the tribological contact analysis of coated systems. This solution can be used as a suitable analytical model for mechanics of scratch test. Despite the lack of fully satisfactory analytical model of its mechanics, the scratch test is widely used to quantitatively evaluate the adhesion of coating and substrate. In this test an indenter is drawn across the surface of a coating under an increasing (continuous or step-wise) load. In order to develop an analytical model for scratch test in elastic zone, the fundamental solutions were obtained for concentrated point forces acting perpendicular and parallel to the layer surface. The stress and displacement fields were calculated for the coatings and the substrate due to these forces. These results were compared with the results of finite element method (FEM) by using ANSYS software, as well as with the results of uncoated elastic half-space. These results are also useful for ranking the coating-substrate adhesion of different coated systems, or for estimating the critical mean stress for interfacial failure. ?? 2007 Elsevier B.V. All rights reserved.
Coating; FEM; Scratch test; Stress analysis
Mechanics analysis of two-dimensionally prestrained elastomeric thin film for stretchable electronics
Acta Mechanica Solida Sinica
23
6
593-599
2010
10.1016/S0894-9166(11)60006-2
Various methods have been developed to fabricate highly stretchable electronics. Recent studies show that over 100 two dimensional stretchability can be achieved by mesh structure of brittle functioning devices interconnected with serpentine bridges. Kim et al show that pressing down an inflated elastomeric thin film during transfer printing introduces two dimensional prestrain, and therefore further improves the system stretchability. This paper gives a theoretical study of this process, through both analytical and numerical approaches. Simple analytical solutions are obtained for meridional and circumferential strains in the thin film, as well as the maximum strain in device islands, which all agree reasonably well with finite element analysis. © 2010 The Chinese Society of Theoretical and Applied Mechanics.
shell; soft materials; stretchable electronics
The mechanics of the tribology of thin film systems
Surface and Coatings Technology
43-44
674-687
1990
10.1016/0257-8972(90)90011-Z
This paper aims to explain both the advantages and the current limitations of thin film systems in tribological situations. It begins with short reviews of the relevant basic concepts of friction and wear, of those elements of contact mechanics which are a necessary introduction to an understanding of tribological behaviour, and of the stresses occurring at uncoated surfaces, initially under normal load only and then under combined normal and tangential loads. It then describes the mechanics underlying the two technologically important systems of hard surfaces covered by soft coatings and relatively soft surfaces covered by hard coatings. The mechanics of the scratch test are then discussed and explanations are offered for the various failure modes observed during such a test. Finally, outlines are given of current and future programmes of work designed to elucidate the factors limiting coating performance.
Shape optimization of thin walled structures governed by geometrically nonlinear mechanics
Computer Methods in Applied Mechanics and Engineering
237-240
107-117
2012
10.1016/j.cma.2012.05.016
This paper introduces a structural optimization strategy that combines FE-based parametrization with nonlinear kinematics in order to optimize the shape of thin shell structures. The optimization is based on gradient based strategies where the required derivatives are formulated by the adjoint approach. The applied solution algorithm combines the well known nonlinear path following strategies with the design update procedure of the shape optimization. This results in robust and flexible methods that require only a minimum of system evaluations. The proposed optimization goals improve the load carrying behavior of the structure and minimize displacements and stresses. It is shown that such efficient designs also exhibit an improved limit load. This contribution illustrates the application of the proposed method by several shape optimization problems. The presented results prove the exceptional performance of the optimized designs even if the optimal design is disturbed by unavoidable imperfections. It is shown that the application of nonlinear kinematics in the shape optimization of thin shell structures allows for a much more realistic system response and gradient data. The proposed approach is applicable to all kind of optimization strategies like topology, sizing or material optimization, respectively. © 2012 Elsevier B.V.
Membrane action; Nonlinear mechanics; Shape optimization; Shells; Thin walled structures
Design and manufacturing considerations for ply drops in composite structures
Composites Part B: Engineering
30
523-534
1999
10.1016/S1359-8368(98)00043-2
Thickness variations are required to optimize the design of modern laminated composite structures. These thickness variations are accomplished by dropping plies along the length to match varying in-plane and bending loads. This results in a structure which is matched to stiffness and loading requirements. Unfortunately, these ply drops produce internal and local stress concentrations as a consequence of geometric discontinuities and shear lag. In this study, we explore various factors for design of composite structures with ply drops. These factors include: thicknesses, ply stacking sequences, ply drop geometries and manufacturing considerations. In addition, fatigue loading is considered with respect to delamination initiation and growth. A strong sensitivity to the position and the manufacturing details of ply drops is shown for fatigue damage initiation and growth. All studies were conducted on a low-cost E-glass/polyester composite system. The results indicate that it will be difficult to completely suppress damage and delamination initiation in service. However, it was found that, in many cases, there is a threshold loading under which there is little growth after initiation is noted. Factors affecting this threshold are analyzed via the virtual crack closure method in Finite Element Analysis and verified experimentally. Design rules for ply dropping are presented on the basis of these results.
b; delamination; fatigue; fracture; ply-drops; strain energy release rate
Compression after impact of thin composite laminates
Composites Science and Technology
65
13
1911-1919
2005
10.1016/j.compscitech.2005.04.009
The damage tolerance of various lay-ups of thin carbon/epoxy laminates (1.6-2.2 mm thick) is examined by compression after impact (CAI) tests, using a new testing device which adapts to the thicknesses of the specimens and does not require tabs nor any modification of the specimen geometry. The compression stress state was not modified by the presence of the device, as was verified by numerical simulation. With this device, CAI tests were done of different carbon/epoxy laminate lay-ups (quasi-isotropic, cross-ply and woven) and the values of the residual strength and the normalized residual strength of the laminates were obtained as a function of the impact energy. The woven laminate was found to offer the highest residual strength under all the impact energies, and the quasi-isotropic laminate the least loss of normalized strength as the impact energy was raised. ?? 2005 Elsevier Ltd. All rights reserved.
A. Carbon fibres; B. Strength; C. Damage tolerance; C. Laminates
Reliability formulation for composite laminates subjected to first-ply failure
Composite Structures
38
1-4
447-452
1997
10.1016/S0263-8223(97)00079-2
Methods formulated on the basis of the concept of first-ply failure and the structural reliability theory are presented for the reliability analysis of laminated composite plates. In the reliability formulation, an appropriate phenomenological failure criterion is used to establish the limit state equation of the laminated composite plates, and different numerical techniques are employed to evaluate the reliability of the plates. Experimental investigations of lamina strengths and first-ply failure loads of laminated composite plates were performed. Baseline probability distributions of lamina strength parameters constructed from the test data are used to study the reliability of the laminated plates. The accuracy of the proposed models in reliability assessment of the laminated plates are verified by the experimental results on first-ply failure load distributions.
First ply failure of G/E laminates under biaxial loadings
Fibre Science and Technology
12
2
97-110
1979
10.1016/0015-0568(79)90023-X
Thin-walled [0/90]s and [±45]s tubes of T300/1034 graphite/epoxy were subjected to static and fatigue biaxial loadings for the purpose of experimentally detecting first ply failure (FPF). FPF envelopes were determined using a replication technique and compared with ultimate strength envelopes and lamination theory predictions of FPF using a maximum strain criterion and accounting for initial strains due to curing. The FPF envelopes compared rather well with lamination theory predictions and lay well within the ultimate strength envelopes. Preliminary experiments were conducted to determine the influence of FPF on fatigue strength. Although some fatigue failures were found at stress ranges within the FPF envelope, the fatigue life of specimens at stress ranges penetrating the FPF envelope were dramatically less.
A finite fracture mechanics model for the prediction of the open-hole strength of composite laminates
Composites Part A: Applied Science and Manufacturing
43
8
1219-1225
2012
10.1016/j.compositesa.2012.03.004
A new model based on finite fracture mechanics is proposed to predict the open-hole tensile strength of composite laminates. Failure is predicted when both stress-based and energy-based criteria are satisfied. The material properties required by the model are the ply elastic properties, and the laminate unnotched strength and fracture toughness. No empirical adjusting parameters are required. Using experimental data obtained in quasi-isotropic carbon-epoxy laminates it is concluded that the model predictions are very accurate, resulting in improvements over the traditional strength prediction methods. It also is shown that the proposed finite fracture mechanics model can be used to predict the brittleness of different combinations of materials and geometries. © 2012 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Fracture; C. Analytical modelling
Multiple transverse cracking and stiffness reduction in cross-ply laminates
Journal of Composites Technology and Research
13
2
97-106
1991
The stiffness reduction as a result of multiple transverse cracking in cross-ply laminates and the crack density dependence on the applied tensile stress are analyzed by linear elastic fracture mechanics. The stress field distribution is obtained by the principle of minimum complementary energy. Two models are suggested which describe the nonuniform stress distribution in the thickness direction of the 0° layer. They contain the variational approach presented by Z. Hashin (1985) as a particular case. Elastic ply properties and the Mode I critical strain energy release rate GIc for transverse cracking are the experimental data needed. Model predictions are compared with experimental data for glass fiber/epoxy, AS4/3502, and AS/3501-06 carbon fiber/epoxy cross-ply laminates. The predictions from the suggested models describe both the constraint effect and the crack saturation phenomenon.
Smart damping of laminated thin cylindrical panels using piezoelectric fiber reinforced composites
International Journal of Solids and Structures
44
2
587-602
2007
10.1016/j.ijsolstr.2006.05.005
In this paper performance of a new piezoelectric fiber reinforced composite (PFRC) material has been investigated for active constrained layer damping (ACLD) of laminated thin simply supported composite cylindrical panels. The constraining layer of the ACLD treatment has been considered to be made of this PFRC material. A finite element model of smart composite panels integrated with the patches of such ACLD treatment has been developed to demonstrate the performance of these patches on enhancing the damping characteristics of thin cross-ply and angle-ply laminated composite cylindrical panels. Particular emphasis has been placed on studying the effect of variation of the piezoelectric fiber orientation in the constraining PFRC layer and the shallowness angle of the panels on the control authority of the patches. © 2006 Elsevier Ltd. All rights reserved.
Active control; Constrained layer damping; Piezoelectric composites; Smart structures
Impact Damage Resistance of CFRP Prepreg Laminates with Dispersed CSP Particles into Ply Interfaces
International Journal of Damage Mechanics
21
8
1106-1127
2011
10.1177/1056789511429143
The effects of incorporating core shell polymer (CSP) particles within interply interfaces on the impact response of CFRP prepreg laminates are investigated. The impact tests were conducted on samples without and with CSP particles into the ply interfaces. The loads versus time curves were examined to determine the impact response and the associated energy absorption by the laminates were studied. The results indicate that both, the peak load of the laminates improved by 41% and damping index (DI) reduced by 90% with the dispersion of 51 g/m2 of CSP particles within the prepreg ply interfaces of the laminates. It was noted that the CSP particles shielded the composites from the initial severity of impact. The energy absorbing mechanisms altered the supercritical response of the laminate to subcritical due to increase in the elastic energy stored within the laminates with CSP particles thereby changing the energy absorption modes. It was observed from macroscopic observations and SEM images of the damage sites that the damage mechanism and patterns changed and the extent of damage reduced with the addition of CSP particles.
Flutter of delaminated cross-ply laminated cylindrical shells
Composite Structures
94
9
2888-2894
2012
http://dx.doi.org/10.1016/j.compstruct.2012.03.042
In this study, the instability of delaminated cross-ply thin laminated cylindrical shells and panels when subjected to supersonic flow parallel to its length edge is investigated. The delamination is parallel to the shell reference and it extends along the entire length of the cylindrical shell. The Love’s shell theory and Von-Karman–Donnell type of kinematic relations along with first-order potential theory have been employed to construct the aeroelastic equations of motion. The effects of several parameters such as length to radius ratio, delamination position, size and thickness on the critical values are discussed in the details. The results indicate that the presence of delamination reduced the overall stiffness of the structure and thereby decreases the flutter critical boundaries.
Analytical method; Composite laminate; Delamination; Flutter
Three-dimensional stress analysis of free-edge effects in a simple composite cross-ply laminate
Composites Science and Technology
33
98
2243-2259
1996
10.1016/S1359-8368(03)00016-7
Composites for space applications such as advanced satellites will require the use of new and/or improved materials so that more stringent dimensional stability requirements can be met. In this work, we study the effect of ply-level initiation of damage under loading and processing stresses and imposed thermal loading. In particular, included in the study is the prediction and demonstration of a condition of steady-state cracking and the temperature change and loading level necessary to create this damage state, thus leading to the possibility of a predetermined loading range over which layer cracking will not propagate. We also consider the influence of the free-edges on the initiation of layer transverse cracking and potential microcracking that may develop at the fiber/matrix interface. The condition of constrained edge cracking is demonstrated where cracks develop but do not propagate across the laminate. To accomplish these studies unidirectional composites and various cross-ply laminates of IM7/5250-4 (graphite/bismaleimide) were produced and characterized.
A. Laminates; A: Polymer-matrix composites; B: Delamination; B. Delamination; C: Interlaminar stresses; C. Laminate mechanics; composites; D: Criterion; free-edge; Interlaminar stresses; mechanics; steady-state cracking; transverse cracks
Frictional behaviour of high performance fibrous tows: A contact mechanics model of tow-metal friction
Wear
305
1-2
78-88
2013
10.1016/j.wear.2013.05.014
Composites forming processes involve mechanical interactions on the ply, tow, and filament level. 0The deformations that occur during forming processes are governed by friction between tows and tooling material on the mesoscopic level and consequently between filaments and a counterface on the microscopic level. A thorough understanding of the frictional properties on the level of individual filaments is important to understand and predict the macroscopic deformations of a fabric during forming. The contact mechanics based friction model in this work confirms an experimentally observed decrease of frictional forces with an increasing roughness of the counterface. The developed model provides a qualitative understanding of the frictional behaviour of filaments on a cylindrical metal counterface. © 2013.
Aramid; Carbon; Contact mechanics; E-glass; Sliding friction; Surface topography
Perforation of high-strength double-ply fabric system by varying shaped projectiles
International Journal of Impact Engineering
27
577-591
2002
10.1016/S0734-743X(02)00004-0
Work done previously on single-ply ballistic resistant fabric systems is now extended to double-ply systems. Experiments were carried out to investigate the impact phenomenon of double-ply systems that consists of Twaron?? CT 716 fabric and projectiles of the following nose shapes: hemispherical, flat, ogival (CRH 2.5) and conical (half-angle of 30??). Results obtained revealed that the increase in energy absorption does not necessarily double when the ply number is increased to two. In fact, the ratio of energy absorbed in the double-ply system to that of the single-ply system varies with impact velocity and projectile geometry. At points corresponding to maximum energy absorption, the ratio for all projectile types scatters about an average of 2.1. The amount of deviation from this value depends on the mechanisms that lead to perforation. Failure mechanisms of a double-ply system are similar to those of a single-ply system, but the degree of damage of the impact and distal plies differs. ?? 2002 Elsevier Science Ltd. All rights reserved.
Ballistic impact; Failure mechanisms; High-speed impact; High-strength fabric; Multi-ply system; Projectile shape
Bending fatigue stiffness and strength degradation in carbon-glass/epoxy hybrid laminates: Cross-ply vs. angle-ply specimens
International Journal of Fatigue
28
8
815-825
2006
10.1016/j.ijfatigue.2005.11.009
A hybrid glass-carbon non-woven fabric reinforced epoxy matrix composite, constituted by layers of biaxial carbon fabrics, biaxial glass fabrics and hybrid carbon-glass fabrics, was considered for its bending fatigue behaviour. Tensile and flexural static tests as well as displacement-controlled bending fatigue tests (ratio of 0.10) were conducted on two sets of standard specimens, having fibre orientation parallel to the loading direction (cross-ply specimens) and at 45?? to the loading direction (angle-ply specimens). Specimens were subjected to different fatigue loading, with the initial maximum load level up to 85% of the laminate ultimate flexural strength, and damage in the laminate was continuously monitored through the loss of bending moment during cycling. After 106 cycles the fatigue test was stopped and residual properties were measured on tested specimens. Stiffness-based stress-number of cycle (SN) curves were drawn for the two sets of specimens. The amount of stiffness loss for cross-ply and angle-ply specimens was observed to depend on the fatigue load level. In particular, cross-ply specimens were observed to damage more significantly than angle-ply specimens only at high fatigue loading. This was attributed to different damage mechanisms for the two sets of specimens. Reduction in material strength and elastic modulus as measured after 106 cycles was also found to depend on the level of fatigue loading and to follow different trends for the two sets of specimens. ?? 2005 Elsevier Ltd. All rights reserved.
Bending fatigue; Fibre orientation; Hybrid composite; Residual strength; Stiffness degradation
Design and Validation of Thin-Walled Composite Deployable Booms with Tape-Spring Hinges
Aerospace
April
1-17
2011
10.2514/6.2011-2019
This paper presents a 1 m long self-deployable boom that could be folded around a spacecraft. Previously developed simulation techniques are used to analyze this two-hinge boom, made from two-ply plain weave carbon fiber laminate. A stress-resultant based failure criterion is used to study safety of the structure during both stowage and dynamic deployment. A safe design that latches without any overshoot is selected and validated by a dynamic deployment experiment.
Mode I interlaminar fracture toughness and fracture mechanism of angle-ply carbon/nylon laminates
Journal of Composite Materials
30
6
650-661
1996
Interlaminar fracture toughness and fracture mechanism in carbon fiber reinforced nylon laminates have been investigated. Mode I interlaminar fracture toughness tests are carried out on the double cantilever beam (DCB) specimens made of four kinds of angle-ply laminates. These laminates exhibit unstable "stick-slip" crack propagation. In order to obtain the continuous G I resistance curve (G I-R curve) describing the stick-slip behavior, one modification is made to Kageyama's (1987) modified compliance method. From the continuous G I-A curves, it is found that the stable delamination is characterized by flat region of G Istable ��� 1200 J/m 2 for all lay-ups except for 60°//-60° specimen which shows a rising G I-R curve to final failure. The interlaminar fracture toughness of these composite laminates is considerably higher than that of carbon/epoxy laminates. Based on the continuous G I-A curves and the observation of the fracture surfaces, a mechanism is proposed in which the unstable stick-slip behavior is explained by the development of the large scale bridging of fiber-bundle or layer and its breakage.
Angle ply laminates; Angle-ply laminates; Beams and girders; Carbon fiber reinforced plastics; Carbon fiber reinforced thermoplastic; Carbon fiber reinforced thermoplastics; Carbon fibers; Crack propagation; Delamination; Double cantilever beam; Failure (mechanical); Fracture mechanics; Fracture testing; Fracture toughness; Interlaminar fracture toughness; Kageyama modified compliance method; Mode I interlaminar fracture toughness; Modified-nylon; Nylon polymers; Stick slip behavior; Stick-slip behavior; Stick slip crack propagation
Stress analysis of ply drop-off in composite structures
Composite Structures
57
235-244
2002
10.1016/S0263-8223(02)00090-9
A combination of analytical and numerical method is employed to solve the ply drop-off problem. The singular stress fields in the drop-off region are characterized by using the eigenfunction expansion method. A global element capable of capturing the singular behavior is developed and incorporated into a general finite element analysis to provide an overall accurate solution of the stress fields in the ply drop-off region. This facilitates the use of a coarse mesh at the ply drop-off location even there are singular fields. The validation of the global-local finite element method has been carried out with the help of numerical examples. ?? 2002 Elsevier Science Ltd. All rights reserved.
Eigenfunction expansion; Global-local finite element; Ply drop-off; Singular stress
Measurement of adherence of residually stressed thin films by indentation. I. Mechanics of interface delamination
Journal of Applied Physics
56
1984
2632-2638
1984
10.1063/1.333794
A fracture analysis of indentation-induced delamination of thin films is presented. The analysis is based on a model system in which the section of film above the delaminating crack is treated as a rigidly clamped disc, and the crack extension force is derived from changes in strain energy of the system as the crack extends. Residual deposition stresses influence the cracking response by inducing buckling of the film above the crack and by providing an additional. crack driving force once buckling occurs. A relation for the equilibrium crack length is derived in terms of the indenter load and geometry, the film thickness and mechanical properties, the residual stress level, and the fracture toughness of the interface. The analysis provides a basis for using controlled indentation cracking as a quantitative measure of interface toughness and for evaluating contact- induced damage in thin films. I.
Analytical solution for buckling and post-buckling of angle-ply laminated plates under thermomechanical loading
International Journal of Non-Linear Mechanics
36
1097-1108
2001
10.1016/S0020-7462(00)00074-3
The present investigation deals with the buckling and post-buckling analysis of the moderately thick angle-ply laminated composite rectangular plates subjected to combined in-plane mechanical load and temperature gradient across the thickness. The geometric non-linearity in the von-Karman sense and first-order shear deformation theory are employed in the formulation of the problem. Non-linear governing differential equations of equilibrium are linearized by quadratic extrapolation technique and resulting linear differential equations are solved iteratively, using Chebyshev polynomials. The boundary conditions consisting of clamped, simply supported and their combinations are considered. An incremental iterative approach is employed to estimate the critical loads. The effects of b/a, boundary conditions and lamination scheme on the buckling and post-buckling behaviour of the laminated composite plates are investigated. ?? 2001 Elsevier Science Ltd.
Chebyshev series; Composite plates; Post-buckling; Shear deformation; Thermomechanical buckling
Contact mechanics and the wear of metals
Wear
190
2
162-170
1995
10.1016/0043-1648(95)06665-9
It is commonly observed that metallic wear debris takes the form of thin platelets, leading to the term ‘delamination wear’. Modelling this phenomenon has proved a stiff challenge in Contact Mechanics since the fractures which give rise to wear particles lie parallel, or nearly so, to the surface; i.e. on planes of maximum compressive stress. Sectioning the surface layer beneath a wear track has revealed it to have acquired severe plastic strains, which suggests that the cracks are ductile fractures, driven by plastic strain rather than elastic stress intensity. The paper reviews recent research into the progressive plastic deformation of surfaces in repeated sliding: the process known as ‘ratchetting’. Included is an analysis of ‘running-in’ of rough surfaces by repeated sliding and a discussion of the criterion of rupture under cyclic plastic strain.
contact mechanics; delamination wear; metals; plastic deformation; ratchetting
Influence of transverse cracking on ply behavior : introduction of a characteristic damage variable
Composite Science and Technology
46
29-37
1993
10.1016/0266-3538(93)90078-U
The most critical types of damage in composite materials are transverse cracking, delamination and fiber breakage. We have studied transverse cracking in a specimen submitted to axial and shear loading. The proposed model, based on damage mechanics, analyses the consequences of this degradation by a decrease of the anisotropic stiffnesses of the damaged layers of a composite structure. A damage variable is introduced to formulate a damage onset criterion and a damage development law. The development of cracks is simulated by a homogenization method and a macroscopic continuum damage mechanics (CDM) approach. The influence of the orientation of adjacent plies, the thickness and the position of the cracked ply in the stacking sequence have been studied. An iterative process is used to introduce the non-linearity of this damage development in a finite element program. The results obtained for beams submitted to axial loading are compared with experimental curves. Some practical applications are presented for laminated plates containing an open hole subjected to axial and biaxial loading.
composite; damage; transverse cracking
Prediction of the stiffness degradation in cross-ply laminates due to transverse matrix-cracking: An energy method approach
Advanced Composite Materials: The Official Journal of the Japan Society of Composite Materials
7
4
325-346
1998
10.1163/156855198X00237
This study deals with transverse cracking in cross-ply laminates. A fracture mechanics analysis, using a strain energy based criterion, was used to model the onset of transverse matrix cracking, and the conditions for further damage development. An admissible displacement field, involving unknown functions was assumed, and the principle of minimum potential energy was used to establish these functions. The crack front shape was a part of the assumed displacement field, thus making it possible to minimise the strain energy with respect to the crack opening displacement function. In this paper the aim was to establish a solution to the transverse cracking problem, to use later in a numerical procedure for the viscoelastic damage predictions for a cross-ply laminate. The model accounts for residual stresses. A number of finite element solutions were performed to verify the accuracy of the presented analytical solution. Predictions of stiffness degradation due to matrix cracking, and matrix cracking as a function of applied stress are presented.
Cross-ply composites; Damage mechanics; Energy methods; Residual stresses; Stiffness degradation; Transverse cracking
Statistical mechanics: Crackling crossover
Nature Physics
3
8
518-519
2007
10.1038/nphys682
Magnetic domains in a thin film grow in a jerky manner as avalanches of spins flip their directions. At low temperatures, the measured distribution of avalanche sizes agrees with one theory; at high temperatures, with another.
Center of gravity and shear center of thin-walled open-section composite beams
Composite Structures
52
2
255-260
2001
10.1016/S0263-8223(00)00177-X
The definition of center of gravity and shear center of a thin-walled open-section laminated composite beam is a function of the geometry and the material properties of the section. The method is applicable to any arbitrary laminate stacking sequence, i.e. unsymmetric as well as symmetric, and shape of the cross section. Numerical results are obtained for singly symmetric channel and monosymmetric sections with antisymmetric angle-ply layups showing that the locations of the center of gravity and shear center are generally affected by fiber angle variations. ?? 2001 Elsevier Science Ltd. All rights reserved.
Center of gravity; Open-section; Shear center; Thin-walled composites
Bursting thin liquid films
Journal of Fluid Mechanics
524
121-130
2005
10.1017/S0022112004002411
The breakup of a free thin liquid film subjected to an impulsive acceleration is investi- gated. A soap film is stretched on a frame at the exit of a shock tube. As the shock impacts the film, the film accelerates within a very short
Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading
Composite Structures
75
121-131
2006
10.1016/j.compstruct.2006.04.048
Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson's ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods. © 2006 Elsevier Ltd. All rights reserved.
Cracks; Interlaminar stress; Laminate; Property degradation; State space; Thermal loading
Mechanics of shear deformable thin-walled beams made of composite materials
Thin-Walled Structures
45
1
37-62
2007
10.1016/j.tws.2006.12.001
In this paper, a new theoretical model is developed for the generalized linear analysis of composite thin-walled beams with open or closed cross-sections. The present model incorporates, in a full form the shear deformability by means of two features. The first one may be addressed as a mechanical aspect where the effect of shear deformability due to both bending and non-uniform warping is considered. The second feature is connected with the constitutive aspects, and it contemplates the use of different hypotheses adopted in the formulation. These topics are treated in a straightforward way by means of the Linearized Principle of Virtual Works. The model is developed by employing a non-linear displacement field, whose rotations are formulated by means of the rule of semitangential transformation. This model allows studying many problems of static's, free vibrations with or without arbitrary initial stresses and linear stability of composite thin-walled beams with general cross-sections. A discussion about the constitutive equations is performed, in order to explain distinctive aspects of the effects included in the theory. This paper presents the theoretical formulation together with finite element procedures that are developed with the aim to obtain solutions to the general equations of thin-walled shear deformable composite beams. A non-locking fourteen-degree-of-freedom finite element is introduced. Numerical examples are carried out in several topics of static's, dynamics and buckling problems, focusing attention in the validation of the theory with respect to experimental data and with 2D and 3D computational approaches. Also, new parametrical studies are performed in order to show the influence of shear flexibility in the mechanics of the thin-walled composite beams as well as to illustrate the usefulness of the model. © 2007 Elsevier Ltd. All rights reserved.
Composite material; Shear flexibility; Thin-walled beams
Identification of damage and plasticity parameters for continuum damage mechanics modelling of carbon and glass fibre-reinforced composite materials
Strain
47
1
105-115
2011
10.1111/j.1475-1305.2009.00649.x
An experimental test series was carried out to determine input parameters for a well- known continuum damage mechanics elementary ply plasticity model. A full suite of data was obtained for a carbon fibre and an S2-glass fibre-reinforced composite material, both currently used in the aerospace industry. Models were implemented using the experimentally determined input parameters and predictions for in-plane behaviour found good agreement with experiments for both material systems. In addition, model predictions for cyclic loading accurately captured reload moduli and plastic strain magnitude.
carbon fibres; composite materials; continuum damage mechanics; mechanical properties; S2-glass fibres
Prediction of ply crack formation and failure in laminates
Composites Science and Technology
62
12-13 SPECIAL ISSUE
1619-1631
2002
10.1016/S0266-3538(01)00204-4
For a [0/90]s cross-ply laminate subject to uniaxial loading, this paper presents the results of comparisons between the model predictions of stress/strain behaviour, carried out in Part A of the Failure Exercise, and the corresponding experimental data provided after the predictions had been made. In addition, because a new model designed for general symmetric laminates has since been developed, comparisons are shown between the stress/strain predictions of the new model applied to quasi-isotropic and [????]s laminates (with ?? = 45 and 55??), and the corresponding experimental data provided to participants in the failure exercise. Very good correlations between the model and experimental stress/strain data have been achieved for both the cross-ply and quasi-isotropic laminates (subject to both uniaxial and biaxial loading), principally because ply cracking in a single orientation is expected to occur for a significant part of the stress/strain curves. The correlation for [????]s laminates is not as good because the model is not able to account for ply crack formation in both the +?? and -?? plies of the laminate. In addition, the model has not yet been modified to deal with mixed-mode ply crack growth, or with non-linear matrix behaviour which could lead to significant deviations between model predictions and experimental results at large strains. It is emphasised that the models used are not able by themselves to predict strength. Additional damage modes must be taken into account (e.g. fibre fracture) before predictions of strength can be made that are based on the modelling of physical micro-mechanisms associated with laminate failure. A rudimentary physically based approach to the prediction of laminate failure is made by considering fibre strain within the laminate in relation to the average failure strain of a single fibre. The ply cracking models that have been assessed in the paper, for cases where they are expected to be valid, have been shown to lead to good predictions of laminate stress/strain behaviour that is consistent with data provided for the Failure Exercise. The reliability of the models is such that they have good potential for being used as the basis of new design methodology to deal with initial ply crack formation in laminates, and the effects of ply cracking on non-linear stress/strain behaviour for parts of stress/strain curves where ply cracking occurs in a single orientation. ?? 2002 Published by Elsevier Science Ltd.
A. Polymer matrix composites; A. Structural materials; B. Matrix cracking; C. Anisotropy; C. Computational simulation
Mechanics condition of thin-walled tubular component with rib hydroforming
Transactions of Nonferrous Metals Society of China (English Edition)
22
SUPPL.2
s280-s286
2012
10.1016/S1003-6326(12)61720-8
To explore the hydroforming possibility of thin-walled tubular component with rib, mechanical analysis and finite element analysis (FEA) were conducted to investigate the rib buckling mechanics conditions. Based on lath-beam assumption, buckling Euler force was derived for rib which is restrained at one end and free at the other. The results indicate that it is possible to achieve a sound thin-walled tubular with rib component through hydroforming process and its expiation ratio can reach 20%. According to FEA, the effects of rib height and inner radius on buckling degree were studied and the threshold values of both rib height and inner radius were given. Simulation results indicate that there is a certain value for buckling and the threshold values of rib height and inner radius to thickness are 14 and 30. The formability deteriorates as rib height and rib inner radius increase. At last, the hydroforming limit diagram was drawn for hydroforming thin-walled tubular component with rib of 1Cr18Ni9. The results are useful for further study of hydroforming regularity of thin-walled tubular component with rib. © 2012 The Nonferrous Metals Society of China.
buckling; hydroforming; integral forming; mechanics condition; thin-walled and height-rib component; tubular component
Examination of ply cracking in composite laminates with open holes: A moire interferometric and numerical study
Composites Part A: Applied Science and Manufacturing
37
282-294
2006
10.1016/j.compositesa.2005.06.004
A moir?? interferometric investigation of surface strain redistribution due to matrix cracking around open holes in two [0/45/90/-45]s composite laminates with differing ply thicknesses was conducted. Both tests revealed significant redistribution of strain as damage developed. The results from the thicker-ply specimen show strain redistribution mostly due to the cracking of the top 0?? ply. This was verified by a mesh-independent displacement discontinuity modeling method based on higher order shape functions. Localized effects of sub-surface-ply cracking were not found. However, due to a thinner surface ply and more extensive damage, the thinner-ply specimen showed significant redistribution of strain as a result of the sub-surface-ply cracking as well as the 0?? ply cracking. Evidence of cracking in the center -45?? plies was present in the strain results. Examination of the strain redistribution and the failure surface of the thinner ply specimen led to the development of a failure scenario, where the initiation of critical 0?? fiber cracking occurs slightly away from the hole edge. Future modeling efforts will attempt to verify this scenario.
A. Laminates
Multiple transverse fracture in 90 cross-ply laminates of a glass fibre-reinforced polyester
Journal of Materials Science
12
1
157-168
1977
10.1007/BF00738481
Specimens of a 90º cross-ply glass-reinforced polyester were tested in tension in a direction parallel to one of the directions of reinforcment. Extensive cracking of the transverse-ply occured at strains much lower than the resin failure strain. These cracks formed in a direction parellel to the transverse reinforcement and showed a remarkably even crack spacing. Result of crack spacing measurements are presented against applied stress for specimens with differing transverse-ply thicknesses. The transverse-crack spacing was found to decrease with increasing applied stress and to increase with increasing transverseply thickness. There was no evidence of debonding between the plies during cracking and a multiple cracking theory in wich the plies remain elastically bonded has been presented which can account for the results.
FAILURE MECHANICS IN LOW-VELOCITY IMPACTS ON THIN COMPOSITE PLATES.
NASA Technical Paper
1983
Composite plates of Thornel 300 graphite in Narmco 5208 epoxy resin were tested to establish the degree of equivalence between low-velocity impact and static testing. Both the deformation and failure mechanics under impact were representable by static indentation tests. Under low-velocity impacts such as tool drops, the dominant deformation mode of the plates was the first, or static, mode. The areas of maximum delamination coincided with the areas of highest peel stresses. The extent of delamination was similar for static and impact tests. Fiber failure damage was established by tensile tests on small fiber bundles obtained by deplying test specimens.
AIRCRAFT MATERIALS - Graphite; MATERIALS TESTING - Failure; PLATES
Determination of Young's modulus for nanofibrillated cellulose multilayer thin films using buckling mechanics
Biomacromolecules
12
961-969
2011
10.1021/bm101330w
The Young's modulus of multilayer films containing nanofibrillated cellulose (NFC) and polyethyleneimine (PEI) was determined using the strain-induced elastic buckling instability for mechanical measurements (SIEBIMM) technique. (1) Multilayer films were built up on polydimethylsiloxane substrates using electrostatic layer-by-layer assembly. At 50% relative humidity, SIEBIMM gave a constant Young's modulus of 1.5 ± 0.2 GPa for 35-75 nm thick films. Conversely, in vacuum, the Young's modulus was 10 times larger, at 17.2 ± 1.2 GPa. A slight decrease in buckling wavelength with increasing strain was observed by scanning electron microscopy with in situ compression, and above 10% strain, extensive cracking parallel to the compressive direction occurred. We conclude that whereas PEI acts as a "glue" to hold multiple layers of NFC together, it prevents full development of hydrogen bonding and specific fibril-fibril interactions, and at high humidity, its hygroscopic nature decreases the elastic modulus when compared with pure NFC films.
Mechanics of sintering thin films II. Cracking due to self-stress
Mech. Mater.
11
221-234
1991
10.1016/0167-6636(91)90004-J
The mechanics of cracks in thin films is examined in this paper, the\nsecond part of a study of sintering thin films constrained by a substrate.\nThe film is analyzed as a compressible viscous fluid with a sliding\ninterface between film and substrate. The analysis can be applied\nto elastic films with a weak interface due to the mathematical analogy\nbetween linear viscous and linear elastic deformations. Asymptotic\nexpressions for the stress intensity factor of a crack in an infinite\nfilm are derived for the limiting cases of low and high interfacial\nfriction. These asymptotic results are verified by finite element\ncomputations which also provide numerical results for intermediate\nvalues of friction. It is assumed that the crack will grow if the\nstress intensity is large enough that the contact area of particles\njust ahead of the crack tip decreases. Expressions for the stress\nintensity factor are used with this fracture criterion to predict\nconditions for crack growth and initiation in sintering thin films.An\ninteresting result is that for sintering films it is possible to\npredict conditions for crack growth in terms of geometrical factors\nalone, such as film thickness, friction, and crack size.
A finite fracture mechanics model for the prediction of the open-hole strength of composite laminates
Composites Part A: Applied Science and Manufacturing
43
8
1219-1225
2012
10.1016/j.compositesa.2012.03.004
A new model based on finite fracture mechanics is proposed to predict the open-hole tensile strength of composite laminates. Failure is predicted when both stress-based and energy-based criteria are satisfied. The material properties required by the model are the ply elastic properties, and the laminate unnotched strength and fracture toughness. No empirical adjusting parameters are required. Using experimental data obtained in quasi-isotropic carbon-epoxy laminates it is concluded that the model predictions are very accurate, resulting in improvements over the traditional strength prediction methods. It also is shown that the proposed finite fracture mechanics model can be used to predict the brittleness of different combinations of materials and geometries. © 2012 Elsevier Ltd. All rights reserved.
Fatigue strengths of cross-ply CFRP laminates at room and high temperatures and its phenomenological modeling
International Journal of Fatigue
28
1297-1306
2006
10.1016/j.ijfatigue.2006.02.013
Fatigue life prediction for a symmetric alternating cross-ply carbon/epoxy laminate subjected to cyclic loading in the fiber direction is attempted on a ply-by-ply basis. First, tension-tension fatigue tests are performed under constant amplitude cycling at room and high temperatures. The normalized S-N relationship for the cross-ply laminate using the normalized stress level agrees with that for the unidirectional laminate made of the same prepreg tape. This implies that the on-axis fatigue behavior of the cross-ply laminate is substantially governed by that of the constituent plies in the laminate. Then, to evaluate the in situ strength of the constituent plies in the cross-ply laminate, static tension and tension-tension fatigue tests are carried out on unidirectional laminates with different number of plies. While the tensile strength of unidirectional laminate significantly depends on the thickness of laminate, the relative fatigue strength is insensitive to the number of plies. Using a modified Tsai-Hill static failure criterion that considers the in situ strength of plies, we can adequately predict the static tensile strength of the cross-ply laminate. Second, based on that fact and the assumption that the final failure of the cross-ply laminate is determined by the failure of axial plies, a simple fatigue failure model for the cross-ply laminate is developed by means of the classical lamination theory and the ply fatigue model considering the in situ static strength of plies. Finally, validity of the proposed model for the fatigue failure of symmetric alternating cross-ply CFRP laminates is evaluated by comparing with experimental results. It is demonstrated that the fatigue strength of the cross-ply laminate in the fiber direction is successfully predicted by the proposed fatigue model with a consideration of the in situ strength of ply. ?? 2006 Elsevier Ltd. All rights reserved.
Carbon/epoxy; Classical lamination theory; Cross-ply laminate; Fatigue; In situ ply strength; Ply-by-ply basis analysis; Ply fatigue model; S-N relationship
A simplified analysis of transverse ply cracking in cross-ply laminates
Composites Science and Technology
31
3
165-177
1988
10.1016/0266-3538(88)90008-5
This paper presents a method of analyzing transverse crack initiation and multiplication in symmetric cross-ply laminates. The method is based on the concept of a through-the-thickness inherent flaw and the energy balance principle. With a second-order polynomial assumed for the crack opening displacement, the perturbed stress field due to the presence of ply cracks is determined from the equilibrium conditions. The energy released as a result of ply cracking is then calculated and used to predict the increase in crack density. Based on an experimental correlation of the analytical result, a resistance curve is proposed to be used as a measure of the resistance to crack multiplication. The resistance to crack multiplication is shown to increase with the increasing crack density.
Interfaces: in fluid mechanics and across disciplines
Journal of Fluid Mechanics
645
1
2010
10.1017/S0022112009994186
The dynamics of fluid–fluid interfaces are important in diverse problems that span many disciplines in science and engineering. A series of snapshots is used to illustrate the breadth of applications that can occur in viscous low-Reynolds-number flows and I highlight theoretical and modelling ideas that are broadly useful for these, as well as other, problems. By way of illustration of unifying quantitative ideas we discuss briefly (i) the use of the Reciprocal Theorem in low-Reynolds-number flows, (ii) the use of the lubrication approximation for characterizing thin-film coating flows sometimes referred to as Landau–Levich–Derjaguin–Bretherton problems and (iii) nearly two-dimensional viscously dominated flows.
Delamination crack originating from transverse cracking in cross-ply composite laminates under extension
International Journal of Solids and Structures
27
1925-1941
1991
10.1016/0020-7683(91)90186-J
Based upon the Stroh formalism for anisotropic elastic materials and upon the method of eigenfunction expansion, the stress redistribution due to delamination cracks originating from transverse cracking is examined from [ 90 0], and [ 0 90], laminates under extension. The structure of the solution, in the form of a series expansion, is determined from the eigenvalue equation resulting from appropriate near-field conditions. To complete the solution, use is made of a boundary collocation technique in conjunction with the eigenfunction series that includes a large number of terms, enough to represent the elastic state throughout the appropriate domain concerned. The fracture mechanics parameters, such as stress intensity factors and energy release rates, are calculated and the major characteristics of stress distribution are discussed. The stability of delamination cracks is examined for varying ratios of ply thickness in terms of the energy release rate. © 1991.
Three-dimensional stress analysis of orthotropic and cross-ply laminated hollow cylinders and cylindrical panels
Computer Methods in Applied Mechanics and Engineering
117
3-4
331-351
1994
10.1016/0045-7825(94)90121-X
This paper deals with a detailed, three-dimensional stress and displacement analysis of transversely loaded, laminated complete hollow cylinders and open cylindrical panels having a symmetric or an antisymmetric cross-ply lay-up. The analysis is based on a refined, static version of a successive approximation approach which was first proposed by Soldatos and Hadjigeorgiou (J. Sound Vibration 137 (1990) 369–384) in connection with corresponding dynamic problems. However, the present refined formulation makes use of a recursive rather than a successive approximation formula. As a result, independently of the number of layers employed, the solution of the bending problem considered always ends with the solution of a sixth order system of simultaneous algebraic equations. The effectivenesss of the approach employed is checked by comparing numerical results with corresponding three-dimensional elasticity results published elsewhere in the literature. Then, the proposed formulation is further used towards a detailed stress and displacement analysis of the afore-mentioned structural elements.
On the mechanics of rim instabilities in viscoelastic polymer thin films
European Physical Journal: Special Topics
166
1
55-61
2009
10.1140/epjst/e2009-00878-x
Abstract Dewetting of polystyrene thin films deposited onto nonwettable silicon wafers displays unusual dynamics and various morphologies.\nThese instability patterns have been shown to be either discrete circular holes or surface undulations, in the case of nucleated\ndewetting or spinodal decomposition repectively. Here, we present the existence of a new rim instability, only effective in\nthe elasticity dominated regime, leading to the propagation of fractures into the rim. The comparison with the viscous fingering\ninstability suggests that, in addition to dewetting dynamics, the study of elasticity and viscous-dominated rim instabilities\nmay lead to improved understanding of the influence of viscoelasticity, slippage and friction at the film/substrate interface.
High-performance two-ply yarn supercapacitors based on carbon nanotubes and polyaniline nanowire arrays
Advanced Materials
25
10
1494-1498
2013
10.1002/adma.201204598
Fine count two-ply yarn supercapacitors are constructed from carbon nanotube yarns and polyaniline nanowires. The thread-like supercapacitor possess excellent electrochemical capacity and are very strong and flexible. When being woven or knitted into wearable electronic devices, alone or in combination with conventional textile yarns, the two-ply yarn supercapacitors can be flexed and stretched repeatedly without significant loss of capacitance.
carbon nanotubes; flexibility; polyaniline nanowire arrays; supercapacitors; wearable electronics
Delamination at Thick Ply Drops in Carbon and Glass Fiber Laminates Under Fatigue Loading
Journal of Solar Energy Engineering
130
3
031001
2008
10.1115/1.2931496
Delamination at ply drops in composites with thickness tapering has been a concern in applications of carbon fibers. This study explored the resistance to delamination under fatigue loading of carbon and glass fiber prepreg laminates with the same resin system, containing various ply drop geometries, and using thicker plies typical of wind turbine blades. Applied stress and strain levels to produce significant delamination at ply drops have been determined, and the experimental results correlated through finite element and analytical models. Carbon fiber laminates with ply drops, while performing adequately under static loads, delaminated in fatigue at low maximum strain levels except for the thinnest ply drops. The lower elastic modulus of the glass fiber laminates resulted in much higher strains to produce delamination for equivalent ply drop geometries. The results indicate that ply drops for carbon fibers should be much thinner than those commonly used for glass fibers in wind turbine blades.
Damage resistance and damage tolerance of dispersed CFRP laminates: Effect of ply clustering
Composite Structures
106
96-103
2013
10.1016/j.compstruct.2013.05.052
In this paper, the effect of introducing ply clustering in a composite stacking sequence on the damage resistance and damage tolerance of CFRP composite plates is investigated. Three stacking sequences are considered. First, a baseline laminate with conventional 0°, ±45° and 90° orientations and without ply clustering. The other two laminates are dispersed laminates with orientations not limited to the conventional ones. In one of them, four layers of 0° fiber orientation are clustered together at the specimen mid-plane, whereas in the last configuration, two clusters of two layers of 0° fiber orientation are introduced at the specimen top and bottom surfaces. The in-plane and the out-of-plane stiffness of the dispersed laminates match within 2% those of the baseline laminate. Ant Colony Optimization algorithm is used to select the stacking sequences with the desirable clustering and stiffness constraints. The results obtained demonstrate that introducing clustering had a negative effect on the maximum peak load recorded at different impact energies and also on the projected delamination area. Regarding damage tolerance, the residual compressive strength can be improved up to 30% with ply clustering. © 2013 Elsevier Ltd.
Damage resistance; Damage tolerance; Dispersed laminates; Low velocity impact; Ply clustering
Amputee socks: how does sock ply relate to sock thickness?
Prosthetics and orthotics international
36
1
77-86
2012
10.1177/0309364611431290
BACKGROUND: The term 'sock ply' may be a source of confusion in prosthetics practice because there may not be a consistent relationship between sock ply and sock thickness.\n\nOBJECTIVES: The purpose of this study was to characterize how sock ply related to sock thickness for different sock materials commonly used in limb prosthetics. We also evaluated how sock thickness changed under loading conditions experienced while wearing a lower limb prosthesis compared with unstressed conditions.\n\nSTUDY DESIGN: Experimental. Mechanical assessment.\n\nMETHODS: Seven sock materials of varying ply and sheaths were tested using a custom instrument. Sock thickness under eight different compressive stress conditions and two different biaxial in-plane tensile strain conditions were measured.\n\nRESULTS: For socks woven from a single material, thickness under walking stance phase conditions averaged 0.7, 1.2 and 1.5 mm for 1, 3 and 5-ply, respectively. For socks woven from several materials, the corresponding results were 0.4, 0.7 and 0.8 mm, respectively. Sock ply did not sum, e.g. a 3-ply sock was not three times the thickness of a 1-ply sock.\n\nCONCLUSIONS: Sock thickness and compressive stiffness are strongly dependent upon sock material, interface pressure, and in-plane biaxial strain.
Amputees; Artificial Limbs; Biomechanical Phenomena; Clothing; Foot; Humans; Lower Extremity; Lower Extremity: surgery; Materials Testing; Materials Testing: methods; Pliability; Pressure; Stress, Mechanical
In situ electro-mechanical experiments and mechanics modeling of tensile cracking in indium tin oxide thin films on polyimide substrates
Journal of Applied Physics
109
10
1-8
2011
10.1063/1.3592341
Indium tin oxide (ITO) thin films supported by polymer substrates have been widely used as transparent electrodes/interconnects in flexible electronics. Understanding the electro-mechanical behaviors of such material system is crucial for reliable operation of flexible devices under large deformation. In this paper, we performed in situ mechanical and electrical tests of ITO thin films with two different thicknesses (200 and 80 nm) deposited on polyimide substrates inside a scanning electron microscope. The crack initiation and propagation, crack density evolution and the corresponding electrical resistance variation were systematically investigated. It was found that cracks initiated at a higher tensile strain level and saturated with a higher density in thinner ITO films. Integrated with a coherently formulated mechanics model, the cohesive toughness and fracture strength of ITO thin films and the ITO/polyimide interfacial toughness were quantitatively determined. The experimentally observed thickness dependence of the saturated crack density in ITO thin films was also quantitatively verified by the model. (C) 2011 American Institute of Physics. [doi:10.1063/1.3592341]
Crack patterns in thin films
Journal of the Mechanics and Physics of Solids
48
6
1107-1131
2000
10.1016/S0022-5096(99)00081-2
A two-dimensional model of a film bonded to an elastic substrate is proposed for simulating crack propagation paths in thin elastic films. Specific examples are presented for films subject to equi-biaxial residual tensile stress. Single and multiple crack geometries are considered with a view to elucidating some of the crack patterns which are observed to develop. Tendencies for propagating cracks to remain straight or curve are explored as a consequence of crack interaction. The existence of spiral paths is demonstrated.
crack propagation; integral equations; lms; thin
Tribo-functional design of double cone drill implications in tool wear during drilling of copper mesh/CFRP/woven ply
Wear
302
1-2
1560-1567
2013
10.1016/j.wear.2013.01.046
This article presents an experimental analysis of drilling using carbide drills on carbon fiber reinforced plastic (CFRP) laminates specially made with copper mesh on one side and woven carbon fabric on the other side using carbide drills. The objective of this study was to improve the machining performance during drilling of sandwiched composite using various dimensions of double cone drill. The drill design in terms of its tribological characteristics (i.e. friction, wear) are analyzed including cutting force, life, chip form and hole quality. Results have shown that double cone drills generated less thrust force compared to standard twist drills. No delamination was found in the holes at high feed rates (above 0.1mm/rev). This could be attributed to the presence of thermoplastic nodules between the layers of the CFRP laminate and the presence of woven fabric ply at the bottom of the laminate. Furthermore a relationship between the feed per cutting edge and the thickness of the thermoplastic layer has been developed to promote the formation of continuous chips during drilling. Finally, SEM observations reveal several damage when standard twist drills were used and less damage was observed with double cone drills. These damaged areas were observed in the plies of fibers oriented at −45° and 90° compared with peripheral cutting speed of the drill.
Damage mechanics; Defects; Delamination; Fiber/matrix bond; Wear
Advanced quantum mechanics
Advanced Quantum Mechanics
1-405
2008
10.1007/3-540-28528-8
The legendary 1951 Dyson Lectures on Advanced Quantum Mechanics are finally LaTeXed, with thorough annotations and an index as an added bonus. See the Typist's Afterward preceding the backmatter for an explanation of this new version, and for the historical context see the website: http://hrst.mit.edu/hrs/renormalization/dyson51-intro/ as well as the author's website at the Princeton Institute for Advanced Study: http://www.sns.ias.edu/~dyson/
Cracking of thin bonded films in residual tension
International Journal of Solids and Structures
29
13
1657-1675
1992
10.1016/0020-7683(92)90015-L
Solutions are obtained for two elastic plane strain problems relevant to the cracking of a thin film bonded to a dissimilar semi-infinite substrate material. The first problem is that of a crack in the film oriented perpendicular to the film/substrate interface with the crack tip touching the interface. The second problem is that of a crack of the same geometry, but with length less than the film thickness, so that the crack tip is within the film. These problems are used to model several modes of crack extension in thin films bonded to thick substrate materials. Complete results from the solution of each problem are given over the full range of practical elastic mismatches. Dimensionless quantities important in describing the cracking of thin films are introduced and accurate approximate formulas based on the solution results are given for them. Applications are discussed, including criteria for avoiding thin film crack extension and a formula for the curvature change induced by the cracking of a thin film bonded to a substrate of finite thickness. The solution results, approximate formulas and information on their application provide the details necessary for the analysis of practical thin film cracking problems.
Time-dependent behaviors of angle-ply laminates with viscous interfaces in cylindrical bending
European Journal of Mechanics, A/Solids
23
2
235-245
2004
10.1016/j.euromechsol.2003.12.004
A simply supported angle-ply laminated plate in cylindrical bending with viscous interfaces under static loading is studied. Because of the presence of viscous interfaces, the behavior of the laminate depends on the time variable, which complicates the analysis. A highly accurate analysis is proposed, in which no assumption on deformation is introduced. Concretely, the state-space formulations, which have been used extensively in laminated structural analyses, are employed. The variations of field variables with time are approximated using the power series expansions. Recurrence formulae that make for easier program are constructed. Numerical examples are finally presented and comparison with existing results shows a good agreement. Results also indicate that the behavior of the laminate is very sensitive to the presence of viscous interfaces. ?? 2004 Elsevier SAS. All rights reserved.
Angle-ply laminate; Cylindrical bending; State-space method; Viscous interface
Beam analysis of angle-ply laminate DCB specimens
Composites Science and Technology
59
February 1998
305-315
1999
10.1016/S0266-3538(98)00069-4
Analysis and experiments on quasi-unidirectional and angle-ply laminate DCB fracture specimens are presented. The analysis treats the DCB specimen as two Bernoulli-Euler-type laminate beams joined at the mid-plane by a Winkler-type elastic foundation to accomodate transverse elasticity of the uncracked region of the specimen. An experimental study was conducted on glass/ polyester quasi-unidirectional and angle-ply laminate DCB specimens. Specifically, [0]6, [??30]5 and [??45]5 laminates with mid-plane delaminations were considered. Compliance values predicted by the elastic-foundation model were in good agreement with experimental data. The initiation fracture toughness was largest for the unidirectional composite and decreased with increased angle in the angle-ply laminates. The fracture toughness, G(c), increased with increased crack length and became steady-state after some crack propagation for the angle-ply laminates. The R-curve behavior is attributed to the work associated with debonding of transversely oriented fiber bundles and fracture of fibers that bridged the crack surfaces. The angle-ply laminates displayed more yarn debonding and bridging, and steep resistance curves. For all laminates it was observed that the crack propagated in a non-uniform manner across the width of the specimen as explained by elastic coupling effects of the laminate beams.
Numerical simulation of interlaminar damage propagation in CFRP cross-ply laminates under transverse loading
International Journal of Solids and Structures
44
10
3101-3113
2007
10.1016/j.ijsolstr.2006.09.007
This paper proposes a numerical simulation of interlaminar damage propagation in FRP laminates under transverse loading, using the finite element method. First, we conducted drop-weight impact tests on CFRP cross-ply laminates. A ply crack was generated at the center of the lowermost ply, and then a butterfly-shaped interlaminar delamination was propagated at the 90/0 ply interface. Based on these experimental observations, we present a numerical simulation of interlaminar damage propagation, using a cohesive zone model to address the energy-based criterion for damage propagation. This simulation can address the interlaminar delamination with high accuracy by locating a fine mesh near the damage process zone, while maintaining computational efficiency with the use of automatic mesh generation. The simulated results of interlaminar delamination agreed well with the experiment results. Moreover, we demonstrated that the proposed method reduces the computational cost of the simulation. © 2006 Elsevier Ltd. All rights reserved.
Composite material; Cross-ply laminate; Delamination; Finite element method; Transverse loading
3-D thermoelastic moduli and saturation crack density for cross-ply laminates with transverse cracks
International Journal of Damage Mechanics
8
3
273-309
1999
10.1177/105678959900800304
For stiffness critical structures, such as those found in space applications, the structural design and functionality may depend on several stiffness components. In this work we study the effect of transverse cracking on the effective Young's moduli, the effective Poisson ratios and the effective coefficient of thermal expansion for glass/epoxy and graphite/epoxy cross-ply laminates. In particular, included in the study are the effect of prescribed boundary conditions on the representative volume element used to describe the problem, the effect of variable crack spacing, and the interaction of transverse crack stress fields. The analysis is accomplished by the use of a model based on Reissner's variational principle that has been shown to accurately model stress fields and energy release rates in flat laminates. The present model predictions are compared to shear lag and finite element predictions from the literature and found to be in good agreement with published experimental data. A criterion to estimate the limiting density for pure transverse cracking damage is presented. Additionally, it is shown that for large crack densities, the model accurately recovers the limiting theory ply-discount effective property values.
The free vibration of symmetrically angle-ply laminated fully clamped skew plates
Journal of Sound and Vibration
323
1–2
444-450
2009
http://dx.doi.org/10.1016/j.jsv.2008.12.027
In this paper, the analysis of the free vibration of thin laminated skew plates with fully clamped edges is investigated. The governing differential equation for skew plate is obtained by transforming the differential equation in Cartesian coordinates into skew coordinates. The natural frequencies of the plate are then calculated by using the finite strip transition matrix method. The numerical results are obtained for different values of skew angles, fiber orientation angles and for different composites laminates. Comparisons have been made with the available results in the literature which show the accuracy and efficiency of the method.
Fractal features of a crumpling network in randomly folded thin matter and mechanics of sheet crushing
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
87
5
1-11
2013
10.1103/PhysRevE.87.052806
We study the static and dynamic properties of networks of crumpled creases formed in hand crushed sheets of paper. The fractal dimensionalities of crumpling networks in the unfolded (flat) and folded configurations are determined. Some other noteworthy features of crumpling networks are established. The physical implications of these findings are discussed. Specifically, we state that self-avoiding interactions introduce a characteristic length scale of sheet crumpling. A framework to model the crumpling phenomena is suggested. Mechanics of sheet crushing under external confinement is developed. The effect of compaction geometry on the crushing mechanics is revealed.
Fracture mechanics of ceramics
Ceramurgia International
4
3
142
1978
10.1016/0390-5519(78)90106-0
The 8th International Symposium on fracture mechanics of ceramics was held on the campus of the University of Houston, Houston, TX, USA, on February 25-28, 2003. This marks three decades of progress in the science and technology develop- ment in ceramics since the first meeting of this group, held at the Pennsylvania State University in 1973, which was published in Volumes 1 and 2 of this series. The meetings continued over approximately four year intervals, held subsequently in Virginia Polytechnic Institute and State University, Japan Fine Ceramics Center, Nagoya, Japan, and Kernforschungszentrum, Karlsruhe, Germany. With the natural maturing of the fields of structural ceramics, the present symposium has focused on nano-scale materials, composites, thin films and coatings as well as glass. The symposium also addressed new issues on fundamentals of fracture mechanics and contact mechanics, and a session on reliability and stand- ardization. The International Organizing Committee gratefully acknowledges the support from the Cullen College of Engineering, and the dedicated help from the local organizing committee. This includes Prof. L. Wheeler, Prashant Haldipur, Jennifer Husmo, Sandra Luna, Charlotte Palm and Jonathan Claydon. Additionally, I wish to thank the materials students who participated in the effort: Duo Liu, Mike Chelf, Marcos Flores, Rafael Longo and Yi Fang. Special thanks are extended to NASA Astronaut Dr. Bonnie Dunbar for her wonderful banquet presentation.
Neuro-musculoskeletal and performance adaptations to lower-extremity plyometric training
Sports Medicine
40
10
859-895
2010
10.2165/11318370-000000000-00000
Plyometric training (PLY) is a very popular form of physical conditioning of healthy individuals that has been extensively studied over the last 3 decades. In this article, we critically review the available literature related to lower-body PLY and its effects on human neural and musculoskeletal systems, athletic performance and injury prevention. We also considered studies that combined lower-body PLY with other popular training modalities, as well as studies that applied PLY on non-rigid surfaces. The available evidence suggests that PLY, either alone or in combination with other typical training modalities, elicits numerous positive changes in the neural and musculoskeletal systems, muscle function and athletic performance of healthy individuals. Specifically, the studies have shown that long-term PLY (i.e. 3-5 sessions a week for 5-12 months) represents an effective training method for enhancing bone mass in prepubertal/early pubertal children, young women and premenopausal women. Furthermore, short-term PLY (i.e. 2-3 sessions a week for 6-15 weeks) can change the stiffness of various elastic components of the muscle-tendon complex of plantar flexors in both athletes and non-athletes. Short-term PLY also improves the lower-extremity strength, power and stretch-shortening cycle (SSC) muscle function in healthy individuals. These adaptive changes in neuromuscular function are likely the result of (i) an increased neural drive to the agonist muscles; (ii) changes in the muscle activation strategies (i.e. improved intermuscular coordination); (iii) changes in the mechanical characteristics of the muscle-tendon complex of plantar flexors; (iv) changes in muscle size and/or architecture; and (v) changes in single-fibre mechanics. Our results also show that PLY, either alone or in combination with other training modalities, has the potential to (i) enhance a wide range of athletic performance (i.e. jumping, sprinting, agility and endurance performance) in children and young adults of both sexes; and (ii) to reduce the risk of lower-extremity injuries in female athletes. Finally, available evidence suggests that short-term PLY on non-rigid surfaces (i.e. aquatic- or sand-based PLY) could elicit similar increases in jumping and sprinting performance as traditional PLY, but with substantially less muscle soreness. Although many issues related to PLY remain to be resolved, the results of this review allow us to recommend the use of PLY as a safe and effective training modality for improving lower-extremity muscle function and functional performance of healthy individuals. For performance enhancement and injury prevention in competitive sports, we recommend an implementation of PLY into a well designed, sport-specific physical conditioning programme.
Training
Modeling delamination migration in cross-ply tape laminates
Composites Part A: Applied Science and Manufacturing
71
192-203
2015
10.1016/j.compositesa.2015.01.021
A novel modeling approach is proposed that combines the Floating Node Method (FNM) with the Virtual Crack Closure Technique (VCCT) to capture delamination migration in cross-ply tape laminates. Delamination migration is the damage process by which a delamination propagating at an interface relocates to a different interface via one or multiple matrix cracks. In the approach proposed, delamination, matrix cracking, and their interaction, are represented in a single element. The kinematics of both delamination and matrix cracks are represented explicitly. Migration onset location, and subsequent path, are determined as part of the solution, in a mesh-independent fashion. Delamination growth, matrix cracking, and migration onset, are all modeled using fracture mechanics based failure and migration criteria. The proposed approach is applied to the modeling of the Delamination Migration (DM) test, showing good qualitative and quantitative agreement with experiments.
B. Delamination; B. Fracture; B. Transverse cracking; C. Finite element analysis
Determination of the elastic moduli of thin samples and adherent cells using conical atomic force microscope tips
Nature Nanotechnology
7
September
733-736
2012
10.1038/nnano.2012.163
The atomic force microscope can detect the mechanical fingerprints of normal and diseased cells at the single-cell level under physiological conditions. However, atomic force microscopy studies of cell mechanics are limited by the 'bottom effect' artefact that arises from the stiff substrates used to culture cells. Because cells adhered to substrates are very thin, this artefact makes cells appear stiffer than they really are. Here, we show an analytical correction that accounts for this artefact when conical tips are used for atomic force microscope measurements of thin samples. Our bottom effect cone correction (BECC) corrects the Sneddon's model, which is widely used to measure Young's modulus, E. Comparing the performance of BECC and Sneddon's model on thin polyacrylamide gels, we find that although Sneddon's model overestimates E, BECC yields E values that are thickness-independent and similar to those obtained on thick regions of the gel. The application of BECC to measurements on live adherent fibroblasts demonstrates a significant improvement on the estimation of their local mechanical properties.
Damage mechanics analysis of transverse cracking behavior in composite laminates
International Journal of Damage Mechanics
9
2
113-129
2000
10.1177/105678950000900201
A damage mechanics analysis is applied to predict transverse cracking in a laminated composite. Two criteria based on the energy release rate and the average ply stress are used to predict transverse cracking. The analytical prediction of transverse crack density as a function of applied laminate strain is favorably compared with the experimental results. An advantage of the present predictive method is that it can be applied to laminates with arbitrary stacking sequences.
Finite width effect of thin-films buckling on compliant substrate: Experimental and theoretical studies
Journal of the Mechanics and Physics of Solids
56
2585-2598
2008
10.1016/j.jmps.2008.03.005
Buckling of stiff thin films on compliant substrates has many important applications ranging from stretchable electronics to precision metrology and sensors. Mechanics plays an indispensable role in the fundamental understanding of such systems. Some existing mechanics models assume plane-strain deformation, which do not agree with experimental observations for narrow thin films. Systematic experimental and analytical studies are presented in this paper for finite-width stiff thin films buckling on compliant substrates. Both experiments and analytical solution show that the buckling amplitude and wavelength increase with the film width. The analytical solution agrees very well with experiments and therefore provides valuable guide to the precise design and control of the buckling profile in many applications. The effect of film spacing is studied via the analytical solutions for two thin films and for periodic thin films. © 2008 Elsevier Ltd. All rights reserved.
Buckling; Compliant substrate; Film width; Stretchable electronics; Thin film
The influence of boundary conditions and transverse shear on the vibration of angle-ply laminated plates, circular cylinders and cylindrical panels
Computer Methods in Applied Mechanics and Engineering
190
2385-2409
2001
10.1016/S0045-7825(00)00242-5
This paper investigates the influence of the edge boundary conditions on the vibration characteristics of transverse shear deformable composite plates, closed cylindrical shells and open cylindrical panels having an arbitrary angle-ply lay-up. The shell model employed for this purpose is equivalent to the unified shear deformable Love-type theory introduced in Refs. [6,7], whereas the analysis is based on the Ritz method. Following some recent relevant developments [1-5], in which the method was applied successfully in connection with vibration problems of shear deformable cross-ply laminates, the Ritz method is employed in conjunction with complete functional bases formed by appropriate orthonormal polynomials. The present vibration study is based on angle-ply laminates having different combinations of simply supported, clamped and free edge boundaries. Apart from the convergence tests performed and the new results presented, the success of the present analysis is verified through comparisons with the corresponding results based on classical plate and shell theories as well as through comparisons with corresponding numerical and experimental results that are available in the literature. ?? 2001 Elsevier Science B.V. All rights reserved.
Evaluation and improvement of real-time PCR assays targeting lytA, ply, and psaA genes for detection of pneumococcal DNA
Journal of Clinical Microbiology
45
8
2460-2466
2007
10.1128/JCM.02498-06
The accurate diagnosis of pneumococcal disease has frequently been hampered not only by the difficulties in obtaining isolates of the organism from patient specimens but also by the misidentification of pneumococcus-like viridans group streptococci (P-LVS) as Streptococcus pneumoniae. This is especially critical when the specimen comes from the respiratory tract. In this study, three novel real-time PCR assays designed for the detection of specific sequence regions of the lytA, ply, and psaA genes were developed (lytA-CDC, ply-CDC, and psaA, respectively). These assays showed high sensitivity (<10 copies for lytA-CDC and ply-CDC and an approximately twofold less sensitivity for psaA). Two additional real-time PCR assays for lytA and ply described previously for pneumococcal DNA detection were also evaluated. A panel of isolates consisting of 67 S. pneumoniae isolates (44 different serotypes and 3 nonencapsulated S. pneumoniae isolates from conjunctivitis outbreaks) and 104 nonpneumococcal isolates was used. The 67 S. pneumoniae isolates were reactive in all five assays. The new real-time detection assays targeting the lytA and psaA genes were the most specific for the detection of isolates confirmed to be S. pneumoniae, with lytA-CDC showing the greatest specificity. Both ply PCRs were positive for all isolates of S. pseudopneumoniae, along with 13 other isolates of other P-LVS isolates confirmed to be non-S. pneumoniae by DNA-DNA reassociation. Thus, the use of the ply gene for the detection of pneumococci can lead to false-positive reactions in the presence of P-LVS. The five assays were applied to 15 culture-positive cerebrospinal fluid specimens with 100% sensitivity; and serum and ear fluid specimens were also evaluated. Both the lytA-CDC and psaA assays, particularly the lytA-CDC assay, have improved specificities compared with those of currently available assays and should therefore be considered the assays of choice for the detection of pneumococcal DNA, particularly when upper respiratory P-LVS might be present in the clinical specimen.
Effects of ply clustering in laminated composite plates under low-velocity impact loading
Composites Science and Technology
71
6
805-817
2011
10.1016/j.compscitech.2010.12.018
This paper presents a study of the effects of ply clustering on polymer-based laminated composite plates subjected to a drop-weight impact loading. The tools used to define the impact configurations, as well as the experimental results obtained, are described in detail. These tools are simplified analytical models for the description of the impact behavior and of the damage thresholds that result in a significant reduction on the structure stiffness and strength, caused by delamination. The results obtained demonstrate that the analytical tools are useful to define the impact configurations, to obtain a preliminary understanding of the effects of each parameter that can influence the response, and to interpret the experimental results. It is concluded that ply clustering reduces the damage resistance of the structure. However, the damage tolerance assessed by the compression after impact tests is unaffected by ply clustering. © 2010 Elsevier Ltd.
A. Laminates; A. Polymer-matrix composite; B. Delamination; B. Impact behavior; C. Damage tolerance
Numerical simulation of delamination in laminated composite components - A combination of a strength criterion and fracture mechanics
Composites Part B: Engineering
40
2
158-165
2009
10.1016/j.compositesb.2008.10.006
An approach for the numerical treatment of delamination in laminated composite components is presented. A first ply failure criterion is employed to predict delamination initiation, while delamination propagation is analyzed using linear elastic fracture mechanics. The combination of initiation and propagation criteria yields a conservative estimation of the load earring capacity of a structure. Furthermore, the growth stability, the sensitivity of the results with respect to a change in the interface properties, and the non-linear structural response caused by the delamination growth process are determined. Two structures are investigated, which show the capability of the proposed approach, a curved laminate and a double lap shear test specimen. ?? 2008 Elsevier Ltd. All rights reserved.
A. Layered structures; B. Delamination; C. Finite element analysis
Mechanics and finite elements for the damped dynamic characteristics of curvilinear laminates and composite shell structures
Journal of Sound and Vibration
263
2
399-414
2003
10.1016/S0022-460X(02)01059-3
Integrated mechanics and a finite element method are presented for predicting the damping of doubly curved laminates and laminated shell composite structures. Damping mechanics are formulated in curvilinear co-ordinates from ply to structural level and the structural modal loss factors are calculated using the energy dissipation method. The modelling of damping at the laminate level is based on first order shear shell theory. An eight-node shell damping finite element is developed. Comparisons of the present model with classical and discrete layer laminate damping theory predictions are shown. Modal damping and natural frequencies of composite plates and open cylindrical shells were measured and correlated with predicted results. Parametric studies illustrate the effect of curvature and lamination on modal damping and natural frequency.
An extensometer for fracture mechanics testing of thin composite laminates
Engineering Fracture Mechanics
30
1
1-4
1988
http://dx.doi.org/10.1016/0013-7944(88)90248-2
In fracture mechanics testing of thin reinforced plastic laminates, an important link in the measurement chain is the displacement transducer, which must be capable of measuring crack tip opening displacement (CTOD) and/or allowing evaluation of the J-integral by the unloading compliance method. The lightweight extensometer designed and calibrated by the authors can be used without any specimen knife edges. Highly deformable, it has the advantage of not rigidifying when used on low-stiffness specimens.
On the mechanics of thin-walled angle column instability
Thin-Walled Structures
52
80-89
2012
10.1016/j.tws.2011.12.007
This paper reports the results of a numerical investigation aimed at providing fresh insight on the mechanics underlying the buckling and (mostly) post-buckling behaviour of short-to-intermediate equal-leg thin-walled angle steel columns exhibiting fixed and pinned (but with the secondary warping prevented) end supports. Although most of the numerical results presented and discussed were obtained through Abaqus shell finite element analyses, the paper also includes some GBT-based critical stresses and buckling mode shapes, whose interpretation help clarifying the distinction between local and global buckling. The shell finite element results displayed consist of (i) elastic post-buckling equilibrium paths and (ii) curves and diagrams providing the evolution, along a given path, of the column deformed configurations and normal stress distributions.
Buckling and post-buckling mechanics; Equal-leg angles; Generalised Beam Theory (GBT); Shell finite element analysis; Thin-walled columns
Strengthening mechanics of thin and thick composite T-joints reinforced with z-pins
Composites Part A: Applied Science and Manufacturing
43
8
1308-1317
2012
10.1016/j.compositesa.2012.03.023
This paper presents an experimental and analytical study into the importance of the skin–flange thickness on the strengthening mechanics and fracture modes of z-pinned composite T-joints. The structural properties of unpinned and z-pinned carbon fibre–epoxy T-joints that had skin–flange thickness values between 2 mm (thin) and 8 mm (thick) were determined under tension (stiffener pull-off) loading. Experimental testing revealed that the capacity of z-pins to improve the structural properties was strongly dependent on the T-joint thickness. The joint properties increased at a quasi-linear rate with the skin–flange thickness, and z-pin pull-out tests showed that this was due to the increased crack bridging traction load and traction energy. The increase to the structural properties of the z-pinned T-joints with increasing thickness is explained using the bridging traction laws for z-pinned laminates.
a. polymer–matrix composites (pmcs); b. mechanical properties; c. analytical modelling; e. joints/joining
Cracking paths at the ply interface in a cross-ply laminate
Composites Part B: Engineering
34
437-445
2003
10.1016/S1359-8368(03)00019-2
It has been observed in both ceramic and polymer-matrix composites that the evolution of transverse matrix cracking shows two distinct stages. When tensile stress is applied in the fiber direction of the 0° ply, cracks are formed in the 90° ply at a load level much lower than the ultimate strength of the laminate. As the load increases, more transverse cracks are initiated. At some critical load, the number of cracks ceases to increase; instead, the existing cracks penetrate into the adjacent 0° layers and eventually fracture the 0° fibers. Catastrophic failure becomes imminent when the 0° fibers are broken. The purpose of this paper is to identify conditions under which transverse cracks are deflected into the ply interfaces at the second stage of damage evolution. To this end, the energy release rates for deflection and penetration are used as a criterion to predict the crack growth paths. It is found that the predicted crack path depends on the geometry, the material properties and the degree of damage. Based on this analysis, a crack path prediction diagram is obtained for crack growth at the ply interface. © 2003 Elsevier Science Ltd. All rights reserved.
Anisotropy; Bimaterials; Crack path; Delamination; Interface crack; Laminate; Transverse cracks
Suppression of Delamination at Ply Drops in Tapered Composites by Ply Chamfering
Journal of Composite Materials
40
2
157-174
2005
10.1177/0021998305053459
The design of structures is often optimized by gradually decreasing the thickness as the load carrying requirement on the components decreases. Such structures in composites are made of tapered laminates involving dropping of plies. However, these structures are often prone to early delamination initiation, which leads to premature failure of the component and therefore limits its useful life. In the past, many routes to circumvent this problem have been evolved, such as the use of adhesive film layers or interleaving the dropped plies between continuous ones. In this work, a novel technique of ply edge chamfering has been developed and employed in the specimen fabrication. Comparisons have been drawn between similarly configured specimens, with and without chamfered ply drops. Static and fatigue test results have shown remarkable improvements, both in terms of complete suppression of delamination around ply drops and in realizing 14.5–77.6% higher strength levels in tapered composite test coupons. The experimental data along with their comparative cases are presented.
Incorporating interlaminar fracture mechanics into design
Proceedings of the I MECH E Part L Journal of Materials:Design and Applications
214
91-97
2000
10.1243/1464420001544870
In laminated composite structures, interlaminar failures or delaminations have continued to be a predominant life-limiting failure mode. The main concern for designers has focused on the damage tolerance of structures in the presence of delamination damage from impact events. The design approach has been to utilize existing stress/strain-based design criteria to design the part, then to impact the part consistent with the threat and to take a knock-down in design loads in the presence of damage. However, delaminations also occur during service in areas where high interlaminar stresses are present. These are generally at required discontinuities in the design, such as cut-outs, holes, joints or ply-drops. The application of interlaminar fracture mechanics as a design tool for optimizing these regions is still in its infancy and is adopted by very few original equipment manufacturers. This paper addresses this issue and presents the more recent developments in incorporating interlaminar fracture mechanics into design. The paper discusses the improvements in global-local modelling to integrate local design features with global stiffness and load considerations and vice versa. It will address the current methods for characterizing interlaminar fracture behaviour and show examples of how predictions can be made to predict the life of a component.
damage tolerance; delamination; durability; fracture mechanics; global; local design
Study of critical buckling loads and modes of cross-ply laminated annular plates
Composites Part B: Engineering
43
2
422-430
2012
10.1016/j.compositesb.2011.08.051
Buckling of composite annular plates under uniform internal and external radial edge loads have been investigated using energy method. Trefftez rule is used in the stability equations. The symmetric buckling of symmetric cross-ply laminates is considered. In this paper, buckling behavior for the three laminates (90/0) 2s, (90/0 2/90) s and (90 2/0 2) s are studied. Influence of some parameters such as thickness, stacking sequence, type of supports and the ratio of hole to sheet radius on buckling loads and modes are investigated. The results of the energy method are compared with the results of numerical method. Based on the results, in the plates with clamped boundary conditions the symmetric buckling assumption is not accurate, contrary to other boundary conditions. ?? 2011 Elsevier Ltd. All rights reserved.
A. Laminates; Annular plates; B. Buckling; C. Laminate mechanics
Stiffness degradation resulting from 90° ply cracking in angle-ply composite laminates
Composites Science and Technology
59
1543-1552
1999
10.1016/S0266-3538(99)00021-4
Stiffness degradation resulting from 90° ply cracking in [±θn/90m]s angle-ply composite laminates has been evaluated by a 3D finite-element method. A control volume having a single simulated transverse crack in 90° ply/plies and intact ±θ outer layers is used for the analysis. The stiffness degradation as a transverse crack extends in the width direction for glass/epoxy angle-ply laminates is calculated for different crack lengths and different fibre orientation angles θ of the outer layers. Effects of the number of 90° layers and number of ±θ layers on the laminate stiffness have also been studied. It has been observed that the available stiffness of the cracked angle-ply laminate largely depends on the fibre orientation angle of the outer layers, the number of cracked cross-ply layers and the number of uncracked outer ±θ layers in the laminate.
Stiffness degradation in cross-ply laminates damaged by transverse cracking and splitting
Composites Part A: Applied Science and Manufacturing
31
4
335-351
2000
10.1016/S1359-835X(99)00077-9
In contrast to the few existing theoretical models (Highsmith and Reifsnider, ASTM STP 1986;907:233-251; Hashin, Trans ASME J Appl Mech 1987;54:872-879; Daniel and Tsai, Comp Eng 1991;1(6):355-362; Tsai and Daniel, Int J Solid Structures...
cross-ply composite laminates
Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a Unified Formulation
Composites Part B: Engineering
58
544-552
2014
10.1016/j.compositesb.2013.10.088
In this paper, the Carrera Unified Formulation and the generalized differential quadrature technique are combined for predicting the static deformations and the free vibration behavior of thin and thick isotropic as well as cross-ply laminated plates. Through numerical experiments, the capability and efficiency of this technique, based on the strong formulation of the problem equations, are demonstrated. The numerical accuracy and convergence are also examined. It is worth noting that all the presented numerical examples are compared with both literature and numerical solutions obtained with a finite element code. The proposed methodology appears to be able to deal not only with uniform boundary conditions, such as fully clamped or completely simply-supported, but also with mixed external conditions, that can be clamped, supported or free. ?? 2013 Elsevier Ltd. All rights reserved.
A. Laminates; B. Vibration; C. Computational modelling
Multi-contrast Light Profile Microscopy for the Depth-Resolved Imaging of the Properties of Multi-ply Thin Films
Applied Spectroscopy
63
6
642-661
2009
Light profile microscopy (LPM) is a direct method for the spectral depth imaging of thin film cross-sections on the micrometer scale. LPM uses a perpendicular viewing configuration that directly images a source beam propagated through a thin film. Images are formed in dark field contrast, which is highly sensitive to subtle interfacial structures that are invisible to reference methods. The independent focusing of illumination and imaging systems allows multiple registered optical sources to be hosted on a single platform. These features make LPM a powerful multi-contrast (MC) imaging technique, demonstrated in this work with six modes of imaging in a single instrument, based on (1) broad-band elastic scatter; (2) laser excited wideband luminescence; (3) coherent elastic scatter; (4) Raman scatter (three channels with RGB illumination); (5) wavelength resolved luminescence; and (6) spectral broadband scatter, resolved in immediate succession. MC-LPM integrates Raman images with a wider optical and morphological picture of the sample than prior art microprobes. Currently, MC-LPM resolves images at an effective spectra resolution better than 9 cm(-1), at a spatial resolution approaching 1 mu m, with optics that operate in air at half the maximum numerical aperture of the prior art microprobes.
blind deconvolution; confocal raman microscopy; depth profiling; light profile microscopy; lpm; mc-lpm; multi-contrast light profile microscopy; multilayer films; point-spread; profilometry; refraction; resolution; scattering
Notch mechanics for plane and thin plate bending problems
Engineering Fracture Mechanics
37
1
87-99
1990
10.1016/0013-7944(90)90333-C
This paper describes the summary of notch mechanics based on the linear elasticity. The V-shaped notch with sharp or round corner and symmetric to the bisector is the object of this study. The plane elastic problem and thin plate bending problem are considered for free and fixed boundary conditions. The following matters are investigated: the stress distributions near the sharp corner; the general expression of the stress concentration at the round corner; the relationship between the intensity of corner and the stress concentration; and the stress intensity factor of a crack initiating from the notch tip. The notch mechanics is connected with the crack mechanics by the expression of stress intensity factor.
The Influence of Ply Waviness with Nonlinear Shear on the Stiffness and Strength Reduction of Composite Laminates
Journal of Thermoplastic Composite Materials
7
2
76-90
1994
10.1177/089270579400700201
The influence of ply waviness with nonlinear shear material response on the mechanical performance of composite laminates is studied. An analytic model, based on a three-dimensional laminated media analysis, is developed to predict the effective nonlinear laminate behavior associated with ply waviness. An undulating [0] ply in a [90/0/90] sublaminate configuration and undulating [±β] plies in a [90/±β/90] sub laminate configuration are two types of ply waviness considered. An incremental loading strategy is employed wherein piece-wise linear solutions are superimposed to obtain the overall nonlinear stress/strain response of composite laminates with wavy plies. The anal ysis also predicts individual ply stress and strain distributions within the wavy ply con figuration. The maximum stress failure criterion is used to predict ply failure in local re gions within the wavy ply configuration and a progressive failure methodology is adopted to permit local load redistribution. Results are presented that offer fundamental insight into the dominant mechanisms for stiffness and strength reduction in composite laminates exhibiting ply waviness and nonlinear shear material behavior.
Elimination of stress-induced curvature in thin-film structures
Journal of Microelectromechanical Systems
11
5
592-597
2002
10.1109/JMEMS.2002.802908
Argon ion machining of released thin-film devices is shown to alter the contour shape of free-standing thin-film structures by affecting their through-thickness stress distributions. In experiments conducted on MEMS thin-film mirrors it is demonstrated that post-release out-of-plane deformation of such structures can be reduced using this ion beam machining method. In doing so optically flat surfaces (curvature <0.001 mm<sup>-1</sup>) are achieved on a number of 3 μm-thick surface micromachined silicon structures, including mirrors with either initially positive curvature or initially negative curvature measuring up to 0.02 mm<sup>-1</sup>. An analytical model incorporating the relevant mechanics of the problem is formulated and used to provide an understanding of the mechanisms behind the planarization process based on ion machining. The principal mechanisms identified are 1) amorphization of a thin surface layer due to ion beam exposure and 2) gradual removal of stressed material by continued exposure to the ion beam. Curvature history predictions based on these mechanisms compare well with experimental observations.
Mechanics and test study of flexible membranes ballooning in three dimensions
Building and Environment
43
11
1871-1881
2008
10.1016/j.buildenv.2007.11.002
Numerous enclosure wall systems employ membranes that are not fully adhered, common examples being mechanically attached housewraps in screen-type exterior wall systems. Many roofing systems also incorporate membranes that are not fully adhered such as mechanically fastened single-ply membranes. Under a negative air pressure differential caused by wind suction, these wall and roof membranes can deform or balloon. Ballooning of the membrane affects many aspects of its performance. For instance, it changes the volume of the air chamber in screen-type wall systems and therefore, affects both the extent of screen pressure moderation and the nature of ventilation within the wall. In case of the single-ply roofing membrane, excessive ballooning can tear or rupture the membrane at the mechanical fastener location and therefore fail the membrane as the primary waterproofing component in the roofing system. This paper develops the structural mechanics for flexible membranes ballooning in three dimensions under a negative air pressure differential. The governing differential equation is derived and solved numerically. A second-order paraboloid of revolution is assumed to describe the ballooning shape. A series of physical tests were conducted to confirm that the ballooning shape follows the second-order paraboloid of revolution and compare the model predict with the test data. ?? 2007 Elsevier Ltd. All rights reserved.
Air pressure differential; Ballooning; Housewrap; Membrane; Screen-type wall system
Analytical Mechanics
American Journal of Physics
68
4
390
2000
10.1119/1.19451
This introductory undergraduate text provides a detailed introduction to the key analytical techniques of classical mechanics, one of the cornerstones of physics. It deals with all the important subjects encountered in an undergraduate course and thoroughly prepares the reader for further study at graduate level. The authors set out the fundamentals of Lagrangian and Hamiltonian mechanics early in the book and go on to cover such topics as linear oscillators, planetary orbits, rigid-body motion, small vibrations, nonlinear dynamics, chaos, and special relativity. A special feature is the inclusion of many "e-mail questions," which are intended to facilitate dialogue between the student and instructor. It includes many worked examples, and there are 250 homework exercises to help students gain confidence and proficiency in problem-solving. It is an ideal textbook for undergraduate courses in classical mechanics, and provides a sound foundation for graduate study.
Mechanics of the interface for carbon nanotube-polymer composites
Thin-Walled Structures
43
1787-1803
2005
10.1016/j.tws.2005.07.003
Carbon nanotubes possess exceptionally superior mechanical properties like high elastic modulus and tensile strength. Hence, they are envisaged to be the ideal reinforcements for polymer composites, especially for enhancement of mechanical properties. However, the superiority of the mechanical properties of nanotubes alone does not ensure mechanically superior composites because the composite properties are strongly influenced by the mechanics that govern the nanotube-polymer interface. The structural strength characteristics of composite materials greatly depend on the mechanical load transfer from the matrix (polymer interface) to the nanotube and the strength of the interface. Hence, the knowledge and understanding of the nature and mechanics of load transfer between nanotube and polymer is critical for manufacturing of enhanced carbon nanotube-polymer composites and will enable in tailoring of the interface for specific applications or superior mechanical properties. In this paper, a review of the state of the art in mechanics of carbon nanotube-polymer composites will be discussed along with some directions for future research in this field. ?? 2005 Elsevier Ltd. All rights reserved.
Putting Mechanics into Quantum Mechanics
Physics Today
July
36-42
2005
10.1063/1.2012461
Nanoelectromechanical structures are starting to approach the ultimate quantum mechanical limits for detecting and exciting motion at the nanoscale. Nonclassical states of a mechanical resonator are also on the horizon.
The peel ply surface treatment for adhesive bonding of composites: A review
International Journal of Adhesion and Adhesives
43
60-69
2013
10.1016/j.ijadhadh.2013.01.014
This paper reviews existing literature related to the peel ply surface treatment of composite materials. A peel ply fabric is used as a removable layer in a composite lay-up and ripped off to modify the surface for adhesive bonding. A peel ply can affect the elemental composition of a surface and it is possible to distinguish between either a polyester or a polyamide peel ply treatment for a specific composite system and application. However, consistent and generalised relationships between the compositional modification or the surface energy and adhesive or resin adherence to treated surfaces are not probable. A compositional analysis and surface energy measurements are affected by the fractured matrix, peel ply fibre cavities and revealed reinforcements. Only a few recent studies have presented results for the regions of the matrix fracture and fibre cavities separately. Resin-impregnated peel plies, namely tear plies, offer additional tailorability for composite surface treatments, but related research is scarce. ?? 2013 Elsevier Ltd.
Composites; Interfaces; Joint design; Surface treatment
Growth, geometry, and mechanics of a blooming lily.
Proceedings of the National Academy of Sciences of the United States of America
108
14
5516-5521
2011
10.1073/pnas.1007808108
Despite the common use of the blooming metaphor, its floral inspiration remains poorly understood. Here we study the physical process of blooming in the asiatic lily Lilium casablanca. Our observations show that the edges of the petals wrinkle as the flower opens, suggesting that differential growth drives the deployment of these laminar shell-like structures. We use a combination of surgical manipulations and quantitative measurements to confirm this hypothesis and provide a simple theory for this change in the shape of a doubly curved thin elastic shell subject to differential growth across its planform. Our experiments and theory overturn previous hypotheses that suggest that blooming is driven by differential growth of the inner layer of the petals and in the midrib by providing a qualitatively different paradigm that highlights the role of edge growth. This functional morphology suggests new biomimetic designs for deployable structures using boundary or edge actuation rather than the usual bulk or surface actuation.
Mechanics of precurved-tube continuum robots
IEEE Transactions on Robotics
25
1
67-78
2009
10.1109/TRO.2008.2006868
This paper presents a new class of thin, dexterous continuum robots, which we call active cannulas due to their potential medical applications. An active cannula is composed of telescoping, concentric, precurved superelastic tubes that can be axially translated and rotated at the base relative to one another. Active cannulas derive bending not from tendon wires or other external mechanisms but from elastic tube interaction in the backbone itself, permitting high dexterity and small size, and dexterity improves with miniaturization. They are designed to traverse narrow and winding environments without relying on ldquoguidingrdquo environmental reaction forces. These features seem ideal for a variety of applications where a very thin robot with tentacle-like dexterity is needed. In this paper, we apply beam mechanics to obtain a kinematic model of active cannula shape and describe design tools that result from the modeling process. After deriving general equations, we apply them to a simple three-link active cannula. Experimental results illustrate the importance of including torsional effects and the ability of our model to predict energy bifurcation and active cannula shape.
Continuum robot; Flexible manipulator; Medical robot; Snake-like robot
Edge Delamination in Angle-Ply Composite Laminates
AIAA Journal
22
2
256-264
1984
doi:10.2514/6.1981-578
Edge delamination has caused significant concern in the design and analysis of advanced composite materials and structures. Owing to its complex nature, only very limited information on this subject is currently available. The composite delamination problem involves not only geometric and material discontinuities but also inherently coupled mode I, II, and III fracture in the layered anisotropic system. Based on the recently developed anisotropic laminate elasticity theory and an eigenfunction expansion method, the exact crack-tip stress singularity and complete field solutions for the composite edge delamination problem are obtained. Fracture mechanics parameters such as mixed-mode stress intensity factors and associated strain energy release rates for a delamination are defined explicitly. For illustrative purposes, results are given for edge-delaminated symmetric [0-/-0/ — 0/0] graphite-epoxy composites subjected to uniform axial extension. Effects of geometric, lamination, and crack variables are examined.
Peel ply surface treatment for composite assemblies: Chemistry and morphology effects
Composites Part A: Applied Science and Manufacturing
36
11
1562-1568
2005
10.1016/j.compositesa.2005.02.012
Glass/epoxy and carbon/epoxy composites were manufactured using a series of polyester and polyamide based peel ply treatments. The influence of peel ply removing upon surface characteristics was assessed with performing contact angle measurements, laser profilometry, SEM and ToF-SIMS analysis. The surface properties of the composite material prior to bonding and the single lap shear performances of resulting assemblies were compared, in order to elucidate the decisive parameters governing adhesion qualities. From a general point of view, the roughness and the chemical nature of the peel ply used strongly influence the properties of the adherent-adhesive system assembly. © 2005 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites; B. Adhesion; B. Surface properties; D. Surface analysis
Alteration of skin mechanics by thin polymer films
Skin Research and Technology
14
3
312-319
2008
10.1111/j.1600-0846.2008.00296.x
BACKGROUND/PURPOSE: High molecular weight polymers such as proteins and polysaccharides have been commonly employed in cosmetic practice to induce skin tightness. The effect is perceived by users as an increase in skin tightness (firmness) accompanied by skin smoothing and elimination of wrinkles and lines. The aim of the study was to assess whether high molecular weight synthetic polymers, in the form of simple skin treatment formulations, could modify mechanical properties of natural skin as well as artificial skin models. METHODS: In experiments involving natural skin, the formulations were employed to treat the inner forearm of five panelists, who ranged in age from mid-20s to mid-40s. Indentometric analysis also included rubber skin models, with various viscoelastic characteristics, modified by deposition of thin polymer films on the surface. Polymers such as polyvinylpyrrolidone, polyquaternium-55, polyimide-1, VP/acrylates/lauryl methacrylate copolymer, and sodium alginate were investigated. The effects of the products were quantified by mechanical skin indentation performed at small deformations. Data analysis was performed using the Hertz theory of contact mechanics, which included the calculation of fundamental parameters such as the modulus of elasticity. RESULTS: The indentometric analysis revealed an increase in the Young's modulae for both artificial and natural skin as a result of treatment with the polymers. The effect was dependent on the amount of deposited product, which was varied in the range from 0.053 to 1.06 mg/cm(2) of polymer. The observed increases in Young's modulae were typically from about 0.7 to 1.4 x 10(4) N/m(2) for untreated skin to 1.4-2.0 x 10(4) N/m(2) for polymer-modified skin, depending on the polymer structure (molecular weight) and the amount of deposition. By the analysis of artificial skin models, it was found that the magnitude of stiffening depends on the mechanical characteristics of the base material. Softer skin models displayed larger increases in Young's modulus after polymer treatment than stiffer skin models. Also, the analysis of skin models suggested that polymeric treatments can lower the viscoelasticity of skin as demonstrated by decreased values of hysteresis loss factors calculated from indentation force vs. penetration depth plots. The performance of the polymers was also shown to be dependent on ambient humidity with the most hygroscopic materials loosing their stiffening effect at high humidity. CONCLUSIONS: The data indicate that high molecular weight polymers can be useful as skin stiffening, firming, or tightening agents. This was demonstrated by indentometric, mechanical analysis of natural skin and artificial skin models, and by determining Young's modulae and viscoelastic parameters.
Indentometry; Polymers; Skin mechanics; Skin tightness; Young's modulae
A model for transverse cracking and delamination in cross-ply laminates
Composites Science and Technology
60
7
1055-1066
2000
http://dx.doi.org/10.1016/S0266-3538(00)00006-3
This paper develops an analytical model to evaluate the stress distibutions in cross-ply laminates subjected to tensile loading and containing transverse cracks and delamination initiated from the transverse crack tips. In the delaminated part the analytical approach is reduced to the usual one-dimensional analysis. In the part without delamination the analytical model is based on a displacement approach which considers that the longitudinal displacement depends on the longitudinal and transverse coordinates in each layer. The stress distributions derived from the analytical model are compared with the results obtained from a finite-element analysis.
B. Modelling; C. Delamination; C. Finite-element analysis; Cross-ply laminates; C. Transverse cracking
Fracture Mechanics and Mechanisms of Impact-Induced Delamination in Laminated Composites
Journal of Composite Materials
29
2
156-178
1995
10.1177/002199839502900202
The fracture mechanism of impact-induced delamination is studied in carbon fiber/PEEK (polyetheretherketone) cross-ply laminates under drop weight impact. The study is based on the energy theory of fracture mechanics and the concept of crack arrest toughness. The damaged laminate is modeled by a finite element method which simulates delaminations and transverse cracks. The numerical results are combined with test data to study the delamination behavior. It is found that the delamination occurs in a deflection-controlled condition and is a process of Mode II dominated unstable crack growth and subsequent arrest. The fracture behavior can be described by strain energy release rate and the delamination size is governed by the delamination arrest toughness of the composite.
Fundamentals of fluid mechanics
Journal of Mechanical Working Technology
16
2
227-228
1988
10.1016/0378-3804(88)90174-X
The number one text in its field, Fundamentals of Fluid Mechanics is respected by professors and students alike for its comprehensive topical coverage, its varied examples and homework problems, its application of the visual component of fluid mechanics, and its strong focus on learning. The authors have designed their presentation to allow for the gradual development of student confidence in problem solving. Each important concept is introduced in simple and easy-to-understand terms before more complicated examples are discussed.
Beam analysis of angle-ply laminate mixed-mode bending specimens
Composites Science and Technology
59
6
937-945
1999
Doi 10.1016/S0266-3538(98)00128-6
An analysis of angle-ply laminated beam fracture specimens loaded in a mixed-mode bending (MMB) apparatus is presented. The analysis is based on superposition of compliance and strain-energy release rate expressions previously derived from laminated beam theory for DCB and ENF angle-ply laminate specimens. Elastic interactions between the two arms of the specimen, asymmetry in lay-up, and interlaminar shear deformation are incorporated in the analysis. It was found that the ratio between G(I) and G(II) is only slightly sensitive to ply angle in the angle-ply laminates, where G(I) and G(II) denote the mode I and mode II components of the strain energy release rate, G. The ratio G(I)/G(II), likewise, is only weakly dependent on crack length. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminates was conducted. Specifically, [0](6), [+/-30](5) and [+/-45](5) laminates with midplane delaminations were tested at various mode ratios (G(I)/G(II)) Predicted compliance values were in good agreement with experimental data. The fracture toughness, G(c), increased with decreased ratio G(I)/G(II). G(c) increased with increased ply angle theta in the angle-ply laminates except for pure mode I conditions. Nonuniform and skewed crack fronts were observed for the angle-ply laminates as a result of elastic coupling in the laminate beams of the cracked region. (C) 1999 Elsevier Science Ltd. All rights reserved.
delamination; double-cantilever beam; glass/epoxy composites; interface crack; singularities; tests; toughness
Cell response to matrix mechanics: focus on collagen.
Biochimica et biophysica acta
1793
5
893-902
2009
10.1016/j.bbamcr.2008.10.012
Many model systems and measurement tools have been engineered for observing and quantifying the effect of mechanics on cellular response. These have contributed greatly to our current knowledge of the molecular events by which mechanical cues affect cell biology. Cell responses to the mechanical properties of type 1 collagen gels are discussed, followed by a description of a model system of very thin, mechanically tunable collagen films that evoke similar responses from cells as do gel systems, but have additional advantages. Cell responses to thin films of collagen suggest that at least some of the mechanical cues that cells can respond to in their environment occur at the sub-micron scale. Mechanical properties of thin films of collagen can be tuned without altering integrin engagement, and in some cases without altering topology, making them useful in addressing questions regarding the roles of specific integrins in transducing or mitigating responses to mechanical cues. The temporal response of cells to differences in ECM may provide insight into mechanisms of signal transduction.
Animals; Cell Line; Collagen Type I; Collagen Type I: metabolism; Extracellular Matrix; Extracellular Matrix: chemistry; Extracellular Matrix: metabolism; Microscopy, Atomic Force; Models, Biological; Signal Transduction; Signal Transduction: physiology; Stress, Mechanical
Cyclic behavior of unidirectional and cross-ply titanium matrix composites
International journal of plasticity
12
3
361-385
1996
10.1016/S0749-6419(96)00012-5
Relatively simple and efficient micromechanical models are used to obtain the uniaxial response of SCS-6/Timetal 21S with [0]4 and [0/90]s laminates when subjected to isothermal and thermomechanical fatigue (TMF) loadings. Features of the modeling that are required to obtain the accurate deformation behavior for this class of materials under these loadings are highlighted. To this end, a comparison is made between the concentric cylinder model and the uniaxial stress model for representing the [0] laminate. The axial stresses from the two models are very similar under mechanical loading. The greatest differences appear under thermal loading alone. The differences on the composite response between a time-independent elastic-plastic and a viscoplastic matrix constitutive model are also examined. The latter is based on the Bodner-Partom unified constitutive model. The [0/90] laminate is treated by adding a parallel element with smeared [90] ply properties to the [0] model and invoking axial strain compatibility as well as stress equilibrium. The proposed constitutive law for the [90] ply includes both matrix viscoplasticity and fiber/matrix separation damage and is based on damage mechanics concepts. The effect of cyclic frequency on TMF behavior is examined. The in-phase TMF life is shown to be very sensitive to frequency due to the relaxation of matrix stress and the attendant increase in fiber stress.
Fatigue of materials; Fatigue testing; Laminated composites; Mathematical models; Metallic matrix composites; Stress analysis; Stress relaxation; Thermal load; Thermomechanical treatment; Titanium alloys; Viscoplasticity
Mechanics of rollable and foldable film-on-foil electronics
Applied Physics Letters
74
8
1177
1999
10.1063/1.123478
The mechanics of film-on-foil devices is presented in the context of thin-film transistors on steel and plastic foils. Provided the substrates are thin, such transistors function well after the foils are rolled to small radii of curvature. When a substrate with a lower elastic modulus is used, smaller radii of curvature can be achieved. Furthermore, when the transistors are placed in the neutral surface by sandwiching between a substrate and an encapsulation layer, even smaller radii of curvature can be attained. Transistor failure clearly shows when externally forced and thermally induced strains add to, or subtract from, each other. (C) 1999 American Institute of Physics. [S0003-6951(99)03608-6].
Herringbone Buckling Patterns of Compressed Thin Films on Compliant Substrates
Journal of Applied Mechanics
71
5
597
2004
10.1115/1.1756141
A thin metal film vapor deposited on thick elastomer substrate develops an equi-biaxial compressive stress state when the system is cooled due to the large thermal expansion mismatch between the elastomer and the metal. At a critical stress, the film undergoes buckling into a family of modes with short wavelengths characteristic of a thin plate on a compliant elastic foundation. As the system is further cooled, a highly ordered herringbone pattern has been observed to develop. Here it is shown that the herringbone mode constitutes a minimum energy configuration among a limited set of competing modes
Variations of Fatigue Damage Growth in Cross-Ply and Quasi-Isotropic laminates Under High-Cycle Fatigue Loading
Journal of Solid Mechanics and Materials Engineering
3
2
138-149
2009
10.1299/jmmp.3.138
The behavior of transverse crack growth and delamination growth under high-cycle fatigue loadings was investigated with cross-ply CFRP laminates, [0/902]s and [0/906]s, and quasi-isotropic CFRP laminates, [45/0/-45/90]s. As a result, it was observed that the behavior of damage growth was different depending on the applied stress level. The growth of local or edge delamination was exacerbated under the test conditions of a low applied stress level and high-cycle loadings, because the areas of stress concentration were applied with high-cyclic loadings. On the other hand, when the fatigue tests were conducted under the applied stress level of 40% of the transverse crack initiation, the growth of transverse cracks was hardly observed until 108 cycles with [0/902]s, [0/906]s and [45/0/-45/90]s laminates.
Composites; Delamination; High-Cycle Fatigue; Transverse Cracks
Mechanics of shaft-loaded blister test for thin film suspended on compliant substrate
International Journal of Solids and Structures
47
18-19
2525-2532
2010
10.1016/j.ijsolstr.2010.05.011
Based on the von Kármán plate theory, the mechanics of a shaft-loaded blister test for thin film/substrate systems is studied by considering elastic substrate deformations and residual stresses in these films. In testing, films are attached to a substrate provided with a circular hole, through which loading is applied to the film by a flat-ended shaft of circular cross-section. The effect of substrate deformation on the deflection of the loaded film is taken into account by using a line spring model. For small deflections, an analytical solution is derived, while for large deflections a numerical solution is obtained using the shooting method. The resulting load-shaft displacement relation, which is essential in blister tests, compares favorably with finite element analysis.
Analytical solution; Compliant substrate; Deflection; Numerical solution; Residual stress; Shaft-loaded blister test; Thin film
Bohmian Mechanics
Bohmian Mechanics
10
2009
10.1007/b99978
Bohmian mechanics is a theory about point particles moving along trajectories. It has the property that in a world governed by Bohmian mechanics, observers see the same statistics for experimental results as predicted by quantum mechanics. Bohmian mechanics thus provides an explanation of quantum mechanics. Moreover, the Bohmian trajectories are defined in a non-conspiratorial way by a few simple laws.
The onset of mixed-mode intralaminar cracking in a cross-ply composite laminate
Mechanics of Composite Materials
44
6
549-556
2008
10.1007/s11029-009-9055-z
The intralaminar fracture toughness of a unidirectionally reinforced glass/epoxy composite is determined experimentally at several mode I and mode II loading ratios. The crack propagation criterion, expressed as a quadratic form in terms of single-mode stress intensity factors (alternatively, linear in terms of energy release rates), approximates the test results reasonably well. The mixed-mode cracking criterion obtained is used to predict the intralaminar crack on set in a cross-ply glass/epoxy composite under off-axis tensile loading. [ABSTRACT FROM AUTHOR] Copyright of Mechanics of Composite Materials is the property of Springer Science & Business Media B.V. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
DEAD loads (Mechanics); EPOXY coatings; fracture toughness; GLACIAL crevasses; GLASS; intralaminar cracking; laminates; mixed-mode loading; polymer-matrix composites; STRAINS & stresses (Mechanics)
An extended finite element method for dislocations in complex geometries: Thin films and nanotubes
Computer Methods in Applied Mechanics and Engineering
198
21-26
1872-1886
2009
10.1016/j.cma.2008.12.025
Dislocation models based on the extended finite element method (XFEM) are developed for thin shells such as carbon nanotubes (CNTs) and thin films. In shells, methods for edge dislocations, which move by glide, and prismatic dislocations, which move by climb, are described. In thin films, methods for dislocations with edge, screw and/or prismatic character are developed in three dimensions. Singular enrichments are proposed which allow the Peach-Koehler force to be computed directly from the stress field along the dislocation line and give improved accuracy. ?? 2009 Elsevier B.V. All rights reserved.
Carbon nanotubes; Dislocations; Extended finite element method; Thin films; Thin shells
A first-ply failure analysis of composite laminates
Computers & Structures
25
371-393
1987
10.1016/0045-7949(87)90130-1
A finite-element computational procedure is developed for the first-ply failure analysis of laminated composite plates. The procedure is based on the first-order shear deformation theory and a tensor polynomial failure criterion that contains the maximum stress, maximum strain, the Hill, Tsai-Wu and Hoffman failure criteria as special cases. By specifying the desired criterion, a first-ply failure analysis of composite laminates subjected to in-plane and/or bending loads can be achieved. A number of problems are presented to evaluate these failure criteria when applied to laminates subjected to in-plane and or bending loads.
Contact mechanics of rough surfaces in tribology: multiple asperity contact
Tribology Letters
4
1-35
1998
10.1023/A:1019186601445
Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic–plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic–plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed.
asperity contact; contact area; contact mechanics; rough surfaces; surface deformation; tribology
Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading
Composite Structures
76
4
314-325
2006
10.1016/j.compstruct.2005.04.021
The interlaminar stresses and displacements near the free-edges and ply cracks are investigated by using the state space equation method for general cross-ply laminates subjected to extension and/or thermal loading. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. Numerical solutions are compared with results obtained from other methods. It is found that the theory provides a satisfactory approximation to the stress singularity occurring in the vicinity of the free-edges and ply cracks. ?? 2005 Elsevier Ltd. All rights reserved.
Free-edge; Interlaminar stress; Laminate; Ply cracking; State space; Thermal loading
Fabrication and Mechanics of Fiber-Reinforced Elastomers
Chemistry & biodiversity
1
11
1829–1841
1998
10.16953/deusbed.74839
Heightened interest in flexible composite applications such as bio-mechanical devices, flexible underwater vehicles, and compliant aircraft structures has revealed a need for improved fabrication techniques, more experimental data, and accurate analytical models for fiber-reinforced elastomeric (FRE) materials. An improved method was developed to fabricate small batches of good quality fiberreinforced elastomer prepreg. Strengths of the method include excellent fiber adhesion, medium to high fiber volume fractions, highly parallel fibers, use of traditional advanced composites fabrication methodologies, and reproducible ply thicknesses. Silicone/cotton, silicone/fiberglass, urethane/cotton, and urethane/fiberglass elastomer/fiber combinations were studied. Balanced angle-ply laminates of each fiber-reinforced elastomer system were laminated from the prepreg with off-axis angles ranging from 0° to 90° in 15° incre-ments. The specimens had fiber volume fractions of 12% to 62%, using fiberglass and cotton fibers, respectively. Tensile stress-strain results of elastomers, dry and elastomer-impregnated cotton fiber, and the fiber-reinforced elastomer specimens are presented and discussed. The axial stiffness of individual cotton fibers increased 74% to 128% when impregnated with an elastomer. The stiffening trend of the silicone rubber and softening trend of the urethane rubber are reflected in the stress-strain response of their respective fiber-reinforced elastomer specimens. Nonlinear shear and transverse properties for each material combination were extracted from 45° and 90° stress-strain data. Nonlinearity of the stress-strain curves are functions of fiber angle, elastomer type and the amount of deformation. An accurate nonlinear FRE model is presented. It is based on classical lamination theory and has been modified to include geometric and material nonlinearity. Geometric nonlinearity is included in the form of nonlinear strain-displacement relations. Material nonlinearity is included in the form of nonlinear orthotropic material properties as a function of extensional strain. The nonlinear strain-displacement relations and the nonlinear material models were added to the FORTRAN code of a pre-existing composites analysis software package. Results from the nonlinear FRE model are compared with test results of balanced angle-ply specimens. Correlation between predicted and experimental results range from good to excellent. A “rubber muscle” which exhibits high contractive forces was also fabricated and modeled as part of the work.
Measurement of the in situ transverse tensile strength of composite plies by means of the real time monitoring of microcracking
Composites Part B: Engineering
65
40-46
2014
10.1016/j.compositesb.2014.02.001
Failure of a ply due to transverse loading is one of the mechanisms that was taken into account in physically-based failure criteria, used in composites design. However, experimental data are scarce and the measurement techniques used in the past are time consuming and involve a lot of specimen handling during testing. While some physical information is currently well consolidated (such as the dependence of the strength on ply thickness, or in situ strength), there still remain relevant open questions. This work presents a methodology, which does not interfere with the tensile test, to detect transverse cracks by optical means. Four different configurations of CFRP are considered. The results show that the in situ strength depends on the thickness of the ply and the orientation of the adjacent layers. In the case of thick transverse plies, the strength is controlled by full-width transverse cracks whereas, in thin plies cracking parallel to the specimen’s mid-plane occurs before transverse matrix cracking.
B. Strength; B. Transverse cracking; C. Damage mechanics; D. Optical microscopy
Thermal buckling of uniformly heated unidirectional and symmetric cross-ply laminated fiber-reinforced composite uniaxial in-plane restrained simply supported rectangular plates
Composites Part A: Applied Science and Manufacturing
36
1355-1367
2005
10.1016/j.compositesa.2005.01.028
Geometrically perfect plates that are restrained from in-plane expansion when slowly and uniformly heated generally develop compressive stresses and then buckle at a specific temperature. The equivalent mechanical loading concept is used to straightforwardly develop solutions to several fundamental thermal buckling problems involving simple laminated plate configurations and the most simple heating environment, namely uniform heating throughout the plate volume. The analysis is restricted to linear elastic stress-strain behavior and constant orthotropic lamina material properties at a specific temperature. Results are obtained for unidirectional and symmetric cross-ply laminated fiber-reinforced composite rectangular plates that are uniaxially restrained in their plane on two of the four edges, but have no edge rotational restraint on any edge. Those boundary conditions constitute two of the four possible types of simply supported edges that differ only in their in-plane conditions. The results are presented in the form of buckling temperature change from the stress-free temperature (at which no stress is generated against the restraint) versus plate aspect ratio curves festooned for different buckling mode shapes for all laminates. Anomalous examples include unidirectionally laminated plates that actually buckle upon cooling instead of heating and cross-ply laminated plates that do not buckle irrespective of whether they are heated or cooled. Those examples are of interest because of their intriguing possible design applications. ?? 2005 Elsevier Ltd. All rights reserved.
A. Plates; B. Buckling; B. Thermal properties; C. Laminate mechanics
Part scaling and mechanics of thin part self-assembly in the fludic phase
MEMS 2011
364-367
2011
10.1109/MEMSYS.2011.5734437
This paper presents an experimental and theoretical study of previously demonstrated high yield self-assembly processes using surface programmable template and specific surface Faraday waves. Here we focus on the combined effect of substrate tilting angle and part size. For 1×1, 3×3 and 5×5 mm2 parts of 100 µm thickness, the maximum substrate tilting angles for effective assembly are experimentally determined and the surface tension induced torques are calculated based on a newly developed model.
Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear
Composites Part A: Applied Science and Manufacturing
37
2
165-176
2006
10.1016/j.compositesa.2005.04.023
A criterion for matrix failure of laminated composite plies in transverse tension and in-plane shear is developed by examining the mechanics of transverse matrix crack growth. Matrix cracks are assumed to initiate from manufacturing defects and can propagate within planes parallel to the fiber direction and normal to the ply mid-plane. Fracture mechanics models of cracks in unidirectional laminates, embedded plies and outer plies are used to determine the onset and direction of propagation of crack growth. The models for each ply configuration relate ply thickness and ply toughness to the corresponding in situ ply strength. Calculated results for several materials are shown to correlate well with experimental results. © 2005 Elsevier Ltd. All rights reserved.
Failure criterion; Fracture; In situ strengths
Intralaminar fracture toughness of a cross-ply laminate and its constituent sub-laminates
Composites Science and Technology
61
8
1115-1122
2001
10.1016/S0266-3538(01)00011-2
The intralaminar mode I fracture toughness values for a M55J/M18 carbon/epoxy cross-ply laminate [0°/90°]15 (alternate 0 and 90° layers) and its constituent sub-laminates, namely the [0°]30 and [90°]30 laminates are theoretically evaluated on the basis of a modified crack-closure integral (MCCI) method corresponding to the fracture loads obtained by testing C(T) specimens. A simple relationship between the intralaminar fracture toughness at the specimen level of a cross ply and its constituent sub-laminates is presented. Test data for fracture loads and crack-opening displacements at the opposite end (far end) to the crack tip of the three types of C(T) specimens are obtained. A comparison of fracture toughness values KIc and crack-opening displacements obtained from tests with theoretical predictions by finite-element analysis shows good agreement for the type of laminates considered. Comparison of the analytically determined KIc of the cross-ply C(T) specimen based on the new relationship using the respective values of KIc of its constituent C(T) specimens shows good agreement with test data.
compact tension specimen; cross-ply laminate; intralaminar fracture toughness; strain energy release rate; translaminar
Utilising fracture mechanics principles for predicting the mixed-mode delamination onset and growth in tapered composite laminates
Composite Structures
102
294-305
2013
10.1016/j.compstruct.2013.03.008
The quasi-static and fatigue performance of carbon and E-glass fibre reinforced tapered laminates was experimentally investigated. Utilising local strain measurements and digital photographs the load levels for delamination initiation were identified. In addition, the fatigue cycles for onset of delamination and growth to a predefined length, which defined the final failure criterion, were accurately evaluated. The data generated served as validation of a predictive methodology for onset of delamination and subsequent growth. The predictive methodology, which was based on a fracture mechanics approach, utilised the mixed mode fatigue delamination behaviour of the materials and finite element analysis of the laminates for evaluation of the strain energy release rate. Satisfactory prediction of the fatigue performance was obtained and the effect of fibre bridging, occurred during the test, on the fatigue life was demonstrated. ?? 2013 Elsevier Ltd.
Delamination; Fatigue; LEFM; Mixed mode; Ply drop-offs
Nonlinear analysis of smart cross-ply composite plates integrated with a distributed piezoelectric fiber reinforced composite actuator
Mechanics of Advanced Materials and Structures
15
1
40-52
2008
10.1080/15376490701426337
This paper is concerned with the static analysis of simply sup- ported cross-ply substrate plates integrated with a layer of piezo- electric fiber reinforced composite material undergoing nonlinear deformations. The vonK´ arm´ an type nonlinear strain displacement relations and first order shear deformation theory are used to for- mulate the variational model of this electromechanical coupled problem. Subsequently, Galerkin procedure is employed to derive the nonlinear algebraic governing equations which are solved by using Newton-Raphson method. The results suggest the potential use of PFRC material for distributed control of nonlinear defor- mations of smart composite structures. The effect of variation of piezoelectric fiber orientation on the actuating capability of the PFRC actuator for counteracting the nonlinear deformations of the smart composite plates has also been investigated.
composite plates; geometrically nonlinear; piezoelectric composite; smart structures
A buckling-based metrology for measuring the elastic moduli of polymeric thin films.
Nature materials
3
8
545-550
2004
10.1038/nmat1175
As technology continues towards smaller, thinner and lighter devices, more stringent demands are placed on thin polymer films as diffusion barriers, dielectric coatings, electronic packaging and so on. Therefore, there is a growing need for testing platforms to rapidly determine the mechanical properties of thin polymer films and coatings. We introduce here an elegant, efficient measurement method that yields the elastic moduli of nanoscale polymer films in a rapid and quantitative manner without the need for expensive equipment or material-specific modelling. The technique exploits a buckling instability that occurs in bilayers consisting of a stiff, thin film coated onto a relatively soft, thick substrate. Using the spacing of these highly periodic wrinkles, we calculate the film's elastic modulus by applying well-established buckling mechanics. We successfully apply this new measurement platform to several systems displaying a wide range of thicknessess (nanometre to micrometre) and moduli (MPa to GPa).
Mechanics of thin ultra-light stainless steel sandwich sheet material: Part I. Stiffness
Acta Materialia
51
5
1341-1350
2003
10.1016/S1359-6454(02)00528-1
Three variants of a novel steel sandwich sheet material have been studied. The geometrical arrangements of the steel fibres in the core have been characterised. Certain mechanical properties of the fibres have also been investigated. The beam stiffnesses of the sheets, and also their through-thickness Young's moduli, have been measured. These results have been compared with model predictions. It is shown that the beam stiffnesses are in all cases significantly lower than expected from simple bending theory. This is attributed to the low through-thickness stiffness of the core and also to a low resistance to shear. Modelling of these properties has facilitated the identification of changes to the core structure, which should lead to improved beam stiffness, while retaining a low density. Increased fibre diameter, and possibly an alteration to the fibre sectional shape, are the most promising changes. Of course, implications for other properties, and for ease of manufacture, will also need to be borne in mind. ?? 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Beam stiffness; Composite materials; Elastic constants; Lightweight materials; Sandwich panels; Single fibre testing; Stainless steel; Steel fibres
Hamiltonian mechanics
Notes
1-10
2010
10.1017/CBO9780511614118.004
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics which predicts the same outcomes as classical mechanics. It uses a different mathematical formalism, providing a more abstract understanding of the theory. Historically, it was an important reformulation of classical mechanics, which later contributed to the formulation of the quantum mechanics.
Elastic and plastic properties of thin films on substrates: nanoindentation techniques
Materials Science and Engineering: A
234-236
1997
37-44
1997
10.1016/S0921-5093(97)00176-7
Recent progress in understanding the mechanical properties of thin films on substrates is briefly reviewed. We describe nanoindentation techniques that have been developed for measuring the elastic and plastic properties of thin films with thickness on the order of micrometers. We also report on efforts to understand the strength properties of thin metal films in terms of the motion and interaction of dislocations within them. The well-known size dependence of the hardness of soft, strain-hardenable metals is described in terms of the geometrically necessary dislocations created in small indentations. The very high strengths typically observed for thin films are interpreted in terms of the mechanics of dislocation motion and interaction in thin metal layers.
1997; 37744; a234-236; elastic and plastic properties; erials science and engineering; of thin films on; substrates
Discontinuous Petrov-Galerkin method with optimal test functions for thin-body problems in solid mechanics
Computer Methods in Applied Mechanics and Engineering
200
9-12
1291-1300
2011
10.1016/j.cma.2010.10.018
We study the applicability of the discontinuous Petrov–Galerkin (DPG) variational framework for thin-body problems in structural mechanics. Our numerical approach is based on discontinuous piecewise polynomial finite element spaces for the trial functions and approximate, local computation of the corresponding ‘optimal’ test functions. In the Timoshenko beam problem, the proposed method is shown to provide the best approximation in an energy-type norm which is equivalent to the L2-norm for all the unknowns, uniformly with respect to the thickness parameter. The same formulation remains valid also for the asymptotic Euler–Bernoulli solution. As another one-dimensional model problem we consider the modelling of the so called basic edge effect in shell deformations. In particular, we derive a special norm for the test space which leads to a robust method in terms of the shell thickness. Finally, we demonstrate how a posteriori error estimator arising directly from the discontinuous variational framework can be utilized to generate an optimal hp-mesh for resolving the boundary layer.
discontinuous petrov-galerkin; hp-adaptivity; thin structures
Contact mechanics and work roll wear in cold rolling of thin strip
Wear
263
7-12 SPEC. ISS.
1447-1453
2007
10.1016/j.wear.2006.12.068
Simulation of cold rolling of thin strip with work roll edge contact was performed using a developed modified influence function method. Surface roughness of the rolled strip on a cold rolling mill was characterized by a surface profilometer. Roll edge contact and related surface roughness transfer are discussed. The focus of this work on cold rolling of thin strip was to justify the roll bite contact mechanics and to analyse the friction in the roll bite and the effect of the friction on the strip profile and the surface finish. The work roll wear and its value are also discussed. The work roll edge contact affects the work roll edge wear significantly. The strip surface finish becomes better after rolling, and the calculated rolling forces are in good agreement with the measured values. ?? 2007 Elsevier B.V. All rights reserved.
Contact mechanics; Friction; Influence function method; Roll wear; Surface roughness
Mechanical response of multicrystalline thin films in mesoscale field dislocation mechanics
Journal of the Mechanics and Physics of Solids
59
11
2400-2417
2011
10.1016/j.jmps.2011.06.009
A continuum model of plasticity, Phenomenological Mesoscopic Field Dislocation Mechanics (PMFDM), is used to study the effect of surface passivation, grain orientation, grain boundary constraints, and film thickness on the mechanical response of multicrystalline thin films. The numerical experiments presented in this paper show that a surface passivation layer on thin films introduces thickness dependence of the mechanical response. However, the effect of passivation decreases in films with impenetrable grain boundaries. The orientation of individual grains of the multicrystal also has a significant effect on the mechanical response. Our results are in qualitative agreement with experimental observations. A primary contribution of this work is the implementation of a jump condition that enables the modeling of important limits of grain boundary constraints to plastic flow, independent of ad-hoc constitutive assumptions and interface conditions.
Bending of cross-ply laminated plates resting on elastic foundations under thermo-mechanical loading
International Journal of Mechanics and Materials in Design
9
3
239-251
2013
10.1007/s10999-012-9212-8
This article investigates the bending response of an orthotropic rectangular plate resting on two-parameter elastic foundations under thermo-mechanical loadings. Analytical solutions for deflection and stresses are investigated by using an unified shear deformation plate theory. The present plate theory enables the trial and testing of different through-the-thickness transverse shear-deformation distributions and, among them, strain distributions that do not involve the undesirable implications of the transverse shear correction factors. The governing equations that include the interaction between the plate and the foundations are obtained. Numerical results are presented to demonstrate the behavior of the system. The influences of aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the thermally induced response are studied.
Orthotropic plates; Pasternak's foundations; Thermo-mechanical loading; Winkler's foundation
Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading
Composite Structures
77
2
249-262
2007
10.1016/j.compstruct.2005.07.002
A two-dimensional global higher-order deformation theory is presented for the free vibration and stability problems of angle-ply laminated composite and sandwich plates subjected to thermal loading. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through Hamilton's principle. Several sets of truncated Mth order approximate theories are applied to solve the eigenvalue problems of a simply supported angle-ply multilayered plate. Natural frequencies and critical temperatures of angle-ply laminated composite and sandwich plates subjected to thermal loading are obtained. Critical temperatures are obtained by increasing the temperature until the natural frequency vanishes. The effects of prebuckling displacements on the natural frequencies and critical temperatures are taken into account. Modal displacement distributions through the transverse direction of the laminates are plotted for the specific temperature parameter. Numerical results are compared with those of the published existing theories. The present global higher-order approximate theories can predict the natural frequencies and critical temperatures of angle-ply laminated composite and sandwich plates subjected to thermal loading accurately within small number of unknowns. ?? 2005 Elsevier Ltd. All rights reserved.
Angle-ply laminated composite and sandwich plates; Free vibration; Global higher-order deformation theory; Thermal buckling; Thermal loading
Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions
International Journal of Mechanical Sciences
44
8
1731-1754
2002
10.1016/S0020-7403(02)00056-5
A postbuckling analysis is presented for a cross-ply laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component Ez only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with a von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators subjected to combined mechanical loading of external pressure and axial compression, and under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.
Boundary layer theory of shell buckling; Hybrid laminated cylindrical shell; Postbuckling; Singular perturbation technique; Thermo-piezoelectric effect
Coupled higher-order layerwise mechanics and finite element for cylindrical composite and sandwich shells with piezoelectric transducers
European Journal of Mechanics - A/Solids
2015
10.1016/j.euromechsol.2015.06.003
Coupled higher-order layerwise piezoelectric laminate mechanics are presented, applicable to shallow cylindrical composite and sandwich shells subjected to static mechanical loads and/or electric voltages. The current formulation enables efficient prediction of (i) global electromechanical response, (ii) local through-thickness distribution of electromechanical variables and (iii) interlaminar shear stress at the interface between adjacent material layers. Using the developed mechanics, the effects of curvature, thickness and ply angle on the global and local through-thickness response of sandwich composite shells are studied.
piezoelectric; sandwich; shells
Cardiac myofilaments: Mechanics and regulation
Journal of Biomechanics
36
5
721-730
2003
10.1016/S0021-9290(02)00450-5
The mechanical properties of the cardiac myofilament are an important determinant of pump function of the heart. This report is focused on the regulation of myofilament function in cardiac muscle. Calcium ions form the trigger that induces activation of the thin filament which, in turn, allows for cross-bridge formation, ATP hydrolysis, and force development. The structure and protein-protein interactions of the cardiac sarcomere that are responsible for these processes will be reviewed. The molecular mechanism that underlies myofilament activation is incompletely understood. Recent experimental approaches have been employed to unravel the mechanism and regulation of myofilament mechanics and energetics by activator calcium and sarcomere length, as well as contractile protein phosphorylation mediated by protein kinase A. Central to these studies is the question whether such factors impact on muscle function simply by altering thin filament activation state, or whether modulation of cross-bridge cycling also plays a part in the responses of muscle to these stimuli. ?? 2003 Elsevier Science Ltd. All rights reserved.
Calcium; Length-dependent activation; Molecular motor; Myofilament; Sarcomere dynamics
Stress and grain growth in thin films
Journal of the Mechanics and Physics of Solids
44
5
657-673
1996
10.1016/0022-5096(96)00022-1
The mechanical properties of polycrystalline thin films with thickness of 1 μm or less depend strongly on the grain geometry, the grain size, and the way in which the crystallographic orientations of the grains are distributed. Grain growth during film formation or during post-deposition annealing can play a dominant role in defining these microstructural characteristics, and therefore, the mechanical properties of films. Stress can suppress or promote grain growth. In the latter case, stress promotes texture evolution during grain growth. Grain growth can serve as a stress relief mechanism in both elastically isotropic and anisotropic materials, and can also promote plastic yielding.
Mechanics of sintering thin films - I. Formulation and analytical results
Mech. Mater.
9
107-119
1990
10.1016/0167-6636(90)90034-D
An analysts of the mechamcs of smtenng thin films i8 presented A two-dimensional\nformulaUon ts obtained by averaging the govermng equattons through\nthe film thtckness The effect of the interracial shear tracuon ~s\nrepresented by a body force winch is related to the m-plane veloctty\nthrough an interface model AnalyUcal results vahd for short times\nhave been obtained for an tmtaally homogeneous annular film on a\nngtd substrate A theoretacal jusuficatlon of the Interface model,\ntogether with a numerical sunulatmn of interface deformatmn based\non the underlying rmcromechamcs is gwen m the Appendax for smtermg\nfilms The analysis xs based on linear vascous material behavior but\ncan be apphed to elastic films with appropriate modlflcaUons
Theoretical Mechanics
Science
14
571-573
1901
10.1126/science.14.354.571-b
Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.
Statistical methodology for assessing manufacturing quality related to transverse cracking in cross ply laminates
Composites Science and Technology
95
100-106
2014
10.1016/j.compscitech.2014.02.010
We present a statistical analysis based methodology for making assessment of the manufacturing quality of cross ply composite laminates as it relates to its effect on transverse cracking evolution. Assuming a two-parameter Weibull distribution of tensile strength of the transverse plies to represent randomly distributed manufacturing defects, multiple crack formation in the plies is simulated in the non-interactive and interactive regimes of cracking using the local stress fields calculated by a variational analysis. The statistical methodology is demonstrated on crack density evolution in cross ply laminates manufactured by four different processing routes and loaded in monotonic tension in the axial direction. The differences in the crack density evolution, supposedly due to different defect population induced by the four manufacturing conditions, could be described by the proposed statistical simulation method.
A. Polymer-matrix composites (PMCs); B. Defects; C. Damage mechanics; C. Probabilistic methods
Mechanics of composite structures
Transformation
1
480
2003
10.1016/0263-8223(94)90053-1
A greater use of composite materials in many areas of engineering has led to a greater demand for engineers versed in the design of structures made from such materials. This text offers students and engineers tools for designing practical composite structures. Among the topics of interest to the designer are stress-strain relationships for a wide range of anisotropic materials; bending, buckling, and vibration of plates; bending, torsion, buckling, and vibration of solid as well as thin-walled beams; shells; hygrothermal stresses and strains; finite element formulation; and failure criteria. More than 300 illustrations, 50 fully worked problems, and material properties data sets are included.
Fluid Mechanics
Book
17
3
864
2009
10.1111/j.1549-8719.2009.00016.x.Mechanobiology
Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situationswhether in the liquid or gaseous state or bothis introduced and comprehensively covered in this widely adopted text. Fully revised and updated with the addition of a new chapter on biofluid mechanics, Fluid Mechanics, Fourth Edition is suitable for both a first or second course in fluid mechanics at the graduate or advanced undergraduate level. The leading advanced general text on fluid mechanics, Fluid Mechanics, 4e guides students from the fundamentals to the analysis and application of fluid mechanics, including compressible flow and such diverse applications as hydraulics and aerodynamics. Updates to several chapters and sections, including Boundary Layers, Turbulence, Geophysical Fluid Dynamics, Thermodynamics and Compressibility. Fully revised and updated chapter on Computational Fluid Dynamics. New chapter on Biofluid Mechanics by Professor Portonovo Ayyaswamy, the Asa Whitney Professor of Dynamical Engineering at the University of Pennsylvania. New Visual Resources appendix provides a list of fluid mechanics films available for viewing online. Additional worked-out examples and end-of-chapter problems. Updated online Solutions Manual for adopting instructors.
cfd; computational fluid dynamics; hutchinson gilford progeria syndrome; nuclear mechanics
An energy based damage mechanics approach to modelling impact onto woven composite materials—Part I: Numerical models
Composites Part A: Applied Science and Manufacturing
37
11
2041-2056
2006
10.1016/j.compositesa.2005.12.013
The increased use of composite materials in a wide spectrum of industries has led to the development of improved predictive techniques, which can aid in the detailed understanding of the behaviour of a composite component or structure to a range of potentially damaging threats. This paper presents an energy based damage mechanics model for woven carbon composites under high strain loading. This damage mechanics approach introduces five damage variables for in plane damage per ply layer. The damage variables are associated with warp and weft fibre damage in both tensile and compressive failure modes, with an additional damage variable to determine the deterioration of the fibre–matrix interface. The damage variables are directly related to the stiffness degradation within the composite laminae and ultimately within the laminate. The evolution of damage in each mode is controlled via a series of damage-strain equations, thus allowing the total energy dissipated for each damage mode to be set as a material parameter, which is mesh size independent. The damage mechanics approach has been implemented into both the LLNL and LS versions of DYNA3D for plane stress (shell) elements. This encompasses both the standard shell element and the solid-shell formulations available within these codes. In the present paper, validation examples are presented for this damage model. The tensile and the tensile-shear responses are modelled at a coupon level, including relevant strain rate effects and tabs, with the proposed damage model. The results show very good agreement with the available experimental data. Suggestions are also presented for additional non-standard experimental tests to derive all material model parameters directly, rather than an inverse modelling approach in which uniqueness may not be guarantee. This paper also presents an interface modelling technique for explicit FE codes. The formulation is again based on damage mechanics and uses only two constants for each delamination mode; firstly, a stress threshold for damage to commence, and secondly, a critical energy release rate for the particular delamination mode. The model has also been implemented into the LLNL DYNA3D Finite Element (FE) code and the LS-DYNA3D commercial FE code. The interface element modelling technique is applied to a series of common fracture toughness based delamination problems, typically the Double Cantilever Beam (DCB) test, and validated for the dynamic case via a simple analytical plate impact simulation. A subsequent part II paper describes the results of simulations using the proposed damage mechanics based models on a series of experimental CRAG plate impact tests.
b; c; composite materials; damage mechanics; fea; finite element analysis; impact behaviour
Variable-stiffness composite panels: Buckling and first-ply failure improvements over straight-fibre laminates
Computers and Structures
86
9
897-907
2008
10.1016/j.compstruc.2007.04.016
One of the primary advantages of using fibre-reinforced laminated composites in structural design is the ability to change the stiffness and strength properties of the laminate by designing the laminate stacking sequence in order to improve its performance. This procedure is typically referred to as laminate tailoring. Traditionally, tailoring is done by keeping the fibre orientation angle within each layer constant throughout a structural component. Allowing the fibres to follow curvilinear paths within the plane of the laminates constitutes an advanced tailoring option that can lead to modification of load paths within the laminate to result in more favourable stress distributions and improve the laminate performance. Based on numerical simulations, the present work demonstrates the advantages of variable-stiffness over straight-fibre laminates in terms of compressive buckling and first-ply failure. A physically based set of failure criteria, able to predict the various modes of failure of a composite laminated structure, is implemented in finite element models of straight and variable-stiffness panels under compression. Non-linear analyses are carried out to simulate first-ply failure in the postbuckling regime. © 2007 Elsevier Ltd. All rights reserved.
Curvilinear-fibre laminates; Damage onset; Failure criteria; Stiffness tailoring; Strength; Tow-placed composites
Spherical indentation of freestanding circular thin films in the membrane regime
Journal of the Mechanics and Physics of Solids
52
9
2005-2023
2004
10.1016/j.jmps.2004.03.002
We present theoretical and experimental results to describe the mechanics of indentation of a clamped circular membrane with a frictionless spherical indenter. Analytical expressions and numerical simulations are presented for the relationships between contact radius, finite indentation strains (and stresses), pre-stretch, loads and deflection. These closed-form solutions are contrasted with point-load models that neglect the contact size (i.e. classical Schwerin-type solutions), and lead to important differences in the indentation strain and load-deflection response. The accuracy of these closed form expressions is illustrated by comparisons with detailed numerical results and experiments on thin elastomer films. We show that the closed-form solutions can be used to extract mechanical properties from indentation testing of freestanding films, with important implications for developing new tests on nanoscale films and/or compliant materials such as polymers and biological substances. (C) 2004 Published by Elsevier Ltd.
Micromechanics modelling of anisotropic damage in cross-ply laminates
International journal of solids and structures
29
10
1303-1328
1992
10.1016/0020-7683(92)90240-T
A micromechanics model is developed to detail various aspects of anisotropic damage behaviour of cross-ply composite laminates. Attention is focused on multi-ply laminates so that a calculation model can be devised, which is composed of a...
A generalized damage model for woven ply laminates under static and fatigue loading conditions
International Journal of Fatigue
32
1
158-165
2010
10.1016/j.ijfatigue.2009.02.016
A generalized non-linear cumulative damage model for woven ply laminates subjected to static and fatigue loading is developed in this paper. The damage, consisting of small cracks running parallel to the fibers, leads to a loss of stiffness in the warp, weft and shear directions. The model presented here describes the evolution of the damage up to failure of the first ply. By replacing the woven ply by two stacked unidirectional plies corresponding to the warp and weft thicknesses, this general model is extended to cover a broad range of plies, from quasi-unidirectional to balanced woven plies. A continuum damage approach (CDM) is then used to define the behaviour of the two virtual unidirectional plies under static and fatigue loading conditions. The model is applied here to an unbalanced woven ply with glass reinforcement and the results of the simulations are compared with experimental data. ?? 2009 Elsevier Ltd. All rights reserved.
Damage; Failure analysis; Laminate; Static fatigue; Textile composite
Structural and failure mechanics of sandwich composites
Solid Mechanics and its Applications
121
1-399
2011
10.1007/978-1-4020-3225-7_1
A structural sandwich typically consists of two thin “face sheets” made from stiff and strong relatively dense material such as metal or fiber composite bonded to a thick lightweight material called “core”. This concept mimics an I-beam, but in two dimensions, where the face sheets support bending loads and the core transfers shear force between the faces in a sandwich panel under load. Figure 1.1 illustrates flat and curved elements from a sandwich structure.
Spontaneous symmetry breaking in quantum mechanics
American Journal of Physics
75
7
635
2007
10.1119/1.2730839
We present a mathematically simple procedure to explain spontaneous symmetry breaking in quantum systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a symmetry broken state in crystals, antiferromagnets, and even superconductors. It has the advantage that it automatically brings to the fore the main players in spontaneous symmetry breaking: the symmetry-breaking field, the thermodynamic limit, and the global excitations of a “thin” spectrum.
Experimental characterization of the impact-damage tolerance of a cross-ply graphite-fiber/epoxy laminate
Polymer Composites
29
5
534-543
2008
10.1002/pc.20373
In this study, the impact-damage tolerance of a graphite-fiber/epoxy composite laminate is studied by examining the correlation between the impact force and the resulting delamination area in the laminate. The cross-ply 0 composite laminate was made of thermosetting P7051S-20Q-1000 prepregs (Toray Composites America). A Hopkinson pressure bar (HPB) was employed to create the impulsive loading with varying magnitude. Transient impact force, displacement, impact power, and transmitted impact energy were calculated using the transient signals recorded from the strain gage mounted on the HPB. Impulsive loads with controllable magnitude were used to induce delamination damage with varying size in the composite samples. Nondestructive evaluation based on a novel ultrasonic pulse-echo reflector technique was used successfully for characterizing the delamination areas in the thin composite samples with thickness ∼2 mm. The present experimental results indicate that there exists a very good linear correlation between the impact force (e.g. the peak force, impact impulse, peak impact power, and the transmitted impact energy of the first impact force pulse exerted by the HPB) and the delamination area of the composite samples. This correlation can be used to determine the threshold of the impact force that initiates the delamination damage in the composite laminate. In contrast to the weight-drop test, the present experimental method successfully examined the impact damage tolerance of polymer matrix composites (PMCs) subjected to impulsive loading with very high force magnitude and ultra short duration such as the typical ballistic impact. The present method and results can be used for the study of impact damage tolerance of PMCs with varying lay-ups and interface modifications. © 2008 Society of Plastics Engineers.
Modelling of the contact mechanics of thin films using analytical linear elastic approaches
Habilitation, Technical University of Chemnitz
2003
In this work the author presents simulation procedures (mathematical\nmodels) with the aim to help determining and analysing the mechanical\nproperties of coating-substrate-systems and finding an optimal coating\nstructure which should protect the compound from inelastic deformation\nunder a given range of load conditions. Such procedures may be used\nas a tool to minimise the search field for experimental work. For\nthis purpose one would need a mathematical model which allows one\nto calculate the complete elastic field with all its displacement\nand stress components within a multilayer film on a substrate under\ngiven mechanical loading and intrinsic stress conditions.\n\nDue to copyright restrictions the author is not allowed to publish\nthe Part II of his habilitation thesis at this place. It concerns\nthe references in meta data.
Mechanics of Composite Materials with
New York
11
337
2005
10.1007/BF00611782
The solutions to most of the given problems appear in an appendix at the end of the book.
On the Stoney Formula for a Thin Film/Substrate System With Nonuniform Substrate Thickness
Journal of Applied Mechanics
74
6
1276
2007
10.1115/1.2745392
Current methodologies used for the inference of thin film stress through system curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis, and co-workers [Acta Mech. Sinica, 21, pp. 362–370 (2005); J. Mech. Phys. Solids, 53, 2483–2500 (2005); Thin Solid Films, 515, pp. 2220–2229 (2006); J. Appl. Mech., in press; J. Mech. Mater. Struct., in press] established methods for the film/substrate system subject to nonuniform misfit strain and temperature changes. The film stresses were found to depend nonlocally on system curvatures (i.e., depend on the full-field curvatures). These methods, however, all assume uniform substrate thickness, which is sometimes violated in the thin film/substrate system. Using the perturbation analysis, we extend the methods to nonuniform substrate thickness for the thin film/substrate system subject to nonuniform misfit strain.
interfacial shears; nonlocal; nonuniform misfit strain; nonuniform substrate thickness; stress-curvature relations; thin films
Origins of primate locomotion: Gait mechanics of the woolly opossum
American Journal of Physical Anthropology
118
3
231-238
2002
10.1002/ajpa.10048
The locomotion of primates differs from that of other mammals in three fundamental ways. During quadrupedal walking, primates use diagonal sequence gaits, protract their arms more at forelimb touchdown, and experience lower vertical substrate reaction forces on their forelimbs relative to their hindlimbs. It is widely held that the unusual walking gaits of primates represent a basal adaptation for movement on thin, flexible branches and reflect a major change in the functional role of the forelimb. However, little data on nonprimate arboreal mammals exist to test this notion. To that end, we examined the gait mechanics of the woolly opossum (Caluromys philander), a marsupial convergent with small-bodied prosimians in ecology, behavior, and morphology. Data on the footfall sequence, relative arm protraction, and peak vertical substrate reaction forces were obtained from videotapes and force records for three adult woolly opossums walking quadrupedally on a wooden runway and a thin pole. For all steps recorded on both substrates, woolly opossums always used diagonal sequence walking gaits, protracted their arms beyond 90 degrees relative to horizontal body axis, and experienced peak vertical substrate reaction forces on forelimbs that were significantly lower than on hindlimbs. The woolly opossum is the first nonprimate mammal to show locomotor mechanics that are identical to those of primates. This case of convergence between primates and a committed fine-branch, arboreal marsupial strongly implies that the earliest primates evolved gait specializations for fine-branch locomotion, which reflect important changes in forelimb function.
Arboreality; Biomechanics; Caluromys philander; Forelimb function; Postcranium
First-ply failure of laminated composite plates
Theoretical and Applied Fracture Mechanics
19
1
29-48
1993
10.1016/0167-8442(93)90031-6
Composite laminates offer superior load carrying capacity. Reliable application of structures requires a knowledge of their stress/strain and failure behavior. past treatments involved assumptions in both the stress and failure analyses; they become increasingly more difficult when the failure of the microstructure constituents is to be included in the continuum analysis of the laminates. Recognizing the conventional failure criteria used for composite material analyses, this work adopts the first-ply failure criterion by application of a polynomial function and the finite element procedure. The laminates are modeled by the Reissner-Mindlin plate theory that accounts for moderate rotation. This is because shear effects are more pronounced in composite laminates whose transverse shear modulus is low relative to the Young's modulus. Failure loads are obtained for different laminate thicknesses, stacking sequences and aspect ratios and different failure criteria. The results show that predictions made from the maximum stress criterion are nearly the same as the others, except for those obtained by the Hill criterion.
Characterization and damage analysis of notched cross-ply and angle-ply fabric GFRP composite material
Composite Structures
102
237-249
2013
10.1016/j.compstruct.2013.03.006
One of the main problems related to composite structure joining is use of mechanical joint that damages continuous fibers and leads to reduction of considerable amount of load carrying capacity of composite structure. To underline this problem, damage initiation and mode of fracture around circular hole of cross-ply and angle-ply of Glass Fiber Reinforced Polymer (GFRP) specimens subjected to tensile loading have been studied experimentally and numerically. A comprehensive notch-edge damage analysis was performed with help of recording test video, digital microscope, Polariscope, and layer by layer SEM (scanning electron microscope) analysis. To understand the effect of manufacturing process on the quality of hole and to avoid its influence on the actual result, a number of manufacturing methods and cutting parameters were used and based on the found result appropriate method was selected for further study. From tensile test, results showed that the tensile strength, crack initiations and propagations around hole are influenced by the quality of notch. Experimental observation showed that the effectiveness of finding of damaged zone is dependent on the damage observation techniques. Predicted damaged zone by numerical solution are in good agreement with experimental observations. © 2013 Elsevier Ltd.
Damage observation; Failure criterion; Failure load; Notch; SEM; Twill GFRP
Shear Coefficient in Orthotropic Thin-Walled Composite Beams
Journal of Composites for Construction
2
1
46-56
1998
10.1061/(ASCE)1090-0268(1998)2:1(46)
The shear coefficient in Timoshenko beam theory is derived for thin-walled beams constructed of orthotropic laminated composite panels and new formulas for the common forms of thin-walled section are presented. The results are identical to Cowper's for the case of isotropic beams. Comparison is also made with the shear coefficient presented by Bank: (1987). A parametric study is conducted to evaluate the effect of cross section dimensions and the mechanical properties of the laminated panels on the shear coefficient. The transverse shear deformation and its relative importance compared to bending deformation is investigated for this class of composite beams. For thin-walled sections constructed from laminated panels made of a combination of 0° unidirectional and angle-ply laminae, the optimal ply angle for different percentages of angle-ply laminae, is found to minimize the total static deflection of the beam. This lay-up configuration is the most practical and effective distribution of plies in laminated composite thin-walled beams to meet the design serviceability re- quirements (Le., deflection and vibration).
Modern Quantum Mechanics
American Journal of Physics
54
7
668
1994
10.1119/1.14491
This best-selling classic provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts. The author, J. J. Sakurai, was a renowned theorist in particle theory. This revision by Jim Napolitano retains the original material and adds topics that extend the text’s usefulness into the 21st century. The introduction of new material, and modification of existing material, appears in a way that better prepares the student for the next course in quantum field theory. You will still find such classic developments as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell’s inequality. The style and treatment of topics is now more consistent across chapters. The Second Edition has been updated for currency and consistency across all topics and has been checked for the right amount of mathematical rigor.
Local versus global buckling of thin films on elastomeric substrates
Applied Physics Letters
93
2
3-5
2008
10.1063/1.2956402
Local buckling can form microcorrugations in thin films on elastomeric substrates, to yield an effective type of mechanical stretchability in otherwise rigid, brittle materials, with many application possibilities. For large area films or relatively thin substrates, however, global (Euler) buckling, as opposed to local buckling, can be observed in experiments. This paper describes analytically the mechanics of local and global buckling of one-dimensional thin films or two-dimensional thin membranes on elastomeric substrates. The critical condition separating these two buckling modes is obtained analytically, and it agrees well with experiments and numerical simulations.
An energy based damage mechanics approach to modelling impact onto woven composite materials-Part I: Numerical models
Composites Part A: Applied Science and Manufacturing
37
11
2041-2056
2006
10.1016/j.compositesa.2005.12.013
The increased use of composite materials in a wide spectrum of industries has led to the development of improved predictive techniques, which can aid in the detailed understanding of the behaviour of a composite component or structure to a range of potentially damaging threats. This paper presents an energy based damage mechanics model for woven carbon composites under high strain loading. This damage mechanics approach introduces five damage variables for in plane damage per ply layer. The damage variables are associated with warp and weft fibre damage in both tensile and compressive failure modes, with an additional damage variable to determine the deterioration of the fibre-matrix interface. The damage variables are directly related to the stiffness degradation within the composite laminae and ultimately within the laminate. The evolution of damage in each mode is controlled via a series of damage-strain equations, thus allowing the total energy dissipated for each damage mode to be set as a material parameter, which is mesh size independent. The damage mechanics approach has been implemented into both the LLNL and LS versions of DYNA3D for plane stress (shell) elements. This encompasses both the standard shell element and the solid-shell formulations available within these codes. In the present paper, validation examples are presented for this damage model. The tensile and the tensile-shear responses are modelled at a coupon level, including relevant strain rate effects and tabs, with the proposed damage model. The results show very good agreement with the available experimental data. Suggestions are also presented for additional non-standard experimental tests to derive all material model parameters directly, rather than an inverse modelling approach in which uniqueness may not be guarantee. This paper also presents an interface modelling technique for explicit FE codes. The formulation is again based on damage mechanics and uses only two constants for each delamination mode; firstly, a stress threshold for damage to commence, and secondly, a critical energy release rate for the particular delamination mode. The model has also been implemented into the LLNL DYNA3D Finite Element (FE) code and the LS-DYNA3D commercial FE code. The interface element modelling technique is applied to a series of common fracture toughness based delamination problems, typically the Double Cantilever Beam (DCB) test, and validated for the dynamic case via a simple analytical plate impact simulation. A subsequent part II paper describes the results of simulations using the proposed damage mechanics based models on a series of experimental CRAG plate impact tests. ?? 2006 Elsevier Ltd. All rights reserved.
B. Impact behaviour; C. Damage mechanics; C. Finite element analysis (FEA); Composite materials
Asymmetric carbon nanotube-MnO₂ two-ply yarn supercapacitors for wearable electronics
Nanotechnology
25
13
135401
2014
10.1088/0957-4484/25/13/135401
Strong and flexible two-ply carbon nanotube yarn supercapacitors are electrical double layer capacitors that possess relatively low energy storage capacity. Pseudocapacitance metal oxides such as MnO₂ are well known for their high electrochemical performance and can be coated on carbon nanotube yarns to significantly improve the performance of two-ply carbon nanotube yarn supercapacitors. We produced a high performance asymmetric two-ply yarn supercapacitor from as-spun CNT yarn and CNT@Mn₂2 composite yarn in aqueous electrolyte. The as-spun CNT yarn serves as negative electrode and the CNT@MnO₂ composite yarn as positive electrode. This asymmetric architecture allows the operating potential window to be extended from 1.0 to 2.0 V and results in much higher energy and power densities than the reference symmetric two-ply yarn supercapacitors, reaching 42.0 Wh kg(-1) at a lower power density of 483.7 W kg(-1), and 28.02 Wh kg(-1) at a higher power density of 19,250 W kg(-1). The asymmetric supercapacitor can sustain cyclic charge-discharge and repeated folding/unfolding actions without suffering significant deterioration of specific capacitance. The combination of high strength, flexibility and electrochemical performance makes the asymmetric two-ply yarn supercapacitor a suitable power source for flexible electronic devices for applications that require high durability and wearer comfort.
asymmetric supercapacitor; carbon nanotube; in colour only in; manganese oxide; some figures may appear; the online journal; two-ply yarn
A Model for Shape Control of Cross-ply Laminated Shells using a Piezoelectric Actuator
Journal of Composite Materials
40
14
1271-1285
2005
10.1177/0021998305057437
This article investigates the technique of using a piezoelectric (P) material as the actuator to control the deformation of thin unsymmetric cross-ply laminated shells. A theoretical model is developed using the Rayleigh-Ritz principle to predict the effect of piezoelectric layer on laminated shell deformation. Several stacking sequences are investigated. Owing to the curvature of the shell, the position of the piezoelectric layer has a great effect on the deformation. The effect of the P-layer as the outer surface or inner surface is investigated. It is found that to achieve the same amount of deformation, different levels of electric fields have to be applied depending on the P-layer configuration. The efficiency of the P-layer on shells with various stacking sequences is also studied and it is observed that the efficiency is determined by the stacking sequence of the composite layers. This model can be used as a guide to design the piezocomposite laminated shell.
Postbuckling analysis of cross-ply laminated cylindrical shell panels under parabolic mechanical edge loading
Thin-Walled Structures
48
8
660-667
2010
10.1016/j.tws.2010.04.010
Postbuckling equilibrium paths of simply supported cross-ply laminated cylindrical shell panels subjected to non-uniform (parabolic) inplane loads are traced in this paper. Love's shell theory with higher order shear deformation theory and von Krmn nonlinear straindisplacement relations are used in the mathematical formulation of the problem. In the first step, the plate membrane problem is solved to evaluate the stress distribution within the prebuckling range as the applied inplane edge load is non-uniform. The governing shell panel postbuckling equations are derived from the principle of minimum total potential energy using the above stress distributions. Adopting multi-term Galerkin's approximation, the governing equations are reduced into a set of non-linear algebraic equations. NewtonRaphson method in conjunction with Riks approach is employed to plot the postbuckling paths through limit points. Numerical results are presented for symmetric (0/90/0) crossply laminated cylindrical shell panels under parabolic inplane load, lateral distributed load and initial imperfections. Limit loads and snap-through behavior of shell panels are studied. ?? 2010 Elsevier Ltd. All rights resvered.
Non-uniform inplane loading; Parabolic loading; Post buckling; Riks approach; Ritz method
Minimization of thermal expansion of symmetric, balanced, angle ply laminates by optimization of fiber path configurations
Composites Science and Technology
71
1105-1109
2011
10.1016/j.compscitech.2011.03.016
Optimal fiber path configurations that minimize the sum of the coefficients of thermal expansion (CTE) values along the principal material directions for a class of laminates are presented. Previous studies suggest that balanced, symmetric, angle ply laminates exhibit negative CTE values along the principal directions. Using the sum of the CTE values along the principal material directions as an effective measure of the coefficient of thermal expansion (CTEeff), we have shown and provided a proof that the smallest value of CTEeff is rendered by straight fiber path configurations. The laminates considered are sufficiently thin so as to neglect the thermal stresses induced through the thickness of the laminate. It is found that the minimal CTEeff values occur for [+45/-45]ns lay-ups. This result is supported by numerical studies that consider curvilinear fiber paths. The possibility of obtaining zero CTE values along both principal material directions and the conditions that render this situation are also examined. © 2011 Elsevier Ltd.
A. Laminate; A. Polymer-matrix composites; B. Thermomechanical properties; C. Deformation; C. Modelling
Design guidelines for ply drop-off in laminated composite structures
Composites Part B: Engineering
32
2
153-164
2001
10.1016/S1359-8368(00)00038-X
The present investigation aims at developing a few guidelines for the design of tapered laminated composites. The tapering in laminated composites is introduced by terminating (dropping-off) plies at different locations. The main objective in designing a drop-off is to reduce stress concentration. At present some thumb rules are used to design the drop-off. In this paper, guidelines have been developed by studying the effect of important parameters that determine the strength of the laminate. The numerical study shows that some of the thumb rules used at present are rather conservative and may be relaxed to an extent.
A. Laminates; B. Delamination; B. Stress concentrations
Introduction to Fracture Mechanics
Journal of the Society of Materials Science, Japan
32
359
935-941
1983
10.2472/jsms.32.935
This text is based on a series of lectures conducted on fracture mechanics. As an introductory course, the test is focused on the essential concepts and analytical methods of fracture mechanics, aiming at painting a broad picture of the theoretical background to fracture mechanics. While a brief review of some important issues in the theory of elasticity is provided in the first chapter, the main focus of the test is centred on stress analysis and energetic approaches to cracked components, local plastic deformation at crack tips, fracture criteria and fatigue life prediction.
Thin-walled structures as impact energy absorbers
Thin-Walled Structures
41
91-107
2003
10.1016/S0263-8231(02)00082-4
The key structural components of the majority of transportation vehicles are designed as thin-walled components. During a crash event, a number of structural components must sustain abnormal loadings in order to meet stringent integrity requirements. At the same time other components must dissipate impact energy in a controlled manner that limits the deceleration of a vehicle to a required safety limit. The present paper focuses on the crushing mechanics of thin-walled components. The analysis method is based on the Superfolding Element (SE) concept, which originates from experimentally observed folding patterns of crushed shell elements. The paper presents milestones of the underlying theory of plastic shells and basic design considerations that are coupled with the SE-based predictive techniques in a CAE software. The paper also presents basic examples of the design process of typical energy absorbing components. ?? 2002 Elsevier Science Ltd. All rights reserved.
Crushing mechanics; Design for crash; Energy absorbing structures; Large plastic deformations of shells
The In Situ Ply Shear Strength Distributions in Graphite/Epoxy Laminated Composites
Journal of Composite Materials
21
708-733
1987
10.1177/002199838702100802
An experimental and analytical investigation was performed to study the in situ ply shear strength in fiber-reinforced laminated composites. The effects of ply orientation and laminate thickness on the ply shear strength in laminates were the major concerns of the study. T300/1034-C Graphite/Epoxy cross-ply laminates were selected for the tests, and a rail shear fixture was used for measuring ply shear strengths. A three-dimensional finite element program was also developed to analyze the interlaminar stress distributions in the specimens. The results of test data strongly indicate that the ply orientation and laminate thickness significantly influence the in-plane shear strengths of the laminates. This effect could be attributed to the inherent flaws introduced during manufacturing processes and to interlaminar stresses in laminates. As a consequence, ply shear strength should not be regarded as an intrinsic property of fiber-reinforced laminates. Due to the free edge effect, the results of shear strength distributions measured from the rail shear fixture were conser vative.
Compression tests on anti-symmetric two-ply GFRP cylinders
Composites Part B: Engineering
30
January
335-350
1999
10.1016/S1359-8368(99)00004-9
This article deals with the experimental buckling behaviour of glass fibre-reinforced plastic (GFRP) cylinders under concentric and eccentric compression. The laminates are of type `Rovimat 1200' consisting of woven glass-fibre roving within a polyester resin matrix. Two-ply cylinders, for which the nominal radius-to-thickness ratio is about 108, with anti-symmetric lay-up of different orientation and overlapping procedure, are examined. In particular, the comparative response of cross-ply and angle-ply configurations is investigated and discussed. The results of experiments on eight models are presented including thickness and imperfection mapping, load and strain measurements as well as salient observations regarding the behaviour of each model. Systematic and automated data acquisition techniques using a laser scanning system and computer-controlled loading procedures were used in order to provide the experimental measurements in a form that can be readily used for further analytical and design studies. The results demonstrate the significant influence of laminate orientation and loading eccentricity on the buckling strength of anti-symmetric cross-ply and angle-ply GFRP cylinders.
b; buckling; glass fibre-reinforced plastics
Fracture mechanics analysis of thin coatings under plane-strain indentation
International Journal of Solids and Structures
40
3
591-610
2003
10.1016/S0020-7683(02)00619-4
A combined experimental/analytical work is carried out to elucidate the fracture resistance of a thin, hard coating bonded to a semi-infinite substrate due to indentation by a cylindrical surface. The bending of the coating under the softer substrate induces concentrated tensile stress regions at the lower and upper surfaces of the coating, from which cracks may ensue. The evolution of such damage in a model transparent system (glass/polycarbonate) is viewed in situ from below and from the side of the specimen. The critical load needed to initiate a crack on the lower coating surface generally increase proportionally to the coatings thickness, d. An interesting departure from this trend occurs for thin coatings, where the fracture load, although marred by a large scatter, increases somewhat with decreasing d. The fracture data for the upper coating surface are limited to relatively thick coatings due to the recurrence of premature failure from the coating edges. The behavior in this range is similar to that for the lower surface crack, albeit with an order of magnitude greater fracture resistance. A fracture mechanics analysis in conjunction with FEM is performed to elucidate the stress intensity factors responsible for crack propagation. A crack normal to the coating surface is assumed to emanate either from the-lower or upper surface of the coating. A major feature of the solution is the occurrence of a bending-induced compression stress field over a region ahead of the crack tip. This effect, which become more dominant as the ratio between the contact length and the coating thickness is increased, tends to delay the onset of crack propagation, especially for the lower surface crack. Consequently, in applications associated with large indenters, thin and/or tough coatings and stiff substrates, cracking from the upper coating surface may precede that from the lower surface. An interesting feature of this crack shielding mechanism is that when the coating surface contains a distribution of flaws rather than a single crack, small flaws in this population may be more detrimental than large ones. Incorporation of these aspects into the analysis leads to a good correlation with the test results. In the special case of line loading, which constitutes a lower bound for the critical loads, a closed-form, approximate solution for the stress intensity factors or the critical loads are obtained. Plane-strain indentation, although less common than spherical indentation, allows for characterizing the fracture resistance of opaque films through observation from the specimen edge. This approach is not easily implemented to thin films (i.e., less than about a hundred microns), however. (C) 2002 Elsevier Science Ltd. All rights reserved.
Bone Mechanics
Standard Handbook of Biomedical Engineering and Design
8.1-8.23
2004
38 Chapters covering Biomechanics, Tissue Mechanics, Product Design - fantastic resource
Effect of off-axis ply orientation on 0??-fibre microbuckling
Composites Part A: Applied Science and Manufacturing
30
10
1197-1207
1999
10.1016/S1359-835X(99)00026-3
The aim of the present work is to study both experimentally and theoretically the compression failure mechanisms in multi-directional composite laminates, and especially the effect of the off-axis ply orientation on fibre microbuckling in the 0??-plies. The critical mechanism in the compressive fracture of unidirectional polymer matrix composites is plastic microbuckling/kinking. In multi-directional composites with internal 0??-plies, catastrophic failure also initiates by kinking of 0??-plies at the free-edges or manufacturing defects, followed by delamination. When 0??-plies are located at the outside, or in the case of cross-ply laminates, failure rather tends to occur by out-of-plane buckling of the ??-plies. T800-924C carbon-fibre-epoxy laminates with a [(????/O2)2]s lay-up are used here to study the effect of the supporting ply angle ?? on the stress initiation of 0??-fibre microbuckling. Experimental data on the compressive strength of laminates with ?? equal to 30, 45, 60 or 75?? are compared to theoretical predictions obtained from a fibre kinking model that incorporates interlaminar shear stresses developed at the free edges at (0/??) interfaces. Initial misalignment of the fibres and non-linear shear behaviour the matrix are also included in the analysis.
compression failure mechanisms
Thermal Stress Analysis of Cross-Ply Laminated Plates Using Refined Shear Deformation Theory
Journal of Experimental & Applied Mechanics
10
5
47-66
2011
A refined shear deformation theory is presented for thermal flexural analysis of cross-ply laminated plates under combined linear and nonlinear thermal loads through the thickness of laminated plates. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Thermal stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to combined linear and nonlinear single sinusoidal thermal load are obtained. The validity of present theory is verified by comparing the results with those of classical plate theory and first order shear deformation theory and higher order shear deformation theory.
Cross-ply laminated plates; non linear thermal loading; orthotropic material; thermal stresses; Trigonometric shear deformation theory
Determination of material parameters for discrete damage mechanics analysis of carbon-epoxy laminates
Composites Part B: Engineering
56
638-646
2014
10.1016/j.compositesb.2013.08.084
Discrete damage mechanics (DDM) refers to micromechanics of damage constitutive models that, when incorporated into commercial finite element software via user material subroutines, are able to predict intralaminar transverse and shear damage initiation and evolution in terms of the fracture toughness of the composite. A methodology for determination of the fracture toughness is presented, based on fitting DDM model results to available experimental data. The applicability of the DDM model is studied by comparison to available experimental data for Carbon Epoxy laminates. Sensitivity of the DDM model to h- and p-refinement is studied. Also, prediction of modulus vs. applied strain is contrasted with ply discount results and the effect of in situ correction of strength is highlighted. ?? 2013 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Transverse cracking; C. Damage mechanics; C. Finite element analysis (FEA); Parameter identification
Mechanics of compressive stress evolution during thin film growth
Journal of the Mechanics and Physics of Solids
51
11-12
2127-2148
2003
10.1016/j.jmps.2003.09.013
Based on recent in situ measurements, Chason et al. (2002) proposed that the evolution of compressive stress during thin film growth by vapor deposition is due to an increase in surface chemical potential in the presence of growth flux and the consequent exchange of adatoms between the free surface and the grain boundaries. Based on this hypothesis, we present a model for grain boundary stress evolution during thin film growth. To illustrate the mechanics of the problem, first it is assumed that the local normal stress on the grain boundary is proportional to the local grain boundary opening only. The resulting "linear spring" model captures all essential features of the experimental observations. A more accurate description of the grain boundary stress evolution is presented by modeling the stress field due to the material inserted into the grain boundary as that resulting from a continuous distribution of dislocations along the grain boundary. The adatom flux between the grain boundary and the free surface is assumed to be proportional to the difference in chemical potential between the two. This model successfully explains a wide range of experimental observations, including the development of compressive stress during room temperature growth, effect of growth rate on the kinetics of compressive stress evolution and the continued tensile stress generation during low-temperature growth. (C) 2003 Elsevier Ltd. All rights reserved.
Determination of elastic moduli of thin layers of soft material using the atomic force microscope.
Biophysical journal
82
5
2798-2810
2002
10.1016/S0006-3495(02)75620-8
We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels.
Numerical modelling of the damage modes in UD thin carbon/glass hybrid laminates
Composites Science and Technology
94
39-47
2014
10.1016/j.compscitech.2014.01.013
This paper proposes a new FE-based approach for modelling all of the possible damage modes in glass/carbon UD hybrid laminates in tensile loading. The damage development is modelled by two sets of cohesive elements, (i) periodically embedded in the carbon layer for modelling carbon fibre failure and (ii) at the glass/carbon interface to capture delamination. The analysis is stopped when the glass layer failure is predicted by integrating the stress distribution over the glass layer to calculate an equivalent stress for unit volume of the glass. The proposed method is validated against the experimental results and then used to simulate the progressive damage process of other hybrid configurations and finally produce a damage-mode map for this material set. The method can easily be applied to other hybrids to assess their performance by producing damage-mode maps. © 2014 Elsevier Ltd.
A. Hybrid composites; B. Delamination; B. Fragmentation; C. Finite element analysis; Thin-ply layer
Fatigue strength of glass fiber/epoxy angle-ply laminates with different matrix ductility
Mechanics of Composite Materials
28
5
439-444
1993
10.1007/bf00608613
Angle ply laminates made up of glass fiber/epoxy plies have a good static strength for laminate angles up to about 45 °. This is due to the limitation of transverse strain in the plies due to constraints exerted by neighboring plies. At laminate angles of 50 ° and above the transverse and shear strains in the plies are not sufficiently constrained and cause failure in the matrix material. The constraint effect is present in fatigue but since the polymeric matrix material is sensitive to fatigue loading fatigue failure will occur at much lower strain levels than in static loading. This effect cannot be offset by increasing the ductility of the matrix material. Thus, strain to failure under fatigue loading will be only a small fraction of the static strain to failure for angle ply laminates with ply angles up to around 45 ° where the static strength is due to the constraint effect.
The significance of effective modulus theory (homogenization) in composite laminate mechanics
Composites Science and Technology
60
2471-2488
2000
10.1016/S0266-3538(00)00042-7
In this work, we consider the issues regarding the homogenization of fiber-reinforced layers in a laminate in the presence of macroscopic (ply-level) stress gradients. This is accomplished by considering a series of (free edge) boundary value problems similar to those treated by Pagano and Rybicki in 1974. Despite our inability to provide such a homogenization theory, if one truly exists, we can devise approaches to predict the fiber/matrix interfacial stresses in an arbitrary cell by applying certain displacements and/or tractions on the cell boundaries. These boundary conditions are those derived by representing each layer in the laminate by conventional effective modulus theory. It is shown that these approximations can lead to reasonably accurate interfacial stresses and offer great promise as a means of solving practical laminate problems reinforced by fibers of moderate diameter. (C) 2000 Elsevier Science Ltd. All rights reserved.
Effective module; Homogenization; Laminates; Micromechanics
Off-axis fatigue behavior of a carbon/epoxy cross-ply laminate and predictions considering inelasticity and in situ strength of embedded plies
International Journal of Fatigue
30
1743-1755
2008
10.1016/j.ijfatigue.2008.02.009
The off-axis fatigue behavior of a carbon/epoxy symmetric cross-ply laminate at room temperature is examined, and a ply basis fatigue life prediction method is tested with a special emphasis on consideration of the inelastic deformation and in situ strength of the inclined plies embedded in the laminate. Constant amplitude tension-tension fatigue tests are first performed on the coupon specimens of the cross-ply laminate for various fiber orientations. The fiber orientation dependence of the off-axis fatigue data on the cross-ply laminate can be removed by normalizing the maximum fatigue stress levels with the help of the associated off-axis static strengths. The distribution of the normalized off-axis fatigue data on the cross-ply laminate almost agrees with the normalized fatigue data on the unidirectional laminate made of the same prepreg tape, indicating that the relative fatigue performance of the cross-ply laminate is almost indistinguishable from that of the unidirectional laminate. A simple off-axis fatigue analysis of the cross-ply laminate is then attempted on a ply basis, in which no effects of progressive damage are assumed. A ply fatigue model that takes into account the in situ principal strengths of the plies embedded in a general laminate is developed to this end, along with an analytical procedure for identifying the in situ strength ratios of the actual principal strengths to reference values. The actual stress components in the plies embedded in the cross-ply laminate are evaluated using a laminate constitutive model based on the classical lamination theory, in which the non-linear plastic deformation of inclined plies under in-plane off-axis loading is taken into account. It is demonstrated that good guesses about in situ strength ratios can be made on the basis of elastoplastic CLT analysis, and the off-axis fatigue lives of the cross-ply laminate predicted using appropriate in situ strength ratios are shown to agree well with the experimental results. ?? 2008 Elsevier Ltd. All rights reserved.
Classical lamination theory; Cross-ply laminate; In situ strengths; Off-axis fatigue; Plastic deformation
Effects of the intralaminar shear loading rate on the damage of multi-ply composites
International Journal of Impact Engineering
18
6
679-699
1996
10.1016/0734-743X(95)00059-J
It is well known that the specific absorption energy of structural elements based on composite materials is higher than those made of steel. However, this capacity may be limited due to localized damage mechanisms, inducing premature failure. Intralaminar shear is one of such mechanisms and is investigated here in a broad range of strain rates using tensile specimens made of E Glass/Epoxy (?? 45)\n s crossply laminate. Several interrupted dynamic tensile tests were performed thanks to modifications in a servo-hydraulic testing machine and in a tensile split Hopkinson bar. The damage caused by shear is investigated under the damage mechanics frame, permitting access to the influence of the strain rate on damage threshold and damage propagation rate. Copyright ?? 1996 Elsevier Science Ltd.
Composites; Intralaminar shear loading; Stress
The statistical distribution of percolation resistance as a probe\ninto the mechanics of ultra-thin oxide breakdown
International Electron Devices Meeting 2000. Technical Digest. IEDM (Cat. No.00CH37138)
00
C
8-11
2000
10.1109/IEDM.2000.904372
Soft and hard breakdown result from the statistical distribution\nof the percolation conductance, rather than any physical difference\nbetween the traps involved. The distribution obtained confirms some\nsubtle and surprising predictions of the percolation model and shows\nthat the effective trap-diameter is less than 1.5 nm. It also\ndemonstrates that 1.5 nm oxides at 1 V can not undergo hard breakdown\n
Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 1993
Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 1993
481-484
1993
10.1016/B978-0-444-81619-1.50053-8
Several kinds of surface thin film thermocouples for instantaneous temperature measurements in metal and ceramic engines were worked out. In this paper, the structures and the characteristics of these thermocouples, the results of real engine measurements will be given.
A multiscale mechanics approach for modeling textured polycrystalline thin films with nanothickness
International Journal of Mechanical Sciences
48
899-906
2006
10.1016/j.ijmecsci.2006.01.003
A multiscale method is proposed for calculating elastic constants of textured polycrystalline thin films of nanothicknesses. In this method the molecular simulation and finite element method are hierarchically employed. The elastic constants for each single crystal are first calculated through the simulations of on- and off-axis tension tests of the single crystal using molecular statics. Subsequently, the constitutive relations for the single crystal are used in conjunction with a finite element code to study the macro-mechanical deformation and stresses in textured polycrystalline nanofilms. The result indicates that both film thickness and grain size influence the macro-Young's modulus and Poisson's ratio of the nanofilm. Specifically, for nickel, the value of the macro-Young's modulus decreases as film thickness decreases and increases as grain size decreases. The value of the macro-in-plane Poisson's ratio increases as the thickness decreases or grain size increases. ?? 2006 Elsevier Ltd. All rights reserved.
Effective Poisson's ratio; Effective Young's modulus; Finite element; Molecular simulation; Multiscale mechanics; Polycrystalline nanofilms
In-plane shear properties of cross-ply composite laminates with different off-axis angles
Composite Structures
65
2
167-177
2004
10.1016/j.compstruct.2003.10.012
A modified Iosipescu test fixture has been designed and manufactured to investigate the in-plane shear properties of cross-ply composite laminates with different off-axis angles. A cross-ply [0/90]2s glass fiber reinforced epoxy composite laminate was manufactured using the hand lay-up technique. This laminate was cut at different off-axis angles (0??, 15??, 30??, 45??, 60??, 75?? and 90??) to give specimens with different stacking sequences ([0/90]2s, [15/-75]2s, [30/-60]2s, [45/-45]2s, [60/-30]2s, [75/-15]2s and [90/0]2s respectively). The tensile properties (strength, modulus and Poisson's ratio) of cross-ply laminate were determined experimentally. Shear modulus and the tensile elastic properties of cross-ply laminate with different off-axis angles were predicted theoretically from the elastic properties of the constituent materials. The results show that Young's modulus measured from the stress-strain diagram drawn using strain gauge readings in the tension test is more than six orders of magnitude higher than those determined from the stress-strain diagram of the testing machine. The predicted value of the Young's modulus of cross-ply specimen, [0/90]2s, has excellent agreement with the experimental results. The maximum in-plane shear strength is found for specimens with 45?? and 60?? off-axis angles, i.e. for [45/-45]2s and [60/-30]2s specimens respectively. On the other hand specimens with 0?? and 90?? off-axis angles have the minimum in-plane shear strength. The predicted values of in-plane shear modulus of cross-ply laminate with different off-axis angles (0-90??) agree very well with the experimental results. Failure modes of cross-ply specimens with different off-axis angles in Iosipescu shear test have been investigated. ?? 2003 Elsevier Ltd. All rights reserved.
Cross-ply; Elastic properties; In-plane shear; Iosipescu shear test; Off-axis; Tension test
A 3-D fracture mechanics approach to the strength of composite materials
Engineering Fracture Mechanics
14
3
637-649
1981
10.1016/0013-7944(81)90050-3
The first ply failure in composite laminates are studied by 3-D fracture mechanic approach. The fracture model is based on a crack embedded in one of the inner layers. Numerical results for the case of “angle ply” laminates are based on a general 3-D finite difference program. Stress intensity factors and fracture energy are evaluated by the J-integral 2-D and 3-D methods as well as by the stresses and energy balance. It was found that the J(2-D) method can be applied to 3-D problems while the J(3-D) method is not suitable for the numerical computation. The influence of geometrical properties of the crack and the layers on the various stress intensity factors is presented and discussed. Change in failure mechanism of the weakest ply was proved by experiments to fit with numerical results. It was found that the weakest layer is strengthened by the others, a fact which has been verified experimentally and hasn't been explained by other approaches.
Fracture mechanics interpretation of thin spray-on liner adhesion tests
International Journal of Adhesion and Adhesives
34
17-23
2012
10.1016/j.ijadhadh.2012.01.001
Thin spray-on liners (TSLs) are relatively thin (2–5mm) fast setting liner materials that are sprayed onto rock surfaces to support mining excavations. The adhesive strength between a TSL and a rock surface is an important property controlling the design and performance of TSL rock support systems. In this study, direct pull-off TSL adhesion tests were interpreted based on a fracture mechanics approach. An edge crack propagation equation for a generic case (ν≠0.5) was derived and the failure modes of TSLs were studied. It was found that the current TSL adhesion test sample geometries show confined behaviour, the failure mode of the tests are edge crack propagation. Bulk cavitation of TSLs can only occur for very compliant samples (E<0.6MPa). Adhesion tests done on a TSL product, Tekflex, applied on concrete substrates were examined to verify the edge crack propagation.
Adhesion test; Crack propagation; Fracture; Rock support; Thin spray-on liner
Vibration of angle-ply laminated plates with twist by Rayleigh-Ritz procedure
Computer Methods in Applied Mechanics and Engineering
193
805-823
2004
10.1016/j.cma.2003.08.003
Considering transverse strain and rotary inertia, an analytical method for vibration of an angle-ply laminated plate with twist is proposed. An accurate strain-displacement relationship of a twisted plate is derived by the Green strain tensor on the general shell theory and the Mindlin plate theory. The equilibrium for free vibration is given out by the principle of virtual work and is solved by using the Rayleigh-Ritz procedure with normalized characteristic orthogonal polynomials generated by the Gram-Schmidt process. The convergence and the accuracy of the present method are investigated. The parametric effects of a fibre angle, a twist angle, a thickness ratio and a stacking sequence on vibration frequencies and mode shapes of laminated plates are studied. © 2003 Elsevier B.V. All rights reserved.
Laminated plate with twist; Mindlin plate theory; Orthogonal polynomials; Principle of virtual work; Rayleigh-Ritz procedure
A new super convergent thin walled composite beam element for analysis of box beam structures
International Journal of Solids and Structures
41
5-6
1491-1518
2004
10.1016/j.ijsolstr.2003.10.024
In this paper, a new composite thin wall beam element of arbitrary cross-section with open or closed contour is developed. The formulation incorporates the effect of elastic coupling, restrained warping, transverse shear deformation associated with thin walled composite structures. A first order shear deformation theory is considered with the beam deformation expressed in terms of axial, spanwise and chordwise bending, corresponding shears and twist. The formulated locking free element uses higher order interpolating polynomial obtained by solving static part of the coupled governing differential equations. The formulated element has super convergent properties as it gives the exact elemental stiffness matrix. Static and free vibration analyses are performed for various beam configuration and compared with experimental and numerical results available in current literature. Good correlation is observed in all cases with extremely small system size. The formulated element is used to study the wave propagation behavior in box beams subjected to high frequency loading such as impact. Simultaneous existence of various propagating modes are graphically captured. Here the effect of transverse shear on wave propagation characteristics in axial and transverse directions are investigated for different ply layup sequences. ?? 2003 Elsevier Ltd. All rights reserved.
Finite element; Free vibration; Thin walled beam; Wave propagation
Introduction to Fluid Mechanics;
Flow Measurement and Instrumentation
11
1
51-52
2000
10.1016/S0955-5986(99)00026-6
The air and the water of rivers and seas are always moving. Such a movement of gas or liquid (collectively called “fluid”) is called the “flow,” the study of which is called “fluid mechanics.” The science of flow has been classified into hydraulics, which developed from experimental studies; and hydrodynamics, which developed through theoretical studies. Hydraulics developed as a purely empirical science with practical techniques beginning in prehistoric times. Leonardo da Vinci made many discoveries and observations in the field of hydraulics. He forecast laws, such as the drag and the movement of a jet or falling water. Furthermore, he advocated the observation of internal flow by floating particles in water, that is, “visualization of the flow.” The advent of hydrodynamics, which tackles fluid movement both mathematically and theoretically, was considerably later than that of hydraulics. This chapter provides details regarding an important paper published in 1869 that connected hydraulics and hydrodynamics..
Buckling of a stiff thin film on a compliant substrate in large deformation
International Journal of Solids and Structures
45
10
3107-3121
2008
10.1016/j.ijsolstr.2008.01.023
A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically. © 2008 Elsevier Ltd. All rights reserved.
Buckling; Finite deformation; Finite element analysis; Perturbation analysis; Thin film
Numerical method to control high levels of damage growth using an implicit finite element solver applied to notched cross-ply laminates
Composite Structures
110
1
51-61
2014
10.1016/j.compstruct.2013.11.003
Numerical modelling of composites is becoming ever more important to commercial aircraft manufacturers for design-phase cost reductions and improved lead times. The implementation of a user-defined numerical model for damage prediction in composites is described. All modelling is conducted in ABAQUS/Standard (an implicit solver) and the models demonstrate stable performance with significant levels of damage. This stability is often difficult to achieve when modelling damage with implicit solvers. The favourable performance is due to the damage variable evaluation, which uses information from the previous iteration of an increment to drive damage development during a given load step. This "pseudo-current" damage evaluation is complex to implement, however, the stable performance and the improved time-step size dependence justifies this approach. The method is applied to analyse cross-ply open-hole tension specimens having similar layups but demonstrating different damage growth and varying failure loads. The analysis includes in-plane damage, delamination and splitting mechanisms and a nonlocal regularisation scheme to mitigate spurious mesh sensitivity. The delamination and splitting mechanisms are essential for differentiating between the various specimen types. The damage evolution method provides stability to the implicit solver allowing significant levels of damage to develop within the laminates, giving a valuable prediction of laminate behaviour. ?? 2013 Elsevier Ltd.
Damage mechanics; Delamination/splitting; Modelling; Notched laminates
Usefulness of real-time PCR for lytA, ply, and Spn9802 on plasma samples for the diagnosis of pneumococcal pneumonia.
Clinical microbiology and infection : the official publication of the European Society of Clinical Microbiology and Infectious Diseases
16
8
1135-41
2010
10.1111/j.1469-0691.2009.03069.x
In the present study, we evaluated rapid real-time PCR assays for ply, Spn9802, and lytA applied to plasma samples for the detection of Streptococcus pneumoniae in patients with community-acquired pneumonia (CAP). In a prospective study of CAP aetiology, an EDTA plasma sample was collected together with blood culture in 92 adult CAP patients and 91 adult controls. Among the 92 CAP patients, lytA PCR was positive in eight (9%), Spn9802 PCR was positive in 11 (12%) and ply PCR was positive in 19 (21%) cases. Of 91 controls, the ply PCR was positive in eight cases (9%), but no positive cases were noted by Spn9802 or lytA PCRs. Ten CAP patients had pneumococcal bacteraemia. Compared to blood culture, PCR for lytA, Spn9802 and ply had sensitivities of 70% (7/10), 60% (6/10) and 70% (7/10), and specificities of 96% (79/82), 94% (77/82) and 85% (70/82) respectively. With blood culture and/or culture of representative sputum, and/or urinary antigen detection, S. pneumoniae was identified in 31 CAP patients. Compared to these tests in combination, PCR for lytA, Spn9802 and ply showed sensitivities of 26% (8/31), 32% (10/31) and 42% (13/31), and specificities of 100% (61/61), 98% (60/61) and 90% (55/61) respectively. We conclude that Spn9802 and lytA PCRs may be useful for the rapid detection of bacteraemic pneumococcal pneumonia, whereas ply PCR is not specific enough for routine use and blood PCR with small plasma volumes is not useful for the detection of nonbacteraemic pneumococcal pneumonia.
Adult; Aged; Aged, 80 and over; Bacterial Proteins; Bacterial Proteins: genetics; Bacteriological Techniques; Bacteriological Techniques: methods; Blood; Blood: microbiology; Community-Acquired Infections; Community-Acquired Infections: microbiology; DNA, Bacterial; DNA, Bacterial: genetics; DNA, Bacterial: isolation & purification; Female; Humans; Male; Middle Aged; Pneumonia, Pneumococcal; Pneumonia, Pneumococcal: diagnosis; Polymerase Chain Reaction; Polymerase Chain Reaction: methods; Prospective Studies; Sensitivity and Specificity; Streptococcus pneumoniae; Streptococcus pneumoniae: genetics; Streptococcus pneumoniae: isolation & purification; Streptolysins; Streptolysins: genetics; Time Factors
Mechanics of highly deformed elastic shells
Thin-Walled Structures
47
6-7
692-700
2009
10.1016/j.tws.2008.11.009
Emergence of new technological applications, in addition to the constantly growing interest in biological materials has accentuated the importance of studying the mechanics of highly deformed shells. The key challenge is the intricate interplay of physics and geometry, which leads to a mechanical response much different from the response of solid objects. The quest to understand the underlying phenomena has spawned theoretical and experimental studies, which have helped in understanding the underlying mechanisms of deformation and response of shells. Here, we use numerical simulations to study the response of shells when they are deformed deeply into the nonlinear regime. We use computational models to study the mechanics of highly deformed elastic shells in several classical problems: indentation of elastic spherical caps by a flat rigid plate and a rigid sharp indenter and pure bending of circular and oval cylinders. These assays are used to highlight some of the key aspects of the mechanics of highly deformed elastic shells, while an overview of the current state-of-the-art and suggestions for future research on this subject are also provided. ?? 2008 Elsevier Ltd. All rights reserved.
Indentation; Localization of deformation; Nonlinear response; Numerical simulations; Shell structures
Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates
Composites Science and Technology
54
4
395-404
1995
10.1016/0266-3538(95)00084-4
In previous papers the microscopic failure process of (0/90n/0) (n = 4,8,12) cross-ply laminates was investigated. Progressive damage parameters, such as the transverse crack density and the delamination ratio, were measured. A simple modified shear-lag analysis including the thermal residual strains was conducted to predict the transverse crack density and the delamination length. The analysis did not consider the interaction between the transverse cracks and the delamination. In the present paper, a prediction is presented for the transverse crack density including the effect of delamination growth. The prediction shows better agreement with the experimental results, especially for laminates with thicker 90 ° plies in which extensive delamination occurs. Loading/unloading tests have also been performed to obtain the Young's modulus reduction and the permanent strain as functions of the damage state. The shear-lag predictions of the Young's modulus reduction and the permanent strain are compared with the experimental data. Better agreement is obtained when the interaction between transverse cracks and delamination is considered.
cross-ply laminates; delamination
Influence of ply-drop location on the fatigue behaviour of tapered composites laminates
Procedia Engineering
2
1
1105-1114
2010
10.1016/j.proeng.2010.03.119
The influence of ply-drop position in thickness direction under fatigue loading (R=-1) has been studied for a highly oriented composite laminate dropping from 20 to 12 plies. Compressive and tensile strengths have been determined for several configurations of ply-drop locations. Fatigue tests at a load ratio of R=-1 have been performed up to rupture. The first damages clearly identified are delaminations close to the drop-offs. Their initial locations and propagations kinetics before final failure were observed. Finite element simulations were performed to find out initiation spots of delamination. An interlaminar stress criterion has been proposed to predict initiation of delaminations. Effects of ply-drops configuration on fatigue are discussed. © 2010 Published by Elsevier Ltd.
Composite; Damage modes; Fatigue; Numerical simulation; Ply-drop
Variational analysis of cracked angle-ply laminates
Composites Science and Technology
70
4
638-646
2010
10.1016/j.compscitech.2009.12.018
Stiffness reduction of angle-ply laminates of the type [??m\n(2) / ??n\n(1)]s containing intralaminar cracks in the middle laminae is analyzed. Using the principle of minimum complementary energy an optimal admissible stress field is derived that satisfies equilibrium, boundary and traction continuity conditions. The method provides a lower bound for the stiffness matrix of a cracked angle-ply. Results for longitudinal stiffness of a cracked Glass/Epoxy [0 ?? / 45 ??]s laminate are in very good agreement with experimental data. Asymptotic behavior of the laminate stiffness when the crack densities are low or high is derived and its importance is discussed. ?? 2009 Elsevier Ltd. All rights reserved.
A. Laminate; B. Matrix cracking; C. Elastic properties; C. Modelling
COUPLING OF DAMAGE MECHANICS AND PROBABILISTIC APPROACH FOR LIFE-TIME PREDICTION OF COMPOSITE STRUCTURES
ICF10, Honolulu, Hawaii - 2001
2001
We propose a damage model with a probabilistic approach for laminates made of unidirectional fibre reinforced plies. Statistical information is collected through multiple cracking tests. The defects are considered as trans- verse matrix cracks and we study them by examining laminates. Parameters of a cumulative distribution function of the failure strength are determined. Probabilistic parameters of the cumulative distribution are chosen to be independent of the ply thickness and multiaxial loading to have intrinsic values for describing the ply. Probabilistic parameters found previously are introduced into a finite element computation of laminates using a Statistical Volume Element (SVE). As experimental results, numerical ones present a dispersion of the failure stress.
carbon; composite laminates; crack density; defects statistics; epoxy fabric laminates; mul-; probabilistic failure criteria; tiaxial loading; transverse cracking
Salt tectonics driven by sediment progradation: Part I - Mechanics and kinematics
AAPG Bulletin
89
March 1991
1071-1079
2005
10.1306/03310503063
Using conceptual reasoning and results from physical models, we describe the mechanical and kinematic characteristics of sediment wedges spreading seaward above a viscous evaporitic layer. Spreading can occur if the distal sediment overburden is thin and weak, or if it comprises preexisting salt bodies. Spreading is accommodated by proximal extension and an associated rise of diapiric ridges, by midslope seaward translation, and by distal shortening. Rapid sediment progradation can lead to the reactivation of older distal folds by later extension. Either retrogradation or renewed sedimentation following a long depositional hiatus can reactivate older grabens and diapirs in shortening. Copyright © 2005. The American Association of Petroleum Geologists. All rights reserved.
diapirism; salt tectonics; thin-skinned extension
Nanomechanical fracture-testing of thin films
Engineering Fracture Mechanics
61
1
1-20
1998
10.1016/S0013-7944(98)00050-2
Nanochemical testing techniques were used to quantitatively assess the adhesion of thin film-substrate systems. These techniques utilized micron-scale diamond tips with instrumentation continuously measuring to sub-nanometer and sub-millinewton resolutions. Delamination was modeled as an interfacial crack propagation problem, utilizing linear elastic fracture mechanics and characterized by the critical strain energy release rate. A 9.1 mu m thick phenol-formaldehyde polymer film on stainless steel was tested with indentation, scratching and edge-loading of fine lines. Also, sputtered copper and tungsten-copper bilayer films on SiO2, 150 to 1500 nm thick, were tested with indentation. (C) 1998 Elsevier Science Ltd. All rights reserved.
indentation; interfacial fracture; nanomechanics; scratch testing; thin films
Improved Smeared and Zigzag Third-Order Theories for Piezoelectric Angle-Ply Laminated Cylindrical Shells under Electrothermomechanical Loads
Journal of Mechanics of Materials and Structures
4
6
1157-1184
2009
DOI 10.2140/jomms.2009.4.1157
An improved efficient zigzag theory (IZIGT) and an improved third-order theory (ITOT) are presented for hybrid piezoelectric angle-ply composite circular cylindrical shells under electrothermomechanical loading. In both theories, the potential and thermal fields are approximated as piecewise linear across a number of sublayers so that the nonlinear potential field and actual temperature profile across the laminate thickness can be captured to any desired degree of accuracy. The transverse displacement is approximated to explicitly account for the transverse normal strain resulting from thermal and electric fields without introducing additional unknowns. The shear traction free conditions on the top and bottom surfaces in both theories and the continuity of transverse shear stresses at layer interfaces in the IZIGT are satisfied exactly considering coupled constitutive equations. The theories are assessed in comparison with the available exact 3D piezothermoelasticity solution for simply supported angle-ply hybrid cylindrical panels under electrothermomechanical loads. The comparisons for a hybrid test panel, a composite panel, and a sandwich panel establish that the IZIGT is very accurate and the ITOT is an improvement over the conventional third-order theory for thermal loads, which assumes uniform deflection across the laminate thickness.
actuator; angle-ply; composite shells; cylindrical shell; finite-element; formulation; piezoelectric composite; piezothermoelastic solution; plates; thermal load; vibration control; zigzag theory
Fatigue behavior of CFRP cross-ply laminates under on-axis and off-axis cyclic loading
International Journal of Fatigue
28
10 SPEC. ISS.
1254-1262
2006
10.1016/j.ijfatigue.2006.02.011
This paper focuses on the damage and fracture process of CFRP cross-ply laminates under on-axis and off-axis cyclic loading. On the semi-log S-N curves obtained by fatigue tests, fatigue fracture is described by a straight line and the fatigue limit is not recognized clearly. In the on-axis fatigue tests, fiber-peeling damage in 0?? plies develops in addition to ply-cracking damage in 90?? plies. The fiber-peeling damage was described by peeling-off of fiber bundles from the specimen surface after micro-scale damage of matrix resin and fiber-matrix interface. Most of the ply-cracking damage develops at an early stage of stress cycles, and slightly increases during fatigue, while the fiber-peeling damage in 0?? plies initiates from the edges of 0?? plies and evolves in the whole area of laminates with an increase in stress cycles. The fatigue fracture seems to occur when the 0?? plies lose their load carrying capacity by the evolution of the fiber-peeling damage. In the off-axis fatigue tests, the fatigue fracture is caused by the initiation and evolution of ply-cracking damage and succeeding delamination. It is concluded that the fatigue strength is governed by the fiber-peeling damage in 0?? plies under on-axis cyclic loading and by the ply-cracking damage and delamination under off-axis cyclic loading. ?? 2006 Elsevier Ltd. All rights reserved.
CFRP cross-ply laminates; Fatigue behavior; Fiber-peeling damage; Ply-cracking damage; S-N curve; Tensile properties
An ultra-thin PDMS membrane as a bio/micro-nano interface: Fabrication and characterization
Biomedical Microdevices
9
4
587-595
2007
10.1007/s10544-007-9070-6
We report a method for making ultra-thin PDMS membrane devices. Freely suspended membranes as thin as 70 nm have been fabricated. Bulging tests were performed with a custom built fluidic cell to characterize large circular membranes. The fluidic cell allows the media (such as air or water) to wet one side of the membrane while maintaining the other side dry. Pressure was applied to the membrane via a liquid manometer through the fluidic cell. The resulting load-deflection curves show membranes that are extremely flexible, and they can be reproducibly loaded and unloaded. Such devices may potentially be used as mechanical and chemical sensors, and as a bio-nano/micro interface to study cellular mechanics in both static and dynamic environments.
Bulging test; Microfabrication; PDMS membrane; Ultra sensitive membrane
An Introduction to Fluid Mechanics
Journal of Applied Mechanics
35
3
624
1968
10.1115/1.3601282
First published in 1967, Professor Batchelor's classic text on fluid dynamics is still one of the foremost texts in the subject. The careful presentation of the underlying theories of fluids is still timely and applicable, even in these days of almost limitless computer power. This re-issue should ensure that a new generation of graduate students see the elegance of Professor Batchelor's presentation.
Damage Mechanics and Fatigue Life Assessment of Composite Materials
International Journal of Damage Mechanics
8
4
339-354
1999
10.1177/105678959900800404
The present state of fatigue life assessment of composite materials is largely empirical. This paper discusses how the discipline of damage mechanics can elevate this status to a mechanisms-based methodology. Specific topics addressed are mechanisms of fatigue damage, characterization of damage and its evolution, criticality of damage and prediction of fatigue life. Data and analysis results for cross ply laminates are used to illustrate and discuss the topics.
Fatigue damage mechanics of composite materials Part IV: Prediction of post-fatigue stiffness
Composites Science and Technology
44
4
309-317
1992
10.1016/0266-3538(92)90068-E
A model has been developed for predicting the stiffness of cross-ply carbon fibre composite laminates containing a notch from which damage, in the form of matrix cracks, splits and delaminations, has grown. A combination of experimental and theoretical results have been used to deduce appropriate degraded stiffness properties for the damaged regions of the laminate. These degraded stiffnesses have then been incorporated into a finite element representation of the notched laminate to predict the overall stiffness. Agreement with experimental data is satisfactory.
finite element analysis; predicting post-fatigue stiffness
Fatigue damage mechanics of composite materials. II: A damage growth model
Composites Science and Technology
44
2
169-177
1992
10.1016/0266-3538(92)90110-O
A fatigue model has been developed for damage growth at a notch tip in carbon fibre/epoxy laminates. The damage is modelled as a series of interacting matrix cracks in various forms: splitting, delamination and transverse ply cracking. The extent of fatigue damage can be successfully predicted for a family of (90i/0j)ns and (90/±45/0)s laminates. In this second paper of four, a damage-based model is proposed which can explain the effect of cyclic tensile loading on the post-fatigue strength and stiffness of a notched laminate.
On the crushing mechanics of thin walled structures
Journal of Applied Mechanics (ASME)
50
727-734
1983
10.1115/1.3167137
A self-consistent theory is presented which describes the crushing behavior of a class of thin-walled structures. Assuming a rigid-plastic material and using the condition of kinematic continuity on the boundaries between rigid and deformable zones, a basic folding mechanism is constructed. This mechanism closely reproduces all the main features of folds and wrinkles actually observed on typical crumpled sheet metal structures. Calculations based on the energy balance postulate show that two-thirds of the plastic energy is always dissipated through inextensional deformations at stationary and moving plastic hinge lines. The extensional deformations are confined to relatively small sections of the shell surface but they account for the remaining one-third of the dissipated energy. The theory is illustrated by application to the problem of progressive folding of thin-walled rectangular columns. A good correlation is obtained with existing experimental data as far as the mean crushing force and the geometry of the local collapse mode is concerned.
axial; box; quasi-inextensional mode; theoretical
Buckling under axial compression of thin-walled composite beams exhibiting extension-twist coupling
Compos Struct
31
3
203-212
1995
DOI: 10.1016/0263-8223(95)00010-0
A study of the flexural buckling of single-cell extension-twist coupled\nbeams under axial compression is presented. The analysis is based\non a recently developed geometrically non-linear thin walled beam\ntheory. The effects of direct transverse shear and the parasitic\nbending-transverse shear coupling as well as those of different boundary\nconditions and ply-angles are discussed.
Mechanics. Buckling cascades in free sheets.
Nature
419
6907
579
2002
10.1038/419579a
The edge of a torn plastic sheet forms a complex three-dimensional\nfractal shape. We have found that the shape results from a simple\nelongation of the sheet in the direction along its edge. Natural\ngrowth processes in some leaves, flowers and vesicles could lead\nto a similar elongation and hence to the generation of characteristic\nwavy shapes.
Effective Thermo-Elastic Constantsof Angle-Ply Laminates Containing90 Degree Ply Cracks
Journal of Composite Materials
35
15
1373-1391
2001
10.1106/RA4L-4FC2-LQX8-LF5J
Effective elastic moduli and thermal expansion coefficients for a composite containing transverse cracks through the middle layers are determined analytically. The laminate portion of the layered composite is treated as a single plate with effective properties (global laminate model), and the ply clusters are modeled as a homogeneous, orthotropic material (local model). The global model is a displacement based, higher order laminated plate theory, while the local model is a stress based homogeneous plate theory. Both models include the effect of transverse shear and normal stresses. This global/local scheme leads to considerable flexibility in modeling cracked laminates without resorting to an inordinate number of degrees of freedom. Numerical results are compared to other approaches.
angle-ply laminates; discount; laminate damage; plate analysis; ply; ply cracking; transverse cracking
Thick vs. thin: thallus morphology and tissue mechanics influence differential drag and dislodgement of two co-dominant seaweeds
Journal of Experimental Marine Biology and Ecology
165
1
23-43
1992
10.1016/0022-0981(92)90287-K
The lower rocky intertidal zone of many moderately exposed and exposed shores in the Gulf of Maine, USA, is co-dominated by two species of red macroalgae, Chondrus crispus Stackhouse and Mastocarpus stellatus (Stack. in With.) Guiry. These species are anatomically, morphologically, ecologically and phylogenetically similar. We quantified: 1.(1) mechanical properties of the stipe; and2.(2) flow forces on the stipe relative to thallus area and biomass of these species, to determine mechanical and morphological characteristics that could explain the greater winter dislodgement of C. crispus thalli in mixed stands. Although stipes of both species broke at the same mean force, C. crispus stipes were relatively thick, weak and extensible compared to the relatively thin, strong and stiff stipes of M. stellatus. Risk of breakage increased with size in both species because: 1.(1) their stipes weakened with increasing cross-sectional area; and2.(2) cross-sectional area of the stipe failed to increase in linear proportion to frond area. Drag on C. crispus thalli of > 3 g fresh weight was greater than on M. stellatus of the same biomass, whereas drag on smaller fronds ( < 3 g fresh weight) of the two species was similar. Drag on large C. crispus thalli was greater mainly because they exhibit greater surface area for a given biomass than do large M. stellatus. Dislodgement by hydrodynamic forces has more severe ecological consequences for M. stellatus because regeneration from holdfasts is slower than in C. crispus. A reduced surface area:biomass ratio coupled with greater strength may lessen wave-induced disturbance and be important to maintaining a high abundance of M. stellatus in the low intertidal zone of wave-swept shores.
Algal morphology; Biomechanics; Chondrus; Drag; Mastocarpus; Scaling
An Introduction to Continuum Mechanics
Journal of Applied Mechanics
51
4
949
1984
10.1115/1.3167763
Formanymaterials the behaviour of large samples can be studied without recourse to the details of atomic levelstructure. A familiar example is the behaviour of fluids, but we can describe solids, glasses etc by making use of the framework provided by continuum mechanics.
Probabilistic Failure Strength Analyses of Graphite/Epoxy Cross-Ply Laminates
Journal of Composite Materials
18
4
339-356
1984
10.1177/002199838401800403
This paper treats the failure characteristics of [0/90/0] and [90/0/90] cross-ply laminates based upon the statistical strength analysis. The stress redistributions at the failure of the 90 {degrees} ply are analyzed using a shear-lag model, taking the thermal residual stresses and Poisson effect into consideration. The formulae for determining first cracking, subsequent multiple cracking and ultimate fracture are derived. The present analysis is compared with the existing experimental results for graphite/epoxy cross-ply laminates, and reasonable agreements have been obtained.
Negative Poisson's ratios in angle-ply laminates: theory and experiment
Composites
25
9
863-868
1994
10.1016/0010-4361(94)90027-2
A series of composite panels has been prepared by laminating unidirectional prepreg tapes of epoxy resin reinforced with continuous carbon fibres. Each panel was a balanced, symmetrical laminate with the plies alternating at ± θ to a reference direction where θ = 0, 10, 15, 20, 25, 30 and 40°. The full set of nine elastic constants was determined for each panel using ultrasonic velocity measurements. The experimentally determined elastic constants were then compared with theoretical predictions obtained using standard laminate theory. The Poisson's ratios of the composites were of particular interest in showing negative values for θ in the range between 15 and 30°, as predicted by the theory.
angle-ply laminates; carbon/epoxy; laminate theory; Poisson's ratios; stiffness constants; ultrasonic velocity technique
Effects of wrap thickness and ply configuration on composite-confined concrete cylinders
Composite Structures
67
4
437-442
2005
10.1016/j.compstruct.2004.02.002
The behavior of small-scale fiber reinforced polymer (FRP) wrapped concrete cylinders under uniaxial compressive loading was investigated through nonlinear finite element analysis. Two parameters were considered for this numerical study: the FRP wrap thickness, and the ply configuration. Performances of numerical models with “hoop-angle-hoop” and “angle-hoop-angle” ply configurations were compared, where the terms “hoop” and “angle” indicate that wraps were oriented at an angle of 0° and 45° in reference to circumferential direction, respectively. The finite element analysis results showed substantial increase in the axial compressive strength and ductility of the FRP confined concrete cylinders as compared to the unconfined ones. The cylinders with “hoop-angle-hoop” ply configuration in general exhibited higher axial stress and strain capacities as compared to the cylinders with the “angle-hoop-angle” ply configuration. The increase in wrap thickness also resulted in enhancement of axial strength and ductility of the concrete cylinders.
Columns; Composite wrap; Concrete; Ductility; Fibers; Ply angle; Strength; Uniaxial compression; Wrap thickness
Effect of surface roughness on nanoindentation test of thin films
Engineering Fracture Mechanics
75
17
4965-4972
2008
10.1016/j.engfracmech.2008.06.016
By using the two-dimensional quasicontinuum method, the nanoindentation process on a single crystal copper thin film with surface roughness is simulated to study the effect of surface morphology on the measurements of mechanical parameters. The nanohardness and elastic modulus are calculated according to Oliver-Pharr's method. The obtained results show a good agreement with relevant theoretical and experimental results. It is found that surface roughness has a significant influence on both the nanohardness and elastic modulus of thin films determined from nanoindentation tests. The effect of such factors as the indenter size, indentation depth and surface morphology are also examined. To rule out the influence of surface morphology, the indentation depth should be much greater than the characteristic size of surface roughness and a reasonable indenter size should be chosen. This study is helpful for identifying the mechanical parameters of rough thin films by nanoindentation test and designing nanoindentation experiments. © 2008 Elsevier Ltd. All rights reserved.
Nanohardness; Nanoindentation; Quasicontinuum method; Surface roughness; Thin films
Mechanics and scaling of thin part assembly at a fluidic interface
Journal of Micromechanics and Microengineering
21
025002
2011
10.1088/0960-1317/21/2/025002
This paper presents an experimental and theoretical study of a high yield self-assembly process with a programmable template. An analysis of the fluidic assembly method at an air–water interface is presented with an emphasis on the combined effect of a substrate tilting angle and part size. For 1 × 1, 3 × 3 and 5 × 5 mm 2 parts with 100 µm thickness, the maximum substrate tilting angles are experimentally determined and the surface tension induced torques are derived from the developed model. The result indicates that there is a limit on the lateral size of the parts that can be assembled when we use just one substrate tilting angle. Based on our analysis, we also propose a novel method that is capable of assembling parts of higher lateral dimensions using parametric changes in the substrate tilting angle.
Transverse cracks in cross-ply laminates 2. Stiffness degradation
Mechanics of Composite Materials
34
2
153-170
1998
10.1007/BF02256035
From the results of stress analysis between two transverse cracks in cross ply laminate [1], a model for the stiffness reduction based on generalized plane strain assumptions has been developed. Simple analytical expressions are obtained for the longitudinal modulus and the Poisson's ratio as a function of the transverse crack density. Apart from the crack density, these expressions depend only on the elastic and geometrical properties of constituent laminae and the average crack opening displacement (ACOD) normalized in the proper way. Calculations of the ACOD are performed and analyzed with the FEM and analytical models used for the stress analysis in [1]. The predicting capabilities of approximate models are discussed in comparison with experimental data and FEM results. In order to predict the stiffness degradation for a wide variety of laminates, a simple procedure requiring only one FEM calculation for some "average laminate" with "average crack spacing" is proposed and has been proved effective.
Flexible, high performance Two-Ply Yarn Supercapacitors based on irradiated Carbon Nanotube Yarn and PEDOT/PSS
Electrochimica Acta
127
433-438
2014
10.1016/j.electacta.2014.02.064
We present a simple design and a fabrication method for a high-performance, flexible, two-ply yarn supercapacitor based on irradiated CNT yarn and conductive polymer Poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT/PSS). The CNT yarn is treated with gamma irradiation and the yarn surface is coated with the PEDOT/PSS to improve the energy storage capacitance of the as-spun yarn supercapacitor. A layer of PVA gel is coated on the surfaces of the CNT yarn and the composite yarn to form a separation layer containing electrolyte. The results show that the gamma irradiation greatly increases the electrical conductivity and improved the gram capacitance of the as-spun CNT two-ply yarn supercapacitor. The coating of PEDOT/PSS on the surface of the pure and irradiated CNT yarns further significantly improves the capacitance of the supercapacitors. The two-ply yarn supercapacitor constructed from the irradiation CNT yarn coated by PEDOT/PSS exhibits the large capacitance and high cyclic charge-discharge stability. Moreover, these two-ply yarn supercapacitors with fine diameters are highly flexible and can be easily woven or knitted into textile fabrics for uses in wearable electronics. ?? 2014 Elsevier Ltd.
Carbon nanotube yarn; Conductive polymer; Flexible supercapacitors; Irradiation
Mechanics of tendon, from an engineering perspective
International Journal of Fatigue
29
6
1001-1009
2007
10.1016/j.ijfatigue.2006.09.020
This is a review of the mechanics of tendon, with new observations on: (i) elastic modulus around zero stress and (ii) the mode of fatigue rupture. The collagenous building-block of tendon is the fibril, long and thin, and more-or-less circular in cross-section. The diameters of fibrils are well-known, but their lengths remain uncertain. The basic structural question is: do fibrils run the whole length of the tendon, or does each fibril have at least one end in the tendon? This is a simple question, with no simple answer. Difficulties in measuring elastic modulus, UTS and hysteresis stem from the problem of clamping the tendon into the test machine. This is circumvented by tests carried out in life. Fatigue is both the focus of this journal, and is also especially important for tendon. Susceptibility to fatigue is such that rupture is only avoided by ongoing repair, with each tendon being only just adequate for its habitual stresses. Fatigue rupture of tendon involves longitudinal cracks leaving long, thin interdigitating fibrous units. At the deepest level, the whole of biology involves forces acting on materials, which puts the Mechanics of Materials at the centre of Biology. ?? 2006 Elsevier Ltd. All rights reserved.
Fatigue; Mechanical properties; Rupture; Structure; Tendon
A continuum mechanics based four-node shell element for general non-linear analysis
Engineering Computations
1
1
77-88
1984
10.1108/eb023562
The element was formulated using three-dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed. This element provides a very attractive basic formulation that could be extended to large strain analysis and analysis of composite shells. Also, the concepts applied here to formulate a 4-node element could equally well be employed in an effective manner to formulate higher-order shell elements.
DOMES AND SHELLS; ELASTICITY - Analysis; MATHEMATICAL TECHNIQUES - Finite Element Method; MECHANICS - Continuous Media
Nanoindentation of polymeric thin films with an interfacial force microscope
Journal of the Mechanics and Physics of Solids
52
10
2329-2354
2004
10.1016/j.jmps.2004.03.005
The mechanical properties of interphase regions at bi-material interfaces can be quite different from the surrounding bulk materials. For composite materials, this interphase region is usually thin but plays an important role in their overall mechanical properties. Nanoindentation has become a commonly used experimental technique for measuring the mechanical properties of materials, especially when one of the dimensions is small. However, the extraction of reduced elastic modulus from the nanoindentation of thin films on substrates can pose challenges due to the influence of the substrate. In this study, the nanoindentation of thin films on substrates has been examined with a view to extracting the reduced modulus of thin polymer films. Thin films of (3-aminopropyl)triethoxysilane (C9H23NO3Si, γ-APS) were deposited on silicon. An interfacial force microscope (IFM) was used to indent the γ-APS films. The effect of the substrate was studied by considering two very different thicknesses (4μm and 46nm). The nanoindentation data were analyzed via contact mechanics theories and a finite element analysis that incorporated surface interactions. The analyses showed that nanoindentation experiments can provide reliable values of film modulus when the film is very different from the substrate. It was found that the commonly used rule of thumb that the indentation depth should be less than 10% of the thickness did not eliminate substrate effects for a wide range of material combinations. Instead, it is proposed that the contact radius should be less than 10% of the thickness so that contact mechanics theories for monolithic materials can be used without considering the presence of the substrate. The modulus of γ-APS polymer films and the surface energy between the tungsten tip of the IFM and γ-APS films were extracted and were related to their cure. A completely cured 46nm thick γ-APS film had a reduced modulus of 3.5±0.5GPa. This value falls in the usual range for polymers due to the amorphous nature of the γ-APS films.
A. Adhesion and adhesives; B. Contact mechanics; C. Finite element analysis; D. Nanoindentation; Layered materials; Polymeric materials
Lectures on quantum mechanics
Lectures on Quantum Mechanics
1-307
2007
10.1007/978-0-387-37744-5
Four concise, brilliant lectures on mathematical methods by the Nobel Laureate and quantum pioneer begin with an introduction to visualizing quantum theory through the use of classical mechanics. The remaining lectures build on that idea, examining the possibility of building a relativistic quantum theory on curved surfaces or flat surfaces.
Fracture mechanism characterization of cross-ply carbon-fiber composites using acoustic emission analysis
NDT & E International
33
2
101-110
2000
10.1016/S0963-8695(99)00030-4
The sequence of microscopic fracture mechanisms in locally loaded cross-ply carbon-fiber composites was studied by analyzing acoustic emission (AE) signals in combination with the modal analysis of Lamb waves, using microscopic and ultrasonic examination of the specimen after load interruption. The first 70 AE events were analyzed, which were detected during the initial loading segment when the first sudden load drop and gradual load recovery were observed. Characteristics of the detected waves were compared with the S0- and A0-mode Lamb waves produced by a spot- or line-focused YAG laser. The internal damage progression of the composite specimen was determined to be the fiber fracture in the front lamina, transverse cracks in the mid-lamina, delamination and splitting.
Acoustic emission; Cross-ply carbon-fiber composites; Fracture mechanisms; Lamb wave analysis
A new mechanism for the formation of ply wrinkles due to shear between plies
Composites Part A: Applied Science and Manufacturing
49
139-147
2013
10.1016/j.compositesa.2013.03.002
The formation of out-of-plane ply deformation causes significant reductions in the mechanical properties of composites. In-plane fibre misalignments also cause reductions in the compressive strength, yet the origins of these defects are misunderstood. This paper presents a new mechanism for the formation of wrinkles, which is based upon the shear forces generated as a result of mismatches in the coefficient of thermal expansion of composite and tool, as well as the process of ply slippage that occurs during consolidation into radii. Using a U-shaped tool, defects in composite spars have been characterised using light microscopy, showing that the tool geometry and prepreg bridging leads to "instability sites," which lead to wrinkles up to 750 μm in height as well as in-plane misalignment of 0 plies of up to 50. Increasing the frictional shear stress through omission of release film prevents the formation of wrinkles, supporting the mechanism presented in this paper. © 2013 Elsevier Ltd. All rights reserved.
A. Prepreg B. Defects D. Optical microscopy E. Aut
Nonlocality and quantum mechanics
Nature Publishing Group
10
4
3
2010
10.1038/nphys2916
A class of nonlocal hidden variable theories is shown to be incompatible with quantum mechanics.
Buckling of Thin Shells: Recent Advances and Trends
Applied Mechanics Reviews
49
4
263
1996
10.1115/1.3101927
This paper provides a review of recent research advances and trends in the area of thin shell buckling. Only the more important and interesting aspects of recent research, judged from a personal view point, are discussed. In particular, the following topics are given emphasis: (a) imperfections in real structures and their influence; (b) buckling of shells under local/non-uniform loads and localized compressive stresses; and (c) the use of computer buckling analysis in the stability design of complex thin shell structures.
The contact mechanics of fractal surfaces.
Nature materials
2
233-236
2003
10.1038/nmat855
The role of surface roughness in contact mechanics is relevant to processes ranging from adhesion to friction, wear and lubrication. It also promises to have a deep impact on applied science, including coatings technology and design of microelectromechanical systems. Despite the considerable results achieved by indentation experiments, particularly in the measurement of bulk hardness on nanometre scales, the contact behaviour of realistic surfaces, showing random multiscale roughness, remains largely unknown. Here we report experimental results concerning the mechanical response of self-affine thin films indented by a micrometric flat probe. The specimens, made of cluster-assembled carbon or of sexithienyl, an organic molecular material, were chosen as prototype systems for the broad class of self-affine fractal interfaces, today including surfaces grown under non-equilibrium conditions, fractures, manufactured metal surfaces and solidified liquid fronts. We observe that a regime exists in which roughness drives the contact mechanics: in this range surface stiffness varies by a few orders of magnitude on small but significant changes of fractal parameters. As a consequence, we demonstrate that soft solid interfaces can be appreciably strengthened by reducing both fractal dimension and surface roughness. This indicates a general route for tailoring the mechanical properties of solid bodies.
Rotation free isogeometric thin shell analysis using PHT-splines
Computer Methods in Applied Mechanics and Engineering
200
3410-3424
2011
10.1016/j.cma.2011.08.014
This paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical T-meshes (PHT-splines). The method exploits the flexibility of T-meshes for local refinement. The main advantage of the PHT-splines in the context of thin shell theory is that it achieves C1 continuity, so the Kirchhoff-Love theory can be used in pristine form. No rotational degrees of freedom are needed. Numerical results show the excellent performance of the present method. © 2011 Elsevier B.V.
Isogeometric analysis; NURBS; PHT-splines; Thin shell; T-meshes
Fracture mechanics analysis of thin coatings under spherical indentation
International Journal of Fracture
119
263-285
2003
Spherical indentation of a thin, hard coating bonded to a thick substrate is investigated. The bending of the coating over the softer substrate induces concentrated tensile stresses on the lower and upper coating surfaces, from which transverse cracks may ensue. This work is primarily concerned with ring cracks originating from the top surface of the coating. In-situ indentation tests are carried out on a model glass/polycarbonate bi-layer, with the coating thickness and the indenter radius being the main test variables. As the coating thickness is decreased, the critical load to initiate ring cracks progressively departs from that associated with a critical surface stress, the effect that increases with increasing the indenter radius. A fracture mechanics approach in conjunction with the FEM technique is used to elucidate the onset of cylindrical ring cracks in thin-film bi-layer structures due to spherical indentation. The analysis, conducted as a function of the coating thickness and the indenter radius, reveals the existence of bending-induced compression stress regions ahead of the crack tip, which tend to shield the crack or increase the fracture resistance. The specific behavior is dictated by a complex interplay between the contact radius, a, the coating thickness, d, and the crack length, c. An interesting manifestation of this shielding mechanism is that when the coating surface contains flaws of various sizes, small flaws in this population may be more detrimental than large ones. Incorporation of this aspect into the analysis led to a good correlation with the experimental results. In the limit case of point-load, a closed-form, approximate solution for the stress intensity factors and the critical loads is obtained. This solution constitutes a lower bound for the critical loads, and is furthermore directly applicable to finite size indenters provided d >> a. In the limit c/d --> 0, a failure stress criterion may be used irrespective of the ball radius, r. The analysis in this case reveals that decreasing either d/r or the coating/substrate modulus ratio tend to favor ring cracking over radial type cracking. The transition between these two failure modes is identified explicitly as a function of the system parameters.
1; a l applications; a m a g; and t e c; a t e d; axisymmetric; e; e is o f; fracture; g; h n o l; including tribology; indentation; interest in a variety; i n t r; o d u c; o f c o; o f industrial; o g i c; resistance; ring crack; structures to contact d; t h e resistance; thermal barrier coat-; thin fihn; t i o n; w e a r
Mechanical properties and interfacial characteristics of carbon-nanotube-reinforced epoxy thin films
Applied Physics Letters
81
15
2833-2835
2002
10.1063/1.1511532
Multiwalled carbon nanotubes (MWNT) reinforced epoxy composite thin films were prepared by a microfabrication process and their elastic modulus was determined using a shaft-loaded blister test and linear and nonlinear elasticity models. Compared to net resin thin films, a 20% increase in elastic modulus was seen when 0.1 wt % MWNTs were added, suggesting MWNT alignment by spin coating. Electron microscopic observations of the fracture surfaces suggested high interfacial shear stress between MWNTs and the epoxy matrix, a result supported by both molecular mechanics simulation and micromechanics calculations. (C) 2002 American Institute of Physics.
Mechanical testing of thin film nanocellulose composites using buckling mechanics
TAPPI JOURNAL
12
4
9-17
2013
The Young’s modulus of multilayer films containing cellulose nanocrystals (CNCs) and polyethyleneimine (PEI) was measured using a buckling-based method and compared to analogous films containing nanofibrillated cellulose (NFC) and PEI [1]. For films 61 nm to 1.7 μm thick, the Young’s modulus was constant but strongly dependent on relative humidity. Films were stiffer at lower relative humidities, with modulus values of 16 ± 5, 12 ± 1, and 3.5 ± 0.3 GPa at 30%, 42%, and 64% relative humidities, respectively. CNC/PEI films had larger elastic moduli than NFC/PEI films. Both types of nanocellulose multilayer films showed the same modulus dependence on relative humidity over the range studied. Results suggest that ambient water might have an even more pronounced role in nanocomposites than in traditional natural fiber-reinforced composites. This straightforward buckling-based method has quantified mechanical properties and provided a useful comparison between CNC and NFC films. Furthermore, it qualitatively assesses that the components in the composite film are highly compatible and that the hydrophilicity and hygroscopicity of cellulose and PEI combined do not allow for the full mechanical potential of crystalline cellulose nanoelements to be exploited. This work is one approach toward finding dependable methods to characterize nanocellulose, specifically cellulosic thin films, which is increasingly important as we extract nanocellulose from wood, plants, algae, bacteria, and animals and enter a new age of cellulose materials.
TAPPI JOURNAL April 2013
Vibration of axially loaded rotating cross-ply laminated cylindrical shells via Ritz method
Journal of Engineering Mechanics
128
9
1001-1007
2002
10.1061/(ASCE)0733-9399(2002)128:9(1001)
This paper presents the free vibration analysis of axially loaded rotating cross-ply laminated cylindrical shells with the consideration of the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to the rotation. The Ritz method is employed for the solution of this problem. Adopting the trigonometric series as the admissible displacement functions, a set of frequency characteristics equations is derived. The frequency characteristic analysis for shells of simply supported boundary conditions is examined and the frequency characteristics of various lamination schemes are investigated. The results from the present analysis are compared with the available solutions to validate its accuracy.
Axial loads; Boundary conditions; Cylindrical shells; Laminates; Loop tension; Rotation; Shells (structures); vibration; Vibration
Theoretical soil mechanics
Géotechnique
Chapter 4
510
1943
10.1016/0167-1987(88)90005-0
Treatment covers general principles involved in theories of soil mechanics, conditions for shear failure in ideal soils, and mechanical interaction between solid and water in soils. Eng Soc Lib, NY. 5.00)
On the tearing of thin sheets
Engineering Fracture Mechanics
77
11
1849-1856
2010
10.1016/j.engfracmech.2010.03.006
We investigate the interaction between two cracks propagating quasistatically in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. A single tear propagates in a straight line independently of its position in the sheet. In contrast, we find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.
Thermal buckling analysis of cross-ply laminated composite beams with general boundary conditions
Composites Science and Technology
67
1096-1104
2007
10.1016/j.compscitech.2006.05.021
The present study is concerned with the thermal buckling analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The requirement of the continuity conditions between layers for symmetric cross-ply laminated beams is satisfied by the use of the shape function incorporated into the theory which also unifies the one dimensional shear deformable beam theories developed previously. The governing equations are obtained by means of minimum energy principle. Three different combinations of clamped and hinged edge boundary conditions are considered. The critical thermal buckling temperatures are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and lay-ups are presented and compared with the ones available in the literature. It is interesting to note that some cross-ply beams buckle upon cooling instead of heating and some of them do not buckle irrespective of whether they are heated or cooled. ?? 2006 Elsevier Ltd. All rights reserved.
A. Cross-ply beams; B. Buckling; C. Shear deformable beam theory; D. Ritz method
In situ observation and probabilistic prediction of microscopic failure processes in CFRP cross-ply laminates
Composites Science and Technology
52
2
183-195
1994
10.1016/0266-3538(94)90204-6
The microscopic failure processes in three different types of cross-ply laminates, (0/90n/0)(n = 4, 8, 12), were investigated at room temperature and 80°C. Materials systems used were toughened T800H/3631 and conventional T300/3601 carbon/epoxy composites. In situ observation of the microscopic failure process was conducted by using a scanning acoustic microscope (SAM) and a scanning electron microscope (SEM) with instrumented tensile loading devices and by the replication technique. Progressive damage parameters such as the transverse crack density and the delamination ratio were measured. Thermal residual strains which had important effects on the failure process were measured by the ply separation method. On the basis of the above data, a simple modified shear-lag analysis including the thermal residual strains was conducted to obtain the transverse crack density as a function of laminate strain, considering the constraint effect and the strength distribution of the transverse layer. The analysis was also extended to the system containing delamination.
cross-ply laminates; delamination; micro-; scopic failure process; temperature effect; transverse
STRAIN ENERGY RELEASE RATES OF COMPOSITE INTERLAMINAR END-NOTCH AND MIXED MODE FRACTURE: A SUBLAMINATE/PLY LEVEL ANALYSIS AND A COMPUTER CODE.
NASA Technical Memorandum
1987
A computer code is presented for the sublaminate/ply level analysis of composite structures. This code is useful for obtaining stresses in regions affected by delaminations, transverse cracks, and discontinuities related to inherent fabrication anomalies, geometric configurations, and loading conditions. Particular attention is focussed on those layers or groups of layers (sublaminates) which are immediately affected by the inherent flaws. These layers are analyzed as homogeneous bodies in equilibrium and in isolation from the rest of the laminate. A theoretical model used to analyze the individual layers allows the relevant stresses and displacements near discontinuities to be represented in the form of pure exponential-decay-type functions which are selected to eliminate the exponential-precision-related difficulties in sublaminate/ply level analysis.
COMPOSITE LAMINATE ANALYSIS; COMPOSITE MATERIALS; COMPUTER PROGRAMS; FRACTURE MECHANICS; INTERLAMINAR FRACTURE; MATHEMATICAL MODELS; PLY LEVEL ANALYSIS; STRAIN ENERGY; STRESSES - Analysis; STRUCTURAL ANALYSIS; SUBLAMINATE ANALYSIS
Intra and interlayer damage analysis of laminated composites usingcoupled continuum damage mechanics with cohesive interface layer
Composite Structures
2014
10.1016/j.compstruct.2014.10.004
In the present article a model based on coupling of continuum damage mechanics with cohesiveinterfacelayer is proposed in order to predict the progressive damages including the large delamination growth in composite laminates. A new interface cohesive constitutive law is developed which is compatible with 3D continuum damage mechanics (CDM). To avoid the difficulties of 3D mesh generation and 3D interface modeling between the layers, the cohesive interface layer is implemented in the Reddy’s full layer-wise plate theory. An angle-ply laminate is analyzed to evaluate the developed CDM+cohesivelayer in edge delamination initiation and evolution during uniaxial tension loading. The proposed approach is demonstrated to predict progressive damage and final failure load of angle-ply laminated composites both accurately and effectively.
Angle-ply laminate; Cohesive interface layer; Continuum damage mechanics; Edge delamination
Fatigue Testing of Thin Films
Key Engineering Materials
465
552-555
2011
10.4028/www.scientific.net/KEM.465.552
Thin film processing has been a driving technology in microelectronics and mechanics for years. The reliability of such devices is often limited by the failure of thin films. Therefore a deeper understanding of fatigue mechanisms of thin films through experiments is necessary to develop physical based lifetime models. Thus, this paper focuses on a novel setup for micro beam bending of thin metal films on Si cantilever substrate and first results will be presented. © (2011) Trans Tech Publications, Switzerland.
experimental mechanics; fatigue; thin films
Characterization of tensile damage and strength in GFRP cross-ply laminates
Materials Science and Engineering A
383
2
381-389
2004
10.1016/j.msea.2004.05.060
This paper investigates the tensile damage process and strength in\nglass fiber reinforced plastics (GFRP) cross-ply laminates experimentally\nand numerically. Detailed observations are conducted with a video\nmicroscope to comprehend the damage process in the 90° ply. Experimental\nresults indicate that the strength can be approximately estimated\nfrom the strength of the 0° ply, independent of the thickness of\nthe 90° ply. Based on these experimental results, we propose a new\nMonte-Carlo simulation for predicting the damage process and strength\nin cross-ply laminates. The transverse cracks are expressed by utilizing\nthe cohesive elements, considering both local strength and fracture\ntoughness of the 90° ply. Consequently, the stress-strain relationship,\nthe crack progress, and some characteristic phenomena, such as the\nconstrained effect and incomplete transverse cracks, observed in\nthe experiments can be expressed with this simulation.
Fracture
Effect of temperature on the tensile strength and failure modes of angle ply aramid fibre (KRP) tubes under hoop loading
Applied Composite Materials
9
2
99-115
2002
A comprehensive study was undertaken to characterise Kevlar reinforced plastic (KRP) angle ply filament wound tubes at different temperatures. Quasi-static burst tests were performed on tubes of 25°, 55° and 75° winding angle. The tubes were burst under internal radial pressure with minimum end constraints. An experimental rig and two conditioning tanks were designed and built to test the specimens at three temperatures; -46°C (low temperature) and +20°C (room temperature) and +70°C (high temperature). For each test the internal pressure and the strains in both circumferential and longitudinal directions were recorded on suitable digital processing equipment. For a particular batch of tubes tested at three different temperatures, an increase in ultimate hoop strain and a decrease in hoop modulus of the 55° tubes with increasing temperatures was recorded; the temperature effect was less pronounced on the corresponding properties of 25° and 75° tubes. The use of a non-structural thin liner during the tests led to a higher ultimate strength of 55° tubes but had negligible effect on the behaviour of 25° and 75° tubes. The 75° tubes failed in a catastrophic fibre fracture under all test conditions. The mode of failure of 55° changed from weeping at 70°C to fibre fracture at -46°C. The 25° tubes failed by weeping with matrix cracking. The matrix cracking was particularly severe when a liner was used.
Angle ply aramid fibre; Cracking (chemical); Failure analysis; Hoop loading; Kevlar reinforced plastic; KRP tubes; Lined test; Lined tests; Matrix cracking; Modes of failure; Nonmetallic matrix composites; Pressure effects; Reinforced plastics; Static burst strength; Temperature; Temperature effects; Tensile strength; Thermal effects
Experimental and numerical investigations on resonant characteristics of a single-layer piezoceramic plate and a cross-ply piezolaminated composite plate
The Journal of the Acoustical Society of America
119
3
1476
2006
10.1121/1.2161428
Piezolaminated composite plates are widely used in many industrial applications such as intelligent structures and advanced aerospace structural applications. To improve the dynamic performance of the piezolaminated composite structures, it is necessary to experimentally investigate the resonant characteristics of these structures. Three measurement techniques are used in this study to investigate the vibration behavior of the tested specimen. The first method, AF-ESPI (amplitude-fluctuation electronic speckle pattern interferometry) is the major technique for measuring the resonant characteristics of a single-layer piezoceramic plate and a multilayer cross-ply GFRP (glass fiber reinforced plastics) piezolaminated composite plate for completely free conditions. The completely free condition is approximated in experiment by placing and partially sticking the specimen on the surface of a very soft sponge. A thin single-layer piezoceramic plate is first investigated and up to the twenty-sixth transverse modes are presented. Excellent quality of interferometric fringe patterns for vibration mode shapes are presented. The second method, LDV (laser Doppler vibrometer), and the third method, impedance analyzer, are both employed to verify the AF-ESPI results for the piezolaminated composite plate. Both in-plane and out-of-plane resonant frequencies and vibration mode shapes of the piezolaminated composite plate are demonstrated. Finally, numerical computations based on the finite element analysis are presented for comparison with the experimental results. Excellent agreement between the measured data and the numerical results is found in resonant frequencies and mode shapes for the single-layer piezoceramic plate and the cross-ply piezolaminated composite plate.
Effect of annealing on the interface microstructure and mechanical properties of a STS-Al-Mg 3-ply clad sheet
Materials Science and Engineering A
556
319-330
2012
10.1016/j.msea.2012.06.094
In this study we investigated the influence of post-rolling heat treatment upon the microstructure evolution at interface and subsequent uniaxial tensile properties of roll-bonded ferritic stainless steel (STS430)-aluminum (Al3004)-magnesium (AZ31) 3-ply clad metal. By utilizing optical, scanning electron and transmission electron microscopes, the generation and growth of interlayer consists of γ (Mg 17Al 12) and Β (Mg 2Al 3) phases was verified between the constituent layers in the Mg/Al with total thicknesses of 4.56 and 11.21μm during annealing at 300°C for 1 and 3h, respectively. Although as-rolled clad metal was somewhat joined by mechanical locking at the interface, annealing-induced generation of thin diffusion layer between AZ31 and Al3004 by annealing at 300°C for 1h resulted in the enhancement of uniaxial tensile properties in terms of elongation. However, further annealing for 3h lead to weakening the interface bonding properties due to the significant generation of brittle intermetallic phases. The mechanism for retarding interface delamination along the direction of tensile axis was confirmed by the observation from the side surfaces of ex-situ stepped tensile-test specimens. © 2012 Elsevier B.V.
Aluminum; Annealing; AZ31; Clad metals; Clad sheets; Composite materials; Composites; Diffusion layers; Ex situ; Ferritic stainless steel; Generation and growth; Interface bonding; Interface delamination; Interface microstructures; Interfaces; Interfaces (materials); Intermetallic phasis; Magnesium; Mechanical characterization; Mechanical characterizations; Mechanical locking; Mechanical properties; Metal cladding; Microstructure; Microstructure evolutions; Post-rolling; Scanning electrons; STS-Al-Mg 3-ply sheet; Tensile-axis; Thermo-mechanical processing; Thermomechanical processing; Transmission electron microscope; Transmission electron microscopy
Fracture mechanics of laminated glass subjected to blast loading
Theoretical and Applied Fracture Mechanics
44
2
157-167
2005
10.1016/j.tafmec.2005.06.004
A failure criterion based on energy balance approach is introduced for the laminated glass panel subjected to blast loading. Based on this failure criterion, a damage factor is developed to assess the failure of the laminated glass panel. If the damage factor is less than one, the plate is safe otherwise unsafe. Trigonometric function is employed to express the transverse deflection and the Airy's stress function in von Karman's large deflection equations of a thin plate. The nonlinear ordinary differential equation of motion obtained using the Galerkin method is solved using Runge-Kutta method. The predicted results indicate that the breakages of the laminated glass may be caused by the negative phase of the blast load if the positive phase blast load is not violent enough to cause failure. Also, the size of glass shards the laminated glass plies breaks in to is predicted using the surface energy based failure model. ?? 2005 Elsevier Ltd. All rights reserved.
Blast load; Energy balance; Geometric nonlinearity; Laminated glass; Linear viscoelasticity
Cell mechanics and the cytoskeleton
Nature
463
7280
485-492
2010
10.1038/nature08908
The ability of a eukaryotic cell to resist deformation, to transport intracellular cargo and to change shape during movement depends on the cytoskeleton, an interconnected network of filamentous polymers and regulatory proteins. Recent work has demonstrated that both internal and external physical forces can act through the cytoskeleton to affect local mechanical properties and cellular behaviour. Attention is now focused on how cytoskeletal networks generate, transmit and respond to mechanical signals over both short and long timescales. An important insight emerging from this work is that long-lived cytoskeletal structures may act as epigenetic determinants of cell shape, function and fate.
Animals; Biomechanical Phenomena; Cell Physiological Phenomena; Cell Physiological Phenomena: physiology; Cell Shape; Cell Shape: physiology; Cytoskeleton; Cytoskeleton: chemistry; Cytoskeleton: physiology; Epigenesis, Genetic; Humans
Spider silk: Super material or thin fibre?
Advanced Materials
25
9
1275-1279
2013
10.1002/adma.201204158
This work challenges the popular view that silk has exceptional intrinsic mechanical properties of strength and toughness. All polymer fibres are shown to follow one fracture mechanics relationship between failure strength and the ratio of elastic modulus to fibre diameter. Predictive structure-property relations are derived for strength and fracture toughness, and small diameter plays a large part in silk properties.
fibre; fracture mechanics; silk; strength; toughness
On the principles of quantum mechanics
Current Surgery
62
27
38
2004
10.1038/192441a0
We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and increatiblity of particles. We deductively develop the formalism of quantum mechanics on the basis of them: we determine the form of the Lagrangian that satisfies requirements of these principles, and obtain the Schroedinger equation from the Lagrangian. We also derive the canonical commutation relations. Then we adopt the following four guide lines. First, we do not premise the relations between dynamical variables in classical mechanics. Second, we define energy, momentum, and angular momentum as the constants of motion that are derived from homogeneity and isotropy in space and time on the basis of principle of space and time. Since energy and momentum are quantitatively defined in classical mechanics, we define them in quantum mechanics so that the corresponding conservation laws are satisfied in a coupling system of a quantum particle and a classical particle. Third, we define Planck's constant and the mass of a particle as proportionality constants between energy and frequency due to one of Einstein-de Broglie formulas and between momentum and velocity, respectively. We shall obtain the canonical commutation relations and the Schroedinger equation for a particle in an external field in the definitive form. We shall also prove that relations between dynamical variables in quantum mechanics have the same forms for those in classical mechanics.
Thermoelastic properties in combined bending and extension of thin composite laminates with transverse matrix cracks
International Journal of Solids and Structures
34
16
2035-2060
1997
10.1016/s0020-7683(96)00156-4
Approximate analytic expressions for the thermoelastic properties in combined bending and extension of composite laminates containing transverse matrix cracks are derived. The model covers two-dimensional laminates of arbitrary lay-up sequences. The derived expressions for the compliances and thermal expansion coefficients merely contain ply property data and crack distributions. In order to check the accuracy and reliability of the presented analytic method, some sample cracked geometries were examined by use of the finite element method. A good agreement was found between the numerically and analytically obtained results for all cases under consideration.
Dynamics and stability of thin liquid films
Reviews of Modern Physics
81
3
1131-1198
2009
10.1103/RevModPhys.81.1131
The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.
Optimization of ply angles in laminated composite structures by a hybrid, asynchronous, parallel evolutionary algorithm
Composite Structures
92
11
2781-2790
2010
10.1016/j.compstruct.2010.04.003
An evolutionary algorithm approach aimed at the global optimization of ply angles in laminated composites is proposed. The algorithm is enriched by first-order local search and a niching strategy. Genetic variation operators are tailored to the special properties of ply angle optimization problems. Cyclic box-constraints are considered in the crossover, mutation, and niching operations. All experiments on three academic benchmark problems are able to identify a global optimal solution. Two case studies illustrate the applicability of the method on typical engineering problems. ?? 2010 Elsevier Ltd.
Evolutionary algorithm; Optimization; Ply angle; Sensitivity analysis
On a shear-deformable theory of anisotropic thin-walled beams: Further contribution and validations
Composite Structures
56
345-358
2002
10.1016/S0263-8223(02)00019-3
Within the framework of an existing anisotropic thin-walled beam model, a number of non-classical effects are further incorporated and the model thereby developed is validated. Three types of lay-ups, namely, the cross-ply, circumferentially uniform stiffness, and circumferentially asymmetric stiffness are investigated. The solution methodology is based on the Extended Galerkin's Method and the non-classical effects on the static responses and natural frequencies are investigated. Comparisons of the predictions by the present model with experimental data and other analytical as well as numerical results are conducted and pertinent conclusions are drawn. This work is the first attempt to validate a class of refined thin-walled beam model that has been extensively used towards the study, among others, of dynamic response, static aeroelasticity and structural/aeroelastic feedback control. ?? 2002 Elsevier Science Ltd. All rights reserved.
Respiratory fluid mechanics.
Physics of fluids (Woodbury, N.Y. : 1994)
23
2
21301
2011
10.1063/1.3517737
This article covers several aspects of respiratory fluid mechanics that have been actively investigated by our group over the years. For the most part, the topics involve two-phase flows in the respiratory system with applications to normal and diseased lungs, as well as therapeutic interventions. Specifically, the topics include liquid plug flow in airways and at airway bifurcations as it relates to surfactant, drug, gene, or stem cell delivery into the lung; liquid plug rupture and its damaging effects on underlying airway epithelial cells as well as a source of crackling sounds in the lung; airway closure from "capillary-elastic instabilities," as well as nonlinear stabilization from oscillatory core flow which we call the "oscillating butter knife;" liquid film, and surfactant dynamics in an oscillating alveolus and the steady streaming, and surfactant spreading on thin viscous films including our discovery of the Grotberg-Borgas-Gaver shock.
On the dynamic motion of a thin flexible cylinder in a viscous stream
Journal of Fluid Mechanics
38
04
713
1969
10.1017/S0022112069002552
On the dynamic motion of a thin flexible cylinder in a viscous stream(Motion stability and time dependent deflections of thin flexible cylinder with zero bending rigidity in viscous stream). J , CR JOURNAL OF FLUID MECHANICS 38, 713-720, 1969.
Fatigue damage mechanics of composite materials. I: Experimental measurement of damage and post-fatigue properties
Composites Science and Technology
44
2
159-168
1992
10.1016/0266-3538(92)90109-G
A new approach for modelling the post-fatigue strength and stiffness of notched fibre composite laminates has been developed. It is based on the observation of notch tip damage which can be quantified by the extent of the individual failure processes, splitting in the 0° plies and delamination between the 0° ply and off-axis plies. The notch tip damage zone grows stably under tensile cyclic loading in a self-similar manner and the size and shape of this damage zone is dependent on laminate geometry and constituent properties of the fibre, matrix and interface. The post-fatigue strength and stiffness of the laminate can be related uniquely to the split length, which defines the extent of damage growth. In this first paper in a series of four, observation is made and measurements taken of the damage growth mechanisms that make up the damage zone in carbon fibre/epoxy laminates. Radiographs are used to characterise the notch tip damage zone and to establish a qualitative relationship between post-fatigue strength (or stiffness), cyclic stress, damage size and numbers of cycles.
Delamination; matrix cracking; notches; post-fatigue strength/stiffness; splitting
Low cost instrumentation for spin-coating deposition of thin films in an undergraduate laboratory.
Latin-American Journal of Physics Education
5
2
368-373
2011
10.1016/j.aca.2007.12.028
We describe the implementation of an inexpensive spin-coating system to deposit thin films of materials dissolved in a volatile solvent. The system can be easily built with interdisciplinary knowledge of mechanics, fluid mechanics and electronics at undergraduate level. The system allows the deposition of thin films of up to 5cm2 in area and is constructed from a commercial DVD player drive motor and an electronic circuit designed to control the spinning speed and spinning time up to 10,000rpm and 60seg, respectively. In our design, both variables can be adjusted manually through an array of micro push button switches and a varistor. To illustrate the use of our spin-coating system, were prepared films of MDMO-PPV conjugated polymer from solutions in chlorobenzene and tetrahydrofuran and their optical absorption and photoluminescence properties are analyzed and discussed. (English) [ABSTRACT FROM AUTHOR]
CHLOROBENZENE; conjugated polymers; ELECTRONICS; FLUID mechanics; Instrumentación; Instrumentation; LIGHT absorption; películas delgadas; PHOTOLUMINESCENCE; polímeros conjugados; recubrimiento por rotación; spin coating; TETRAHYDROFURAN; thin films
Defining Game Mechanics
Game Studies
8
1-14
2008
1604-7982
This article defines game mechanics in relation to rules and challenges. Game mechanics are methods invoked by agents for interacting with the game world. I apply this definition to a comparative analysis of the games Rez, Every Extend Extra and Shadow of the Colossus that will show the relevance of a formal definition of game mechanics.
Coupled instability of thin-walled columns based on multi-scale continuum mechanics
Thin-Walled Structures
48
10-11
763-770
2010
10.1016/j.tws.2010.07.001
The authors have proposed a concept of micro-mode materials from the standpoint of multi-scale continuum mechanics, which is suitable to express warping deformation of thin-walled beams. In the present study, the concept of micro-mode materials is extended to express bifurcation buckling. Using the second Piola-Kirhhoff stress and hierarchical multi-scales for integration, the authors derive the balance equations for buckling. The obtained equations, including the newly discovered local-bimoment, are presented herein. These equations may enable the derivation of the bucking equations with every bucking mode. The application of the derivation of Euler buckling is also demonstrated using the concept of micro-mode materials. ?? 2010 Elsevier Ltd. All rights reserved.
Balance equations; Bimoment; Micro-mode materials; Polar materials; Structural mechanics; Thin-walled beams
A numerical study of ply orientation on ballistic impact resistance of multi-ply fabric panels
Composites Part B: Engineering
68
259-265
2015
10.1016/j.compositesb.2014.08.049
This paper presents a detailed finite element (FE) analysis aiming to investigate numerically the impact deformation of multi-ply fabric panels with angled plies. The purpose of the investigation described in this paper is to study numerically the way in which the multi-ply panels deform and to identify the energy absorption in different panel constructions. The FE model was created using ABAQUS to simulate the transverse impact of a projectile onto various woven fabric panels. Influencing factors such as the impact velocity, panel construction and the number of plies are taken into account in the FE simulations. The numerical predictions show that the orientation of plies significantly affects the energy-absorbing capacity of the multi-ply fabric panels. The angled panels always increase the energy-absorbing capacity, compared with the aligned panel, by as much as 20%, depending on the number of plies in the panel. In addition, the stacking sequence of oriented plies also plays an important role in absorbing the energy. For the multi-ply fabric panel with large numbers of plies, there is an optimised sequence of plies which can maximise the energy-absorbing capacity of the panel. An important aspect of the work is validation of the numerical technique. It is shown that the FE predictions are highly consistent with the experimental study [1].
aramid fiber; FEA; finite element analysis; impact behavior; impact behaviour; ply-oriented ballistic panel; stress transfer
Microscopic fatigue failure process in interleaved and toughness-improved CFRP cross-ply laminates
Advanced Composite Materials
6
4
309-326
1997
10.1016/S0266-3538(96)00118-2
The microscopic failure process in CFRP cross-ply laminates under quasi-static tensile loading has been investigated at ambient temperature and 80 °C. Material systems considered were interleaved T800H/3631-FM300 and toughness-improved T800H/3900-2 with selectively toughened interlaminar layers. In situ observation of the microscopic failure process was conducted by using an optical microscope (OM) and a scanning acoustic microscope (SAM) with an ‘instrumented tensile loading device’ together with the replication technique. The transverse crack density was measured as a function of the applied laminate strain. On the basis of the above data, a variational stress analysis and a probabilistic approach were used to calculate the transverse crack density as a function of laminate strain. Failure mechanisms after transverse cracking were also discussed.
cross-ply laminates; effect; inter-; microscopic failure; process; temperature; transverse crack
Intra-ply shear locking in finite element analyses of woven fabric forming processes
Composites Part A: Applied Science and Manufacturing
37
5
790-803
2006
10.1016/j.compositesa.2005.04.024
This study was motivated by the observation of physically unrealistic wrinkles, named spurious wrinkles, seen in finite element simulations of diaphragm forming of woven fabrics. Essential intra-ply shear modes for 4-node and 3-node shell elements were investigated. When these essential modes, which show dependency on mesh orientations, are not fully implemented, the stiffness of an element may be overestimated. The phenomenon is termed intra-ply shear locking. It explains the spurious wrinkles in the forming simulations. A simple remedy, based on aligned meshes, is suggested to eliminate the locking problem. The effectiveness of the remedy is demonstrated by simulations of small patches, a bias extension test and diaphragm forming of a 3-ply simple cup. © 2005 Elsevier Ltd. All rights reserved.
A. Fabrics/textiles; C. Finite element analysis; E. Forming; Intra-ply shear locking
Damage mechanics of composite materials: I— Measurements of damage and strength
Composites Science and Technology
39
4
289-301
1990
10.1016/0266-3538(90)90077-I
A new approach for modelling the strength of notched composites has been developed. The approach is based on the assumption that subcritical damage modifies the notch-tip stress field and that the state of subcritical damage just before failure, referred to as the terminal damage state (TDS), must have a significant influence on notched strength. The TDS was monitored for a wide range of cross-ply graphite reinforced epoxy specimens using real-time radiography. A finite element model incorporating the TDS was used to determine the modified notch-tip stress field. A simple tensile stress failure criterion has been found to predict failure very well provided that the effect of subcritical damage is considered in this way. The effect of both layup and notch size on strength can be entirely accounted for by the effect these parameters have on the terminal damage state. In the first paper of a four-part series, radiographs of c. 60 specimens have been used to characterize the notch-tip damage zone and to establish a qualitative relationship between terminal damage and notched strength.
Lung parenchymal mechanics
Comprehensive Physiology
1
3
1317-1351
2011
10.1002/cphy.c100033
The lung parenchyma comprises a large number of thin-walled alveoli, forming an enormous surface area, which serves to maintain proper gas exchange. The alveoli are held open by the transpulmonary pressure, or prestress, which is balanced by tissues forces and alveolar surface film forces. Gas exchange efficiency is thus inextricably linked to three fundamental features of the lung: parenchymal architecture, prestress, and the mechanical properties of the parenchyma. The prestress is a key determinant of lung deformability that influences many phenomena including local ventilation, regional blood flow, tissue stiffness, smooth muscle contractility, and alveolar stability. The main pathway for stress transmission is through the extracellular matrix. Thus, the mechanical properties of the matrix play a key role both in lung function and biology. These mechanical properties in turn are determined by the constituents of the tissue, including elastin, collagen, and proteoglycans. In addition, the macroscopic mechanical properties are also influenced by the surface tension and, to some extent, the contractile state of the adherent cells. This chapter focuses on the biomechanical properties of the main constituents of the parenchyma in the presence of prestress and how these properties define normal function or change in disease. An integrated view of lung mechanics is presented and the utility of parenchymal mechanics at the bedside as well as its possible future role in lung physiology and medicine are discussed.
Experimental investigation and characterisation techniques of compressive fatigue failure of composites with fibre waviness at ply drops
Composite Structures
100
398-403
2013
10.1016/j.compstruct.2013.01.010
Internal features, such as fibre waviness and ply drops, have an impact on fatigue performance of composite structures. In this investigation, specimens were manufactured with wavy plies sandwiched between straight plies by placing blocks of discontinuous plies anti-symmetrically on either side of the continuous wavy plies. The specimens were representative of the kind of fibre misalignment that can occur in components at ply drops and resin rich areas. Experimental characterisation techniques using strain gauge software were also developed for detecting the initiation of delamination and its propagation, by measuring interlaminar transverse displacements. Specimens with longitudinal discontinuous plies did not fail in compression but rather failed by delamination initiating at the ply drops. None of specimens with transverse discontinuous plies failed directly in compression due to misalignment in the wavy plies. The fatigue failure mechanisms are the same as those observed under static loading in previous work, which facilitates development of a fatigue model.
Composites manufacturing; Compressive fatigue failure mechanisms; Defects; Delamination; Fibre waviness; Ply drops
A physically based continuum damage mechanics model for thin laminated composite structures
International Journal of Solids and Structures
40
9
2267-2300
2003
10.1016/S0020-7683(03)00016-7
The present work focuses on the development, implementation, and verification of a plane-stress continuum damage mechanics (CDM) based model for composite materials. A physical treatment of damage growth based on the extensive body of experimental literature on the subject is combined with the mathematical rigour of a CDM description to form the foundation of the model. The model has been implemented in the commercial finite element code, LS-DYNA and the results of the application of the model to the prediction of impact damage growth and its effects on the impact force histories in carbon fibre reinforced plastic laminates are shown to be physically meaningful and accurate. Furthermore, it is demonstrated that the material characterization parameters can be extracted from the results of standard test methodologies for which a large body of published data already exists for many composite materials.
composites; constitutive model; continuum damage mechanics; damage growth; energy absorption; impact
Instabilities in gravity driven flow of thin liquid films
SIAM Review
45
1
95-115
2003
10.1137/S003614450240135
This paper presents theoretical, computational, and experimental aspects\nof the instability development in the flow of thin fluid films. The\ntheoretical part involves basic fluid mechanics and presents derivation\nof the thin film equation using lubrication approximation. A simplified\nversion of this equation is then analyzed analytically using linear\nstability analysis, and also numerically. The results are then compared\ndirectly to experiments. The experimental part outlines the setup,\nas well as data acquisitionand analysis. This immediate comparison\nto experiments is very useful for gaining better insight into the\ninterpretation of various theoretical and computational results.
driven; falling; film; flow; gravity; kondic
A refined dynamic stiffness element for free vibration analysis of cross-ply laminated composite cylindrical and spherical shallow shells
Composites Part B: Engineering
62
143-158
2014
10.1016/j.compositesb.2014.02.021
An exact free vibration analysis of doubly-curved laminated composite shallow shells has been carried out by combining the dynamic stiffness method (DSM) and a higher order shear deformation theory (HSDT). In essence, the HSDT has been exploited to develop first the dynamic stiffness (DS) element matrix and then the global DS matrix of composite cylindrical and spherical shallow shell structures by assembling the individual DS elements. As an essential prerequisite, Hamilton's principle is used to derive the governing differential equations and the related natural boundary conditions. The equations are solved symbolically in an exact sense and the DS matrix is formulated by imposing the natural boundary conditions in algebraic form. The Wittrick-Williams algorithm is used as a solution technique to compute the eigenvalues of the overall DS matrix. The effect of several parameters such as boundary conditions, orthotropic ratio, length-to-thickness ratio, radius-to-length ratio and stacking sequence on the natural frequencies and mode shapes is investigated in details. Results are compared with those available in the literature. Finally some concluding remarks are drawn. ?? 2014 Elsevier Ltd. All rights reserved.
A. Layered structures; B. Vibration; C. Analytical modeling; C. Laminate mechanics; Dynamic stiffness method
Electrical technique for monitoring crack growth in thin-film fracture mechanics specimens
Journal of materials research
19
11
3139-3144
2004
10.1557/JMR.2004.0421
An accurate and reliable electrical technique for continuous monitoring of crack growth in fracture specimens containing technologically relevant thin-film device structures has been developed. Both adhesive and cohesive crack growth measurements are reported using a SiO2 passivation layer and a conducting titanium film deposited on the side face of fracture specimens. Crack velocity measurements approaching 10(-12) m/s were achieved, representing nearly an order of magnitude improvement over commonly used compliance-based techniques. The technique may be particularly useful for elucidating near threshold crack velocity behavior, which is important for thin-film reliability.
Vibration analysis of cross-ply laminated square plates with general boundary conditions
Composites Science and Technology
63
7
1061-1070
2003
10.1016/S0266-3538(03)00016-2
This study is concerned with the vibration analysis of cross-ply laminated square plates subjected to different sets of boundary conditions. The analysis is based on a five-degree-of-freedom shear deformable plate theory. The requirement of the continuity conditions among the layers for the symmetric cross-ply laminated plates are fulfilled by the use of the shape functions incorporated into this theory which, also, unifies the two-dimensional shear deformable plate theories developed previously. Initially, the governing equations obtained by use of Hamilton's principle for the vibration of cross-ply laminated plates with simply supported boundary conditions at all of their edges are solved by an exact analytical method. In the case of cross-ply laminated square plates subjected to twelve different combinations of free, clamped and simply supported edge boundary conditions, the free vibration frequencies are obtained by applying the Ritz method where the five displacement components are assummed as the series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and material arrangements are presented and compared with the ones available in the literature. ?? 2003 Elsevier Science Ltd. All rights reserved.
B. Vibration; Cross-ply laminated plates; C. Shear deformable plate theory; Ritz method
A study of transverse ply cracking using a discrete element method
Computational Materials Science
28
3-4
608-619
2003
10.1016/j.commatsci.2003.08.017
We study the transverse cracking of the 90degrees ply in {[}0/90](S)\ncross-ply laminates by means of a discrete element method. To model the\n90degrees ply a two-dimensional triangular lattice of springs is\nconstructed where nodes of the lattice model fibers, and springs with\nrandom breaking thresholds represent the disordered matrix material in\nbetween. The spring-lattice is coupled by interface springs to two rigid\nbars which represent the two 0degrees plies in the model, which could be\nsublaminate as well. Molecular dynamics simulation is used to follow the\ntime evolution of the model system. It was found that under gradual\nloading of the specimen, after some distributed cracking, segmentation\ncracks occur in the 90degrees ply which then develop into a saturated\nstate where the ply cannot support additional load. The stress\ndistribution between two neighboring segmentation cracks was determined,\nfurthermore, the dependence of the microstructure of damage on the ply\nthickness was also studied. To give a quantitative characterization of\nstiffness degradation, the Young modulus of the system is monitored as a\nfunction of the density of segmentation cracks. The results of the\nsimulations are in satisfactory agreement with experimental findings and\nwith the results of analytic calculations. (C) 2003 Elsevier B.V. All\nrights reserved.
composites; damage evolution; discrete element; failure criterion; fracture
Stress and moisture effects on thin film buckling delamination
Experimental Mechanics
47
1
163-170
2007
10.1007/s11340-006-9346-4
Deposition processes control the properties of thin films; they can also introduce high residual stresses, which can be relieved by delamination and fracture. Tungsten films with high 1-2 GPa compressive residual stresses were sputter deposited on top of thin (below 100 nm) copper and diamond-like carbon (DLC) films. Highly stressed films store large amounts of strain energy. When the strain energy release rate exceeds the films' interfacial toughness, delamination occurs. Compressive residual stresses cause film buckling and debonding, forming open channels. Profiles of the buckling delaminations were used to calculate the films' interfacial toughness and then were compared to the adhesion results obtained from the superlayer indentation test. Tests were conducted in both dry and wet environments and a significant drop in film adhesion, up to 100 times was noticed due to the presence of moisture at the film/substrate interface. © Society for Experimental Mechanics 2007.
Adhesion; Buckling delamination; Environmentally assisted fracture; Stress; Telephone cord; Thin films
Fabrication and material properties of fibrous PHBV scaffolds depending on the cross-ply angle for tissue engineering
Journal of Biomaterials Applications
27
4
457-468
2012
10.1177/0885328211411956
Fibrous PHBV cross-ply scaffolds were fabricated using the electrospinning technique. The electrospun fibers were arranged depending on angles of alignment, which were 180°, 90°, 60°, and 45°. The stress and strain values of the fibrous PHBV cross-ply scaffolds increased as the cross-ply angle increased. At 180°, the strength and strain values of the fibers depended on tensile loading directions. At an alignment of 90°, the PHBV scaffolds had a stress value of 3.5 MPa, which was more than two times higher than the random structure. The cell morphology and proliferation of L-929 cells was strongly dependant on the fiber alignment and the best results were observed when the angle alignment was high. The results of this study showed that the cross-ply structure of the PHBV scaffold affected not only the cell adhesion and spreading properties but also dictated the mechanical properties, which were dependent on the angles of alignment.
alignment; electrospinning; fiber cross-ply; phbv
Characterization of the interactions of the pneumolysoid, ??6 PLY, with human neutrophils in vitro
Vaccine
29
48
8780-8782
2011
10.1016/j.vaccine.2011.09.080
The pneumolysin toxoid, ??6 PLY, is a prototype pneumococcal protein vaccine candidate. However, its potentially detrimental residual pro-inflammatory interactions with human neutrophils are unknown. In the current study the effects of the toxoid (8-1000ng/ml) have been compared with those of wild-type pneumolysin (WT/PLY, 8ng/ml) on neutrophil cytosolic Ca \n 2+ fluxes, generation of leukotriene B \n 4 (LTB \n 4), and release of matrix metalloproteinase-9 (MMP-9), using spectrofluorimetric, and ELISA procedures (LTB \n 4 and MMP-9) respectively. Exposure of neutrophils to WT/PLY resulted in influx of Ca \n 2+ and significant (P<0.05) release of MMP-9 and generation of LTB \n 4. However, treatment of the cells with ??6 PLY at concentrations of up to 1000ng/ml had only trivial effects on Ca \n 2+ influx and no effects on either release of MMP-9 or LTB \n 4 production. The observed absence of pro-inflammatory interactions of ??6 PLY with neutrophils is clearly an important property of this pneumococcal protein vaccine candidate. ?? 2011 Elsevier Ltd.
Calcium; Leukotriene B \n 4; Matrix metalloproteinase-9; Neutrophils; Pneumolysin
Interpretation of the ultrafast photoinduced processes in pentacene thin films
Journal of the American Chemical Society
132
10
3431-3439
2010
10.1021/ja909166s
Ambiguity remains in the models explaining the photoinduced dynamics in pentacene thin films as observed in pump-probe experiments. One model advocates exciton fission as governing the evolution of the initially excited species, whereas the other advocates the formation of an excimeric species subsequent to excitation. On the basis of calculations by a combined quantum mechanics and molecular mechanics (QM/MM) method and general considerations regarding the excited states of pentacene we propose an alternative, where the initially excited species instead undergoes internal conversion to a doubly excited exciton. The conjecture is supported by the observed photophysical properties of pentacene from both static as well as time-resolved experiments.
Continuum Mechanics for Engineers
New York
1
400s
1999
10.1061/(ASCE)0733-9399(2001)127:3(310)
The second edition of this popular text continues to provide a solid, fundamental introduction to the mathematics, laws, and applications of continuum mechanics. With the addition of three new chapters and eight new sections to existing chapters, the authors now provide even better coverage of continuum mechanics basics and focus even more attention on its applications.Beginning with the basic mathematical tools needed-including matrix methods and the algebra and calculus of Cartesian tensors-the authors develop the principles of stress, strain, and motion and derive the fundamental physical laws relating to continuity, energy, and momentum. With this basis established, they move to their expanded treatment of applications, including linear and nonlinear elasticity, fluids, and linear viscoelasticity. This book provides the reader with the foundation necessary to be a skilled user of todays advanced design tools, such as sophisticated simulation programs that use nonlinear kinematics and a variety of constitutive relationships. With its ample illustrations and exercises, it offers the ideal self-study vehicle for practicing engineers and an excellent introductory text for advanced engineering students.
Elementary Engineering Fracture Mechanics
Journal of Applied Mechanics
42
3
751
1975
10.1115/1.3423697
When asked to start teaching a course on engineering fracture mechanics, I realized that a concise textbook, giving a general oversight of the field, did not exist. The explanation is undoubtedly that the subject is still in a stage of early development, and that the methodologies have still a very limited applicability. It is not possible to give rules for general application of fracture mechanics concepts. Yet our comprehension of cracking and fracture beha viour of materials and structures is steadily increasing. Further developments may be expected in the not too distant future, enabling useful prediction of fracture safety and fracture characteristics on the basis of advanced fracture mechanics procedures. The user of such advanced procedures m\lst have a general understanding of the elementary concepts, which are provided by this volume. Emphasis was placed on the practical application of fracture mechanics, but it was aimed to treat the subject in a way that may interest both metallurgists and engineers. For the latter, some general knowledge of fracture mechanisms and fracture criteria is indispensable for an apprecia tion of the limita tions of fracture mechanics. Therefore a general discussion is provided on fracture mechanisms, fracture criteria, and other metal lurgical aspects, without going into much detail. Numerous references are provided to enable a more detailed study of these subjects which are still in a stage of speculative treatment.
Optimum design of a composite structure with ply-interleaving constraints
Thin-Walled Structures
17
185-202
1993
The application of composite materials to aircraft construction has provided the designer with increased flexibility. The orientation of plies can be tailored to provide additional aeroelastic performance unobtainable with an isotropic material. A tailored laminate is made up of plies of several orientations, usually 0 deg, 45 deg, -45 deg, and 90 deg. The direction of the 0 deg plies, does not need to be oriented with the leading edge, but can be varied to obtain a wide variety of structural properties. Also, the number of plies of each orientation varies from one zone to another on the planform. Thus, a thick laminate with mainly 0 deg plies may form the root zone, and a thinner laminate with mainly +45 deg plies may form the leading edge zone. Tailored laminates were designed using complicated optimization programs. Unfortunately, many tailored designs must be modified before they are manufactured. The modification adds weight and decreases performance. One type of modification is ply interleaving, an overlap of plies between zones on the laminate. These interleaves are added to ensure that zones with varying ply percentages can be connected without loss of strength. In this paper, the constraints needed to eliminate interleaves in the laminate optimization process will be described and implemented in a structural optimization problem. The method used has the potential to prevent changes to composite laminates late in the design cycle.
Residual stiffness in cross-ply laminates subjected to cyclic loading
Composite Structures
85
205-212
2008
10.1016/j.compstruct.2007.10.025
A new approach has been developed to evaluate the residual stiffness of cross-ply laminates under tensile fatigue loading. In the present research, a stiffness degradation model is generalized by using a new fatigue life measure and shear-lag analyses to improve correlation at low fatigue cycles and high stress states. The developed model is integrated into a progressive approach to predict the transverse stiffness degradation of 30?? unidirectional plies made of AS4/3501-6 carbon/epoxy under both constant and variable amplitude cyclic tensile loading. Also, the stress history in 0?? and 90?? plies and transverse stiffness degradation in 90?? plies of a cross-ply laminate are predicted by using the developed model. The generalized model, in contrast to original one, is capable of simulating stiffness reduction under high stress states where failure occurs in transverse plies of a cross-ply laminate during the first cycles of the fatigue loading. Predicted results by the model show a good correlation with the experimental data. ?? 2007 Elsevier Ltd. All rights reserved.
Cross-ply laminates; Progressive damage modeling; Stiffness degradation; Stress history
Optimum design of a composite structure with ply-interleaving constraints
Thin-Walled Structures
17
3
185-202
1990
The application of composite materials to aircraft construction has provided the designer with increased flexibility. The orientation of plies can be tailored to provide additional aeroelastic performance unobtainable with an isotropic material. A tailored laminate is made up of plies of several orientations, usually 0 deg, 45 deg, -45 deg, and 90 deg. The direction of the 0 deg plies, does not need to be oriented with the leading edge, but can be varied to obtain a wide variety of structural properties. Also, the number of plies of each orientation varies from one zone to another on the planform. Thus, a thick laminate with mainly 0 deg plies may form the root zone, and a thinner laminate with mainly +45 deg plies may form the leading edge zone. Tailored laminates were designed using complicated optimization programs. Unfortunately, many tailored designs must be modified before they are manufactured. The modification adds weight and decreases performance. One type of modification is ply interleaving, an overlap of plies between zones on the laminate. These interleaves are added to ensure that zones with varying ply percentages can be connected without loss of strength. In this paper, the constraints needed to eliminate interleaves in the laminate optimization process will be described and implemented in a structural optimization problem. The method used has the potential to prevent changes to composite laminates late in the design cycle.
Introduction To Contact Mechanics
Analysis
226
2007
10.1007/978-0-387-68188-7
Introduction to Contact Mechanics, Second Edition is a gentle introduction to the mechanics of solid bodies in contact for graduate students, post doctoral individuals, and the beginning researcher. This second edition maintains the introductory character of the first with a focus on materials science as distinct from straight solid mechanics theory. Every chapter has been updated to make the book easier to read and more informative. A new chapter on depth sensing indentation has been added, and the contents of the other chapters have been completely overhauled with added figures, formulae and explanations. The author begins with an introduction to the mechanical properties of materials, general fracture mechanics and the fracture of brittle solids. This is followed by a detailed description of indentation stress fields for both elastic and elastic-plastic contact. The discussion then turns to the formation of Hertzian cone cracks in brittle materials, subsurface damage in ductile materials, and the meaning of hardness. The author concludes with an overview of practical methods of indentation.
Low-velocity impact response of doubly curved symmetric cross-ply laminated panel with embedded SMA wires
Composite Structures
105
216-226
2013
10.1016/j.compstruct.2013.04.041
In this paper, the dynamic response of thin smart curved composite panel subjected to low-velocity transverse impact is investigated. Shape memory wires are used to reinforce the curved composite panel in a smart way. One-dimensional thermodynamic constitutive model by Liang and Rogers is used for estimating the structural recovery stress. The two degrees-of-freedom springs-masses model is used for evaluation of the contact force between the curved composite panel and the impactor. This work is benefited from the linear Hertzian contact model which is linearized for the impact analysis of the curved composite panel. The governing equations of the curved panel are provided by the first-order shear deformation theory and solved by Fourier series related to simply supported boundary condition. For this purpose, the equation of doubly curved panel motion included the uniform in-plane forces is obtained. By the present analysis, the curved composite panel behavior under low-velocity impact, and also the effect of the impact parameters, the shape memory wire and the curved panel dimensions are studied. ?? 2013 Elsevier Ltd.
Composite materials; Doubly curved panel; Impact response; Liang and Rogers model; SMA wire
The mechanics of penetration of projectiles into targets
International Journal of Engineering Science
16
1
1-99
1978
10.1016/0020-7225(78)90002-2
The present survey is concerned with the terminal ballistics aspects and the penetration mechanics viewpoint of the inIeraction of penetrators and targets. The fatter are categorized as semiinfinite, thick, intermediate and thin. Initial velocity ranges are established for the partial purpose of separating physical effects in various regimes. Target damage mechanisms are described and the concept of a phase diagram distinguishing between the domains of embedment (or perforation) and ricochet is presented. Methods for describing or observing the process are indicated: these include empirical relations, analytical models for ballistic velocities based on rather simple damage mechanisms (primarily for targets, but in some instances for the striker), hypervelocity descriptions, numerical techniques and experimental methods. Projectile and target characteristics are described and the penetration into the targets is examined for the various thickness categories. Finally, some unsolved problems in this area are indicated that require further investigation.
Influence of localized imperfection on the instability of isotropic/cross-ply cylindrical shells/rings under external pressure
Composite Structures
67
1
57-70
2005
10.1016/j.compstruct.2004.01.003
Compressive response of two extreme cases of cylindrical shell type structures weakened by the presence of localized imperfections is investigated. These two extreme cases are (i) thin metallic cylindrical shells, which are characterized by the absence of transverse shear deformation, and (ii) thick laminated advanced fiber reinforced composite rings (very long cylindrical shells), whose response is dominated by the interlaminar or transverse (primarily shear) deformation. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element, and is based on the assumption of layerwise linear displacements distribution through thickness (LLDT) or linear displacements distribution through thickness (LDT), is utilized in the analysis of afore-mentioned cross-ply ring or thin homogeneous isotropic cylindrical shell, respectively. Hitherto unavailable numerical results pertaining to the two cases are also presented.
Free flexural vibration behavior of bimodular material angle-ply laminated composite plates
Journal of Sound and Vibration
286
1-2
167-186
2005
10.1016/j.jsv.2004.10.004
In this paper, the free flexural vibration behavior of bimodular laminated angle-ply composite plates is studied. The formulation is based on the theory that accounts for the transverse shear and transverse normal deformations, and incorporates higher order through the thickness approximations of the in-plane and transverse displacements. The governing equations obtained using Lagrange's equations of motion are solved through the finite element approach. A detailed parametric study is carried out to study the influences of plate geometry, lay-up, ply-angle and material properties on the free flexural vibration response and frequencies, neutral surface locations and mode shapes of bimodulus angle-ply composite laminated plates. ?? 2004 Elsevier Ltd. All rights reserved.
Analysis of thin-walled composite box beam under torsional load without external restraint
Thin-Walled Structures
40
4
385-397
2002
10.1016/S0263-8231(01)00064-7
A procedure for analyzing the mechanical behavior of laminated thin-walled composite box beam under torsional load without external restraint is presented. The method is based on the theory of composite laminated plates and is deduced by means of the free torsion theory of thin-walled beams, which makes the procedure simple and practical. In the present theory, the stresses are considered distributing unequally along the wall thickness and various coupling effects are taken into account. The calculation formulas of torsional angle and stress given by this method are concise and easy to use. The present analysis results indicate that by reason of coupling effects, in general, the free torsion of composite box beams may not exist definitely, so a concept of torsion without external restraint is suggested. Finally, the examples are given and their numerical results are analyzed and discussed. The values of torsional angle, ply stresses (including their variation with the off-axis ply angle) obtained by this paper are compared with those obtained by model test or finite element method (FEM). ?? 2002 Published by Elsevier Science Ltd.
Composite box beam; The theory of composite laminated plates; Torsion without external restraint
Mechanics of Rubber Bearings for Seismic and Vibration Isolation
Mechanics of Rubber Bearings for Seismic and Vibration Isolation
2011
10.1002/9781119971870
Widely used in civil, mechanical and automotive engineering since the early 1980s, multilayer rubber bearings have been used as seismic isolation devices for buildings in highly seismic areas in many countries. Their appeal in these applications comes from their ability to provide a component with high stiffness in one direction with high flexibility in one or more orthogonal directions. This combination of vertical stiffness with horizontal flexibility, achieved by reinforcing the rubber by thin steel shims perpendicular to the vertical load, enables them to be used as seismic and vibration isolators for machinery, buildings and bridges.
Print ISBN: 9781119994015\r\nePDF ISBN: 978111997188
Intermediate mechanics of materials
Solid Mechanics and its Applications
175
1978
1-633
2011
10.1007/978-94-007-0295-0_1
This book covers the essential topics for a second-level course in strength of materials or mechanics of materials, with an emphasis on techniques that are useful for mechanical design. Design typically involves an initial conceptual stage during which many options are considered. At this stage, quick approximate analytical methods are crucial in determining which of the initial proposals are feasible. The ideal would be to get within 30% with a few lines of calculation. The designer also needs to develop experience as to the kinds of features in the geometry or the loading that are most likely to lead to critical conditions. With this in mind, the author tries wherever possible to give a physical and even an intuitive interpretation to the problems under investigation. For example, students are encouraged to estimate the location of weak and strong bending axes and the resulting neutral axis of bending before performing calculations, and the author discusses ways of getting good accuracy with a simple one degree of freedom Rayleigh-Ritz approximation. Students are also encouraged to develop a feeling for structural deformation by performing simple experiments in their outside environment, such as estimating the radius to which an initially straight bar can be bent without producing permanent deformation, or convincing themselves of the dramatic difference between torsional and bending stiffness for a thin-walled open beam section by trying to bend and then twist a structural steel beam by hand-applied loads at one end. In choosing dimensions for mechanical components, designers will expect to be guided by criteria of minimum weight, which with elementary calculations, generally leads to a thin-walled structure as an optimal solution. This consideration motivates the emphasis on thin-walled structures, but also demands that students be introduced to the limits imposed by structural instability. Emphasis is also placed on the effect of manufacturing errors on such highly-designed structures - for example, the effect of load misalignment on a beam with a large ratio between principal stiffness and the large magnification of initial alignment or loading errors in a strut below, but not too far below the buckling load.
Brownian motion in thin sheets of viscous fluid
Journal of Fluid Mechanics
73
593
1976
10.1017/S0022112076001511
The drag on a cylindrical particle moving in a thin sheet of viscous fluid is calculated. It is supposed that the sheet is embedded in fluid of much lower viscosity. A finite steady drag is obtained, which depends logarithmically on the ratio of the viscosities. The Einstein relation is used to determine the diffusion coefficient for Brownian motion of the particle, with application to the movement of molecules in biological membranes. In addition, the Brownian motion is calculated using the Langevin equation, and a logarithmically time-dependent diffusivity is obtained for the case when the embedding fluid has zero viscosity.
Optimal design of laminated composite structures with ply drops using stacking sequence tables
Composite Structures
107
559-569
2014
10.1016/j.compstruct.2013.08.030
This article introduces the concept of stacking sequence table (SST) for the optimal design of laminated composite structures with ply drops. The SST describes the sequence of ply-drops ensuring the transition between a thick guide laminate and a thinner one. A blended design is represented by a SST combined with a thickness distribution over the regions of the structure. An evolutionary algorithm is specialized for SST-based blending optimization. Optimization of the sequence of ply-drops with the proposed algorithm enables satisfying design guidelines that could not have been considered in previous studies. An extensive set of design guidelines representative of the actual industrial requirements is introduced. The method is applied to an 18-panel benchmark problem from the literature with convincing results. In particular, the present results show that strength-related guidelines can be enforced without significantly penalizing the stiffness behavior and consequently the mass of the structure. © 2013 Elsevier Ltd.
Blending; Composite laminate; Evolutionary optimization; Stacking sequence table (SST)
Development of transverse cracking in cross-ply laminates during fatigue tests
Composites Science and Technology
61
12
1711-1721
2001
10.1016/S0266-3538(01)00068-9
The purpose of this paper is to analyse the progressive development of transverse cracking in cross-ply laminates subjected to uniaxial fatigue tests. First, a finite-element analysis shows how an analytical model which considers a progressive shear through the thickness of the O° layers can be used for evaluating the stress field in the case of progressive cracking across the specimen width. The paper then presents a simulation of the progression of the transverse cracking, based on statistical distributions along the specimen length for crack initiation and across the specimen width for crack growth across the specimen width. The simulation process is applied to glass-fibre/epoxy cross-ply laminates and the results obtained are compared with experimental results. © 2001 Published by Elsevier Science Ltd. All rights reserved.
A. Cross-ply laminates; B. Fatigue; C. Transverse cracking
Mechanics of Foamed Elastic Materials
Rubber Chemistry and Technology
36
3
597-610
1963
10.5254/1.3539591
Abstract The deformation of a foamed elastic material, both in tension and compression, and its resistance to tearing and to tensile rupture, have recently been derived on the basis of a model consisting of a large number of thin threads joined at their ends to form a three-dimensional network. A general account of this theoretical treatment, and the evidence for it, is presented. The theory is extended to deal with small deformations of closed-cell foams; relations for Young's modulus and Poisson's ratio are derived. The viscous damping of open-cell foams due to air flow through the network of threads is also discussed.
Bending mechanics and mode selection in free subduction: a thin-sheet analysis
Geophysical Journal International
180
2
559-576
2010
DOI 10.1111/j.1365-246X.2009.04460.x
To elucidate the dynamics of free (buoyancy-driven) subduction of oceanic lithosphere, I study a model in which a 2-D sheet of viscous fluid with thickness h and viscosity gamma eta(1) subducts in an infinitely deep ambient fluid with viscosity eta(1). Numerical solutions for the sheet's evolution are obtained using the boundary-element method (BEM), starting from an initial configuration comprising a short 'protoslab' attached to a longer horizontal 'plate' that is free to move laterally beneath an impermeable traction-free surface. Interpretation of the solutions using thin viscous sheet theory shows that the fundamental length scale controlling the subduction is the 'bending length' l(b), defined at each instant as the length of the portion of the sheet's midsurface where the rate of change of curvature is significant. Geophysically speaking, l(b) is the sum of the lengths of the slab and of the region seaward of the trench where flexural bulging occurs. The bending length in turn enters into the definition of the sheet's dimensionless 'stiffness' S equivalent to gamma(h/l(b))3, which controls whether the sinking speed of the slab is determined by the viscosity of the sheet itself (S 1) or by that of the ambient fluid (S < 1). Motivated by laboratory observations of different modes of subduction (retreating versus advancing trench, folding versus no folding, etc.) in fluid layers with finite depth, I calculate numerically the dip theta(D) of the slab's leading end as a function of gamma and the normalized depth D/h to which it has penetrated. The contours of the function theta(D)(gamma, D/h) strongly resemble the intermode boundaries in the laboratory-based regime diagram of Schellart, supporting the hypothesis that the mode of subduction observed at long times in experiments is controlled by the dip of the slab's leading end when it reaches the bottom of the layer. In particular, the BEM solutions explain why trenches advance in the laboratory only when gamma lies in an intermediate range, and why they retreat when gamma is either smaller or larger than this. Application of the BEM model to Wu et al.'s compilation of the minimum curvature radii of subducted slabs suggests gamma is an element of [140, 510] for the Earth. This is too small to permit the laboratory-type 'trench advancing' mode, in agreement with the lack of tomographic evidence for slabs that are 'bent over backwards'.
dynamics; dynamics of lithosphere and mantle; insights; laboratory experiments; lithosphere; lower-mantle; mechanics, theory, and modelling; plate motions; slab penetration; subduction zone processes; trench migration; viscous sheets; zones
Thermal buckling of cross-ply laminated composite shallow shells according to a global higher-order deformation theory
Composite Structures
81
2
210-221
2007
10.1016/j.compstruct.2006.08.008
A two-dimensional global higher-order deformation theory is presented for the evaluation of critical temperatures in cross-ply laminated composite shallow shells subjected to thermal loading. The effects of prebuckling deformations of the shells subjected to a temperature change that is independent of the in-plane coordinates are taken into account in the present analysis. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses are derived through the principle of virtual work. Several sets of truncated Mth order approximate theories are applied to solve the thermal buckling problems of a simply supported multilayered shell. Critical temperatures are shown for two cases of including the effects of prebuckling displacements and neglecting these effects. The modal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. The present results are verified to be accurate enough for cross-ply laminated composite shallow shells through the convergence study and energy balance computations. ?? 2006 Elsevier Ltd. All rights reserved.
Critical temperature; Cross-ply laminated composite shells; Global higher-order deformation theory; Orthotropic materials; Thermal buckling
Numerical investigation of the ballistic efficiency of multi-ply fabric armours during the early stages of impact
International Journal of Impact Engineering
34
1
71-88
2007
10.1016/j.ijimpeng.2006.07.001
The early impact behaviour of single and multi-ply Kevlar® 129 fabric armour systems is investigated using an explicit finite element code, TEXIM, developed in-house. This numerical model is carefully validated using continuous temporal data obtained from an instrumented experimental setup. The model is then used to explore the loss in ballistic efficiency of woven fabric targets, as experienced early in the impact event, when either the number of layers in the panel or the yarn denier is increased.
Ballistic response; Discrete pin-jointed model; Energy absorption; Multi-layer woven fabrics; Wave propagation
Effect of Curing Stresses on the First Ply-failure in Composite Laminates
Journal of Composite Materials
13
1
2-16
1979
10.1177/002199837901300101
This paper describes an experimental technique of detecting the first ply-failure in laminated composites using a combination of long strain gages and acoustic emission measurement.
Why were Matrix Mechanics and Wave Mechanics considered equivalent?
Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
39
2
444-461
2008
10.1016/j.shpsb.2008.01.004
A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schr??dinger's 1926 proof, a myth. Schr??dinger supposedly failed to prove isomorphism, or even a weaker equivalence ("Schr??dinger-equivalence") of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent on this equivalence, was deemed a myth as well. In response, I argue that Schr??dinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schr??dinger in his first and second communications of 1926. Schr??dinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schr??dinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schr??dinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it. ?? 2008 Elsevier Ltd. All rights reserved.
Equivalence; Isomorphism; Matrix Mechanics; Niels Bohr's atom; Quantum Mechanics; Wave Mechanics
Cardiac thin filament regulation
Pflugers Archiv European Journal of Physiology
457
1
37-46
2008
10.1007/s00424-008-0511-8
Myocardial contraction is initiated upon the release of calcium into the cytosol from the sarcoplasmic reticulum following membrane depolarization. The fundamental physiological role of the heart is to pump an amount blood that is determined by the prevailing requirements of the body. The physiological control systems employed to accomplish this task include regulation of heart rate, the amount of calcium release, and the response of the cardiac myofilaments to activator calcium ions. Thin filament activation and relaxation dynamics has emerged as a pivotal regulatory system tuning myofilament function to the beat-to-beat regulation of cardiac output. Maladaptation of thin filament dynamics, in addition to dysfunctional calcium cycling, is now recognized as an important cellular mechanism causing reduced cardiac pump function in a variety of cardiac diseases. Here, we review current knowledge regarding protein-protein interactions involved in the dynamics of thin filament activation and relaxation and the regulation of these processes by protein kinase-mediated phosphorylation.
Actin; Cardiac function; Muscle mechanics; Myocardial contractility; Thin filament; Troponin
A Layerwise Shear Deformation Theory for Two-Layered Cross-Ply Laminated Plates
Mechanics of Advanced Materials and Structures
7
4
331-353
2000
10.1080/10759410050201690
A layerwise trigonometric shear deformation theory for flexural analysis\nof two-layered laminated plates, taking into account transverse shear\ndeformation effects, is presented. The present theory has only three\nvariables, that is, two variables less than those in the first-order\nshear deformation theory. The displacement field uses a sinusoidal\nfunction in terms of thickness coordinate to represent the shear\ndeformation. The noteworthy feature of the theory is that the transverse\nshear stresses can be obtained directly from the use of constitutive\nrelations with reasonable accuracy, satisfying the shear stress free\nsurface conditions at the top and bottom surfaces of the plate and\ncontinuity conditions at interface between the layers. The transverse\nshear stresses can also be obtained, with better accuracy, by integrating\nequilibrium equations. The theory obviates the need for a shear correction\nfactor. The governing equations and boundary conditions are obtained\nusing the principle of virtual work. A two-layered cross-ply laminated\nplate is considered for the numerical study to demonstrate the efficacy\nof the theory. The results obtained using the present theory are\ndiscussed critically with those of other theories and are found to\nagree well with the exact elasticity results.
Mechanics of bacteriophage maturation
Proceedings of the National Academy of Sciences
109
7
2342-2347
2012
10.1073/pnas.1109590109
Capsid maturation with large-scale subunit reorganization occurs in virtually all viruses that use a motor to package nucleic acid into preformed particles. A variety of ensemble studies indicate that the particles gain greater stability during this process, however, it is unknown which material properties of the fragile procapsids change. Using Atomic Force Microscopy-based nano-indentation, we study the development of the mechanical properties during maturation of bacteriophage HK97, a λ-like phage of which the maturation-induced morphological changes are well described. We show that mechanical stabilization and strengthening occurs in three independent ways: (i) an increase of the Young's modulus, (ii) a strong rise of the capsid's ultimate strength, and (iii) a growth of the resistance against material fatigue. The Young's modulus of immature and mature capsids, as determined from thin shell theory, fit with the values calculated using a new multiscale simulation approach. This multiscale calculation shows that the increase in Young's modulus isn't dependent on the crosslinking between capsomers. In contrast, the ultimate strength of the capsids does increase even when a limited number of cross-links are formed while full crosslinking appears to protect the shell against material fatigue. Compared to phage λ, the covalent crosslinking at the icosahedral and quasi threefold axes of HK97 yields a mechanically more robust particle than the addition of the gpD protein during maturation of phage λ. These results corroborate the expected increase in capsid stability and strength during maturation, however in an unexpected intricate way, underlining the complex structure of these self-assembling nanocontainers.
Contact Mechanics
Handouts
1-8
1985
10.1017/CBO9781139171731
What is Contact Mechanics? The two different kind of contacts. Boussinesq and Cerruti Potential Functions The specific case of an Applied Normal Force Hertz Equations- Derivation, Assumptions Rigid Sphere Contacting a Deformable Plate Deformable Sphere Contacting a Rigid Plate
Tuning heterogeneous poly(dopamine) structures and mechanics: in silico covalent cross-linking and thin film nanoindentation.
Soft matter
10
3
457-64
2014
10.1039/c3sm51810h
Mussel-inspired synthetic poly(dopamine) thin films from dihydroxyphenylalanine (DOPA) and lysine, structurally similar to natural melanin, have drawn extensive interest as a versatile surface functionalization and coating material for use in a broad range of applications. In order to gain a better understanding of its complex and heterogeneous polymeric structure and mechanical properties, we report a computational model of poly(dopamine) by mimicking the polymerization process of the intermediate oxidized product of dopamine, 5,6-dihydroxyindole (DHI), via controlled in silico covalent cross-linking under the two most possible reaction schemes proposed in experiments. To validate our results using experiment, we synthesize poly(dopamine) thin films and perform experimental nanoindentations on the film. We observe an overall linear behavior for Young's modulus as a function of the degree of cross-linking, demonstrating the possibility of enhancing the mechanical robustness of poly(dopamine) materials by increasing the extent of polymerization. At the highest degree of polymerization considered (70%), the model mimics the linear tetrameric model for poly(dopamine) and melanin. At this degree of polymerization, we find a Young's modulus of 4.1-4.4 GPa, in agreement with our nanoindentation results of 4.3-10.5 GPa, previous experiments for natural melanin, as well as simulation results for the cyclic tetrameric melanin model (Chen et al., ACS Nano, 2013). Our results suggest that the non-covalent DHI aggregate model might not be appropriate to represent the structure of poly(dopamine) and melanin-like materials, since it gives a much smaller Young's modulus than the experimental lower bound. Our model not only nicely complements the previous computational work, but also provides new computational tools to study the heterogeneous structural and physicochemical properties of poly(dopamine) and melanin, as well as their formation pathways.
Dihydroxyphenylalanine; Dihydroxyphenylalanine: chemistry; Dihydroxyphenylalanine: metabolism; Elastic Modulus; Indoles; Indoles: chemistry; Indoles: metabolism; Lysine; Lysine: chemistry; Lysine: metabolism; Melanins; Melanins: chemistry; Melanins: metabolism; Polymers; Polymers: chemistry; Polymers: metabolism
A discrete model of thin shells
ACM Symposium on Computer Animation
62--67
2003
10.1145/1198555.1198663
In this paper we introduce a discrete shell model describing the behavior of thin flexible structures, such as hats, leaves, and aluminum cans, which are characterized by a curved undeformed configuration. Previously such models required complex continuum mechanics formulations and correspondingly complex algorithms. We show that a simple shellmodel can be derived geometrically for trianglemeshes and implemented quickly bymodifying a standard cloth simulator. Our technique convincingly simulates a variety of curved objects with materials ranging from paper to metal, as we demonstrate with several examples including a comparison of a real and simulated falling hat.
Influence of Interface Ply Orientation on Fatigue Damage of Adhesively Bonded Composite Joints
Journal of Composites Technology & Research
8
1
3-7
1986
An experimental study of cracked-lap-shear specimens was conducted to determine the influence of adherend stacking se quence on debond initiation and damage growth in a composite-to composite bonded joint. Specimens consisted of quasi-isotropic graph ite/epoxy adherends bonded together with either FM-300 or EC 3445 adhesives. The stacking sequence of the adherends was varied such that 0°, 45°, or 90° plies were present at the adherend-adhesive interfaces. Fatigue damage initiated in the adhesive layer in those specimens with 0° and 45° interface plies. Damage initiated in the form of ply cracking in the strap ·adherend for the specimens with 90° interface plies. The fatigue-damage growth was in the form of delamination within the com posite adherends for specimens with the 90° and 45° plies next to the adhesive, while debonding in the adhesive resulted for the specimens with 0° plies next to the adhesive. Those joints with the 0° and 45° plies next to either adhesive had essentially the same fatigue-damage-initia tion stress levels. These stress levels were 13 and 71% higher, respec tively, than those for specimens with 90° plies next to the EC 3445 and FM-300 adhesives.
adhesivebonding; composite materials; debonding; delamination; fatigue (materials); fracture mechanics; stacking sequence
A large deformation–small strain formulation for the mechanics of geometrically exact thin-walled composite beams
Thin-Walled Structures
84
443-451
2014
10.1016/j.tws.2014.05.014
This work presents a new formulation of the geometrically exact thin walled composite beam theory. The formulation assumes that the beam can undergo arbitrary kinematical changes while the strains remain small, thus compatibilizing the hypotheses of the strain measure and the constitutive law of the composite material. A key point of the formulation is the development of a pure small strain measure written solely in terms of scalar products of position and director vectors; the latter is accomplished through the obtention of a generalized small strain vector by decomposition of the deformation gradient. The resulting small strain measure is objective under rigid body motion. The finite element implementation of the proposed formulation is simpler than the finite strain theory implementation previously developed by the authors. Numerical experiments show that the present formulation is very accurate and computationally more efficient than the finite strain formulation, thus it is more convenient for most practical applications.
Composite beams; Finite elements; Finite rotations; Thin-walled beams; Wind turbines
Crack Development in Graphite-epoxy Cross-ply Laminates Under Uniaxial Tension
Composites Science and Technology
24
1-31
1985
10.1016/0266-3538(85)90058-2
When a graphite-epoxy laminate ofcross-ply (0/90) lamination is subjected to uniaxial tension, transverse cracks in the 90° ply can be induced at strains as low as 0·3% .These cracks will continue to form in increasing numbers if the applied tension increases. At some late stage of loading, and before the breaking of fibers in the 0° ply, several other matrix-dominant cracking modes may emerge. All seem to be precipitated by the transverse cracks. The late-stage matrix cracks propagate individually in a stable manner, but can coalesce and thus cause disintegration of the laminate. The objective of this paper is to describe analytically the various cracking events in the cross-ply laminates as they occur during the course of loading. The particular laminates considered belong to the [0 2/90n]1, n = 1, 2 and 4, family. Emphasis is placed on determining why a certain mode of cracking occurs while some other modes do not. Especially for the cracking modes which occur during late-stage loading, an analysis will be made to explain why they are critical to the final strength of the laminate. The analytical results are compared with experiments on laminates made from a graphite-epoxy system.
Numerical approach to the interlaminar crack formation process in cross-ply laminates due to transverse loading
Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
62
593
18-25
1996
Interlaminar crack extension in continuous fiber-reinforced laminates due to accidental transverse loading is one of the most serious problems in actual service applications of this kind of composite. Here we attempt to numerically obtain the relation between the in-plane two-dimensional extent of interlaminar cracks and the transverse load applied to the laminate by quasi-static indentation. Our attention is focused on the local energy release rate along the interlaminar crack front. The two-dimensional multi-layered finite-element method is developed, which employs two-dimensional bending elements of each lamina stacked to represent the laminate. This FEM enables us to easily estimate the energy release rate at any point on the interlaminar crack front. Under the condition of a constant critical energy release rate, we carry out the computational simulation of interlaminar crack extension for the case of a three-layered cross-ply laminate. Simulated extension behavior of interlaminar cracks under increasing indentation load appears to be in good agreement with the experimental observations.
Computer simulation; Crack propagation; Cross ply laminates; Fiber reinforced materials; Finite element method; Fracture mechanics; Interlaminar crack formation; Laminated composites; Loads (forces); Multilayered finite element method; Transverse loading
Two-scale convergence for thin domains and its applications to some lower-dimensional models in fluid mechanics
Asymptotic Analysis
23
1
23-57
2000
Inspired by the similar ideas from the homogenization theory, in this paper we introduce the notion of two-scale convergence for thin domains that allow lower-dimensional approximations. We prove the compactness theorem, analogous to the one in homogenization theory. Using those results we derive the lower-dimensional models for potential flow in thin (possibly degenerated) pipe, the degenerated Reynold's equation for viscous flow in degenerated thin domain and the 1-dimensional approximation for the non-Newtonian (power-law) flow in a thin pipe.
Dynamics and stability of thin liquid films
Reviews of Modern Physics
81
3
1131-1198
2009
10.1103/RevModPhys.81.1131
The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.
Short-Term Plyometric Training Improves Running Economy in Highly Trained Middle and Long Distance Runners
The Journal of Strength & Conditioning Research
20
4
947-954
2006
10.1519/R-18235.1
Saunders, P.U., R.D. Telford, D.B. Pyne, E.M. Peltola, R.B. Cunningham, C.J. Gore, and J.A. Hawley. Short-term plyometric training improves running economy in highly trained middle and long distance runners. J. Strength Cond. Res. 20(4): 947–954. 2006.—Fifteen highly trained distance runners (V˙ O2max 71.1 6.0 ml·min1·kg1, mean SD) were randomly assigned to a plyometric training (PLY; n 7) or control (CON; n 8) group. In addition to their normal training, the PLY group undertook 3 30 minutes PLY sessions per week for 9 weeks. Running economy (RE) was assessed during 3 4 minute treadmill runs (14, 16, and 18 km·h1), followed by an incremental test to measure V˙ O2max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km·h1 (4.1%, p 0.02), but not at 14 or 16 km·h1. This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p 0.09), and a lower V˙ O2-speed slope (14%, p 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or V˙ O2max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics.
Crescent singularities and stress focusing in a buckled thin sheet: mechanics of developable cones.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
60
5 Pt B
6091-103
1999
10.1103/PhysRevE.60.6091
The localization of deformation is a simple consequence of the fact that bending a thin sheet is energetically cheaper than stretching it. In this paper we investigate conical singularities that appear on a crumpled sheet and called developable cones (d cones). We found that for a sample of a finite thickness the singularity is never pointlike but has a spatial extension in the form of a crescent. A further deformation of the d cone leads to a transition to a plastic deformation equivalent to a decrease in the singularity size characterized from curvature and profile analysis. The crescent radius of curvature is measured both at small deformations and at large deformations. It is found that, during the buckling process, the curvature of the crescent exhibits two different scalings versus the deformation. From the cone profile, we measured the reaction force of the plate to deformation; and from force measurements, the energy that is necessary to create the singularity is characterized.
Dynamics of thin vortex rings
Journal of Fluid Mechanics
609
319-347
2008
10.1017/S0022112008002292
As part of a long-range study of vortex rings, their dynamics, interactions with boundaries and with each other, we present the results of experiments on thin core rings generated by a piston gun in water. We characterize the dynamics of these rings by means of the traditional equations for such rings in an inviscid fluid suitably modifying them to be applicable to a viscous fluid. We develop expressions for the radius, core size, circulation and bubble dimensions of these rings. We report the direct measurement of the impulse of a vortex ring by means of a physical pendulum.
Determination of GIC in Angle Ply Composites Using a Cantilever Beam Test Method
Journal of Reinforced Plastics and Composites
2
1
2-17
1983
10.1177/073168448300200101
This paper discusses a study conducted to determine the changes that occurred when the crack was initiated between angle plies in an angle ply laminate. A double cantilever beam test is used to measure G//I//C values in angle ply composites. It is demonstrated that the G//I//C values determined with this method are independent of the compliance of the specimen. In the angle ply composites, four different crack morphologies are observed, each with different G//I//C values associated with crack growth
Hamiltonian Fluid Mechanics
Annual Review of Fluid Mechanics
20
225-256
1988
10.1146/annurev.fluid.20.1.225
... The particle-relabeling symmetry property corresponds, by Noether's theorem, to a conservation ... Asymptotic approximations, conservation laws , stability the orems, and useful variable transformations all ... The utility of Hamiltonian methods seems to originate from several factors. ...
Advanced Fracture Mechanics
Journal of Engineering Materials and Technology
108
2
199
1986
10.1115/1.3225862
This book presents an extensive, unified, and up-to-date approach to the still developing subject of fracture mechanics from an applied mechanics perspective. Progressing from the simple to the more advanced topics, it goes beyond the well developed area of linear elastic fracture mechanics to consider the dynamic and elastic-plastic regimes, and in doing so, extends the subject into a broader range of realistic engineering applications.
Natural vibration analysis of symmetrical cross-ply laminated plates using a mixed variational formulation
European Journal of Mechanics - A/Solids
19
3
469-485
2000
10.1016/S0997-7538(00)00169-8
A mixed variational formulation based upon Hamilton's principle and Lagrange's multipliers is generally obtained to deduce the governing equations of laminated composite structures. The additional work, as a function of stresses only, is introduced in the variational statement by using Legendre's transformation. A rational higher-order displacement-based two-dimensional theory for the analysis of laminated plates is presented. This theory is established using the mixed variational formulation to study the vibration behaviour of symmetric laminated orthotropic plates subjected to normal traction fields. The accuracy of the present theory is demonstrated via a bending problem for which the exact solution is available. Natural frequencies are obtained according to the classical, first- and higher-order plate theories. The effects of boundary conditions, transverse shear, aspect ratio, orthotropy ratio, and number of layers on natural frequencies are investigated. The obtained results are compared with other exact results available in the field literature. (C) 2000 Editions scientifiques et medicales Elsevier SAS.
An experimental investigation of the sequence effect in block amplitude loading of cross-ply composite laminates
International Journal of Fatigue
24
2-4
437-446
2002
10.1016/S0142-1123(01)00099-8
The Palmgren-Miner rule has been shown to be inexact in many cases for various composite materials. Several empirical models have been conceived to account for this discrepancy, as well as the effect of block sequence. The approach taken here is based on the underlying mechanisms. A cross-ply laminate was used as a model material. In general, composites show both initiatory and progressive mechanisms under fatigue loading. The former is active at high static stresses, whereas the latter predominates at lower stress amplitudes where they are given sufficient time to propagate, Initiatory mechanisms give rise to damage from which the progressive mechanisms can start, and conversely the progressive mechanisms continually alter the local stress state which results in further damage accumulation caused by the initiation controlled mechanisms. In a cross-ply laminate, the initiatory mechanism is the formation of transverse cracks, and the progressive mechanism is mainly delamination growth initiated from the transverse cracks. In an experimental investigation of carbon fiber/epoxy cross-ply laminates, the interaction of these mechanisms has shown why a sequence of high-low amplitude levels results in shorter lifetimes than a low-high order. Such a sequence effect seems to be a common behavior for many other composite materials, and can be mechanistically explained by a similar kind of interaction. Advantages and drawbacks of the mechanistic approach compared with empirical rules are also discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.
block loading; CRACKING; cross-ply laminates; damage mechanisms; DELAMINATION; FATIGUE LIFE; fractography; GROWTH; INITIATION; LIFE PREDICTION; MODEL; polymer matrix composites; sequence effect; STRENGTH; variable amplitude fatigue
Thickness dependence of cracking resistance in thin aluminium plates
Journal of the Mechanics and Physics of Solids
47
10
2093-2123
1999
10.1016/S0022-5096(99)00011-3
The influence of thickness on the fracture toughness of aluminium 6082T0 thin plates of 1-6 mm thicknesses was studied experimentally and numerically from tensile testing of cracked DENT specimens. Results are discussed in terms of the observations of critical J-integral, critical CTOD and essential work of fracture.
A shear-locking free robust isoparametric three-node triangular finite element for moderately-thick and thin arbitrarily laminated plates
Computers & Structures
57
4
589-597
1995
http://dx.doi.org/10.1016/0045-7949(95)00071-N
A shear-locking free robust isoparametric three-node triangular finite element is developed for advanced fiber-reinforced arbitrarily laminated moderately-thick and thin plates. The strain-displacement relations are based on Reissner and Mindlin plate theory that accounts for transverse shear deformations into the plate formulation. A shear correction term is introduced into the finite element formulation to circumvent the shear locking effect. Numerical results, for illustration purposes, are presented for a simply-supported plate with cross-ply laminations subjected to uniform transverse loads, constituting study of convergence and shear locking effects on transverse displacement and moment, and their variations for various parametric effects.
First ply failure analysis of laminated stiffened plates
Composite Structures
2003
10.1016/S0263-8223(02)00350-1
A new laminated stiffened plate element is presented for the first ply failure analysis of laminated stiffened plates. The plate element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffener. Therefore the mesh generation is no longer constrained by the disposition of the stiffener and a computationally economic mesh can be generated without any loss of accuracy. The first ply failure loads of cross-ply stiffened plates is estimated with the present formulation under uniformly distributed load and sinusoidal load using various prominent failure theories and compared with the published results. The results are found to be in good agreement. A few parametric studies are carried out on laminated plates stiffened with blade, I- and hat section stiffeners for varying fibre angles ranging from 15?? to 75??. ?? 2002 Elsevier Science Ltd. All rights reserved.
Finite element analysis; First ply failure; Laminates; Stiffened plates
Numerical study of the mechanics of indentation bending tests of thin membranes and inverse materials parameters prediction
Computational Materials Science
52
1
123-127
2012
10.1016/j.commatsci.2011.03.025
Indentation bending tests are an important testing method for thin rubber-like materials. The choice of material laws in finite element (FE) simulations of the test directly influences the accuracy of the numerical model and material properties predicted through inverse FE modelling. In this work, the effect of using a linear elastic or hyperelastic model on the material parameters predicted from indentation bending tests of a thin rubber sheet over a low strain range were studied. An inverse program has been developed based on the Kalman filter method to predict the material properties from experimental tests and to assess the uniqueness of the converged results for different material models. The predicted results were compared to standard tests carried out on the same material. Results showed that the Young's modulus of the material with the linear elastic model can be accurately predicted while the converged parameters (C\n 10 and C\n 01) for the Mooney-Rivlin model were not unique; data analysis showed that parameters C\n 10 and C\n 01 of the converged data were associated with the shear modulus of the material. ?? 2011 Elsevier B.V. All rights reserved.
Deformation limits for corrugated cross-ply laminates
Composite Structures
92
6
1458-1468
2010
10.1016/j.compstruct.2009.11.015
This work determines the maximal possible deformations of a corrugated sheet where the corrugation pattern consists of two circular segments. The influence of the lay-up of cross-ply laminates and the influence of the geometry is investigated. The calculations are based on considerations of layerwise strains that are calculated with the help of an analytical singly-curved shell model. For the evaluation of the influence of geometric nonlinearities according finite element simulations are performed and compared to the linear strain limit calculations. The influence of scalable geometry parameters is also investigated. ?? 2009 Elsevier Ltd. All rights reserved.
Composite laminates; Corrugated sheets; Deformation limit; Homogenization model; Shell theory
Acoustic emission monitoring of degradation of cross ply laminates.
The Journal of the Acoustical Society of America
127
6
EL246-L251
2010
10.1121/1.3425752
The scope of this study is to relate the acoustic activity of damage in composites to the failure mechanisms associated with these materials. Cross ply fiber reinforced composites were subjected to tensile loading with recording of their acoustic activity. Acoustic emission (AE) parameters were employed to monitor the transition of the damage mechanism from transverse cracking (mode I) to delamination (mode II). Wave propagation measurements in between loading steps revealed an increase in the relative amplitude of the propagated wave, which was attributed to the development of delamination that confined the wave to the top longitudinal plies of the composite.
Principles of Quantum Mechanics
American Journal of Physics
20
7
460
1952
10.1119/1.1933288
Reviews from the First Edition: "An excellent text &8230; The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist) "No matter how gently one introduces students to the concept of Dirac&8217;s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin) Reviews of the Second Edition: "This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details--all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. &8230; It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews) R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book&8217;s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.
Engineering Mechanics: Statics
Applied Mechanics Reviews
55
1
B7
2002
10.1115/1.1445323
Focusing on the conceptual understanding of mechanics, this exciting new text addresses developments in the methods of analyzing mechanics problems. It fully incorporates the highly sophisticated computational software packages currently available to students. The text provides transition material to higher level courses, as well as a wealth of problems to foster understanding. All sample problems and the use of computational software (Mathcad, MATLAB, Mathematica and Maple) are presented in four separate manuals (one for each software program). Each manual explains how to use the software package to solve the example problems in the book.
Free-Vibration of Fiber-Composite Thin Shells in a Hot Environment
Journal of Reinforced Plastics and Composites
14
2
143-163
1995
Results are presented of parametric studies to assess the effects of various parameters on the free vibration behavior (natural frequencies) of [+/-theta](2) angle-ply fiber composite thin shells in a hot environment. These results were obtained by using a three-dimensional finite element structural analysis computer code. The fiber composite shell is assumed to be cylindrical and made from T300 graphite fibers embedded in an intermediate-modulus high-strength matrix (IMHS). The residual stresses induced into the laminated structure during the curing are taken into account. The following parameters are investigated: the length and the thickness of the shell, the fiber orientations, the fiber volume fraction, the temperature profile through the thickness of the laminate and the different ply thicknesses. Results obtained indicate that: the fiber orientations and the length of the laminated shell had significant effect on the natural frequencies. The fiber volume fraction, the laminate thickness and the temperature profile through the shell thickness had a weak effect on the natural frequencies. Finally, the laminates with different ply thicknesses had insignificant influence on the behavior of the vibrated laminated shell.
angle-ply laminates; composite structures; computational simulation; fiber composites; finite element analysis; free vibration; high temperature; laminated cylinders; mode shape; moisture; natural frequencies; residual stresses; structural analysis
Mechanics of neutrophil phagocytosis: experiments and quantitative models.
Journal of cell science
119
4
1903-1913
2006
10.1242/jcs.02876
To quantitatively characterize the mechanical processes that drive phagocytosis, we observed the FcgammaR-driven engulfment of antibody-coated beads of diameters 3 mum to 11 mum by initially spherical neutrophils. In particular, the time course of cell morphology, of bead motion and of cortical tension were determined. Here, we introduce a number of mechanistic models for phagocytosis and test their validity by comparing the experimental data with finite element computations for multiple bead sizes. We find that the optimal models involve two key mechanical interactions: a repulsion or pressure between cytoskeleton and free membrane that drives protrusion, and an attraction between cytoskeleton and membrane newly adherent to the bead that flattens the cell into a thin lamella. Other models such as cytoskeletal expansion or swelling appear to be ruled out as main drivers of phagocytosis because of the characteristics of bead motion during engulfment. We finally show that the protrusive force necessary for the engulfment of large beads points towards storage of strain energy in the cytoskeleton over a large distance from the leading edge ( approximately 0.5 microm), and that the flattening force can plausibly be generated by the known concentrations of unconventional myosins at the leading edge.
cell; cell mechanics; finite element simulations; lamella; membrane tension; motility
Optimization of multilaminated structures using higher-order deformation models
Computer Methods in Applied Mechanics and Engineering
149
1-4
133-152
1997
10.1016/S0045-7825(97)00066-2
A refined shear deformation theory assuming a non-linear variation for the displacement field is used to develop discrete models for the sensitivity analysis and optimization of thick and thin multilayered angle ply composite plate structures. The structural and sensitivity analysis formulation is developed for a family of C0 Lagrangian elements, with eleven, nine and seven degrees of freedom per node using a single layer formulation. The design sensitivities of structural response for static, free vibrations and buckling situations for objective and/or constraint functions with respect to ply angles and ply thicknesses are developed. These different objectives and/or constraints can be generalized displacements at specified nodes, Hoffman's stress failure criterion, elastic strain energy, natural frequencies of chosen vibration modes, buckling load parameter or the volume of structural material. The design sensitivities are evaluated either analytically or semi-analytically. The accuracy and relative performance of the proposed discrete models are compared and discussed among the developed elements and with alternative models. A few illustrative test designs are discussed to show the applicability of the proposed models.
Droplet impact on a thin fluid layer
Journal of Fluid Mechanics
542
1-23
2005
10.1017/s0022112005006282
The initial stages of high-velocity droplet impact on a shallow water layer are described, with special emphasis given to the spray jet mechanics. Four stages of impact are delineated, with appropriate scalings, and the successively more important influence of the base is analysed. In particular, there is a finite time before which part of the water in the layer remains under the droplet and after which all of the layer is ejected in the splash jet.
liquid; small deadrise angles; water-entry
Fundamentals of rock mechanics
Tectonophysics
38
3-4
367-368
1977
10.1016/0040-1951(77)90223-2
Widely regarded as the most authoritative and comprehensive book in its field, the fourth edition of Fundamentals of Rock Mechanics includes new and substantially updated chapters to this highly praised text.Extensively updated throughout, this new edition contains substantially expanded chapters on poroelasticity, wave propogation, and subsurface stressesFeatures entirely new chapters on rock fractures and micromechanical models of rock behaviourDiscusses fundamental concepts such as stress and strainOffers a thorough introduction to the subject before expertly delving into a fundamental, self-contained discussion of specific topicsUnavailable for many years, now back by popular demand. An Instructor manual CD-ROM for this title is available. Please contact our Higher Education team at HigherEducation@wiley.com for more information.Reviews:“With this attention to detail, and rigorous adherence to clarity and exactness in description, this edition will consolidate the standing achieved by the earlier editions as a most authoritative and comprehensive book in its field. It will continue to serve as a leading reference work for geoscientists interested in structural geology, tectonics and petrophysics as well as for civil, mining and petroleum engineers.” (Petroleum Geoscience)"...I consider this book to be an invaluable reference for studying and understanding the fundamental science at the base of rock mechanics. I believe this to be a must-have textbook and I strongly recommend it to anyone, student or professional, interested in the subject." (Rock Mechanics and Rock Engineering)"An excellent book, very well presented, and is a must for the shelves of serious engineers and scientists active or interested in the fields of rock mechanics and rock engineering.... Highly recommended." (South African Geographical Journal, 2008)
The whole truth: comparative analysis of diaphragmatic hernia repair using 4-ply vs 8-ply small intestinal submucosa in a growing animal model.
Journal of pediatric surgery
41
3
518-23
2006
10.1016/j.jpedsurg.2005.11.068
BACKGROUND: Diaphragmatic reconstruction remains a challenging problem. There is limited information concerning the use of small intestinal submucosa (SIS) in congenital diaphragmatic hernia repair. A canine model was used to evaluate the use of a SIS patch in diaphragmatic reconstruction.\n\nMETHODS: Eleven beagle puppies (1.6-4.2 kg, 8 weeks old) underwent left subcostal laparotomy, central left hemidiaphragm excision (2 x 7 cm, 50% loss), and reconstruction with a 4-ply group I (n = 5) or 8-ply group II (n = 6) SIS patch. Chest radiographs were taken at time of operation and 3 and 6 months postoperatively. Animals were killed at 6 months. Adhesion formation (both pleural and abdominal), gross visual evaluation of the patch, and histology were compared.\n\nRESULTS: In group I (4-ply), 1 animal died at 3 months from patch deterioration accompanied by stomach herniation that resulted in respiratory failure. In the 4 remaining animals, chest radiographs showed no evidence of herniation or eventration. On physical examination, there was no evidence of chest wall deformity. During gross surgical examination, the 4-ply patches showed thinning, multiple defects, and liver herniation in 3 animals. In 1 pup, the patch was thickened, intact, well incorporated at the repair site, and adherent to the liver and spleen. In group II (8-ply), 1 animal died of cardiopulmonary failure in the early postoperative period. In the other 5 animals, chest radiographs showed evidence of eventration in 1. On gross examination the patch adhered to the liver in all 5 surviving animals. In 4, the patches were thickened, viable, but had some shrinkage. One patch pulled away from the native diaphragm laterally; however, no visceral herniation was present. In the 1 animal with eventration, there was no evidence of a patch. Adhesion scores (AS) were graded and determined by the sum of extent (0-4), type (0-4), and tenacity (0-3). Average abdominal AS in group I was 5.6 +/- 0.8 vs 10.2 +/- 0.2 (P = .079) for group II. Average lung AS was 0.6 +/- 0.6 in group I vs 3.8 +/- 1.1 (P = .0476) for group II. Histological examination showed group II patches had greater collagen deposition with central calcification and mild inflammation within the residual graft, whereas group I patches were much thinner and were composed of granulation tissue without evidence of residual graft.\n\nCONCLUSIONS: These data indicate that 8-ply SIS repair of diaphragmatic defects was superior (80%; 4/5 to 4-ply, 20%; 1/5, success). Organ adherence appears to be necessary for neovascularization of the SIS composite. Eight-ply grafts appear to be more durable and persist for a longer period, which may improve neovascularization. Long-term follow-up to evaluate remodeling characteristics of the patch material is required.
Animals; Disease Models, Animal; Dogs; Hernia, Diaphragmatic; Hernia, Diaphragmatic: congenital; Hernia, Diaphragmatic: surgery; Intestine, Small; Intestine, Small: blood supply; Intestine, Small: transplantation; Neovascularization, Physiologic; Postoperative Complications
Stiffness reduction analysis of cracked cross-ply laminates by using integral equation approach
Engineering Fracture Mechanics
34
1
245-251
1989
10.1016/0013-7944(89)90257-9
The multiple transverse crack problem of [ laminates is considered. Combined with the expansion of series of Fourier-hyperbolic functions the problem is formulated in terms of a singular integral equation. From this solution, stiffness reduction of such laminates is obtained. Through numerical computation, the effects of the crack density and crack length on the Young's modulus of the cracked laminates are given. A comparison is made with the corresponding results obtained by different approach.
Postbuckling characteristics of angle-ply laminated truncated circular conical shells
Communications in Nonlinear Science and Numerical Simulation
13
7
1411-1430
2008
10.1016/j.cnsns.2007.01.001
The postbuckling characteristics of the angle-ply laminated composite conical shells subjected to the torsion, the external pressure, the axial compression, and the thermal loading considering uniform temperature change are studied using the semi-analytical finite element approach. The finite element formulation is based on the first-order shear deformation theory and the field consistency principle. The variations in the stiffness coefficients along the meridional direction due to the changes in the ply-angle and the ply-thickness of the filament wound conical shells are incorporated in the finite element formulation. The nonlinear governing equations are solved using the Newton–Raphson iteration procedure coupled with the displacement control method to trace the prebuckling followed by the postbuckling equilibrium path. The presence of asymmetric perturbation in the form of a small magnitude load spatially proportional to the linear buckling mode shape is considered to initiate the bifurcation of the shell deformation. The influence of semi-cone angle, ply-angle and number of circumferential waves on the prebuckling/postbuckling response of the anti-symmetric angle-ply laminated circular conical shells is investigated.
02.70.Dc; 46.32.+x; 46.70.De; Angle-ply; Conical shell; Critical load; Postbuckling; Semi-analytical finite element; Variation of stiffness coefficients
Effects of matrix and interface on damage in GRP cross-ply laminates
Composites Science and Technology
60
1
9-21
2000
10.1016/S0266-3538(99)00096-2
A study has been made of the transverse cracking behavior of a series of cross-ply laminates with different matrices, fiber coatings (sizes) and fiber volume fractions. On the basis of unpublished results, a correlation was assumed between material effects on leakage pressure in pressure vessels of given stacking sequence and transverse cracking behavior in cross-ply laminates. Mechanisms for crack initiation and growth were studied by optical microscopy. The strain at the onset of transverse cracking, ε\n TOS, increased and the slope, K, of the curve of crack density as a function of strain decreased as the G\n IC of the matrix increased. Improved fiber/matrix adhesion and lower fiber content had similar effects. The properties of polyester-based composites were usually inferior to those of vinylester composites as a consequence of pre-existing debonds and subcritical cracks resulting from microlevel curing stresses. From observations of failure mechanisms one may infer that proof testing of pipes or pressure vessels will increase the extent of subcritical damage in the material.
b; c; fiber content; interface; matrix toughness; micromechanisms; transverse cracking
Lateral buckling analysis of thin-walled laminated composite beams with monosymmetric sections
Engineering Structures
28
14
1997-2009
2006
10.1016/j.engstruct.2006.03.024
Lateral buckling of thin-walled composite beams with monosymmetric sections is studied. A general geometrically nonlinear model for thin-walled laminated composites with arbitrary open cross-section and general laminate stacking sequences is given by using systematic variational formulation based on the classical lamination theory. All the stress resultants concerning bar and shell forces are defined, and nonlinear strain tensor is derived. General nonlinear governing equations are given, and the lateral buckling equations are derived by linearizing the nonlinear governing equations. Based on the analytical model, a displacement-based one-dimensional finite element model is developed to formulate the problem. Numerical examples are obtained for thin-walled composite beams with monosymmetric cross-sections and angle-ply laminates. The effects of fiber orientation, location of applied load, modulus ratio, and height-to-span ratio on the lateral buckling load are investigated. The torsion parameter and a newly-defined composite monosymmetry parameter are also investigated for various cases. ?? 2006 Elsevier Ltd. All rights reserved.
Classical lamination theory; Lateral buckling; Nonlinear theory; Thin-walled composites
A first course in continuum mechanics
Englewood Cliffs, NJ, Prentice-Hall, Inc., 1977. 351 p.
329
1977
10.1017/CBO9780511619571
A first course in continuum mechanics for Physical an Biological Engineers and scientis
Proffesor of applied Mechanics And Bioengineering; San Diego
Lung Mechanics
Anesthesiology
33
2
283
1970
10.1097/00000542-197008000-00026
A modern quantitative study of lung mechanics, relating mathematical modeling and engineering principles to lung function, structure, mechanics, and disease.
Unit cell modelling of textile laminates with arbitrary inter-ply shifts
Composites Science and Technology
72
1
14-20
2011
10.1016/j.compscitech.2011.08.003
Deformation and failure mechanisms of textile laminates are strongly affected by mutual shift of the plies. To model arbitrarily stacked laminate within a traditional framework of multi-scale modelling, one must construct a representative volume element (RVE), which includes all the plies. This is a time consuming and computationally expensive work. As an alternative, the paper suggests a technique that allows setting problems on one unit cell of a single ply, i.e. a volume smaller than RVE of the laminate. The technique approximates the stress field in a ply by combination of stress fields obtained in two additional problems. Boundary conditions (BC) in these problems imitate the interaction of the unit cell with surrounding media. Once these problems are solved, the solution for arbitrary number of plies is composed analytically. The proposed technique respects inter-ply configurations, accounts for the number of plies, distinguishes the ply position, and reproduces the meso stress state with a good accuracy. The technique is validated against reference solutions obtained for the entire laminate. ?? 2011 Elsevier Ltd.
A. Laminate; A. Textile composites; Boundary conditions; C. Multiscale modelling; C. Stress transfer
Inter-ply stitching optimisation of highly drapeable multi-ply preforms
Composites Part A: Applied Science and Manufacturing
71
144-156
2015
10.1016/j.compositesa.2015.01.016
An efficient finite element model has been developed in Abaqus/Explicit to solve highly non-linear fabric forming problems, using a non-orthogonal constitutive relation and membrane elements to model bi-axial fabrics. 1D cable-spring elements have been defined to model localised inter-ply stitch-bonds, introduced to facilitate automated handling of multi-ply preforms. Forming simulation results indicate that stitch placement cannot be optimised intuitively to avoid forming defects. A genetic algorithm has been developed to optimise the stitch pattern, minimising shear deformation in multi-ply stitched preforms. The quality of the shear angle distribution has been assessed using a maximum value criterion (MAXVC) and a Weibull distribution quantile criterion (WBLQC). Both criteria are suitable for local stitch optimisation, producing acceptable solutions towards the global optimum. The convergence rate is higher for MAXVC, while WBLQC is more effective for finding a solution closer to the global optimum. The derived solutions show that optimised patterns of through-thickness stitches can improve the formability of multi-ply preforms compared with an unstitched reference case, as strain re-distribution homogenises the shear angles in each ply.
A. Fabrics/textiles; E. Forming; E. Preform; E. Stitching
Transverse cracking of cross-ply laminates: Part 2. Progressive widthwise cracking
Composites Part A: Applied Science and Manufacturing
27
96
1003-1010
1996
10.1016/1359-835X(96)00064-4
The purpose of the paper is to investigate the progressive transverse cracking across the width of cross-ply laminates, subjected to uniaxial fatigue tests. First a finite element analysis is implemented for a crack partly spanning the width of an elementary cell. The influence of the crack length across the specimen width is studied. Then, it is shown how the results can be used in the case of a random distribution of transverse cracks observed in fatigue tests. Copyright ?? 1996 Elsevier Science Ltd.
Analytical models; Crack distributions; Cross-ply laminates; Damage accumulation; Finite element analysis; Progressive transverse cracking
Asymptotic analysis of the non-linear behavior of long anisotropic tubes
International Journal of Non-Linear Mechanics
34
6
1003-1018
1999
10.1016/S0020-7462(98)00070-5
An asymptotically correct beam model is obtained for a long, thin-walled,\ncircular tube with circumferentially uniform stiffness (CUS) and\nmade of generally anisotropic materials. By virtue of its special\ngeometry certain small parameters cause unusual non-linear phenomena,\nsuch as the Brazier effect, to be exhibited. The model is constructed\nwithout ad hoc approximations from 3D elasticity by deriving its\nstrain energy functional in terms of generalized 1D strains corresponding\nto extension, bending, and torsion. Large displacement and rotation\nare allowed but strain is assumed to be small. Closed-form expressions\nare provided for the 3D non-linear warping and stress fields, the\n1D non-linear stiffness matrix and the bending moment-curvature relationship.\nIn bending, failure could be caused by limit-moment instability,\nlocal buckling or material failure of a ply. A procedure to determine\nthe failure load is provided based on the non-linear response, neglecting\nmicro-mechanical failure modes, post-failure behavior, and hygrothermal\neffects. Asymptotic considerations lead to the neglect of local shell\ninterlaminar and transverse shear stresses for the thin-walled configuration.\nResults of the theory are illustrated for a few symmetric, antisymmetric\nangle-ply and unsymmetric layups and show that some previously published\ntheories are not asymptotically correct.
Interfacial toughness measurements for thin films on substrates
Acta Materialia
50
3
441-466
2002
10.1016/S1359-6454(01)00354-8
There are more than 200 different methods for measuring adhesion, suggesting it to be material, geometry and even industry specific. This availability has exploded at least partly due to the arrival of dissimilar material interfaces and thin films and the ease with which microfabrication techniques apply to silicon technology. Having an eye toward those tests utilized for thin films, this paper reviews only a few of these techniques. The emphasis is on measuring thin film adhesion from the standpoint of fracture mechanics, when the film is mechanically or by other means removed from the substrate, and the amount of energy necessary for this process is calculated per unit area of the removed film. This tends to give values approaching the true work of adhesion at small thickness and greater values of the practical work of adhesion at larger thickness, all being in the 30-30,000 nm range. The resulting large range of toughnesses is shown to be dependent on the scale of plasticity achieved as controlled by film thickness, microstructure, chemistry and test temperature. While the tests reviewed largely address the measurement of elastic strain energy release rates, we also briefly address a few theoretical models which are specific to the resistance side of the delamination equation. The weight of the evidence suggests for ductile metallic films that the major extrinsic variables are film stress, extent of delamination, thickness and temperature while the major intrinsic ones are modulus, yield strength, the thermodynamic work of adhesion and one or more length scales. For some 25 film/substrate multilayers, with emphasis on Al, Au and Cu, the comparison of several theoretical models as to how the extrinsic and intrinsic variables intertwine is made. ?? 2002 Published by Elsevier Science Ltd. on behalf of Acta Materialia Inc.
Adhesion energies; Fracture & fracture toughness; Interfaces; Thin films
Fracture mechanics
International Journal of Solids and Structures
37
1-2
171-183
2000
10.1016/S0020-7683(99)00086-4
In this article, after a brief description of some significant catastrophic structural failures going back to the period when iron and steel began to replace wood and masonry as the primary structural materials, the historical development of the field of fracture mechanics is discussed. First, the basic concepts of the field, the motivation underlying their development and the key contributions made in the area are briefly described. A summary of the key engineering applications of fracture mechanics, its methods, some recent important contributions and areas of future research is is then presented.
Introduction to Mechanics and Symmetry
Physics Today
48
July
70
1998
10.1063/1.2808303
Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability and bifurcation, and the study of specific rigid, fluid, plasma and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous specific applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, expecially senior undergraduate and graduate students in mathematics, physics and engineering. For this second edition, the text has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available on-line.
Mechanics and thermodynamics of interfaces, thin liquid films and membranes
Journal of Dispersion Science and Technology
18
6-7
609-623
1997
First we review some recent studies devoted to the role of surface moments (torques) in the mechanics and thermodynamics of fluid interfaces of arbitrary shape. The presence of bending and torsion moments leads to a difference between the mechanical and thermodynamical surface tensions and shear stresses. Next we review recent results in the mechanics of thin liquid films and the transition region film-Plateau border. Line and transversal tensions are assigned as excesses on the contact line. The transversal tension accounts for the attractive forces in the transition zone. Experiments with floating bubbles show that the movement of the contact line can lead to non-equilibrium values of the line tension, which can be interpreted in terms of a plastic deformation.
bending moment; bubbles; contact-angle; curved interfaces; deformable emulsion droplets; energy; flocculation; foam films; line tension; surface-tension
Supersymmetry and Quantum Mechanics
Physics Reports
251
5-6
159
1994
10.1016/0370-1573(94)00080-M
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large $N$ expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order $p$.
Information theory and statistical mechanics
Physical Review
106
4
620-630
1957
10.1103/PhysRev.106.620
It is concluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). ... \n
Structural modeling of SMA fiber hybrid active thin-walled composite beams
Composite Structures
91
1
120-130
2009
http://dx.doi.org/10.1016/j.compstruct.2009.04.038
The constitutive equations relating cross-sectional loads (forces and moments) to cross-sectional displacements (stretching, bending, twisting) of thin-walled laminated beams with integral shape memory alloy (SMA) active fibers is presented. The variational asymptotic method is used to formulate the force-deformation relationships equations accounting for the presence of active SMA fibers distributed along the cross-section of the beam. The constitutive relationships for evaluation of the properties of a hybrid SMA composite ply are obtained following the rule of mixtures. The analytical expressions of the actuation components for the active beam are derived based on Tanaka’s constitutive equation and Lin’s linear phase transformation kinetics for SMA fiber. The general form of constitutive relation is applied to the cases of extension-twist coupling, corresponding to Circumferentially Uniform (CUS) and bending-twist coupling, corresponding to Circumferentially Anti-Symmetric (CAS). The present analysis extends the previous work done for modeling generic passive thin-walled laminated beams. Numerical results show that significant extension, bending and twisting deflection occur during the phase transformation due to SMA actuation. The effects of temperature on structural response behavior during phase transformation from martensite to austenite are significant. The effects of the volume fraction of the SMA fiber, the martensitic residual strain and ply angle are also addressed.
Active closed cross-sections beam; Blade; Shape memory alloy fiber composite; Static deformation control
Reflections on the mechanics of granular matter
Physica A: Statistical Mechanics and its Applications
261
267-293
1998
10.1016/S0378-4371(98)00438-5
During recent years, a rather basic conflict has emerged between departments of mechanics/ physics concerning the description of granular media. Experts from mechanics measure stress/ strain relations, using the so-called triaxial tests, and then use these data to predict the behavior of a sample under given boundary conditions. Some physicists have a different view: they have claimed that it is not possible to define a proper displacement field in a heap of sand, and that the notion of strains is thus ambiguous. In the present text, we conclude that the crucial features are the following: (a) a heap is usually formed from a flowing phase of sand, (b) there is (empirically) a sharp interface between the flowing phase and the frozen heap below, (c) we may define for each grain a displacement, which is measured from the moment when it froze. (This displacement is due, for instance, to a compaction of the heap under its own weight.) We also present some aspects of the dynamics, including dune motions and surface flows of grains. Bouchaud, Cates and coworkers have constructed a very compact description for thin flows. We discuss the practical consequences of this picture, emphasizing some possible extensions for thicker flows. This suggests a number of possible experiments on avalanches.
Axisymmetric indentation of an incompressible elastic thin film
Mechanics of Materials
30
275-286
1998
10.1088/0022-3727/38/7/C02
The problem of impressing a rigid flat-ended cylindrical indenter onto an incompressible elastic film is considered. An integral transform solution is developed to reduce the solution of the problem to a Fredholm integral equation of the second kind with a symmetrical kernel depending on the boundary conditions (frictionless/bonded) in the areas of contact. The relationship between the applied load and the indentation depth is derived, which provides a guideline for measuring the elastic constants of thin films and determining the degree of adhesion between a thin film and a stiffer substrate.
The fatigue damage mechanics of notched carbon fibre/PEEK laminates
Composites
23
5
305-311
1992
10.1016/0010-4361(92)90329-S
A model is presented for the strength, post-fatigue residual strength and damage propagation in notched, cross-ply carbon fibre/polyetheretherketone (PEEK) laminates. Fracture mechanics principles are used to predict quasi-static damage growth, and the application of a Paris law permits extension to fatigue damage. Strength is predicted by applying a failure criterion based on the tensile stress distribution in the 0° plies, as modified by damage (either quasi-static or fatigue). The volume dependence of strength is included by using a simple Weibull distribution. The parameters of the model are determined from independent experiments. Good agreement with experimental results is obtained. Comparisons are made with previous results from carbon fibre/epoxy laminates. The behaviour of the carbon fibre/PEEK is similar, although the extent of delamination and matrix cracking is reduced owing to the higher inherent toughness of the matrix.
Stiffness and fracture analysis of laminated composites with off-axis ply matrix cracking
Composites Part A: Applied Science and Manufacturing
38
4
1262-1269
2007
10.1016/j.compositesa.2006.07.001
Matrix cracks parallel to the fibres in the off-axis plies is the first intralaminar damage mode observed in laminated composites subjected to static or fatigue in-plane tensile loading. They reduce laminate stiffness and strength and trigger development of other damage modes, such as delaminations. This paper is concerned with theoretical modelling of unbalanced symmetric laminates with off-axis ply cracks. Closed-form analytical expressions are derived for Mode I, Mode II and the total strain energy release rates associated with off-axis ply cracking in [0/??]s laminates. Stiffness reduction due to matrix cracking is also predicted analytically using the Equivalent Constraint Model (ECM) of the damaged laminate. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy and carbon/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed. ?? 2006 Elsevier Ltd. All rights reserved.
A. Laminates; B. Fracture; B. Mechanical properties; C. Analytical modelling
A new layerwise trigonometric shear deformation theory for two-layered cross-ply beams
Composites Science and Technology
61
1271-1283
2001
10.1016/S0266-3538(01)00024-0
A new layerwise trigonometric shear deformation theory for the analysis of two-layered cross-ply laminated beams is presented. The number of primary variables in this theory is even less than that of first-order shear deformation theory, and moreover, it obviates the need for a shear correction factor. The sinusoidal function in terms of thickness coordinate is used in the displacement field to account for shear deformation. The novel feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutive relationships, satisfying the shear-stress-free boundary conditions at top and bottom of the beam and satisfying continuity of shear stress at the interface. The principle of virtual work is used to obtain the governing equations and boundary conditions of the theory. The effectiveness of the theory is demonstrated by applying it to a two-layered cross-ply laminated beam. ?? 2001 Elsevier Science Ltd. All rights reserved.
Cross-ply beam; Interface shear continuity; Laminated thick beam; Shear deformation; Transverse shear stress
Impact strength of angle ply fiber reinforced materials
Journal of Composite Materials
10
1
92
1976
10.1177/002199837601000108
Tensile strength of angle ply balanced laminated made of glass fibers\n\nand epoxy matrix has been investigated under dynamic loading using\nan\n\ninstrumented drop weight apparatus. A comparison of theoretical and\n\nexperimental stress-strain curves reveals that good agreement exists\nfor a\n\ncertain range of fiber orientation. Different failure criteria have\nto be used\n\nfor each range. Failure stresses in the dynamic case are found to\nbe considerably\n\nhigher than the corresponding static values for the complete\n\nrange of fiber orientation. Failure strains and initial effective\nmoduli are\n\nthe same for static and for impact loadings.
angle ply fiber reinforced materials; composite materials; Impact strength
Novel two-ply composite membranes of chitosan and sodium alginate for the pervaporation dehydration of isopropanol and ethanol
Journal of Membrane Science
156
17-27
1999
10.1016/S0376-7388(98)00322-6
Novel two-ply dense composite membranes were prepared using successive castings of sodium alginate and chitosan solutions for the pervaporation dehydration of isopropanol and ethanol. Preparation and operating parameters namely polymer types facing to the feed stream, NaOH treatment for the regeneration of chitosan, and crosslinking system types were investigated using the factorial design method. It was shown that these parameters were all critical to the performance of the membrane in the form of the main and interaction effects. The pervaporation performance of the two-ply membrane with its sodium alginate layer facing the feed side and crosslinked or insolubilized in sulfuric acid solution was compared with the pure sodium alginate and the chitosan membranes in terms of the flux and separation factors. It was shown that although its flux was lower than that of the pure sodium alginate and chitosan membranes, the separation factors at various alcohol concentrations were in between values for the two pure membranes. For the dehydration of 90wt% isopropanol-water mixtures the performance of the two-ply membrane which was moderately crosslinked in formaldehyde was found to match the high performance of the pure sodium alginate membrane. This two-ply membrane had fluxes of 70g/m2h at 95% EtOH, 554g/m2h at 90% PrOH and separation factors of 1110 at 95% EtOH, 2010 at 90% PrOH and its mechanical properties were better than that of the pure sodium alginate membrane. Copyright (C) 1999 Elsevier Science B.V.
Chitosan; Crosslinking; Ethanol-water mixture; Isopropanol-water mixture; Pervaporation; Sodium alginate; Two-ply membrane
Mixed micromechanics and continuum damage mechanics approach to transverse cracking in $[S,90_n]_s$ laminates
Mechanics of Composite Materials
37
2
115-126
2001
10.1023/a:1010665401860
The stiffness reduction in [S, 90(n)](s) laminates due to transverse cracking in 90-layers is analyzed using the synergistic continuum damage mechanics (SCDM) and a micromechanics approach. The material constants involved in the SCDM model are determined using the stiffness reduction data for a reference cross ply laminate. The constraint efficiency factor, which depends on the stiffness and geometry of neighboring layers, is assumed to be proportional to the average crack opening displacement (COD). The COD as a function of the constraint effect of adjacent layers and crack spacing is described by a simple power law. The crack closure technique and Monte Carlo simulations are used to model the damage evolution: the 90-layer is divided into a large number of elements and the critical strain energy rate Gc having the Weibull distribution is randomly assigned to each element. The crash density data for a [0(2)/90(4)](s) cross plan laminate are used to determine the Weibull parameters. The simulated crack density curves are combined with the CDM stiffness reduction predictions to obtain the stiffness versus strain. The methodology, developed is successfully used to predict the stiffness reduction as a junction of crack density in [+/- theta /90(4)](s) laminates.
cracking; experiment; laminates; material constants; MODEL; modeling; MULTIPLE MATRIX CRACKING; PARAMETER; PLIES; PLY; PROPERTIES; stiffness reduction; STRENGTH DISTRIBUTION; THERMOELASTIC
The Effect of Moisture, Matrix and Ply Orientation on Delamination Resistance, Failure Criteria and Fracture Morphology in CFRP
Composite Materials : Testing, Design, and Acceptance Criteria, ASTM STP1416
221-234
2002
10.1520/STP1416-EB
The objective of this work was to relate damage mechanisms, gleaned through electron microscopy, to delamination loci generated using fracture toughness (Mixed-Mode Bend) tests. From this, mixed-mode criteria were ranked using the x<sup>2</sup> method (goodness of fit). The shapes of the failure loci (G <sub>T</sub> versus %G<sub>I</sub>) were related to the damage mechanisms, and to the moisture content, fibre type and ply orientation. Due to cusp formation, the delamination toughness increased as the proportion of Mode II increased. A further finding was that a 'hump' which was observed in the failure loci under Mode I dominated loading was due to fibre bridging. Ply orientation also had a significant effect on the toughness; 0°/90° interface was about 45% tougher than the 0°/0° interface due to secondary matrix cracking parallel to the crack front. The presence of such additional mechanisms indicates' that delamination toughness is not a material property but is dependent on ply orientation
The mechanics of spin coating of polymer films
Physics of Fluids
31
10
2786
1988
10.1063/1.866986
The process of spin coating is described, with particular attention to applications in microelectronics. The physical mechanisms involved in the process are discussed and those mechanisms that affect the final state are identified, viz., centrifugal and viscous forces, solute diffusion, and solvent evaporation: A model is proposed that incorporates only the latter mechanisms, with viscosity and diffusivity depending on solute concentration. The evaporation of solvent during spinning causes the solution viscosity to increase and the flow is reduced. The thickness of the final solid film is related to the thickness of a diffusion boundary layer near the free surface. The model predicts the final dry film thickness in terms of the primary process variables, spin speed, and initial polymer concentration. A similarity boundary‐layer analysis leads to a simple approximate result for the final film thickness that is consistent with limited experimental data, h ∼ K C0 (ν0 D0)^1/4 / Ω^1/2, where K is a number of order unity and the other quantities are, respectively, the initial polymer concentration, the kinematic viscosity, the solute diffusivity, and the spin speed. The dependence on diffusivity has not previously been described theoretically. The total spin time is shown to be proportional to Ω− 1, in agreement with experiment. The rate of solvent evaporation is shown to be proportional to Ω, which contradicts previous assumptions.
Fracture and Frictional Mechanics - Theory
Treatise on Geophysics
4
83-106
2007
10.1016/B978-044452748-6.00062-6
Fracture mechanics considers conditions for the onset, propagation, and arrest of shear and tensile ruptures. Because earthquakes can be naturally represented as elastodynamic shear instabilities, fracture mechanics forms a theoretical basis of earthquake seismology. Earthquake ruptures involve a number of mechanical processes, including yielding and material breakdown around the propagating rupture front, complex time-dependent evolution of friction on a slipping interface behind the rupture front, radiation of seismic waves, wear, communition, and heating of the fault zone material, etc. These processes are intrinsically coupled, and must be considered in a unified fashion. Recent theoretical, experimental, and field data suggest that fracture mechanics models assuming small-scale yielding and constant residual friction on a fault surface may not be an adequate theoretical description of earthquake ruptures. This is because the fault interface may undergo a continuous weakening with rapid slip (e.g., due to thermal effects), so that the effective displacement corresponding to fault weakening may (1) scale with the rupture length and (2) be non-negligible compared to the overall coseismic offset. Also, an assumption that the inelastic yielding is confined to the slip plane is likely violated, especially at high rupture speeds approaching the shear wave velocity. It follows that the earthquake fracture energy is expected to scale with the rupture size, and may not be a negligible part of the earthquake energy balance, perhaps even for large earthquakes. In the presence of significant variations in the dynamic friction during fault slip, a distinction between the fracture energy and the energy loss due to friction is not well defined. Both terms represent inelastic work done on a fault that is ultimately spent on fracturing, communition, and heating of the fault zone material. If the fracture energy is formally defined as work required to evolve friction from the maximum static level in the breakdown zone at the rupture front to the minimum dynamic level, a continuous dynamic weakening implies repartitioning of the total inelastic work between the fracture energy and the 'residual' frictional losses. The coseismic heating is one of the likely mechanisms that control the dynamic fault strength, and thus the stress drop and seismic radiation. The instantaneous along-fault temperature distribution is governed by the details of slip history, as well as the characteristic thickness and thermophysical properties of a slipping zone. Faults that are thin compared to the thermal diffusion length scale are predicted to produce maximum temperatures near the rupture front, while thicker faults are likely hottest in the central part of the rupture. These patterns may affect the rupture dynamics. Theoretical models that fully couple heat transfer, thermally activated friction, elastodynamics, and off-fault damage may be necessary for realistic simulations of earthquake ruptures. ?? 2007 Elsevier B.V. All rights reserved.
Analytic solutions; Crack propagation theory; Dynamic friction; Earthquake; Fracture energy; Fracture mechanics; Frictional heating; Nucleation; Process zone; Rupture; Shear; Weakening; Yielding
Fluid Mechanics
Image Rochester NY
6
539
1987
10.1007/b138775
Mjog god kennslubok. Agaet fyrir byrjendur sem og lengra komna
Game Studies - Defining Game Mechanics Game Studies - Defining Game Mechanics
Game Studies
8
1-15
2008
1604-7982
This article defines game mechanics in relation to rules and challenges. Game mechanics are methods invoked by agents for interacting with the game world. I apply this definition to a comparative analysis of the games Rez, Every Extend Extra and Shadow of the Colossus that will show the relevance of a formal definition of game mechanics.
game design; game mechanics; game research; rules
Mechanics of roll edge contact in cold rolling of thin strip
International Journal of Mechanical Sciences
48
7
697-706
2006
10.1016/j.ijmecsci.2006.01.017
Simulation of cold rolling of thin strip due to roll edge contact with oil lubrication was performed successfully using a developed influence function method. Roll edge contact and related surface roughness was discussed in this paper. The calculated rolling force, intermediate force and work roll edge contact force increase significantly when the reduction increases. The strip profile becomes poor with a higher reduction, and the calculated rolling forces are consistent with the measured values. A modified edge shape of work roll determined from the roll edge contact length and roll edge flattening value is helpful to reduce the work roll edge wear and to extend the work roll life. Surface roughness and asperity of the rolled strip are characterized by surface profilometer and atomic force microscope. The research shows that the surface roughness reduces with a higher reduction or rolling speed. The effect of the strip width on surface roughness is not significant. ?? 2006 Elsevier Ltd. All rights reserved.
Influence function method; Roll edge contact; Roll wear; Surface asperity
Matrix Cracking of Cross-Ply Ceramic Composites
Acta Metallurgica Et Materialia
42
6
1933-1945
1994
Doi 10.1016/0956-7151(94)90018-3
A micromechanics study is presented of the matrix cracking behavior of laminated, fiber-reinforced ceramic cross-ply composites when subject to tensile stressing parallel to fibers in the 0-degrees plies. Cracks extending across the 90-degrees plies are assumed to exist, having developed at relatively low tensile stresses by the tunnel cracking mechanism. The problem addressed in this study is the subsequent extension of these intital cracks into and across the 0-degrees plies. Of special interest is the relation between the stress level at which the matrix cracks are able to extend all the way through the 0-degrees plies and the well known matrix cracking stress for steady-state crack extension through a uni-directional fiber-reinforced composite. Depending on the initial crack distribution in the 90-degrees plies, this stress level can be as large as the uni-directional matrix cracking stress or it can be as low as about one half that value. The cracking process involves a competition between crack bridging by the fibers in the 0-degrees plies and interaction among multiple cracks. Crack bridging is modeled by a line-spring formulation where the nonlinear springs characterize the sliding resistance between fibers and matrix. Crack interaction is modeled by two representative doubly periodic crack patterns, one with collinear arrays and the other with staggered arrays. Material heterogeneity and anisotropy are addressed, and it is shown that a homogeneous, isotropic average approximation can be employed. In addition to conditions for matrix cracking, the study provides results which enable the tensile stress-strain behavior of the cross-ply to be predicted, and it provides estimates of the maximum stress concentration in the bridging fibers. Residual stress effects are included.
brittle-matrix; fiber; fracture; transverse cracking
The molecular structure ordering and orientation of the metallophthalocyanine CoPc, ZnPc, CuPc, and MgPc thin layers deposited on silicon substrate, as studied by micro-Raman spectroscopy
Journal of Materials Science
46
20
6589-6595
2011
10.1007/s10853-011-5607-4
In this article, we present orientation study of metallophthalocyanine (MPcs) (CoPc, ZnPc, CuPc, and MgPc) thin films deposited on silicon substrate. The MPc’s thin layers were obtained by the quasi-molecular beam evaporation. The micro-Raman scattering spectra of MPc’s thin films were investigated in the spectral range 550–1650 cm−1 using 488 nm excitation wavelength. Raman scattering studies were performed at room temperature before and after annealing process. Annealing process of thin layers was carried out at 200 °C for 6 h. From polarized Raman spectra using surface Raman mapping, the information on polymorphic phase of MPc’s layers has been obtained. The chosen Raman modes A1g and B1g are connected with different polymorphic phases of MPc (α and β form) thin layers. Moreover, the obtained results showed the influence of the annealing process on the ordering of the molecular structure. Following the annealing process, it was observed arrangement of the thin layers structure being revealed in Raman spectra. The obtained results indicate that the annealing process has a significant influence on the structure of thin layers being under study.
Fundamentals of Solid Mechanics
Petroleum Rock Mechanics
1-12
2011
10.1016/B978-0-12-385546-6/00001-2
Course at the European School for Advanced Studies in Earthquake Risk Reduction
Chevron Limited; University of Stavanger
Underwater breathing: the mechanics of plastron respiration
Journal of Fluid Mechanics
608
275-296
2008
10.1017/S0022112008002048
The rough, hairy surfaces of many insects and spiders serve to render them water-repellent; consequently, when submerged, many are able to survive by virtue of a thin air layer trapped along their exteriors. The diffusion of dissolved oxygen from the ambient water may allow this layer to function as a respiratory bubble or 'plastron', and so enable certain species to remain underwater indefinitely. Maintenance of the plastron requires that the curvature pressure balance the pressure difference between the plastron and ambient. Moreover, viable plastrons must be of sufficient area to accommodate the interfacial exchange Of 02 and C02 necessary to meet metabolic demands. By coupling the bubble mechanics, surface and gas-phase chemistry, we enumerate criteria for plastron viability and thereby deduce the range of environmental conditions and dive depths over which plastron breathers can survive. The influence of an external flow on plastron breathing is also examined. Dynamic pressure may become significant for respiration in fast-flowing, shallow and well-aerated streams. Moreover, flow effects are generally significant because they sharpen chemical gradients and so enhance mass transfer across the plastron interface. Modelling this process provides a rationale for the ventilation movements documented in the biology literature, whereby arthropods enhance plastron respiration by flapping their limbs or antennae. Biornimetic implications of our results are discussed.
The influence of mechanical couplings on the compressive stability of anti-symmetric angle-ply laminates
Composite Structures
57
1-4
473-482
2002
10.1016/S0263-8223(02)00116-2
The compressive stability of anti-symmetric angle-ply laminated plates with particular reference to the degrading influence of membrane-flexural coupling is reported in this paper. The degree of membrane-flexural coupling in the laminated composite plates is varied, essentially, by altering the ply-angle and the number of plies in the laminated stack for a given composite material system. The coupled compressive buckling solutions are determined in the paper using the finite strip method of analysis and the buckling displacement fields of the strip formulation are those which are able to provide zero in-plane normal movement at the edge boundaries of the laminated plates. Results are given for anti-symmetric angle-ply laminated plates subjected to uniaxial compression and these have been obtained from fully converged finite strip structural models. Validation of the finite strip formulation is indicated in the paper through comparisons with exact solutions where appropriate. Increasing the number of plies in the laminated system is seen to reduce the degree of coupling and the critical stress levels are noted to tend towards the plate orthotropic solutions. The ply-angle corresponding to the optimised buckling stress for any particular laminate is noted in the paper to be influenced by the support boundary conditions at the plates unloaded edges. For any particular laminate the minimum critical buckling stress and corresponding natural half-wavelength of the buckling mode are shown to be highly sensitive to ply-angle variation. Some post-buckling results are presented in the paper and these have been determined using the finite element method of analysis. The influence of membrane-flexural coupling is shown to be significant throughout the compressive post-buckling history of the laminated plates. The optimised ply-angle with regard to the critical compressive buckling stress of square simply supported anti-symmetric angle-ply laminates is shown to be less effective in the post-buckling range with regard to post-buckled compressional stiffness. ?? 2002 Elsevier Science Ltd. All rights reserved.
Angle-ply; Anti-symmetric; Compressive stability; Critical stress; Finite strip method; Laminated plates; Membrane-flexural coupling
Comparison of models for transverse ply cracks in composite laminates
Composites Science and Technology
60
2347-2359
2000
10.1016/S0266-3538(00)00030-0
Ply-level transverse cracking often results in the loss of strength and stiffness and changes in the coefficients of thermal expansion (CTE), and it also provides pathways for moisture or other corrosive agents. In stiffness critical structures, the loss of stiffness and/ or change in CTE may result in the loss of structural functionality. These matrix-dominated failure modes can lead to delamination and fiber breakage in highly loaded plies and eventually to failure of the laminate. It is vitally important that predictive methods are developed that will be accepted, following thorough validation, by the composites engineering community. This paper is one attempt to achieve sound validation for four different methods of prediction, one of which is finite-element analysis. The three distinct cross-ply laminate models discussed here have been shown to be consistent with each other, and with FEA predictions. Additionally, model predictions for the effective moduli of transversely cracked laminates have been shown to be in good agreement with experimental measurements. The excellent correlation of the model predictions and the agreement with experimental data provides the basis for these models to be seriously considered for use in the development of new design tools and procedures. (C) 2000 Elsevier Science Ltd. All rights reserved.
C. Laminates; Composites; C. Stress transfer; C. Transverse cracks
The effects of feeding Karlodinium veneficum (PLY # 103; Gymnodinium veneficum Ballantine) to the blue mussel Mytilus edulis
Harmful Algae
7
1
91-98
2008
10.1016/j.hal.2007.05.004
The effects of exposure to the type species for Karlodinium veneficum (PLY # 103) on immune function and histopathology in the blue mussel Mytilus edulis were investigated. Mussels from Whitsand Bay, Cornwall (UK) were exposed to K. veneficum (PLY # 103) for 3 and 6 days. Assays for immune function included total and differential cells counts, phagocytosis and release of extra cellular reactive oxygen species. Histology was carried out on digestive gland and mantle tissues. The toxin cell quota for K. veneficum (PLY # 103) was measured by liquid chromatography–mass spectrometry detecting two separable toxins KvTx1 (11.6±5.4ng/ml) and KvTx2 (47.7±4.2ng/ml). There were significant effects of K. veneficum exposure with increasing phagocytosis and release of reactive oxygen species following 6 days exposure. There were no significant effects on total cell counts. However, differential cell counts did show significant effects after 3 days exposure to the toxic alga. All mussels produced faeces but not pseudofaeces indicating that algae were not rejected prior to ingestion. Digestive glands showed ingestion of the algae and hemocyte infiltration after 3 days of exposure, whereas mantle tissue did not show differences between treatments. As the effects of K. veneficum were not observed in the mantle tissue it can be hypothesized that the algal concentration was not high enough, or exposure long enough, to affect all the tissues. Despite being in culture for more than 50 years the original K. veneficum isolate obtained by Mary Parke still showed toxic effects on mussels.
Blue mussel; Harmful algal blooms; Histopathology; Immunology; Karlodinium veneficum
Simulation of multiple delaminations in impacted cross-ply laminates using a finite element model based on cohesive interface elements
Composites Science and Technology
69
11-12
1699-1709
2009
10.1016/j.compscitech.2008.10.025
The paper investigates the capability of a finite element model based on cohesive interface elements to simulate complex three-dimensional damage patterns in composite laminates subjected to low-velocity impact. The impact response and the damage process of cross-ply laminated plates with grouped ([03/903]s and [903/03]s) and interspersed ([0/90]3s) ply stacking was simulated using a FE model developed by the authors in a previous study and the numerical results were compared to experimental observations. The model provided a correct simulation of size, shape and location of the principal fracture modes occurring in impacted [03/903]s and [903/03]s laminates. In [0/90]3s laminates, characterized by a complex spatial damage distribution, the model was able to predict the approximately circular shape of the overall projected damage area and to capture the typical shape features of individual delaminations; significant discrepancies between experiments and predictions were however observed in terms of delamination sizes at single interfaces. Further investigations are needed to clarify the main reasons of these discrepancies. ?? 2008 Elsevier Ltd. All rights reserved.
B. Impact behaviour; C. Computational simulation; C. Delamination
The giant protein titin: a major player in myocardial mechanics, signaling, and disease.
Circulation research
94
3
284-95
2004
10.1161/01.RES.0000117769.88862.F8
The sarcomere contains, in addition to thin and thick filaments, a filament composed of the giant protein titin (also known as connectin). Titin molecules anchor in the Z-disc and extend to the M-line region of the sarcomere. The majority of titin's I-band region functions as a molecular spring. This spring maintains the precise structural arrangement of thick and thin filaments, and gives rise to passive muscle stiffness; an important determinant of diastolic filling. Earlier work on titin has been reviewed before. In this study, our main focus is on recent findings vis-à-vis titin's molecular spring segments in cardiac titins, including the discovery of fetal cardiac isoforms with novel spring elements. We also discuss new insights regarding the role of titin as a biomechanical sensor and signaling molecule. We will end with focusing on the rapidly growing knowledge regarding titinopathies.
Animal; Animals; Biomechanical Phenomena; Biomechanics; Connectin; Contractility; Disease Models; Heart; Heart Diseases; Heart Diseases: physiopathology; Heart: physiology; Humans; Mice; Muscle Proteins; Muscle Proteins: genetics; Muscle Proteins: physiology; Myocardial stiffness; Passive stiffness; Protein Kinases; Protein Kinases: genetics; Protein Kinases: physiology; Signal Transduction; Signal Transduction: physiology; Stretch
TRACKS : Toward Directable Thin Shells
ACM Transactions on Graphics
26
50
2007
10.1145/1239451.1239501
We combine the often opposing forces of artistic freedomandmath- ematical determinism to enrich a given animation or simulation of a surface with physically based detail. We present a process called tracking, which takes as input a rough animation or simula- tion and enhances it with physically simulated detail. Building on the foundation of constrained Lagrangian mechanics, we propose weak-form constraints for tracking the input motion. This method allows the artist to choose where to add details such as characteris- tic wrinkles and folds of various thin shell materials and dynamical effects of physical forces. We demonstrate multiple applications ranging from enhancing an artists animated character to guiding a simulated inanimate object.
add fine scale details without; artist sets; computes equations; deviating from artist; directable animation; finer scales; galerkin; left intact; motion remaining; our solver; rigging; scale features; s intentions; thin shells; tracking
Prediction of impact-induced delamination in cross-ply composite laminates using cohesive interface elements
Composites Science and Technology
68
12
2383-2390
2008
10.1016/j.compscitech.2007.06.015
The paper investigates the potential of cohesive interface elements for damage prediction in laminates subjected to low-velocity impact. FE models with interface elements adopting a bilinear cohesive law were first calibrated and validated by simulation of standard fracture toughness tests and then employed to model the impact response of cross-ply graphite/epoxy laminated plates. The developed model provided a correct simulation of the impact response of laminates in a wide range of energy values and successfully predicted size, shape and location of main damage mechanisms. The results of the analyses also pointed out the importance of employing a damage criterion capable of accounting for the constraining effect of out-of-plane compression on the initiation of the decohesion phase. ?? 2007 Elsevier Ltd. All rights reserved.
B. Impact behaviour; C. Computational simulation; C. Delamination
A consistent thin-layer theory for Bingham plastics
Journal of Non-Newtonian Fluid Mechanics
84
1
65-81
1999
10.1016/S0377-0257(98)00133-5
Thin-layer theory is developed for Bingham plastic fluids; the specific case of a fluid flowing down an inclined plane is considered. In contrast to previous work it is indicated how the Bingham model leads directly to a self-consistent thin-layer theory; this does not rely upon adopting a bi-viscous approximation. The theory describes the fluid in terms of regions of fully plastic flow bounded by a "fake" yield surface. Above this fake yield surface are "pesudo-plugs" - regions in which the leading-order equations predict a plug, but which are seen to be weakly yielded at higher order.
Quantum mechanics. Non-relativistic theory
Course of Theoretical Physics
3
677
1977
10.1063/1.3062347
Quantum Mechanics, Third Edition: Non-relativistic Theory is devoted to non-relativistic quantum mechanics. The theory of the addition of angular momenta, collision theory, and the theory of symmetry are examined, together with spin, nuclear structure, motion in a magnetic field, and diatomic and polyatomic molecules. This book is comprised of 18 chapters and begins with an introduction to the basic concepts of quantum mechanics, with emphasis on the uncertainty principle, the principle of superposition, and operators, as well as the continuous spectrum and the wave function. The following chapters explore energy and momentum; Schrödinger's equation; angular momentum; and motion in a centrally symmetric field and in a magnetic field. Perturbation theory, spin, and the properties of quasi-classical systems are also considered. The remaining chapters deal with the identity of particles, atoms, and diatomic and polyatomic molecules. The final two chapters describe elastic and inelastic collisions. This monograph will be a valuable source of information for physicists.
Thin and strong! The bioengineering dilemma in the structural and functional design of the blood-gas barrier
Physiol Rev
85
3
811-844
2005
10.1152/physrev.00022.2004
In gas exchangers, the tissue barrier, the partition that separates the respiratory media (water/air and hemolymph/blood), is exceptional for its remarkable thinness, striking strength, and vast surface area. These properties formed to meet conflicting roles: thinness was essential for efficient flux of oxygen by passive diffusion, and strength was crucial for maintaining structural integrity. What we have designated as "three-ply" or "laminated tripartite" architecture of the barrier appeared very early in the evolution of the vertebrate gas exchanger. The design is conspicuous in the water-blood barrier of the fish gills through the lungs of air-breathing vertebrates, where the plan first appeared in lungfishes (Dipnoi) some 400 million years ago. The similarity of the structural design of the barrier in respiratory organs of animals that remarkably differ phylogenetically, behaviorally, and ecologically shows that the construction has been highly conserved both vertically and horizontally, i.e., along and across the evolutionary continuum. It is conceivable that the blueprint may have been the only practical construction that could simultaneously grant satisfactory strength and promote gas exchange. In view of the very narrow allometric range of the thickness of the blood-gas barrier in the lungs of different-sized vertebrate groups, the measurement has seemingly been optimized. There is convincing, though indirect, evidence that the extracellular matrix and particularly the type IV collagen in the lamina densa of the basement membrane is the main stress-bearing component of the blood-gas barrier. Under extreme conditions of operation and in some disease states, the barrier fails with serious consequences. The lamina densa which in many parts of the blood-gas barrier is <50 nm thin is a lifeline in the true sense of the word.
Animals; Biomechanical Phenomena; Biophysical Phenomena; *Biophysics; Blood-Air Barrier/*physiology; Extracellular Matrix/physiology/ultrastructure; Gases/*metabolism; Humans; Lung/physiology/ultrastructure; Oxygen Consumption; Pulmonary Gas Exchange/physiology; Stress, Mechanical
Delamination of compressed thin films
Advances in Applied Mechanics
33
119-192
1997
10.1016/S0065-2156(08)70386-7
[Publisher summary] This chapter elaborates the delamination of compressed thin films. Blisters may grow by interfacial fracture, a process which, under the appropriate conditions, may result in the catastrophic failure of the component. Blisters are often observed to adopt convoluted-even bizarre shapes and to fold into intricate patterns. Some developments based on the use of direct methods of the calculus of variations, which have proven useful for understanding the mechanics of folding of thin films are reviewed. Preferred growth directions have been reported in films grown epitaxially on crystallographic planes. These cords may branch forming webs of regular geometries. The experimental evidence suggests that the direction of the cords in these arrays is determined by the anisotropy of the state of stress in the film, which favors cords that are perpendicular to the axis of highest compressive stress. It is found that a boundary-layer analysis permits one to assign a well-defined width to the sharp edges exhibited by the membrane solution. This width sets the minimum spacing between folds, and is found to correlate closely with the wavelength of the boundary undulations observed in large blisters. The energetics of blister growth and growth of telephone-cord blister are also described.
Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method
Composites Science and Technology
66
1248-1255
2006
10.1016/j.compscitech.2005.10.029
The present study is concerned with the buckling analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The requirement of the continuity conditions between layers for symmetric cross-ply laminated beams are satisfied by the use of the shape function incorporated into the theory which also unifies the one-dimensional shear deformable beam theories developed previously. The governing equations are obtained by means of Minimum Energy Principle. Three different combinations of free, clamped and simply supported edge boundary conditions are considered. The critical buckling loads are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results were obtained for different length-to-thickness ratios and lay-ups are presented and compared with the ones available in the literature. ?? 2005 Elsevier Ltd. All rights reserved.
A. Cross-ply beams; B. Buckling; C. Shear deformable beam theory; D. Ritz method
Fatigue damage mechanics of composite materials. II: A damage growth model
Composites Science and Technology
44
2
169-177
1992
10.1016/0266-3538(92)90110-O
A fatigue model has been developed for damage growth at a notch tip in carbon fibre/epoxy laminates. The damage is modelled as a series of interacting matrix cracks in various forms: splitting, delamination and transverse ply cracking. The extent of fatigue damage can be successfully predicted for a family of (90i/0j)ns and (90/±45/0)s laminates. In this second paper of four, a damage-based model is proposed which can explain the effect of cyclic tensile loading on the post-fatigue strength and stiffness of a notched laminate. © 1992.
Cyclic Tensile Loading; Damage Growth Models; damage prediction; Delamination; Epoxy Resins - Fiber Reinforcement; fatigue damage model; Fatigue of Materials - Mathematical Models; notches; Notch Tip; Plastics Laminates; Plastics Laminates - Crack Propagation; Plastics, Reinforced - Carbon Fiber; Plastics, Reinforced - Cracks; Ply Cracking; Post Fatigue Strength
STRAINED FERROELECTRIC THIN FILMS
International Journal of Applied Mechanics
01
01
21-40
2009
10.1142/S1758825109000046
Using thermodynamics approach, the present work analytically studies the effect of mismatch strains on the material properties of ferroelectric thin films. A one-dimensional model is first developed to illustrate the physical picture and the procedure of the theoretical approach. Then, the effect of non-equal mismatch strains is investigated by using the same theoretical approach.
Monolayer flow on a thin film
Journal of Fluid Mechanics
193
151
1988
10.1017/S0022112088002095
\nTwo-dimensional flow of a surface-active monolayer on a thin viscous \nfilm is considered. Simplifications of negligible gravity and \npressure forces are made. Interfacial properties are described by \nsimple model equations of state. Solutions are obtained for when the \nmonolayer is scraped along the interface by a barrier and a steady \nstate exists where surface advection is balanced by surface \ndiffusion. Surface velocity, film thickness and spreading rate \ndependence on surface diffusivity are examined.
Quantum mechanics: Get real
Nature Physics
8
6
443-444
2012
10.1038/nphys2325
Do quantum states offer a faithful representation of reality or merely encode the partial knowledge of the experimenter? A new theorem illustrates how the latter can lead to a contradiction with quantum mechanics.
Effects of pretwist and presetting on coupled bending vibrations of rotating thin-walled composite beams
International Journal of Solids and Structures
40
1203-1224
2003
10.1016/S0020-7683(02)00605-4
A refined dynamic theory of rotating blades modeled as anisotropic composite thin-walled beams, experiencing the flapping-lagging-transverse shear coupling is presented. The structural model encompasses a number of non-standard features, such as anisotropy and transverse shear, pretwist and presetting angles, the presence of a rigid hub on which the beam is mounted, and the rotatory inertia. The developed theory and the methodology used to determine the eigenfrequency characteristics are validated against the results available in the literature, and new results emphasizing the influence played by the ply-angle, pretwist and presetting, coupled with that of the rotating speed on blade free vibration characteristics are supplied, and pertinent conclusions are outlined. ?? 2002 Elsevier Science Ltd. All rights reserved.
Free vibration; Presetting and pretwist; Rotating beams; Shearable beam model; Thin-walled composite beams
Buckling of symmetrical cross-ply composite rectangular plates under a linearly varying in-plane load
Composite Structures
80
1
42-48
2007
10.1016/j.compstruct.2006.02.030
An exact solution for buckling of simply supported symmetrical cross-ply composite rectangular plates under a linearly varying edge load is presented. It is developed based on the first-order shear deformation theory for moderately thick laminated plates. Buckling loads of cross-ply rectangular plates with various aspect ratios are obtained and the effects of load intensity variation and layup configuration on the buckling load are investigated. The results are verified using the computer code ABAQUS. ?? 2006 Elsevier Ltd. All rights reserved.
Buckling; Cross-ply; Exact solution; Linearly varying load; Rectangular plate
Short-term plyometric training improves running economy in highly trained middle and long distance runners.
Journal of strength and conditioning research / National Strength & Conditioning Association
20
947-954
2006
10.1519/R-18235.1
Fifteen highly trained distance runners VO(2)max 71.1 +/- 6.0 ml.min(-1).kg(-1), mean +/- SD) were randomly assigned to a plyometric training (PLY; n = 7) or control (CON; n = 8) group. In addition to their normal training, the PLY group undertook 3 x 30 minutes PLY sessions per week for 9 weeks. Running economy (RE) was assessed during 3 x 4 minute treadmill runs (14, 16, and 18 km.h(-1)), followed by an incremental test to measure VO(2)max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km.h(-1) (4.1%, p = 0.02), but not at 14 or 16 km.h(-1). This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p = 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p = 0.09), and a lower VO(2)-speed slope (14%, p = 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or VO(2)max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics.
Notes on Quantum Mechanics
Notes
1-60
2004
10.1063/1.3057981
Quantum Mechanics is introduced using state vectors, linear operators and canonical quantisation rules. Spectra of some operators are calculated algebraically. The Schr¨ odinger Equation, is introduced and applied to problems of a single particle in a potential field and then to some three dimensional problems.
Fundamental Mechanics of Fluids
Mechanical Engineering
1
xiv, 525 p
2003
Retaining the features that made previous editions perennial favorites, Fundamental Mechanics of Fluids, Third Edition illustrates basic equations and strategies used to analyze fluid dynamics, mechanisms, and behavior, and offers solutions to fluid flow dilemmas encountered in common engineering applications. The new edition contains completely reworked line drawings, revised problems, and extended end-of-chapter questions for clarification and expansion of key concepts. Includes appendices summarizing vectors, tensors, complex variables, and governing equations in common coordinate systems Comprehensive in scope and breadth, the Third Edition of Fundamental Mechanics of Fluids discusses: Continuity, mass, momentum, and energy One-, two-, and three-dimensional flows Low Reynolds number solutions Buoyancy-driven flows Boundary layer theory Flow measurement Surface waves Shock waves
13. Biofluid Mechanics
Annual Review of Fluid Mechanics
21
1
167-204
1989
10.1146/annurev.fluid.21.1.167
This article is primarily devoted to various aspects of the circulation of blood, but it also provides a brief guide to the literature of other biofluid- mechanics topics.
Optimization of a composite scarf repair patch under tensile loading
Composites Part A: Applied Science and Manufacturing
40
12
1921-1930
2009
10.1016/j.compositesa.2009.04.033
Mechanics of the composite repair under tensile loading with and without overlay plies was examined for nontraditional patch ply orientations. Three-dimensional nonlinear analysis was performed for repair failure prediction and good baseline comparison for open hole scarfed panels and panels repaired by using standard ply-by-ply replacement patch composition was achieved. Multidimensional optimization was performed to calculate the repair patch ply orientations which minimize the von Mises stresses in the adhesive. These optimal stacking sequences achieved significant reduction of the stress levels and resulted in predicted up to 85% and 90% strength restoration for flush and single ply thickness over-ply repair. These results are intended to illustrate additional design variables available for efficient composite repair design, namely the composition of the repair patch.
A. Polymer-matrix composites (PMCs); B. Strength; C. Numerical analysis; E. Joints/joining
Mechanics of soft interfaces studied with displacement-controlled scanning force microscopy
Progress in Surface Science
85
9-12
347-397
2010
10.1016/j.progsurf.2010.07.003
The development of scanning force microscopes that maintain precise control of the tip position using displacement control (DC-SFM) has allowed significant progress in understanding the relationships between the chemical and mechanical properties of soft interfaces. Here, developments in DC-SFM techniques and their applications are reviewed. Examples of material systems that have been investigated are discussed and compared to measurements with other techniques involving nanoprobe geometries to illustrate the achievements and promise in this area. Specifically discussed are applications to soft interfaces, including SAMs, lipid bilayers, confined fluids, polymer surfaces, ligand-receptor bonds, and soft metallic films. ?? 2010 Elsevier Ltd. All rights reserved.
Contact mechanics; Nanoindentation; Scanning probe microscopy; Surface forces; Thin films
The motion of a thin oil sheet under the steady boundary layer on a body
Journal of Fluid Mechanics
11
02
161
1961
10.1017/S0022112061000445
161 of a steady on a By L. C. SQUIRE Royal Aircraft Establbhment, Bedford (Received 10 March 1961)
Determination of damage micromechanisms and fracture resistance of glass fiber/epoxy cross-ply laminate by means of X-ray computed microtomography
Composites Science and Technology
72
2
350-359
2012
10.1016/j.compscitech.2011.11.025
The onset and evolution of the damage in three dimensions was studied by X-ray computed micro-tomography (XCT) in a notched glass fiber/epoxy cross-ply laminate subjected to three-point bending. It was found that damage began by formation of intraply cracks in the 90° plies followed by intraply cracking the 0° plies. Fiber fracture in front of the notch tip occurred at 65% of the maximum load and finally fiber kinking and interply delamination took place under the loading point. Finite element (FE) simulations were carried out to understand crack initiation and the redistribution of stresses upon crack propagation. The crack area corresponding to each damage mechanism was quantified from the XCT images, and this information was used to determine the effective fracture resistance curve of the cross-ply laminate. © 2011 Elsevier Ltd.
A. Polymer-matrix composites; B. Fracture; B. Fracture toughness; C. Crack; X-ray computed tomography
New directions in mechanics
Mechanics of Materials
37
2-3 SPEC. ISS.
231-259
2005
10.1016/j.mechmat.2004.04.009
The Division of Materials Sciences and Engineering of the US Department of Energy (DOE) sponsored a workshop to identify cutting-edge research needs and opportunities, enabled by the application of theoretical and applied mechanics. The workshop also included input from biochemical, surface science, and computational disciplines, on approaching scientific issues at the nanoscale, and the linkage of atomistic-scale with nano-, meso-, and continuum-scale mechanics. This paper is a summary of the outcome of the workshop, consisting of three main sections, each put together by a team of workshop participants. Section 1 addresses research opportunities that can be realized by the application of mechanics fundamentals to the general area of self-assembly, directed self-assembly, and fluidics. Section 2 examines the role of mechanics in biological, bioinspired, and biohybrid material systems, closely relating to and complementing the material covered in Section 1. In this manner, it was made dear that mechanics plays a fundamental role in understanding the biological functions at all scales, in seeking to utilize biology and biological techniques to develop new materials and devices, and in the general area of bionanotechnology. While direct observational investigations are an essential ingredient of new discoveries and will continue to open new exciting research doors, it is the basic need for controlled experimentation and fundamentally-based modeling and computational simulations that will be truly empowered by a systematic use of the fundamentals of mechanics. Section 3 brings into focus new challenging issues in inelastic deformation and fracturing of materials that have emerged as a result of the development of nanodevices, biopolymers, and hybrid bio-abio systems. Each section begins with some introductory overview comments, and then provides illustrative examples that were presented at the workshop and which are believed to highlight the enabling research areas and, particularly, the impact that mechanics can make in enhancing the fundamental understanding that can lead to new technologies. © 2004 Elsevier Ltd. All rights reserved.
A mechanical model of damage and delamination in corrugated board during folding
Engineering Fracture Mechanics
72
15
2299-2315
2005
10.1016/j.engfracmech.2005.03.002
The mechanical behavior of a layered paper structure subjected to a combined load of bending and tension is studied. A finite element analysis is performed to include a gradient enhanced continuum damage theory since a non-local theory has to be used when stress gradients are present. Despite the anisotropic nature of paper materials, each layer is modeled as isotropic and homogenous where material parameters are estimated from the in-plane properties of the paper sheet. The two failure modes, material failure and delamination between top and base layer is analyzed within the frameworks of fracture and continuum damage mechanics. Delamination is assumed to be in shearing mode since the crack surfaces are predominantly sliding and crack opening is vanishing. An analytic solution for the fracture energy release rate is derived utilizing engineering beam theory assuming small deformations. Different combinations of stiffness and thickness ratios between the top and base layer are examined in order to judge the risk for having material failure or delamination failure of the multi-ply linerboard. Having a thick and weak top layer, compared to the base layer, increases the probability to obtain through-thickness damage failure in favor of delamination. On the other hand, having a stiff and thin top layer, compared to the base layer, increases the probability to obtain delamination prior to rupture of the top layer. Experiments performed on two-ply linerboards consisting of one ply of mainly virgin fibers and one ply of recycled fibers confirm the predictions made by the model.
Delamination; Linerboard; Material damage
Transverse cracks in cross-ply laminates. 1. Stress analysis
Mechanics of Composite Materials
33
6
565-582
1997
During service loading of cross ply laminates, transverse cracks occur in plies. The cracks parallel to the fiber direction are extended over the full thickness of transverse plies and often cross the entire test specimen width. It is widely recognized that the changes of laminate thermomechanical constants, caused by the transverse cracking of composite laminates, can be significant. Theoretical stress analysis in the cross ply laminates in the vicinity of cracks is performed using numerical (FE) and analytical methods. The effect of transverse cracks on the degradation of elastic properties will be discussed in Part 2 [1]. Approximate analytical micromechanical models based on shear lag predictions, variational analysis, and numerical 2D finite element calculations were verified in their predictive abilities. The three variational models used are based on the principle of minimum complementary energy and have different degrees of accuracy with respect to the stress assumptions used (Hashin's, 2D 0° and 2D 0°/90° models). Using FEM, the plane stress and strain state were analyzed. The effect of material properties and layer thickness on the stress distribution in a 90° layer was evaluated by varying the crack spacing. The crack opening displacement (COD), normalized with respect to the far field strain, is proposed as a measure of reduction of the mechanical properties. Since the CODs are rather insensitive to the crack spacing (crack density) in a wide region, they will be used in modeling the stiffness reduction in these laminates [1].
Vascular mechanics of the coronary artery.
Zeitschrift fur Kardiologie
89 Suppl 2
92-100
2000
10.1007/s003920070106
This paper describes our research into the vascular mechanics of the coronary artery and plaque. The three sections describe the determination of arterial mechanical properties using intravascular ultrasound (IVUS), a constitutive relation for the arterial wall, and finite element method (FEM) models of the arterial wall and atheroma. METHODS: Inflation testing of porcine left anterior descending coronary arteries was conducted. The changes in the vessel geometry were monitored using IVUS, and intracoronary pressure was recorded using a pressure transducer. The creep and quasistatic stress/strain responses were determined. A Standard Linear Solid (SLS) was modified to reproduce the non-linear elastic behavior of the arterial wall. This Standard Non-linear Solid (SNS) was implemented into an axisymetric thick-walled cylinder numerical model. Finite element analysis models were created for five age groups and four levels of stenosis using the Pathobiological Determinants of Atherosclerosis Youth (PDAY) database. RESULTS: The arteries exhibited non-linear elastic behavior. The total tissue creep strain was epsilon creep = 0.082 +/- 0.018 mm/mm. The numerical model could reproduce both the non-linearity of the porcine data and time dependent behavior of the arterial wall found in the literature with a correlation coefficient of 0.985. Increasing age had a strong positive correlation with the shoulder stress level, (r = 0.95). The 30% stenosis had the highest shoulder stress due to the combination of a fully formed lipid pool and a thin cap. CONCLUSIONS: Studying the solid mechanics of the arterial wall and the atheroma provide important insights into the mechanisms involved in plaque rupture.
NASA Discipline Cardiopulmonary; NASA Program Biomedical Research and Countermeasur; Non-NASA Center
Initiation and propagation of interfacial delamination in integrated thin-film structures
2010 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, ITherm 2010
m
2010
10.1109/ITHERM.2010.5501290
Interfacial delamination has been a major reliability issue for both BEoL and packaging systems. The failure is often due to poor adhesion of interfaces. Thus characterization of interfacial properties is critical for material selection and process control. Conventional methods for interfacial adhesion and fracture toughness measurements are generally based on linear elastic fracture mechanics. More detailed local measurements are required to fully characterize the interfaces based on a nonlinear cohesive interface model. With the experimentally determined interfacial properties, cohesive interface modeling can be set up to predict the initiation and evolution of interfacial failure in chip-package systems. In this study, two model systems are considered by approaches of both linear elastic fracture mechanics (LEFM) and cohesive interface modeling (CIM). First, for a brittle thin film on a compliant substrate, the initiation and propagation of delamination from the root of a channel crack is simulated. The effects of the cohesive strength and fracture toughness of the interface on channel cracking of thin films on compliant substrates are analyzed. Second, a four-point bend test is considered, in comparison with experimental measurements of the local crack opening displacements.
Delamination; Fracture; Interface
MECHANICS OF THE PEEL TEST FOR THIN FILM ADHESION
Materials Research Society Symposium Proceedings
119
31-41
1988
10.1557/PROC-119-31
bility of the peel test for thin film adhesion have been investigated. Firstly, the effect of plasticity in the peel test of thin metallic films is analyzed. The analysis has given a closed ABSTRACT The mechanics aspects of the peel test are analyzed. In this analysis, the limitation and form solution for the partitioning of peel strength between the energy expenditure rate for the decohesion process and the internal work expenditure rate caused by plastic deformation (bending) of the film. The results predicted the variation of peel strength as a function of the film thickness, the film yield stress and the compliance of the substrate. This analysis shows that the peel strength is very sensitive to the thickness of the film and the yield stress of the film. As observed in the experiment, the peel strength has a peak value at a certain thickness of the film. This is explained for both L and T peel tests. Unlike the L peel test, the peak phenomenon in the T peel test (of metallic films) is due to the hardening of the adhered film. Secondly, the effect of plasticity and viscoelasticity in the peel test of thin polymer films is analyzed. Unlike the peel test of metallic films, tension and shear effect of the film deformation is very important in the analysis of the polymer peel test. An integral equation is formulated for the viscoelastic models of the adhered film. The solution of the integral equation reveals the important parameters in polymer peeling and their contribution to the peel force as well as to the viscoelastic dissipation. In addition, the meaning of the interface toughness is reexamined and the interface toughness is evaluated by the peel test. Based on these analyses, a Universal Peel Diagram has been constructed, which accounts for the hardening behavior of the film. On this diagram, objective interfacial decohesion toughness can be readily obtained using very simple peel tests. The analysis includes not only the 900 peel test but also the general angle peel test. Comparison between the theory and experiment has been made with the experimental data provided by J. Kim of IBM. The comparison shows good agreement.
Collapse of thin–wall composite sections subjected to high speed axial loading
International Journal of Vehicle Design
13
5-6
564-579
1992
10.1504/IJVD.1992.061748
In this paper, static and dynamic crushing tests in a speed range of 18?24 m/s were conducted on specimens of different geometries: square tube, circular tube, and circular cone specimens made of three different composite materials. Two of the composite materials consist of fibreglass and vinylester resin, but with different fibre contents and ply lay?up. The third is made of fibreglass and polyester resin. This study investigated the effects of specimen geometry and crush speed on the specific energy absorption of these composite materials. It was found that for specimens showing stable crushing, greater thickness lends to reduce the specific energy absorption; square tubes have less specific energy absorption than circular tubes, and greater cone angle results in lower specific energy. Crushing speed does not have significant effect on the specific energy absorption of thin?walled circular or square tubes made of the three kinds of composite materials. However, specific energy of thin?walled circular conical specimens made of polyester resin and random chopped strand mat of glass fibre were reduced by some 35% under a crushing speed of about 21 m/s. It is also clear from this study that at higher crush speeds the crushing mechanisms of tubular specimens with large thickness differ from the static cases.
The Cracking and Decohesion of Thin Brittle Films
MRS Proceedings
130
May
1043-1049
1988
10.1557/PROC-130-213
Film cracking and decohesion and two typical failure modes observed\nin thin coatings. In this investigation, failures were initiated\nin brittle Cr films deposited on both ductile and brittle substrates\nto study these phenomena. Fracture mechanics models were proposed\nto interpret the experimental observations. Excellent agreement between\ntheory and experiment has been demonstrated.
Free Vibration of Two-layered Cross-Ply Laminated Plates Using Layer-wise Trigonometric Shear Deformation Theory
Journal of Reinforced Plastics and Composites
23
4
389-405
2004
10.1177/0731684404031893
In this paper, variationally consistent layer-wise trigonometric shear\ndeformation theory has been extended to deal with free vibration\nof two-layered laminated cross-ply plates. Governing differential\nequations are derived by making use of a displacement field which\nallows a sinusoidal variation of the in-plane displacements through\nthe laminate thickness. In this displacement based theory, constitutive\nrelations between shear-stress and shear-strains are satisfied in\nboth the layers, and, therefore, shear correction factor is not required.\nCompatibility at the layer interface in respect of in-plane displacement\nand compatibility in respect of transverse shear-stress is satisfied,\nyet present theory contains fewer unknown variables than that of\nthe first order shear deformation theory. Effects of rotary inertia\nand other inertias are also included. Efficacy of the present theory\nis demonstrated through illustrative examples.
cross-ply plate; free vibration; laminated thick; layer-wise theory; plate; rotary inertia; shear deformation
Free vibration of anti-symmetric angle-ply laminated conical shells
Composite Structures
122
488-495
2015
http://dx.doi.org/10.1016/j.compstruct.2014.11.075
Abstract Free vibration of anti-symmetric angle-ply composite laminated conical shells is studied including shear deformation using spline function approximation. The equilibrium equations are formulated in terms of displacement and rotational functions. These functions are approximated using Bickley-type splines to obtain the generalised eigenvalue problem with suitable boundary conditions. Parametric studies are made to analyse the effects of circumferential node number, length ratio and cone angle on the frequency parameter for different number of layers and materials with different ply orientations under two types of boundary conditions.
Angle-ply; Conical shells; Free vibration; Shear deformation; Spline
The fracture of brittle thin films on compliant substrates in flexible displays
Engineering Fracture Mechanics
69
5
597-603
2002
10.1016/S0013-7944(01)00104-7
One mechanical issue in flexible organic light emitting displays (OLED) is the fracture of extremely thin brittle conducting transparent oxide films deposited on thin flexible substrates. Understanding the behaviour of these films under flexed condition is essential for designer of flexible OLED. Controlled buckling experiments on the film and substrate have been designed to study the fracture of the films under both tension and compression. Fracture of the film is superficially similar in both tension and compression. However, under tension a channelling crack is formed, while under compression, the film delaminates, buckles and cracks in a tunnelling motion. The fracture toughness of the film and the delamination toughness have been estimated from these experiments. Design to maximise the flexibility of the device is discussed. ?? 2002 Elsevier Science Ltd. All rights reserved.
Delamination; Flexible displays; Fracture toughness; Indium-tin oxide; Thin film
The macroscopic delamination of thin films from elastic substrates.
Proceedings of the National Academy of Sciences of the United States of America
106
27
10901-6
2009
10.1073/pnas.0902160106
The wrinkling and delamination of stiff thin films adhered to a polymer substrate have important applications in "flexible electronics." The resulting periodic structures, when used for circuitry, have remarkable mechanical properties because stretching or twisting of the substrate is mostly accommodated through bending of the film, which minimizes fatigue or fracture. To date, applications in this context have used substrate patterning to create an anisotropic substrate-film adhesion energy, thereby producing a controlled array of delamination "blisters." However, even in the absence of such patterning, blisters appear spontaneously, with a characteristic size. Here, we perform well-controlled experiments at macroscopic scales to study what sets the dimensions of these blisters in terms of the material properties and explain our results by using a combination of scaling and analytical methods. Besides pointing to a method for determining the interfacial toughness, our analysis suggests a number of design guidelines for the thin films used in flexible electronic applications. Crucially, we show that, to avoid the possibility that delamination may cause fatigue damage, the thin film thickness must be greater than a critical value, which we determine.
Determination of the first ply failure load for a cross ply laminate subjected to uniaxial tension through computational micromechanics
International Journal of Solids and Structures
51
13
2549-2556
2014
10.1016/j.ijsolstr.2014.03.030
A method for determining the in situ strength of fiber-reinforced laminas for three types of transverse loading including compression, tension and shear is presented. In the framework of this method, an analysis of local stresses that are responsible for the coalescence of matrix cracks is carried out by using a multi-fiber unit cell model and finite element method. The random distribution of fibers, fiber–matrix decohesion and matrix plastic deformations are taken into account in the micromechanical simulations. The present study also shows that the nonlinear hardening behavior of matrix reflects more realistically the influence of plastic deformations on the in situ transverse strength of lamina than the perfectly plastic behavior of matrix. The prediction of the in situ transverse strength is verified against the experimental data for a cross ply laminate subjected to uniaxial tension.
Computational micromechanics; First ply failure; Matrix cracking; Polymer–matrix composites
Damage Detection in Thin Composite Laminates Using Piezoelectric Phased Sensor Arrays and Guided Lamb Wave Interrogation
Journal of Intelligent Material Systems and Structures
21
July
995-1010
2010
10.1177/1045389X10372003
Damage detection in composite laminated panels using Lamb waves is demonstrated with an innovative use of a sensor array and processing algorithm. Two models were developed to characterize the Lamb wave propagation properties of orthotropic panels. Predictions of the dispersion relations were made for a fiber-reinforced composite laminate. Experiments were conducted to empirically characterize the wave propagation behavior in a manufactured laminate. Piezoelectric patches were used as sensors and actuators in the experiments. Comparisons were made between analytical predictions and experimental results, which demonstrate that the higher order model captured essential wave propagation behavior at frequencies of interest. Sensor arrays and associated processing were used for wavenumber decomposition and filtering of the Lamb wave modes. Composite laminates were manufactured with an embedded defect to simulate inter-ply delamination. Experiments were conducted to detect the presence of delamination damage in a composite laminate.
piezoelectric; sensor; structural health monitoring
Free vibration of cross-ply laminated beams with arbitrary boundary conditions
International Journal of Engineering Science
32
12
1971-1980
1994
http://dx.doi.org/10.1016/0020-7225(94)90093-0
Analytical solutions of refined beam theories are developed to study the free vibration behavior of cross-ply rectangular beams with arbitrary boundary conditions in conjunction with the state space approach. The study concludes that the disagreement between different shear deformation theories is much less than the disagreement between any of them and Euler-Bernoulli theory.
Evolution of Wrinkles in Elastic-Viscoelastic Bilayer Thin Films
Journal of Applied Mechanics
72
6
955
2005
10.1115/1.2043191
This paper develops a model for evolving wrinkles in a bilayer thin\nfilm consisting of an\n\nelastic layer and a viscoelastic layer. The elastic layer is subjected\nto a compressive\n\nresidual stress and is modeled by the nonlinear von Karman plate theory.\nA thin-layer\n\napproximation is developed for the viscoelastic layer. The stability\nof the bilayer and the\n\nevolution of wrinkles are studied first by a linear perturbation analysis\nand then by\n\nnumerical simulations. Three stages of the wrinkle evolution are identified:\ninitial growth\n\nof the fastest growing mode, intermediate growth with mode transition,\nand, finally, an\n\nequilibrium wrinkle state.
Analysis of local delaminations in composite laminates with angle-ply matrix cracks
International Journal of Solids and Structures
39
6
1515-1537
2002
10.1016/S0020-7683(02)00007-0
In this paper, local delaminations growing uniformly from the tips of angle-ply matrix cracks in composite laminates loaded in tension are modelled theoretically. A 2-D shear lag method is used to determine stresses in a laminate representative segment containing one crack and two crack tip delaminations. For the calculation of the strain-energy release rate (SERR) associated with delaminations, the damaged layer is replaced with an equivalent homogeneous one with effective elastic properties. Closed-form expressions for the total SERR and its mode I and mode II components as a linear function of the first partial derivatives of the effective elastic properties of the damaged layer with respect to delamination area are derived. Dependence of SERRs and the laminate stiffness properties on delamination area, crack density and ply orientation angle is examined for balanced [O2/??2/-??2]5 and unbalanced [O2/??2]5 carbon/ epoxy laminates. The total SERR obtained in this study is compared to a simple closed-form expression for a uniform local delamination derived in earlier work by O'Brien (Local delamination in laminates with angle-ply matrix cracks: Part II Delamination Fracture Analysis and Fatigue Characterization. NASA Technical Memorandum 104076/AVS-COM Technical Report 91-B-011). It appears that matrix crack density and delamination size influence the SERR value significantly. ?? 2002 Elsevier Science Ltd. All rights reserved.
Composite materials; Delamination; Fracture; Micromechanics; Modelling; Shear lag; Stiffness
On the transverse cracking and stiffness degradation of aged angle-ply laminates
Materials Letters
60
21-22
2561-2564
2006
10.1016/j.matlet.2006.01.037
A modified shear lag analysis, taking into account the concept of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in aged angle-ply laminated composites. The results of this paper represent well the dependence of the degradation of elastic properties on the cracks density, hygrothermal conditions and the fibre orientation of the outer layers.
Angle-ply laminates; Hygrothermal effect; Stiffness reduction; Stress perturbation function; Transverse cracking
Fracture mechanics analysis on Smart-Cut® technology. Part 2: Effect of bonding flaws
Acta Mechanica Sinica/Lixue Xuebao
25
2
197-203
2009
10.1007/s10409-008-0193-7
In Part 2 of the paper on the Smart-Cut process, the effects of bonding flaws characterized by the size and internal pressure before and after splitting are studied by using fracture mechanics models. It is found that the bonding flaws with large size are prone to cause severe deviation of defect growth, leading to a non-transferred area of thin layer when splitting. In a practical Smart-Cut process where the internal pressure of bonding flaws is very small, large interfacial defects always promote defect growth in the splitting process. Meanwhile, increasing the internal pressure of the bonding flaws decreases the defect growth and its deviation before splitting. The mechanism of relaxation of stiffener constraint is proposed to clarify the effect of bonding flaws. Moreover, the progress of the splitting process is analyzed when bonding flaws are present. After splitting, those bonding flaws with large size and high internal pressure are vulnerable for the blistering of the thin film during high-temperature annealing. © 2008 The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH.
Asphalt pavements; Before and after; Defect growths; Defects; Fracture; Fracture mechanics; Fracture mechanics analysis; Fracture mechanics models; High-temperature annealing; Interfacial defect; Internal pressures; Large sizes; Smart-Cut technology; Splitting process; Strength of materials; Stress intensity factor; Stress intensity factors; Thin layers
A meso-scale unit-cell based material model for the single-ply flexible-fabric armor
Materials and Design
30
9
3690-3704
2009
10.1016/j.matdes.2009.02.008
A meso-scale unit-cell based material model for a prototypical plain-woven single-ply flexible armor is developed and implemented in a material user subroutine for use in commercial explicit finite element programs. The main intent of the model is to attain computational efficiency when calculating the mechanical response of the multi-ply fabric-based flexible armor material during its impact with various projectiles without significantly sacrificing the key physical aspects of the fabric microstructure, architecture and behavior. To validate the new model, a comparative finite element method (FEM) analysis is carried out in which: (a) the plain-woven single-ply fabric is modeled using conventional shell elements and weaving is done in an explicit manner by snaking the yarns through the fabric and (b) the fabric is treated as a planar continuum surface composed of conventional shell elements to which the new meso-scale unit-cell based material model is assigned. The results obtained show that the material model provides a reasonably good description for the fabric deformation and fracture behavior under different combinations of fixed and free boundary conditions. ?? 2009 Elsevier Ltd.
Ballistic performance; Flexible armor; High-performance fibers; Material model; Meso scale; Unit cell
High Strain Rate Response of Angle-Ply Glass/Epoxy Laminates
Journal of Composite Materials
29
1308-1320
1995
10.1177/002199839502901003
The effects of strain rate on the mechanical behavior of Scotchply Type 1002 glass/epoxy angle-ply laminates is investigated. High strain rate tests (approximately 103 sec-1) using a direct tension split Hopkinson bar apparatus and quasi-static tests (strain rate of approximately 10-4 sec-1) using a servo-hydraulic testing machine have been conducted. Results indicate that the maximum normal stress experienced by glass/epoxy laminates is higher for dynamic than for quasi-static loading conditions. Although both fibers and matrix are sensitive to the strain rate, the fibers influence laminate rate sensitivity more than the matrix.
Numerical modeling of progressive damage in fiber reinforced plastic cross-ply laminates
Composites Science and Technology
68
10-11
2282-2289
2008
10.1016/j.compscitech.2008.04.021
A numerical model of the progressive damage in cross-ply laminates (e.g., transverse cracks, interlaminar delaminations, and fiber breaks) is proposed. In this model, the embedded process zone (EPZ) model is used for the transverse cracks and interlaminar delaminations; the truss elements are used to express the fiber breaks. First, we describe the formulation and algorithm of this model. Second, we calculate the transverse cracking stress in CFRP [0/90]s laminates and compare it with the experiments by Boniface et al. The comparison validates that our model can appropriately simulate the onset and accumulation of transverse cracks for an arbitrary thickness of the 90?? ply to the 0?? ply with a set of parameters. Finally, this model is applied to our experiments for GFRP [90/0]s laminates. The simulated results reproduce the complicated progressive damage in GFRP [90/0]s laminates very well. ?? 2008 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); C. Computational simulation; C. Embedded process zone (EPZ) model; C. Finite-element analysis (FEA); C. Transverse cracking
Riveting process modeling and simulating for deformation analysis of aircraft's thin-walled sheet-metal parts
Chinese Journal of Aeronautics
24
3
369-377
2011
10.1016/S1000-9361(11)60044-7
The riveting joint is one of the important joint methods to permanently fasten two thin-walled sheet-metal parts. It is most basic to efficiently analyze and estimate the deformation of the riveting joint for the performance, fatigue durability and damage of the riveting structure in the aircraft. This paper researches the riveting process mathematics modeling and simulating to more accurately analyze deformation of thin-walled sheet-metal parts. First, the mathematics and mechanics models for the elastic deformation, plastic deformation and springback of the rivet are built by mechanics theory. Second, on the basis of ABAQUS system, a finite element system, an instance made up of the rivet and two thin-walled sheet-metal parts of aluminum alloy is used to analyze and simulate the stress and deformation. What's more, a comparison is made between the results obtained by the mathematics and mechanics models and those by finite element method (FEM). The models are proved true by the calculating and simulation results of the instance. ?? 2011 Elsevier Ltd. All rights reserved.
aircraft; deformation; finite element method; mechanics modeling; riveting; thin-walled structure
Modified Listeria bacteriophage lysin genes (ply) allow efficient overexpression and one-step purification of biochemically active fusion proteins
Applied and Environmental Microbiology
62
8
3057-3060
1996
Listeria bacteriophage lytic enzymes are useful for in vitro applications such as rapid, gentle cell disruption, and they provide new approaches as selective antimicrobial agents for destruction of Listeria monocytogenes in contaminated foods. We describe here the amino-terminal modification of three cloned Listeria phage lysin genes (ply), resulting in fusion proteins with a 12-amino-acid leader containing six consecutive histidine residues. The recombinant enzymes retain their native specific activity and can be efficiently overproduced in Escherichia coli. By one-step metal chelate affinity chromatography, active lysins could be purified to more than 90% homogeneity.
Out-of-plane hygroinstability of multi-ply paperboard
Fibre Science and Technology
14
3
201-212
1981
10.1016/0015-0568(81)90012-9
An equation for predicting the out-of-plane dimensional instability (curl) of a hygroscopic multi-ply paperboard subjected to a variable environment has been derived. The analysis is based on classical lamination theory combined with Hooke's law modified for swelling. Each constituent ply of the material is considered as a macroscopic homogeneous medium with properties described by the orthotropic model. The application of the derived equation for multi-ply paper was tested for two-ply boards. The data required are those relating to the elastic and expansional properties as a function of the moisture content for each ply. A general agreement is established between predicted and measured changes in curvature at different relative humidities in experiments where the sheet forming, drying and subsequent evaluation of the sheets are fully controlled.
Kindergarten Quantum Mechanics
Quantum Theory: Reconsiderations of the Foundations III
81-98
2005
10.1109/TSG.2010.2091656
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.
category theory; dirac notation; graphical calculus; logic; quantum formalism; quantum information; quantum mechanics
Experimental and theoretical analyses of first-ply failure of laminated composite pressure vessels
Composite Structures
49
2
237-243
2000
10.1016/S0263-8223(99)00133-6
Experimental and analytical approaches are studied via the first-ply failure strength on symmetrically laminated composite pressure vessels with various material properties, radius-to-thickness ratios, and different numbers of layers subjected to uniform internal pressure loads. Optimal angle-ply orientations of generally laminated symmetric [[theta]/-[theta]/...]S shells designed for maximum stiffness were investigated. A hand lay-up technique was used to laminate composite pressure vessels by the stacking of pieces of prepreg in the desired orientations and subsequent curing. The first-ply failure pressure loads of the laminated composite pressure vessels are determined using the acoustic emission AMS3 (AE) system. The experimental results have been proved to be efficient and effective in the theoretical prediction of first-ply failure strengths of laminated composite pressure vessels.
experimental and analytical approaches; first-ply failure strength; laminated composite pressure vessels
Damage Mechanics Analysis of Transverse Cracking Evolution in Delaminated CFRP Laminates
Journal of Reinforced Plastics and Composites
18
1360-1366
1999
10.1177/073168449901801501
A damage mechanics analysis was applied to predict transverse crack evolution in a laminated composite. The analysis was originally developed to predict thermoelastic properties of a laminate containing transverse cracks. Two criteria based on both critical average ply stress and critical energy release rate were used to discuss the transverse cracking behavior. The effect of delamination was also considered in the present study. The predictions of transverse crack density based on both criteria were successfully compared with experimental results. This analysis can be applied to laminate with arbitrary lay-up configuration.
MODELLING AND IDENTIFICATION OF TEMPERATURE- ELEMENTARY PLY IN CARBON / EPOXY
Composites Science and Technology
56
883-888
1996
This paper develops, at the elementary-ply level, a mode1 of the mechanical behaviour of continuous-fibre carbon/epoxy composite laminates subject to in-plane loads at temperatures in the range -120 to +12O”C. Attention is focused on the influence of temperature on the mechanical behaviour for load intensities extending to material failure. Damage mechanisms are introduced via meso-damage variables associated with the softening of ply stifiess. Inelastic strains are accounted for through a plasticity model coupled with damage. A careful analysis of the influence of temperature shows that experiments performed at three suitably chosen temperatures are suflcient to yield a precise identification of the single layer mode1 within the full temperature range.
laminates; temperature-dependent
The behaviour of cross-ply hybrid matrix composite laminates
Composites
23
6
397-405
1992
10.1016/0010-4361(92)90002-C
Two types of cross-ply laminate have been made from prepreg: (a) hybrid matrix laminates consisting of longitudinal plies of glass fibres in epoxy resin and transverse plies of glass fibres in epoxy resin/urethane elastomer blend; and (b) uniform matrix laminates with the same resin in both the longitudinal and transverse plies. The presence of the urethane in the transverse plies increases the applied strains necessary for the initiation and development of transverse cracking during the extension of both hybrid matrix and uniform matrix laminates. The effect is greater with increasing amounts of urethane. The cracking data, stress/strain behaviour, acoustic emission response and ply thickness effects on crack development are discussed in the light of existing theories concerning transverse cracking.
The Non-Linear Field Theories of Mechanics
Journal of Applied Mechanics
33
4
958
1966
10.1115/1.3625229
Matter is commonly found in the form of materials Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber,... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.
The effects of creep and fatigue stress ratio on the long-term behaviour of angle-ply CFRP
Composite Structures
57
205-210
2002
10.1016/S0263-8223(02)00084-3
The long-term behaviour of ??45??-angle-ply laminates of carbon/epoxy was studied. Due to the absence of 0??-layers angle-ply laminates are subject to cyclic creep. The creep strain evolution was investigated by experimental and analytical means. To predict the total strain depending on the applied stress level and load time an empirical creep law based on power law functions was adopted. Good agreement between experiment and prediction was found. The interaction between creep and fatigue was used to estimate a lower bound of the endurance limit based on creep predictions exclusively. ?? 2002 Elsevier Science Ltd. All rights reserved.
Characterizing viscoelastic properties of thin elastomeric membrane
Mechanics of Materials
34
8
485-491
2002
10.1016/S0167-6636(02)00176-X
We present a new method to characterize the viscoelastic properties of a thin polymeric film. A sensitive microscope visualization instrument was used for measuring the time-dependent deformation, i.e. creep, of the circular thin membrane under a constant load. The elastic deformation of the thin membrane was measured laterally. The elastic modulus as a function of time can be explicitly determined by our recently developed equations. A viscoelastic theory, Zener model, was applied to interpret the measured time-dependent deformation of the membrane under various temperatures, and the creep parameters can therefore be quantitatively estimated. The results show the elastic constants and viscosity coefficient of the membrane materials decrease with the increasing temperatures.
Creep; Elasticity; Mechanical characterization; Polymeric membrane; Viscoelasticity
Modelling and finite element treatment of intra-ply shearing of woven fabric
Journal of Materials Processing Technology
138
1-3
47-52
2003
10.1016/S0924-0136(03)00047-5
Diaphragm forming of fibre/epoxy materials is a potential cost-effective approach in manufacturing aerospace components. Significant intra-ply shearing is essential in diaphragm forming a double-curvature geometry. In previous studies, the intra-ply shearing was addressed based on an ideal fibre reinforced fluid (IFRF) model. The IFRF model was tried in the present study for a thermoset material. However, it fails to interpret the experimental results. New models, namely general hinge model and restrained membrane model were thus suggested for intra-ply shearing simulations. The concept of the restrained membrane model was demonstrated using finite element simulations with determined material properties. The proposed model provided a good reproduction of the experimental results. Discussions were given on inherent limitations of the IFRF model and the effects of fibre in-plane bending.
Diaphragm forming; Finite element simulation; Intra-ply shearing; Modelling
Fracture-Mechanics for Thin-Film Adhesion
Ibm Journal of Research and Development
38
4
367-377
1994
The essential elements of the mechanics of delamination are reviewed and their implications for design are discussed. Two important concepts for the prediction of the reliability of thin-film systems are emphasized: 1) limiting solutions for the crack-driving force that are independent of flaw size, and 2) ''mixed-mode fracture.'' Consideration of the first concept highlights the possibility of flaw-tolerant design in which the statistical effects associated with flaw distributions can be eliminated. The significance of mode-mixedness includes its effect on crack trajectories and on the interface toughness, two key variables in determining failure mechanisms. Theoretical predictions are given for some cases of delamination of thin films under compressive stresses, and the results are compared with experimental observations to illustrate appropriate design criteria for the model systems studied.
bimaterial interfaces; blister test; brittle films; cracking; decohesion; delamination; mixed-mode fracture; peel-test; resistance; substrate
Mechanics of fluids
Nature
272
5648
109-109
1978
10.1038/272109a0
Massey, B. S. (1983). Mechanics of Fluids (Fifth ed.). Van Nostrand Reinhold
Probabilistic energy based model for prediction of transverse cracking in cross-ply laminates
International Journal of Solids and Structures
42
2
365-392
2005
10.1016/j.ijsolstr.2004.06.043
In the present paper an attempt is made to describe transverse cracking of cross-ply ([0??n/90??m]s) laminates subjected to an external applied load and a temperature change. For this purpose a new method is suggested which was developed on the basis of the energy balance based finite fracture criterion suggested by Hashin (1996) [Hashin, Z., 1996. J. Mech. Phys. Solids 44, 1129]. In this approach the value of the specific surface energy (the critical energy release rate) is assumed to be dependent on a random microdamage distribution in the material. Hence, it is assumed to be a random function of location. A new probabilistic technique is developed to take this randomness into consideration. It is shown that only one unknown probabilistic function is required, namely the probability density function of the specific surface energy. This is determined by fitting the external stress and the corresponding crack density to experimental data for any specific laminated system. The cracking process for any other laminate made of the same material may be predicted by the suggested method. Numerical simulation of progressive cracking process is described, which provides the probability density function for inter-crack distances as well as the crack density growth with increasing external loading. A simple probabilistic progressive cracking criterion is developed as well. The predicted crack density growth calculated for various laminates is in good agreement with published experimental results. ?? 2004 Elsevier Ltd. All rights reserved.
Brittle fracture; Crack density; Cross ply laminates; Finite fracture criterion; Probability of fracture; Transverse cracks; Variational stress analysis
Finite element analysis of substrate effects on indentation behaviour of thin films
Thin Solid Films
447-448
03
399-405
2004
10.1016/S0040-6090(03)01071-X
The substrate effects on indentation behaviour of thin films are analysed using finite element (FE) method. There is no universal critical penetration depth beyond which the substrate effects come in. The critical penetration depth is dependent on the combination of the film and the substrate and more sensitive to differences in the elastic properties than in the plastic properties of the filmysubstrate system. The FE simulation results of the effects of the substrate on the elastic modulus and the hardness of the filmysubstrate system have also been compared with the empirical models of Doerner and Bhattacharya, respectively.
finite element method; indentation; thin films
Polymer microlenses for quantifying cell sheet mechanics
Soft Matter
6
2
398
2010
10.1039/b916385a
Mechanical interactions between individual cells and their substrate have been studied extensively over the past decade; however, understanding how these interactions change as cells interact with neighboring cells in the development of a cell sheet, or early stage tissue, is less developed. We use a recently developed experimental technique for quantifying the mechanics of confluent cell sheets. Living cells are cultured on a thin film of polystyrene [PS], which is attached to a patterned substrate of crosslinked poly(dimethyl siloxane) [PDMS] microwells. As cells attach to the substrate and begin to form a sheet, they apply sufficient contractile force to buckle the PS film over individual microwells to form a microlens array. The curvature for each microlens is measured by confocal microscopy and can be related to the strain and stress applied by the cell sheet using simple mechanical analysis for the buckling of thin films. We demonstrate that this technique can provide insight into the important materials properties and length scales that govern cell sheet responses, especially the role of stiffness of the substrate. We show that intercellular forces can lead to significantly different behaviors than the ones observed for individual cells, where focal adhesion is the relevant parameter.
Ultrasonic Evaluation of Thin, Fiber-Reinforced Laminates
J. Composite Materials
28
4
329-342
1994
This paper reports on the characterization of one- or two-ply, unidirectional and left bracket 0,90,0 right bracket //t, cross-ply graphite/epoxy laminates whose thicknesses were approximately 145 mu m, 275 mu m and 400 mu m, respectively. The measurements are based on the application of the ultrasonic point-source/point-receiver technique (PS/PR) using either a focused laser beam operating as a dipole source or a small aperture, piezoceramic shear transducer serving as a monopole source. Detection of the signals is with a piezoceramic sensor that directly responds to the lateral or shear motions of the specimen surface. The detected time signals represent the detailed spatial and temporal characteristics of the elastic wave field. The experimental group velocity data is analyzed using a simple plane-wave, plane-stress model that describes the propagation of quasi-longitudinal and quasi-transverse membrane waves in the plane of the plate. We demonstrate in this paper the strength of the PS/PR measurement technique when coupled with appropriate signal processing to recover the stiffness tensor of thin, fiber-reinforced laminates. Additionally, preliminary experimental results on the detection of flaws in thin specimens from in-situ measurements are included. (Author abstract) 18 Refs.
Communication: quantum mechanics without wavefunctions.
The Journal of chemical physics
136
3
031102
2012
10.1063/1.3680558
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications-theoretical, computational, and interpretational-are discussed.
Quantum Theory
Mechanics of the human femoral adventitia including the high-pressure response.
American journal of physiology. Heart and circulatory physiology
282
6
H2427-H2440
2002
10.1152/ajpheart.00397.2001
Adventitial mechanics were studied on the basis of adventitial tube tests and associated stress analyses utilizing a thin-walled model. Inflation tests of 11 nonstenotic human femoral arteries (79.3 +/- 8.2 yr, means +/- SD) were performed during autopsy. Adventitial tubes were separated anatomically and underwent cyclic, quasistatic extension-inflation tests using physiological pressures and high pressures up to 100 kPa. Associated circumferential and axial stretches were typically <20%, indicating "adventitiosclerosis." Adventitias behaved nearly elastically for both loading domains, demonstrating high tensile strengths (>1 MPa). The anisotropic and strongly nonlinear mechanical responses were represented appropriately by two-dimensional Fung-type stored-energy functions. At physiological pressure (13.3 kPa), adventitias carry ~25% of the pressure load in situ, whereas their circumferential and axial stresses were similar to the total wall stresses (~50 kPa in both directions), supporting a "uniform stress hypothesis." At higher pressures, they became the mechanically predominant layer, carrying >50% of the pressure load. These significant load-carrying capabilities depended strongly on circumferential and axial in-vessel prestretches (mean values: 0.95 and 1.08). On the basis of these results, the mechanical role of the adventitia at physiological and hypertensive states and during balloon angioplasty was characterized.
Quantum Mechanics - A Modern Development - L. Ballentine.pdf
American Journal of Physics
59
1153
1998
10.1119/1.16631
Although there are many textbooks that deal with the formal apparatus of quantum mechanics and its application to standard problems, before the first edition of this book (PrenticeHall, 1990) none took into account the devel- opments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the founda- tions of quantum mechanics, but they do not integrate those topics into the standard pedagogical material. I hope to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpreta- tion and broader implications of the theory. This book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of quantum mechanics. Parts of the book could be used by senior undergraduates.
Experiments on elastic cloaking in thin plates
Physical Review Letters
108
1
1-5
2012
10.1103/PhysRevLett.108.014301
Following a theoretical proposal [ M. Farhat et al. Phys. Rev. Lett. 103 024301 (2009)], we design, fabricate, and characterize a cloaking structure for elastic waves in 1 mm thin structured polymer plates. The cloak consists of 20 concentric rings of 16 different metamaterials, each being a tailored composite of polyvinyl chloride and polydimethylsiloxane. By using stroboscopic imaging with a camera from the direction normal to the plate, we record movies of the elastic waves for monochromatic plane-wave excitation. We observe good cloaking behavior for carrier frequencies in the range from 200 to 400 Hz (one octave), in good agreement with a complete continuum-mechanics numerical treatment. This system is thus ideally suited for demonstration experiments conveying the ideas of transformation optics.
Thermodynamics and Statistical Mechanics
Journal of The Electrochemical Society
104
10
226C
1957
10.1149/1.2428420
By detailed molecular dynamics and Monte Carlo simulations of a model system we show that granular materials at rest can be described as thermodynamics systems. First, we show that granular packs can be characterized by few parameters, as much as fluids or solids. Then, in a second independent step, we demonstrate that these states can be described in terms of equilibrium distributions which coincide with the statistical mechanics of powders first proposed by Edwards. We also derive the system equation of state as a function of the "configurational temperature," its new intensive thermodynamic parameter.
Thin film deposition: fundamentals and modeling
Computational Materials Science
12
4
354-380
1998
10.1016/S0927-0256(98)00022-6
We review some of the principles of thin film growth. We begin with a description of the growth modes of films and relate the different structures to the thermodynamic driving forces and to kinetics. The influence of misfit strain, surface free energies, and interface energies are discussed in detail. In particular, we treat the instability of a moving crystal-vapor surface resulting from stress, and the stabilizing influence of step energies in the case where the surface is coincident with a low-index orientation below its surface roughening transition temperature. The introduction of defects by strain, high growth rates, and shadowing instabilities are described. A Monte Carlo model of Al is developed; the model parameters are derived from molecular dynamics calculations of atomic level energetics and kinetics. Anisotropies in surface energies and surface mobilities are found to be large, and have a strong influence on film structures. An extension of the model to polycrystalline films is included. Some of the issues involved in metallization of silicon devices are discussed using results from this model. (C) 1998 Published by Elsevier Science B.V. All rights reserved.
Lattice mechanics of origami tessellations
Physical Review E
92
1
013205
2015
10.1103/PhysRevE.92.013205
Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there has been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid mechanics need to be developed to understand their long-wavelength behavior. We introduce here a lattice theory for examining the mechanics of origami tessellations in terms of the topology of their crease pattern and the relationship between the folds at each vertex. This formulation provides a general method for associating mechanical properties with periodic folded structures, and allows for a concrete connection between more conventional materials and the mechanical metamaterials constructed using origami-based design.
Residual Tensile Strength Prediction on a Ply-by-Ply Basis for Laminates Containing Impact Damage
Journal of Composite Materials
26
8 PG - 1193
-1206
1992
10.1177/002199839202600807
Impact loading on composite laminates can cause surface or internal damage in the form of fiber breakage, delamination and matrix cracking. Such damage can reduce laminate tensile strength.
Nanometer-scale mechanics of gold films
Physical Review Letters
71
20
3319-3322
1993
10.1103/PhysRevLett.71.3319
We have used interfacial force microscopy (IFM) to monitor the mechanical deformation of single nanometer-size grains in Au thin films. Our results show that protruding grains, which represent early-stage delamination, display multiple deformation mechanisms including grain boundary sliding and intragranular plasticity. The unprecedented load-displacement control capability of the IFM provides data that are used for the first time to quantitatively distinguish and evaluate individual deformation processes
atomic force microscopy; gold; metallic thin films; nanostructured materials; plastic deformation; slip
Application of the substructured finite element/extended finite element method (S-FE/XFE) to the analysis of cracks in aircraft thin walled structures
Engineering Fracture Mechanics
76
1
44-58
2009
10.1016/j.engfracmech.2008.04.025
The substructured finite element/extended finite element (S-FE/XFE) approach is used to compute stress intensity factors in large aircraft thin walled structures containing cracks. The structure is decomposed into a 'safe' domain modeled with classical shell elements and a 'cracked' domain modeled using three-dimensional extended finite elements. Two applications are presented and discussed, supported by validation test cases. First a section of stiffened panel containing a through-thickness crack is investigated. Second, small surface cracks are simulated in the case of a generic 'pressure membrane' with realistic crack configurations. These two semi-industrial benchmarks demonstrate the accuracy, robustness and computational efficiency of the substructured finite element/extended finite element approach to address complex three-dimensional crack problems within thin walled structures. ?? 2008 Elsevier Ltd. All rights reserved.
Domain decomposition; Extended finite element method; Fracture mechanics; Stress intensity factor; Thin walled structure
Contact Mechanics
Journal of the American Chemical Society
37
1-17
1985
10.1115/1.3261297
This treatise is concerned with the stresses and deformation of solid\nbodies in contact with each other, along curved surfaces which touch\ninitially at a point or along a line. Examples are a railway wheel\nand rail, or a pair of gear wheel teeth. Professor Johnson first\nreviews the development of the theory of contact stresses since the\nproblem was originally addressed by H. Hertz in 1882. Next he discusses\nthe influence of friction and the topographical roughness of surfaces,\nand this is incorporated into the theory of contact mechanics. An\nimportant feature is the treatment of bodies which deform plastically\nor viscoelastically. In addition to stationary contact, an appreciable\nsection of the book is concerned with bodies which are in sliding\nor rolling contact, or which collide.
Fluctuating filaments: statistical mechanics of helices
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
62
5 Pt B
7135-46
2000
10.1103/PhysRevE.62.7135
We examine the effects of thermal fluctuations on thin elastic filaments with noncircular cross section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies nonmonotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long-wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix "melts" and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross section leads to resonant dependence of the persistence length on the twist rate.
A Fracture-Mechanics-Based Approach to fracture control in biomedical devices manufactured from superelastic nitinol tube
Journal of biomedical materials research. Part B, Applied biomaterials
84B
26-33
2008
10.1002/jbmb
Several key fracture-mechanics parameters associated with the onset of subcritical and critical cracking, specifically the fracture toughness, crack-resistance curve, and fatigue threshold, have recently been reported for the superelastic alloy Nitinol, in the product form of the thin-walled tube that is used to manufacture several biomedical devices, most notably endovascular stents. In this study, we use these critical parameters to construct simple decision criteria for assessing the quantitative effect of crack-like defects in such Nitinol devices with respect to their resistance to failure by deformation or fracture. The criteria are based on the (equivalent) crack-initiation fracture toughness and fatigue threshold stress-intensity range, together with the general yield strength and fatigue endurance strength, and are used to construct a basis for design against single-event (overload) failures as well as for time-/cycle- delayed failures associated with fatigue
fatigue; fracture mechanics; fracture toughness; nitinol
Experimental investigation of the contact mechanics of rough fractal surfaces.
IEEE transactions on nanobioscience
3
1
27-31
2004
10.1109/TNB.2003.820264
The nonstationary character of roughness is a widely recognized property of surface morphology and suggests modeling several solid surfaces by fractal geometry. In the field of contact mechanics, this demands novel investigations attempting to clarify the role of multiscale roughness during physical contact. Here we review the results we recently obtained in the characterization of the contact mechanics of fractal surfaces by depth-sensing indentation. One class of experiments was conducted on organic thin films, load-displacement curves being acquired by atomic force microscopy using custom-designed tips. Another class of experiments focused on well-defined crystalline and mechanically polished ceramic substrates probed by a traditional nanoindenter. We observed the first-loading cycle to be considerably affected by surface roughness. Plastic failure was found to dominate incipient contact while contact stiffness increased on decreasing fractal dimension and roughness. Our findings suggest fractal parameters to drive contact mechanics whenever the penetration depth is kept below the interface width.
Carbon; Carbon: chemistry; Fractals; Materials Testing; Materials Testing: methods; Mechanics; Microscopy, Atomic Force; Nanotechnology; Oxides; Oxides: chemistry; Strontium; Strontium: chemistry; Surface Properties; Titanium; Titanium: chemistry
Quantum mechanics of a constrained particle
Physical Review A
23
4
1982-1987
1981
10.1103/PhysRevA.23.1982
The motion of a particle rigidly bounded to a surface is discussed, considering the Schrödinger equation of a free particle constrained to move, by the action of an external potential, in an infinitely thin sheet of the ordinary three-dimensional space. Contrary to what seems to be the general belief expressed in the literature, this limiting process gives a perfectly well-defined result, provided that we take some simple precautions in the definition of the potentials and wave functions. It can then be shown that the wave function splits into two parts: the normal part, which contains the infinite energies required by the uncertainty principle, and a tangent part which contains "surface potentials" depending both on the Gaussian and mean curvatures. An immediate consequence of these results is the existence of different quantum mechanical properties for two isometric surfaces, as can be seen from the bound state which appears along the edge of a folded (but not stretched) plane. The fact that this surface potential is not a bending invariant (cannot be expressed as a function of the components of the metric tensor and their derivatives) is also interesting from the more general point of view of the quantum mechanics in curved spaces, since it can never be obtained from the classical Lagrangian of an a priori constrained particle without substantial modifications in the usual quantization procedures. Similar calculations are also presented for the case of a particle bounded to a curve. The properties of the constraining spatial potential, necessary to a meaningful limiting process, are discussed in some detail, and, as expected, the resulting Schrödinger equation contains a "linear potential" which is a function of the curvature.
doi:10.1103/PhysRevA.23.1982 url:http://dx.doi.org
Two- and three-dimensional folding of thin film single-crystalline silicon for photovoltaic power applications.
Proceedings of the National Academy of Sciences of the United States of America
106
48
20149-20154
2009
10.1073/pnas.0907390106
Fabrication of 3D electronic structures in the micrometer-to-millimeter range is extremely challenging due to the inherently 2D nature of most conventional wafer-based fabrication methods. Self-assembly, and the related method of self-folding of planar patterned membranes, provide a promising means to solve this problem. Here, we investigate self-assembly processes driven by wetting interactions to shape the contour of a functional, nonplanar photovoltaic (PV) device. A mechanics model based on the theory of thin plates is developed to identify the critical conditions for self-folding of different 2D geometrical shapes. This strategy is demonstrated for specifically designed millimeter-scale silicon objects, which are self-assembled into spherical, and other 3D shapes and integrated into fully functional light-trapping PV devices. The resulting 3D devices offer a promising way to efficiently harvest solar energy in thin cells using concentrator microarrays that function without active light tracking systems.
Natural frequencies of FSDT cross-ply composite shells by multiquadrics
Composite Structures
77
3
296-305
2007
10.1016/j.compstruct.2005.07.009
The first-order theory of Donnell is applied to evaluate the natural frequencies of doubly curved cross-ply composite shells. In this paper a meshless method based on multiquadric radial basis functions is used for discretization of equations of motion and boundary conditions. It is shown that natural frequencies obtained by this approach are very accurately determined.
Composite shells; Free vibrations; Multiquadrics; Shear-deformation theories
River Mechanics
Applied Mechanics Reviews
56
2
B30
2003
10.1115/1.1553449
Understanding the mechanism and behaviour of rivers flowing in alluvium is a most challenging subject. The conditions presented by a natural river are far from simple: the flow varies with location and time, and the granular structure and cohesive properties of the alluvium are rarely homogeneous. River Mechanics addresses this subject and aims to improve the understanding and formulation of the fluvial processes which occur in rivers. Topics covered include the interpretation of turbulence in the light of recent advances in the field, and current thinking on the regime concept.
Contact-line mechanics for pattern control
Soft Matter
6
22
5789
2010
10.1039/c0sm00165a
Wrinkled surfaces are ubiquitous in Nature and can be used in a large\nrange of applications such as improved adhesives, microfluidic patterns,\nor as metrology instruments. Despite wide-ranging applications, existing\nmethods do not permit local pattern control since all existing methods\nimpose extensive compressive strains. In this article, we describe a new\nprocess that exploits the local deformation of a soft substrate as it\nstretches to form an adhesive interface with a thin polymer film. The\nwrinkle pattern is effectively a measurement of the strain-field created\nduring the adhesion process, which shows a strong dependence on the\nspeed of attachment. We develop simple scaling arguments to describe\nthis velocity dependence and a critical velocity above which wrinkles do\nnot form. Notably, our approach allows us to define the surface pattern\n``wrinkle-by-wrinkle{''}, thus permitting the creation of single\nwrinkles. Intricate patterns on laterally extensive length scales can\nalso be produced by exploiting the shape of the contact line between the\nfilm and the substrate. This level of control-the placement of single\nfeatures of prescribed trajectory-which is not present in any other\nmethod of thin film wrinkling, is absolutely necessary for any\nrealistic, scalable application.
Deformation and failure in thin films/substrate systems: Methods of theoretical analysis
Applied Mechanics Reviews
58
1-6
338-353
2005
10.1115/1.1995717
This paper reviews the theoretical models and methods of analysis of deformation, damage and fracture in thin film/substrate systems. The mechanisms and models of the plastic deformation of thin films, as well as the effects of the dislocation formation and movement on the strength and deformation of thin films are reviewed. The concepts and methods of the theoretical and numerical analysis of the crack propagation in thin films are discussed. The mechanisms and models of cracking, decohesion and delamination, the effects of the substrate properties, as well as of cracking in a thin film between two substrates are analyzed. Continuum mechanical, probabilistic, and lattice models of damage evolution in brittle thin films, the fragmentation of thin films on a substrate, and the formation of the crack patterns are reviewed as well. Numerical models of nanoindentation are discussed. This review article contains 106 references. Copyright © 2005 by ASME.
Brittle thin films; Crack patterns; Crack propagation; Deformation; Dislocation formation; Mathematical models; Strength of materials; Substrates; Thin films
Determination of longitudinal compressive strength of long fiber composites by three-point bending of [0m/90n/0p] cross-ply laminated strips
Polymer Testing
28
6
618-626
2009
10.1016/j.polymertesting.2009.05.005
A new test method is proposed for measuring longitudinal compressive strength of composite laminates by three-point bending of cross-ply laminates. Optimal cross-ply configuration has been designed in order to get compressive stresses higher than tensile stresses. Thermal and mechanical stresses have been calculated based on the hypothesis of Classical Beam Theory. Cross-ply carbon/epoxy strips with different thicknesses and spans have been tested by three-point bending. Failures on the compressive side have been observed in all cases and no evidence of transverse cracking has been found. Experimental results agree well with compressive strength reference values. The possibility of determination of compressive and tensile strengths by three-point bending from a unique cross-ply lay-up has been also analyzed.
compressive strength
Quantum mechanics and symmetries
Annalen der Physik (Leipzig)
9
11-12
937
2000
10.1002/1521-3889(200011)9:11/12<937::AID-ANDP937>3.0.CO;2-G
Quantum Mechanics (Symmetries) deals with a particularly appealing and successful concept in advanced quantum mechanics. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry, and the general theory of Lie groups. The isospin group, hypercharge, SU(3) and their applications are all dealt with in depth before chapters on charm, SU(4), and dynamical symmetries lead to the frontiers of research in particle physics. This unique text comprises more than 120 detailed, worked examples and problems.As the third reprint of the second edition, this book has been revised to bring the text up to date.
Fatigue behaviour of thermoset and thermoplastic cross-ply laminates
Composites
23
2
109-116
1992
10.1016/0010-4361(92)90111-7
This paper compares the fatigue behaviour of two carbon fibre-reinforced plastics (cfrp)-a conventional T300/914 material with an epoxy resin matrix, and the more recently developed material APC2 with a toughened thermoplastic polyetheretherketone matrix. Monotonic and cyclic tensile tests were carried out on [07/90]s and [03/90/04]s cross-ply lay-ups. Under monotonic tensile loading the behaviour of APC2 has been found to be slightly superior to that of T300/914. Surprisingly, during tension-tension fatigue tests, the observed specimen fatigue lives are far shorter in APC2 than in T300/914. Observations of damage evolution in both materials by means of X-ray radiography throughout the fatigue tests and by scanning electron microscopy at the end of the test make these results clearer.
carbon fibres; composite materials; damage; epoxy matrix; fatigue testing; fractography; PEEK matrix
Effect of ply stacking sequence on buckling behavior of E-glass/epoxy laminated composites
Computational Materials Science
89
89-96
2014
10.1016/j.commatsci.2014.03.017
The aim of this study is to find a comprehensive viewpoint about the results of analytical and finite element methods usually used for prediction of buckling behavior, including critical buckling load and modes of failure, of thin laminated composites with different stacking sequences. To this end, a semi-analytical Rayleigh–Ritz approach is first developed to calculate the critical buckling loads of square composite laminates with SFSF (S: simply-support, F: free) boundary conditions. Then, these laminates are simulated under axially compression loading using the commercial finite element software, ABAQUS. Critical buckling loads and failure modes are predicted by both eigenvalue linear and nonlinear analysis in conjunction with three well-known failure criteria, i.e., Hashin, Tsai-Wu and Tsai-Hill criteria. To validate the analytical and numerical results, layups of [0°/90°]s, [±30°]s and [±45°]s are tested under uniaxial buckling load. Since there is no standard for buckling test of composite plates with simply-supported boundary conditions, a new test setup is designed. Results showed that nonlinear finite element analysis predicts the critical bucking loads of multidirectional laminates with a good accuracy in comparison to experiments. In addition, non-linear finite element analysis associated with the Tsai-Wu and Tsai-Hill failure criteria are more efficient in prediction of buckling modes of failure in comparison to the Hashin criterion.
On the equivalence between the $$s$$ s -method, the XFEM and the ply-by-ply discretization for delamination analyses of laminated composites
International Journal of Fracture
2015
10.1007/s10704-015-9996-2
Two hierarchical approaches, the (Formula presented.)-method and the extended finite element method (XFEM), are compared to the classical ply-by-ply discretization approach in terms of their effectiveness in modeling delamination in laminated composites. In the two hierarchical approaches, a smooth approximation field based on the mesh made of through-the-thickness solid laminated elements is first introduced to resolve a delamination-free response of the composite structure. The initiation and propagation of delamination is modeled by either superposition of element patches (s-method) or by enrichment functions (XFEM). A cohesive zone model is employed to model decohesion at the inter-ply interfaces. In terms of representing strong discontinuities, the two hierarchical methods have been shown to represent an identical approximation space as the classical ply-by-ply discretization approach, even though the s-method gives rise to sparser matrix structure. In terms of representing weak discontinuities, the s-method has been shown to be equivalent to the ply-by-ply discretization approach and provides a seamless transition from weak to strong discontinuity.
Cohesive zone model; Delamination; Finite element analysis; Hierarchical enrichment; Laminated composites; Mesh superposition; s-method; XFEM
Applied quantum mechanics
Cambridge University Press
558
2006
10.1063/1.1881905
Electrical and mechanical engineers, materials scientists and applied physicists will find Levi's uniquely practical 2006 explanation of quantum mechanics invaluable. This updated and expanded edition of the bestselling original text covers quantization of angular momentum and quantum communication, and problems and additional references are included. Using real-world engineering examples to engage the reader, the author makes quantum mechanics accessible and relevant to the engineering student. Numerous illustrations, exercises, worked examples and problems are included; Matlab source codes to support the text are available from www.cambridge.org//9780521183994
Hole flanging with ironing of two-ply thick sheet metals
Journal of Materials Processing Technology
89–90
51-57
1999
http://dx.doi.org/10.1016/S0924-0136(99)00025-4
Two-ply sheet metals are used in the manufacturing of electronic equipment, chemical instruments, transportation works and so on. Two-ply sheet metals are generally composed of metals that have different mechanical properties. Thus the forming process of these materials is complicated. The forming characteristics in hole flanging with ironing for two-ply sheet metals were studied. An explosively welded Al/Cu bi-metallic sheet metal was used as a model material throughout the experiments. The thickness of the matrix A1 was 2.20 mm and that of the cladding Cu was 0.83 mm. A number of experiments were performed using a conical punch with a cone angle of 45°. The experimental results were compared with FEM-simulated results, from which it was demonstrated that the rigid–plastic FEM can be used effectively for predicting the forming process and the finished shape of bi-metallic sheet metals.
FEM; Hole flanging; Ironing; Two-ply sheet metals
The effect of thin film/substrate radii on the Stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature
Journal of Mechanics of Materials and Structures
1
6
1041-1053
2006
10.2140/jomms.2006.1.1041
Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. There are recent studies of film/substrate systems subjected to nonuniform but axisymmetric misfit strain and temperature changes. The film stresses were found to depend nonlocally on system curvatures (that is, depend on the full-field curvatures). A very simple stress-curvature relation was established, but it is limited to thin film and substrate of same radius. We extend the analysis to thin film and substrate of different radii. Remarkably the same simple stress-curvature relation still holds regardless of the film/substrate radii mismatch.
thin film radius, nonuniform misfit strain, nonuni
Closed Form Solutions for the Interlaminar Stress Field in Angle-Ply and Cross-Ply Laminates
Journal of Composite Materials
21
4
292-308
1987
10.1177/002199838702100401
The solution to the problem of interlaminar stresses at a straight free edge in a com posite laminate is obtained in closed form for two special and important cases: angle-ply and cross-ply laminates. These solutions are derived using the Force Balance Method and the principle of minimum complementary energy. The results are favorably compared to the predictions of other analyses found in the literature. The solution procedure is found to be simpler and more efficient than other analytical methods. In addition, for some special cases of cross-ply laminates, the solution is shown to be identical to the predictions of a modified plate theory that includes through-the-thickness stretching.
Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes
International Journal for Numerical Methods in Engineering
59
3
419–456
2004
10.1002/nme.944
The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard crystal elasticity to curved monolayer lattices by means of the exponential Cauchy–Born rule. The constitutive model for a two-dimensional continuum deforming in three dimensions (a surface) is written explicitly in terms of the underlying atomistic model. The resulting hyper-elastic potential depends on the stretch and the curvature of the surface, as well as on internal elastic variables describing the rearrangements of the crystal within the unit cell. Coarse grained calculations of carbon nanotubes (CNTs) are performed by discretizing this continuum mechanics theory by finite elements. A smooth discrete representation of the surface is required, and subdivision finite elements, proposed for thin-shell analysis, are used. A detailed set of numerical experiments, in which the continuum/finite element solutions are compared to the corresponding full atomistic calculations of CNTs, involving very large deformations and geometric instabilities, demonstrates the accuracy of the proposed approach. Simulations for large multi-million systems illustrate the computational savings which can be achieved. Copyright © 2003 John Wiley & Sons, Ltd.
carbon nanotubes; continuum surface model; hyperelasticity; ÿnite elements
Nanosphere embedding into polymer surfaces: A viscoelastic contact mechanics analysis
Physical Review Letters
94
7
1-4
2005
10.1103/PhysRevLett.94.076103
Teichroeb and Forrest [Phys. Rev. Lett. 91, 016104 (2003)] image gold nanosphere embedment into a polystyrene surface and imply the existence of a liquid surface layer. We use a viscoelastic contact mechanics model of their results to give a contrary interpretation. The surface interactions between gold and polystyrene and the indentation depth determine the loads on the nanospheres. Using bulk properties, quantitative agreement between the model and the data is obtained, implying little or no depression in the glass temperature or existence of a liquid layer at the polystyrene surface.
The phase-change kinetics of amorphous Ge2Sb2Te5 and device characteristics investigated by thin-film mechanics
Acta Materialia
94
143-151
2015
10.1016/j.actamat.2015.04.058
For high switching speed and high reliability of phase-change random access memory (PcRAM), we need to identify materials that enable fast crystallization at elevated temperatures but are stable at and above room temperature. Achieving this goal requires a breakthrough in our understanding of the unique crystallization kinetics of amorphous phase change materials as a fragile glass, described as the non-Arrhenius behavior of atomic mobility. It is a highly rewarding task to unravel the unconventional crystallization kinetics and related properties, because these properties can be utilized to predict the device characteristics. This manuscript utilizes the thin-film mechanics to investigate the crystallization kinetics of amorphous Ge2Sb2Te5 phase-change materials doped with Al, Bi, C and N, which is an effective method to analyze the structural changes in amorphous materials. Crystallization temperature, super-cooled liquid region, glass transition temperature and fragility are measured to describe the crystallization kinetics tuned by doping; characteristic fragile-to-strong transition is observed for C and N dopings due to their structural feature as an interstitial dopant. Consequently, doping effects on the phase stability and atomic mobility manifested by the crystallization temperature and the super-cooled liquid region (or 1/fragility) successfully correspond with PcRAM characteristics, i.e., reliability and switching speed, respectively.
crystallization; doping; fragility; ge 2 sb 2; te 5; thin-film mechanics
Thermoviscoelastic deformations of functionally graded thin plates
European Journal of Mechanics - A/Solids
26
5
872-886
2007
http://dx.doi.org/10.1016/j.euromechsol.2007.03.002
By considering the influence of the mid-plane strains due to the inhomogeneous property of FGMs across the thickness, a constitutive equation of thermoviscoelastic functionally graded thin plates is reduced on the basis of the Kirchhoff's hypothesis for the classical plate theory. The corresponding simplified Gurtin's type variational principle of functionally graded thin plates is presented by means of the modern convolution bilinear forms. By using the Navier analytic method or combining the Ritz method in the spatial domain and the Legendre interpolation method in the temporal domain, the static thermoelastic deformations or quasi-static thermoviscoelastic deformations of functionally graded thin plates under mechanical or thermal loads are studied.
Analytic method; Functionally graded plate; Legendre interpolation method; Ritz method; Thermoviscoelastic bending; Variational principle
Buckling modes of elastic thin films on elastic substrates
Applied Physics Letters
90
15
1-3
2007
10.1063/1.2720759
Two buckling modes have been observed in thin films: buckle delamination and wrinkling. This letter identifies the conditions for selecting the favored buckling modes for elasticfilms on elastic substrates. Transition from one buckling mode to another is predicted as the stiffness ratio between the substrate and the film or is predicted for variation of the stiffness ratio between the substrate and the film or variation of theinterfacial defect size. The theoretical results are demonstrated experimentally by observing the coexistence of both buckling modes and mode transition in one film-substrate system.
151902 ͑ 2007 ͒; and engineering mechanics; buckling modes of elastic; department of aerospace engineering; haixia mei and rui; huang a ͒; lied physics letters 90; substrates; thin films on elastic; university of texas
Finite deformation of thin shells in the context of analytical mechanics of material surfaces
Acta Mechanica
209
1-2
43-57
2010
10.1007/s00707-009-0154-7
In the framework of the direct approach shells are considered as deformable\nsurfaces consisting of particles, and the relations of the theory\nare obtained with the methods of analytical mechanics. In the present\nwork we assign to each particle five degrees of freedom, namely three\ntranslations and two in-plane rotations. The principle of virtual\nwork produces all the relations of the theory of shells: equations\nof equilibrium, boundary conditions, definition of the force factors\nand the general form of constitutive equations. Remarkable consistency\nand clarity is achieved both in the relations of the theory and in\nthe derivation process. A new formulation of the Piola tensors for\na shell is suggested in order to transform the equations to the reference\nconfiguration. To analyze the effects of buckling or geometric stiffening,\nwe linearize these equations in the vicinity of a pre-deformed configuration.\nSome new semi-analytical results on buckling and supercritical behavior\nof an axially compressed cylindrical shell are presented. The correspondence\nbetween the equations and the variational formulation is discussed\nin view of development of efficient numerical procedures for modeling\nnonlinear deformations of shells. Results of finite element modeling\nof the nonlinear deformation of a shell structure are discussed in\ncomparison with the fully three-dimensional solution of the problem.
Tailoring the elastic postbuckling response of thin-walled cylindrical composite shells under axial compression
Thin-Walled Structures
84
14-25
2014
10.1016/j.tws.2014.05.009
The buckling of cylindrical shells has long been regarded as an undesirable phenomenon, but increasing interests on the development of active and controllable structures open new opportunities to utilize such unstable behavior. In this paper, approaches for modifying and controlling the elastic response of axially compressed laminated composite cylindrical shells in the far postbuckling regime are presented and evaluated. Three methods are explored (1) varying ply orientation and laminate stacking sequence; (2) introducing patterned material stiffness distributions; and (3) providing internal lateral constraints. Experimental data and numerical results show that the static and kinematic response of unstable mode branch switching during postbuckling response can be modified and potentially tailored.
Axial compression; Cylindrical shells; Experiments; Laminated composites; Postbuckling; Tailoring
Quantum Mechanical Simulations of Nanoindentation of Al Thin Film
Computational Materials Science
47
3
16
2009
10.1016/j.commatsci.2009.11.002
QCDFT is a multiscale modeling approach that can simulate multi-million atoms effectively via density functional theory (DFT). The method is based on the framework of quasicontinuum (QC) approach with DFT as its sole energetics formulation. The local QC energy is calculated by DFT with Cauchy-Born hypothesis and the nonlocal QC energy is determined by a self-consistent embedding approach, which couples nonlocal QC atoms to the vertices of the finite-elements at the local QC region. The QCDFT method is applied to a nanoindentation study of an Al thin film in the presence and absence of Mg impurities. The results show that the randomly distributed Mg impurities can significantly increase the ideal and yield strength of the Al thin film.
molecular mechanics; quantum mechanics
Low velocity impact properties of intra-ply hybrid composites based on basalt and nylon woven fabrics
Materials & Design
31
8
3835-3844
2010
10.1016/j.matdes.2010.03.033
In this paper, the low velocity impact behavior of homogenous and hybrid composite laminates reinforced by basalt–nylon intra-ply fabrics was experimentally investigated. Epoxy resin was used as matrix material. The purpose of using this hybrid composite is to combine the good mechanical properties of basalt fiber with the excellent impact resistant of nylon fiber. Five different types of woven fabrics were used as reinforcement with different volume percentages of nylon (0%, 25%, 33.3%, 50% and 100%). The effect of nylon/basalt fiber content on maximum force, maximum deflection, residual deflection, total absorbed energy, elastic energy, size and type of damage were studied at several low velocity impact nominal energy levels (16, 30 and 40J). The results indicate that impact performance of these composites is significantly affected by the nylon/basalt fiber content. The visual inspection and ultrasonic C-scan of the impact damaged specimens reveals that content of nylon/basalt fiber controls the type and size of damage.
Statistical mechanics of networks
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
70
6 2
1-13
2004
10.1103/PhysRevE.70.066117
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the same role in the study of networks as is played by the Boltzmann distribution in classical statistical mechanics; they offer the best prediction of network properties subject to the constraints imposed by a given set of observations. We give exact solutions of models within this class that incorporate arbitrary degree distributions and arbitrary but independent edge probabilities. We also discuss some more complex examples with correlated edges that can be solved approximately or exactly by adapting various familiar methods, including mean-field theory, perturbation theory, and saddle-point expansions.
Microbridge testing of thin films
Materials Science and Engineering: A
409
1-2
329-339
2005
10.1016/j.msea.2005.03.118
In the present work, we describe a novel microbridge testing method for thin films. The single-layer, bilayer and trilayer thin film microbridge samples were prepared with the microelectromechanical fabrication technique such that they were easy to handle. The microbridge test was conducted with a load- and displacement-sensing nanoindenter system equipped with a microwedge probe. In the mechanics analysis, we considered residual stress in each layer, modeled the substrate deformation with three coupled springs and derived the load–deflection formula in a closed form. For brittle thin films, the microbridge testing method allows us to evaluate simultaneously the Young's modulus, the residual stress and the bending fracture strength. In addition, the microbridge test can characterize the yield strength for ductile thin films.
Bending fracture strength; Microbridge testing method; Residual stress; Thin films; Young's modulus
The application of a ply-refinement technique to the analysis of microscopic deformation in interlaminar-toughened laminates with transverse cracks
Composites Science and Technology
60
231-240
2000
10.1016/S0266-3538(99)00121-9
Predictions of a stress-transfer model proposed by McCartney for calculating the stress and displacement distributions in a symmetric laminate having cracks in 90° plies are compared with experimental results. A ply-refinement technique is used where each ply of the laminate is subdivided into layers having the same properties in order that through-thickness variations of the stress and displacement components can be taken into account. The transverse crack-opening displacement and shear deformation near ply interfaces are calculated and compared with the corresponding experimental results. Cross-ply laminates made of two material systems are used in the experiment. One is interleaved CFRP, T800H/3631-FM300, with epoxy resin (FM300) layers about 100 μm thick between 0 and 90° plies. The other is toughness-improved CFRP, T800H/3900-2, with selectively toughened interlaminar layers about 30 μm thick at all the ply interfaces. It is found that the new model with the ply-refinement technique is more accurate than a previous approximate analysis.
Integration of the Kohonen's self-organising map and k-means algorithm for the segmentation of the AE data collected during tensile tests on cross-ply composites
NDT and E International
38
4
299-309
2005
10.1016/j.ndteint.2004.09.006
The acoustic emission (AE) technique is a useful way for the investigation of local damage in materials. This study deals with the ability of a Kohonen's map to classify recorded AE signals collected during tensile tests on cross-ply glass/epoxy composites in order to monitor the chronology of the damaging process. An unsupervised clustering analysis shows that AE signals are distributed into three clusters. The proposed two-stage procedure is a combination of the Self-Organising Map (SOM) and the k-means methods. In the present work, Kohonen's map is applied as an unsupervised clustering method for the AE signals generated in cross-ply composite specimens during tensile tests. The input vectors of the signal descriptors used in the clustering procedure are calculated from the signal waveforms. The k-means method is then applied on the neurones of the map in order to delimit the clusters and to visualise the topology of the map. ?? 2004 Elsevier Ltd. All rights reserved.
Acoustic emission; Damage; k-means method; Kohonen's map; Polymer-matrix composites (PMCs)
Bone Mechanics Handbook, 2nd Edition. -
Applied Mechanics Reviews
56
4
B61
2003
10.1115/1.1579463
This text summarizes the understanding of bone mechanics with comprehensive coverage of the histology, physiology, and the cell and molecular biology of the bone. It covers mechanical techniques, mechanical properties of cortical and cancellous bone, bone adaptation, and clincally related issues.
Nonlinear solid mechanics
Solid Mechanics and its Applications
160
1-594
2009
10.1007/978-90-481-2331-5_1
This volume provides insight into modelling and ultimate limit computation\nof complex structures, with their components represented by solid\ndeformable bodies. The book examines practically all the important\nquestions of current interests for nonlinear solid mechanics: plasticity,\ndamage, large deformations, contact, dynamics, instability, localisation\nand failure, discrete models, multi-scale, multi-physics and parallel\ncomputing, with special attention given to finite element solution\nmethods. The presentation of topics is structured around different\naspects of typical boundary value problems in nonlinear solid mechanics,\nwhich provides the best pedagogical approach while keeping the book\nsize reasonable despite its very broad contents. Other strong points\nare the exhaustive treatment of subjects, with each question studied\nfrom different angles of mechanics, mathematics and computation,\nas well as a successful merger of scientific cultures and heritage\nfrom Europe and the USA. The book content and style is also the product\nof rich international experience in teaching Master and Doctoral\nlevel courses, as well as the courses organized for participants\nfrom industry (IPSI courses) in France, and similar courses in Germany\nand Italy. Every effort was made to make the contents accessible\nto non-specialists and users of computer programs.
CAPLib—a ‘thin layer’ message passing library to support computational mechanics codes on distributed memory parallel systems
Advances in Engineering Software
32
1
61-83
2001
http://dx.doi.org/10.1016/S0965-9978(00)00056-9
The Computer Aided Parallelisation Tools (CAPTools) [Ierotheou, C, Johnson SP, Cross M, Leggett PF, Computer aided parallelisation tools (CAPTools)—conceptual overview and performance on the parallelisation of structured mesh codes, Parallel Computing, 1996;22:163–195] is a set of interactive tools aimed to provide automatic parallelisation of serial FORTRAN Computational Mechanics (CM) programs. CAPTools analyses the user's serial code and then through stages of array partitioning, mask and communication calculation, generates parallel SPMD (Single Program Multiple Data) messages passing FORTRAN. The parallel code generated by CAPTools contains calls to a collection of routines that form the CAPTools communications Library (CAPLib). The library provides a portable layer and user friendly abstraction over the underlying parallel environment. CAPLib contains optimised message passing routines for data exchange between parallel processes and other utility routines for parallel execution control, initialisation and debugging. By compiling and linking with different implementations of the library, the user is able to run on many different parallel environments. Even with today's parallel systems the concept of a single version of a parallel application code is more of an aspiration than a reality. However for CM codes the data partitioning SPMD paradigm requires a relatively small set of message-passing communication calls. This set can be implemented as an intermediate ‘thin layer’ library of message-passing calls that enables the parallel code (especially that generated automatically by a parallelisation tool such as CAPTools) to be as generic as possible. CAPLib is just such a ‘thin layer’ message passing library that supports parallel CM codes, by mapping generic calls onto machine specific libraries (such as CRAY SHMEM) and portable general purpose libraries (such as PVM an MPI). This paper describe CAPLib together with its three perceived advantages over other routes:• as a high level abstraction, it is both easy to understand (especially when generated automatically by tools) and to implement by hand, for the CM community (who are not generally parallel computing specialists); • the one parallel version of the application code is truly generic and portable; • the parallel application can readily utilise whatever message passing libraries on a given machine yield optimum performance.
CAPTools; Computational mechanics software; Distributed memory parallel systems
Damage in composite laminates with off-axis plies
Composites Science and Technology
59
14
2139-2147
1999
10.1016/S0266-3538(99)00070-6
Damage in off-axis plies of composite laminates is studied by examining the configuration [0/ ?? ??4/0( 1/2 )](s) with ??=25, 40, 55, 70 and 90 subjected to tensile loading in the axial direction. It is found that for the values of ??, where the stress in the off-axis plies normal to the fibers is tensile, ply cracks lying along fibers initiate and increase in number, while for other ?? values the plies do not undergo this damage, as expected. However, the overall laminate elastic moduli are also found to change for the ?? values where no ply cracks exist. It is postulated that a shear-induced degradation of the off-axis plies is responsible for the observed laminate moduli changes. The prediction of changes in these moduli by using the ply shear modulus measured on [????4](s) appears to support this postulate. For the case of moduli changes caused by ply cracks the recently proposed synergistic damage-mechanics approach [1] is applied. The implications of the findings of this work on a class of continuum damage-mechanics formulations proposed in the literature are discussed.
Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply
International Journal of Solids and Structures
50
20-21
3308-3318
2013
10.1016/j.ijsolstr.2013.06.014
This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks.
Cohesive zone modeling; Composite laminates; Extended finite element method; Fracture; In situ strength; Transverse cracking
Mechanics of fold-and-thrust belts and accretionary wedges Cohesive Coulomb theory
Journal of Geophysical Research
89
10087-10101
1984
10.1029/JB089iB12p10087
A critically tapered fold-and-thrust belt or submarine accretionary wedge is one that is on the verge of Coulomb failure everywhere, including its base where frictional sliding along a decollement is assumed to be occurring. Cohesion within a wedge can add significantly to the overall strength near the toe; the effect of this is to decrease the near-toe taper, leading to a critical topographic profile that is concave upward if the decollement is planar. We obtain an approximate self-consistent solution for the state of stress within a thin-skinned cohesive critical Coulomb wedge, and determine the relationship between the wedge taper and its strength and basal friction. The theory is then applied to the presently deforming fold-and-thrust belt of western Taiwan. Fitting of theoretical critical wedge shapes to topographic pro- files and measurements of the step-up angles of thrust faults from the basal decollement are used to constrain the Taiwan wedge strength parameters. An attractive assertion fully consistent with all the observations is that the mechanics of fold-and-thrust belts and accretionary wedges is governed by normal frictional and fracture strengths of rocks measured in the laboratory. In particular, if Byerlee's law/•b = 0.85 is adopted as the coefficient of sliding friction on the base, we find a coefficient of internal friction/• - 0.9-1.0 in the wedge and a wedge cohesion S O - 5-20 MPa. Other solutions having strengths and ambient stresses up to 4 times lower than this can also, however, satisfy the data. INTRODUCTION
Applied Biofluid Mechanics
Applied biofluid mechanics
314p.
2007
10.1036/0071472177
Applied Biofluid Mechanics features a solid grasp of the role of fluid mechanics in the human circulatory system that will help in the research and design of new medical instruments, equipment, and procedures. Filled with 100 detailed illustrations, the book examines cardiovascular anatomy and physiology, pulmonary anatomy and physiology, hematology, histology and function of blood vessels, heart valve mechanics and prosthetic heart valves, stents, pulsatile flow in large arteries, flow and pressure measurement, modeling, and dimensional analysis.
On the adhesion mechanics of multi-layer elastic systems
Surface and Coatings Technology
167
2-3
181-187
2003
10.1016/S0257-8972(02)00893-9
Local-probe instruments such as surface force apparatus or atomic force microscope are routinely used to extract the mechanical properties of thin-layers by subjecting them to indentation loading. Inadvertently, at these micro- or nano-indentation loads, the adhesive surface forces operating between the indenter and the thin-layer will contribute to the deformation. The well-established Johnson–Kendal–Roberts (JKR) theory is applied to extract the surface energy of the contacting solids. For this thin-layer system, the JKR theory should be an error as it is based on the indentation of an elastic half-space with an elastic sphere. A continuum mechanics approach coupled with non-dimensional analysis and finite elements simulation is presented to explain the indentation process of multi-layer elastic systems under the presence of adhesion. The emphasis is on spherical and flat punch probes. Computations of contact size and contact stiffness as a function of load are presented for a range of values of adhesion energies.
Adhesion; Atomic force microscope; Elastic properties; Finite element method; Indentation; Surface force apparatus
The essential mechanics of conchoidal flaking
International Journal of Fracture
29
4
205-221
1985
10.1007/bf00125471
Flaked stone tools are the most durable and therefore the most common artifacts available to archaeologists for tracing the development of early Man. However, the essential mechanics of conchoidal flake formation has not yet been described. In order to successfully create a relatively thin flake that does not terminate prematurely, the direction of the flaking force has to be reasonably precise. We show that the direction of the flaking force is determined mainly by the stiffness of the flake, the actual angle of the blow or impulse having relatively little effect. Long thin flakes can be easily produced because this direction of the flaking force is very close to that necessary to produce local symmetry at the tip of the crack propagating parallel to the surface of the stone.
Transverse cracking in fiber-reinforced brittle matrix, cross-ply laminates
Acta Metallurgica et Materialia
41
2365-2376
1993
10.1016/0956-7151(93)90316-K
The topic addressed in this paper is transverse cracking in the matrix of the 90° layers of a cross-ply laminate loaded in tension. Several aspects of the problem are considered, including conditions for the onset of matrix cracking, the evolution of crack spacing, the compliance of the cracked laminate, and the overall strain contributed by residual stress when matrix cracking occurs. The heart of the analysis is the plane strain problem for a doubly periodic array of cracks in the 90° layers. A fairly complete solution to this problem is presented based on finite element calculations. In addition, a useful, accurate closed form representation is also included. This solution permits the estimation of compliance change and strain due to release of residual stress. It can also be used to predict the energy release rate of cracks tunneling through the matrix. In turn, this energy release rate can be used to predict both the onset of matrix cracking and the evolution of crack spacing in the 90° layers as a function of applied stress. All these results are used to construct overall stress-strain behavior of a laminate undergoing matrix cracking in the presence of initial residual stress.
Three-dimensional interlaminar stress analysis at free edges of general cross-ply composite laminates
Materials & Design
24
121-130
2003
10.1016/S0261-3069(02)00107-3
A layerwise theory is used to investigate analytically the interlaminar\nstresses near the free edges of general cross-ply composite laminates\nunder uniform axial extension. Laminates with finite dimensions are\nconsidered and full three-dimensional stresses in the interior and\nthe boundary-layer regions are calculated. The results obtained from\nthis theory are compared with those available in the literature.\nIt is found that the edge-effect problem of general cross-ply laminates\nis actually a quasi three-dimensional problem and its stress analysis\ncan be restricted to a generic two-dimensional cross-section of the\nlaminates.
composite laminates; free edge effect; layerwise theory
The non-linear buckling analysis of cross-ply laminated orthotropic truncated conical shells
Composite Structures
93
3006-3012
2011
10.1016/j.compstruct.2011.04.035
In this study, the non-linear buckling behavior of cross-ply laminated orthotropic truncated conical shells under axial load has been investigated. The basic relations of the cross-ply laminated orthotropic truncated conical shells are derived using the von Karman-Donnell-type of kinematic non-linearity. Then modified Donnell type non-linear stability and compatibility equations are obtained and are solved. Finally, the influences of the number and ordering of layers and the variations of the conical shell characteristics on the non-linear axial buckling load are investigated. Comparison with available results is satisfactorily good. ?? 2011 Elsevier Ltd.
Axial load; Conical shells; Critical loads; Laminated orthotropic materials; Non-linear buckling
Measuring mechanical properties of thin flexible films by a shaft-loaded blister test
Thin Solid Films
352
1-2
167-172
1999
10.1016/S0040-6090(99)00355-7
Mechanical properties of a thin circular flexible membrane are directly measured by applying an external load to the film center via a rigid spherical capped shaft. Constitutive equations are proposed for the shaft-loaded blister configuration based on linear elasticity. The dependence on the ratio of shaft radius to blister dimension is reflected in the load versus shaft displacement relation. (C) 1999 Elsevier Science S.A. All rights reserved.
coatings; constitutive equations; lm; mechanical properties and measurements; mechanics of thin; shaft-loaded blister test; thin
Springer Handbook of Experimental Solid Mechanics
Springer Handbook of Experimental Solid Mechanics
409 - 443
2008
10.2514/1.38773
As a reference book, the Springer Handbook provides a comprehensive exposition of the techniques and tools of experimental mechanics. An informative introduction to each topic is provided, which advises the reader on suitable techniques for practical applications. New topics include biological materials, MEMS and NEMS, nanoindentation, digital photomechanics, photoacoustic characterization, and atomic force microscopy in experimental solid mechanics. Written and compiled by internationally renowned experts in the field, this book is a timely, updated reference for both practitioners and researchers in science and engineering.
MICROMECHANISMS OF INTERLAMINAR FRACTURE IN CARBON-EPOXY COMPOSITES AT MULTIDIRECTIONAL PLY INTERFACES
The international conference on deformation and fracture composites
1997
The micromechanisms of delamination growth at 0°/0° and 0°/90° ply interfaces under mixed-mode static and cyclic loading have been investigated by examination of fracture surfaces using scanning electron microscopy. Improved delamination resistance with an increasing mode II component was mainly due to an increase in the total surface area generated. There was a secondary cracking mechanism at 0°/90° ply interfaces which gave rise to slightly higher mixed-mode toughnesses. The relatively high scatter in composite toughness was explained in terms of variations in the spatial arrangement of fibres. Examination of shear cusps can be used to identify crack growth directions in post-mortem failure investigations
Thin films with many small cracks
Proceedings of the Royal Society of London. Series A
458
2020
823-840
2002
10.1098/rspa.2001.0821
We show with an example that the limiting theory as thickness goes to zero of a thin fi-lm with many small cracks can be three dimensional rather than two dimensional.
Mechanics; Thin film; Homogenization; Cracks
A damping mechanics model and a beam finite element for the free-vibration of laminated composite strips under in-plane loading
Journal of Sound and Vibration
330
23
5660-5677
2011
10.1016/j.jsv.2011.06.025
A theoretical framework is presented for predicting the nonlinear damping and damped vibration of laminated composite strips due to large in-plane forces. Nonlinear GreenLagrange axial strains are introduced in the governing equations of a viscoelastic composite and new nonlinear damping and stiffness matrices are formulated including initial stress effects. Building upon the nonlinear laminate mechanics, a damped beam finite element is developed. Finite element stiffness and damping matrices are synthesized and the static equilibrium is predicted using a NewtonRaphson solver. The corresponding linearized damped free-vibration response is predicted and modal frequencies and damping of the in-plane deflected strip are calculated. Numerical results quantify the nonlinear effect of in-plane loads on structural modal damping of various laminated composite strips. The modal loss-factors and natural frequencies of cross-ply Glass/Epoxy beams subject to in-plane loading are measured and correlated with numerical results. ?? 2011 Elsevier Ltd. All rights reserved.
Modern mechanics
American Journal of Physics
72
December 2003
439
2004
10.1119/1.1646134
We consider the goals of the introductory course in classical mechanics taken by physics majors and argue both that these goals are not well met in actual courses and that the goals themselves should be rethought. We propose alternative goals and describe an introductory ‘‘modern mechanics’’ course that addresses these alternative goals. Included in the description are several genres of homework problems that are nearly absent from traditional mechanics courses at both the introductory and intermediate levels. The intermediate mechanics course could be restructured to exploit a broader foundation laid by the introductory course.
Discrete mechanics and variational integrators
Acta Numerica 2001
10
1
357-514
2003
10.1017/S096249290100006X
This paper gives a review of integration algorithms for finite dimensionalmechanical systems that are based on discrete variational principles. Thevariational technique gives a unified treatment of many symplectic schemes,including those of higher order, as well as a natural treatment of the discreteNoether theorem. The approach also allows us to include forces, dissipationand constraints in a natural way. Amongst the many specific schemes treatedas examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplecticpartitioned Runge-Kutta schemes are presented.CONTENTSPART 1: Discrete variational mechanics1.1 Introduction 3591.2 Background: Lagrangian mechanics 3651.3 Discrete variational mechanics:Lagrangian viewpoint 3701.4 Background: Hamiltonian mechanics 3761.5 Discrete variational mechanics:Hamiltonian viewpoint 3831.6 Correspondence between discrete andcontinuous mechanics 3861.7 Background: Hamilton-Jacobi theory 3901.8 Discrete variational mechanics:Hamilton-Jacobi viewpoint 392358 J. E. Marsden and M. WestPART 2: Variational integrators2.1 Introduction 3942.2 Background: Error analysis 3972.3 Variational error analysis 3992.4 The adjoint of a method and symmetric methods 4022.5 Composition methods 4052.6 Examples of variational integrators 408PART 3: Forcing and constraints3.1 Background: Forced systems 4213.2 Discrete variational mechanics with forces 4233.3 Background: Constrained systems 4303.4 Discrete variational mechanics with constraints 4383.5 Constrained variational integrators 4443.6 Background: Forced and constrained systems 4523.7 Discrete variational mechanics with forcesand constraints 456PART 4: Time-dependent mechanics4.1 Introduction 4634.2 Background: Extended Lagrangian mechanics 4644.3 Discrete va...
Mechanics and physics of disclinations in solids
European Journal of Mechanics - A/Solids
22
5
727-741
2003
10.1016/S0997-7538(03)00089-5
An overview of recent achievements of the disclination approach in mechanics and physics of solids is given and the use of disclination modeling in materials science is demonstrated. Disclinations are defined as linear defects in solids, which manifest themselves as the sources of characteristic singularities in the fields of displacement and rotation. Necessary terminilogy and designations: Volterra dislocations, Frank (rotation) vector of a disclination, wedge and twist disclinations, are provided and discussed. The properties of screened disclination configurations (loops, dipoles, defects in small particles, etc.) with relatively small energies are considered. The methods and results of calculation of elastic energies for screened disclinations (for example, near a free surface) are presented. On the basis of properties of screened disclinations a series of models for the processes in the structure of plastically deformed materials is developed. The bands with misorientated crystal lattice in metals and other materials are described as a result of partial wedge disclination dipole motion. Disclination models are applied to the analysis of workhardening at large strains and to the theory of grain boundaries and their junctions in polycrystals. Disclination models for the structure and properties of nanostructured materials and nanoparticles are also delivered. Finally, the role of disclinations in relaxation of elastic stresses in epitaxial thin films is highlighted.
Probabilistic first-ply failure analysis of a laminate in composite material
International Journal for Engineering Modelling
13
1-2
35-40
2000
10.4028/www.scientific.net/KEM.221-222.233
A general procedure to develop a probabilistic analysis of composite materials is presented. The second order of the Taylor series has been used in order to determine the statistics of the first ply failure for a symmetric equilibrate composite. The Monte Carlo Method has been used to validate the accuracy of the procedure
Composite first ply failure; Probabilistic analysis; Taylor Series method
Effect of tight corners and ply terminations on quality in out-of-autoclave parts
Proceedings of the SAMPE 2011 Conference
2011
The use of carbon fibre reinforced composites for aerospace structures has seen a high increase in recent years, and is still growing. The high stiffness-to-weight ratio of this material makes it ideal for primary structures on airplanes, satellites, and spacecrafts. Nevertheless, the manufacturing of such composites remains very costly since it requires equipment investment such as an autoclave or an automated fibre placement machine, and very qualified workers. Out- of-autoclave manufacturing technology is very promising since it only requires a traditional oven, while still aiming at similar part quality. However, the absence of positive pressure compared with an autoclave makes it more difficult to achieve low porosity parts. This article investigates the manufacturing of complex features with out-of-autoclave prepreg technology. The features investigated are tight-radius corners with a curvature change, and ply terminations. Ply drop tests were conducted to identify if porosity is higher at ply terminations. The bagging arrangement was modified to achieve the most uniform thickness in areas of curvature change, even with small radii. The conclusions from these studies provide us with guidelines to manufacture a larger part, which includes these features.
Low-velocity impact and static behaviors of high-resilience thermal-bonding inter/intra-ply hybrid composites
Composites Part B: Engineering
69
58-68
2015
10.1016/j.compositesb.2014.09.021
This study prepared inter/intra-ply hybrid composites reinforced with sandwich-structure recycled Kevlar nonwoven/glass woven compound fabric. Negative-depth needle punching and thermal bonding were applied to strengthen the structure with two compound cover plies and a fluffy cushioning center ply. The effects of center ply areal density, needle punching depth, and fiber blending ratio on the static and dynamic impact resistance behaviors of the composites were investigated. The results indicated that areal density significantly influenced the static and dynamic impact behaviors, which were both enhanced by the promotion of thermal-bonding points. As the needle punching deepened, the static and dynamic puncture resistances represented opposite tendencies because of different failure mecha- nisms. Static friction was the dominant factor for static puncture resistance, whereas kinetic friction was the dominant factor for dynamic puncture resistance. A similar phenomenon was observed when fiber blending ratio was varied. In terms of the non-penetrating dynamic cushioning test, areal density was the most distinct influence factor on cushioning behavior and the hybrid composites sample with an areal density of 700 g/m2 could eliminate up to 66.5% of the incident force. Therefore, the inter/ intra-ply hybrid composites showed high impact resistance and excellent dynamic cushioning property.
hybrid; mechanical properties; mechanical testing; recycling
A constitutive ply model for stiffness degradation and plastic strain accumulation: Its application to the Third World Wide Failure Exercise (Part A)
Journal of Composite Materials
47
20-21
2575-2593
2013
10.1177/0021998313484075
This paper represents the authors' contribution to Part A of the third World Wide Failure Exercise where a constitutive model is proposed which considers stiffness degradation and plastic strain accumulation for the prediction of stress-strain curves and failure envelopes of 13 test cases, involving various continuous fiber-reinforced laminates with polymeric matrix materials. The model calibration by means of the provided material data is described and the limits of applicability of the proposed constitutive model are discussed. Finally, the predictions are presented as being obtained without any experimental results available. The test cases consider unidirectional and multidirectional laminates under biaxial loads, laminates under various loading conditions (uniaxial, bending, thermal, loading and unloading) and laminates with open hole under tension or compression. Most of the predictions are documented in terms of stress-strain curves and curves presenting the evolution of brittle damage and of plastic strains.
anisotropic constitutive model; continuum damage mechanics; plasticity; wwfe-iii
An analysis of crack growth in thin-sheet metal via a cohesive zone model
Engineering Fracture Mechanics
69
18
2073-2093
2002
10.1016/S0013-7944(02)00013-9
A cohesive zone model (CZM) is applied to crack growth in thin sheet metal. CZM parameters are determined from results of global measurements and micromechanical damage models. Crack propagation in constrained center-cracked panels is analyzed to verify the choice of CZM parameters. Special attention is paid to the interaction between buckling and crack growth and to crack link-up in multi-site damaged specimens. The good agreement found between the predicted and experimental data demonstrates that the approach is attractive in investigation of structural integrity of thin-walled structures and does not require assumptions regarding the geometry and size dependence of crack growth parameters. ?? 2002 Elsevier Science Ltd. All rights reserved.
Aluminum; Buckling; Cohesive zone model; Crack growth; Crack tip opening angle; FEM; Multi-site-damage
A mechanics baseline test
The Physics Teacher
30
3
159
1992
10.1119/1.2343498
... References 1. D. Hestenes , M. Wells , and G. Swackhamer , " Force concept inventory ," Phys. Teach. 30, 141 (1992). 2. R. Thornton and D. Sokoloff, "Learning motion concepts using real-time microcomputer-based laboratory tools," Am. J. Phys. 58,858 (1990). ...
Large Elastic Deformations of Isotropic Materials. IX. The Deformation of Thin Shells
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
244
888
505-531
1952
10.1098/rsta.1952.0013
The theory of the large elastic deformation of incompressible isotropic\nmaterials is applied to problems involving thin shells. The inflation\nof a circular diaphragm of such a material is studied in detail.\nIt is found that the manner in which the extension ratios and curvatures\nvary in the immediate neighbourhood of the pole of the inflated diaphragm\ncan be determined analytically. However, in order to determine their\nvariation throughout the inflated diaphragm a method of numerical\nintegration has to be employed. Although this is, in principle, valid\nfor any form of the stored-energy function, the calculations are\ncarried through only for the Mooney form. Finally, the problem of\nthe inflation of a spherical balloon, which has already been dealt\nwith by Green & Shield (1950), is discussed in further detail.
Contact mechanics
Tribology International
19
2
109-110
1986
10.1016/0301-679X(86)90085-X
This treatise is concerned with the stresses and deformation of solid bodies in contact with each other, along curved surfaces which touch initially at a point or along a line. Examples are a railway wheel and rail, or a pair of gear wheel teeth. Professor Johnson first reviews the development of the theory of contact stresses since the problem was originally addressed by H. Hertz in 1882. Next he discusses the influence of friction and the topographical roughness of surfaces, and this is incorporated into the theory of contact mechanics. An important feature is the treatment of bodies which deform plastically or viscoelastically. In addition to stationary contact, an appreciable section of the book is concerned with bodies which are in sliding or rolling contact, or which collide.
Hygrothermal effects on the bending of angle-ply composite plates using a sinusoidal theory
Composite Structures
94
12
3685-3696
2012
10.1016/j.compstruct.2012.05.033
The sinusoidal shear deformation plate theory is presented to study the response of multilayered angle-ply composite plates due to a variation in temperature and moisture concentrations. The classical, uniform and parabolic shear deformation plate theories are also considered. The effects of temperature and moisture concentrations on the material properties and the hygrothermal response of multilayered angle-ply composite plates are studied. A number of examples are solved to illustrate the numerical results concerning bending response of multilayered angle-ply composite plates subjected to hygro-thermo-mechanical effects. Hygrothermal response due to a variation in temperature and moisture concentrations has been investigated for different material types sensitive to changing hygrothermal environment conditions. Numerical results suggest that temperature-dependent and/or moisture-dependent material properties ought to be used in the analysis of laminated plates subjected to hygrothermal loads. ?? 2012 Elsevier Ltd.
Dependent elastic properties; Hygrothermal; Rectangular plate
Study on intra/inter-ply shear deformation of three dimensional woven preforms for composite materials
Materials and Design
49
151-159
2013
10.1016/j.matdes.2013.02.025
This study presents the in-plane shear and interlaminar shear behavior of the three dimensional (3D) angle interlock preforms with different fabric densities. Picture frame shear tests for the 3D woven preform were carried out, the non-linear curves of shear stress versus shear angle and the deformation mechanism were analyzed. A new test method was designed to characterize the inter-ply shear property. The samples after interlaminar shear tests were also investigated through the yarn pulling-out and meso-structure to discover their deformation and failure mechanism. The results have shown that the fabric density has significant influence on the in-plane shear and inter-ply shear properties of 3D angle interlock preforms and the shear performance decreases with the increasing of the fabric density. The lower fabric density, the better deformability. The inter-ply shear damage mode is the binder yarn pulling out from the fabric. It is expected that the study can provide an experimental basis for building up the theoretical model. © 2013 Elsevier Ltd.
3D angle interlock preform; Deformation mechanism; In-plane shear; Interlaminar shear; Mechanical property
Deformation of the cell nucleus under indentation: Mechanics and mechanisms
Journal of Materials Research
21
08
2126-2135
2006
10.1557/jmr.2006.0262
Computational models of the cell nucleus, along with experimental observations, can help in understanding the biomechanics of force-induced nuclear deformation and mechanisms of stress transition throughout the nucleus. Here, we develop a computational model for an isolated nucleus undergoing indentation, which includes separate components representing the nucleoplasm and the nuclear envelope. The nuclear envelope itself is composed of three separate layers: two thin elastic layers representing the inner and outer nuclear membranes and one thicker layer representing the nuclear lamina. The proposed model is capable of separating the structural role of major nuclear components in the force-induced biological response of the nucleus (and ultimately the cell). A systematic analysis is carried out to explore the role of major individual nuclear elements, namely inner and outer membranes, nuclear lamina, and nucleoplasm, as well as the loading and experimental factors such as indentation rate and probe angle, on the biomechanical response of an isolated nucleus in atomic force microscopy indentation experiment
Animal Mechanics
Science
24
611
339-340
1906
10.1126/science.24.611.339
Basic mechanics, Hydrodynamics of swimming, The aerodynamics of flight, Principles of walking and running, Empirical studies of walking and running, Locomotion of soft bodied animals, Muscle function in locomotion, Energetics of locomotion, Optimization of locomotion
A filament winding technique for manufacturing cement based cross-ply laminates
Cement and Concrete Composites
20
5
405-415
1998
10.1016/S0958-9465(98)00011-0
A filament winding system was developed for manufacturing various types of fiber/cement composite materials. The system may be easily configured using the computer software to use continuous fiber composite laminates, cross-ply and angle ply laminates, pipes, and pultruded sections. The electrical and mechanical components of the system are discussed in detail. Cement based composite laminates are manufactured using continuous glass and polypropylene fibers. Tensile stress-strain response was measured using closed-loop strain controlled tests. Results indicate that tensile strength of composites can exceed 50 MPa using 5% alkali-resistant (AR) glass fibers. The ultimate strain capacity can also be increased by varying the stacking sequences. Ultimate strain capacities of the order of 2% were obtained. The experimental observations agree favorably with the theoretical predictions based on the ply discount method.
cememt composites; fiber reinforced concrete; fibers; glass fibers; laminated composites; manufacturing; mechanical testing; microcracking; polopropylene fibers; strength; toughening; toughness
Effects of PZT particle-enhanced ply interfaces on the vibration damping behavior of CFRP composites
Composites Part A: Applied Science and Manufacturing
42
10
1477-1482
2011
10.1016/j.compositesa.2011.06.014
In this study, vibration damping behavior of carbon fiber reinforced polymer composites was investigated when ply interfaces were enhanced by lead zirconate titanate (PZT) particles. The influence of particle loading and carbon black coating of particles was analyzed using the dynamic mechanical analysis. When plain PZT particles were distributed in the ply interfaces, the loss factor increased but suddenly dropped with increased particle loading, producing a threshold effect. As the loss factor represents the joule heat of electric current between PZT particles and carbon fibers, the sudden drop implies that there exists incomplete connectivity. To demonstrate the effect of incomplete connectivity, plain PZT particles were coated with carbon black of various weight fraction and the experiments were repeated. The results show there exists an optimal coating ratio of carbon black where the loss factor reaches its maximum value. When the optimal coating was applied to plain PZT particles, the loss factors of composites continuously increased, eliminating the threshold effect.
Carbon black; Lead zirconate titanate; Loss factor; Ply interface
Capillary induced self-assembly of thin foils into 3D structures
Journal of the Mechanics and Physics of Solids
58
12
2033-2042
2010
DOI 10.1016/j.jmps.2010.09.011
Self-assembly of complex structures is common in nature. Self-assembly principles provide a promising way to fabricate three-dimensional, micro- or millimeter scale devices. In the present paper, we present a generalized analytical study of the self-folding of thin plates into deterministic 3D shapes through fluid-solid interactions. Based on the beam theory, a mechanics model is developed, incorporating the two competing components-a capillary force promoting folding and the beinding rigidity of the foil that resists folding into a 3D structure. Through an equivalence argument of thin foils of different geometry, an effective folding parameter, which uniquely characterizes the driving force for folding, has been identified. A criterion for spontaneous folding of any shaped 2D patterned foil based on the effective folding parameter is thus established. The model predictions show excellent agreement with experimental measurements made on a variety of materials, indicating that the assumptions used in the analysis are valid. (C) 2010 Elsevier Ltd. All rights reserved.
bending rigidity; capillary force; folding; self-assembly; thin films
Axial compression and energy absorption characteristics of high-strength thin-walled cylinders under impact load
Theoretical and Applied Fracture Mechanics
53
1
1-8
2010
10.1016/j.tafmec.2009.12.001
Non-linear finite element software LS-DYNA is used to analyze the axial compression behavior and energy absorption of a high-strength thin-walled member under an impact load. To elucidate the effect of dynamic impact on the strain rate, the Cowper-Symonds equation is applied to analyze the plastic state of stress and the onset of dynamic yielding under different strain rates, such that the modeled deformation behavior of the member is consistent with the actual situation. Results for the thin-walled members made of mild steel and dual phase steel are compared. Assuming two different materials with equal sectional areas, an analysis confirms that the energy absorption of high-strength steel thin-walled component is better than the mild steel thin-walled component. Hence, thin-walled tubes made of high-strength steel are investigated using a series of analysis. The relationships between displacement and load, average load and energy absorption properties are obtained. © 2009 Elsevier Ltd. All rights reserved.
Axial compression; High-strength steel; Impact; Thin-walled cylinders
Exact lateral buckling analysis for thin-walled composite beam under end moment
Engineering Structures
29
8
1739-1751
2007
10.1016/j.engstruct.2006.09.017
An improved numerical method to evaluate exactly the element stiffness matrix is proposed for the lateral buckling analysis of thin-walled composite I- and channel-section beams with symmetric and arbitrary laminations subjected to end moments. For this, the bifurcation type buckling theory of thin-walled composite beams subjected to pure bending is developed based on the energy functional. Stability equations and force–deformation relationships are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Then the exact element stiffness matrix is determined using force–deformation relationships. In addition, analytical solutions for lateral buckling moments of unidirectional and cross-ply laminated composite beams with various boundary conditions are derived, as a special case. Finally, the finite element procedure based on Hermitian interpolation polynomials is developed. In order to verify the accuracy of this study, numerical solutions are presented and compared with the analytical solutions and the finite element solutions using the Hermitian beam elements, ABAQUS’s shell elements and the results by other researchers. Also, the effects of fiber orientation and the Wagner effect on the lateral buckling moments are studied.
Arbitrary lamination; Exact stiffness matrix; Lateral buckling moments; Thin-walled composite beam
The Principles of Statistical Mechanics
Journal of Applied Physics
660
1938
10.1063/1.1707250
This is the definitive treatise on the fundamentals of statistical mechanics. A concise exposition of classical statistical mechanics is followed by a thorough elucidation of quantum statistical mechanics: postulates, theorems, statistical ensembles, changes in quantum mechanical systems with time, and more. The final two chapters discuss applications of statistical mechanics to thermodynamic behavior. 1930 edition.
Plastic deformation of freestanding thin films: Experiments and modeling
Journal of the Mechanics and Physics of Solids
54
10
2089-2110
2006
10.1016/j.jmps.2006.04.005
Experimental measurements and computational results for the evolution of plastic deformation in freestanding thin films are compared. In the experiments, the stress-strain response of two sets of Cu films is determined in the plane-strain bulge test. One set of samples consists of electroplated Cu films, while the other set is sputter-deposited. Unpassivated films, films passivated on one side and films passivated on both sides are considered. The calculations are carried out within a two-dimensional plane strain framework with the dislocations modeled as line singularities in an isotropic elastic solid. The film is modeled by a unit cell consisting of eight grains, each of which has three slip systems. The film is initially free of dislocations which then nucleate from a specified distribution of Frank-Read sources. The grain boundaries and any film-passivation layer interfaces are taken to be impenetrable to dislocations. Both the experiments and the computations show: (i) a flow strength for the passivated films that is greater than for the unpassivated films and (ii) hysteresis and a Bauschinger effect that increases with increasing pre-strain for passivated films, while for unpassivated films hysteresis and a Bauschinger effect are small or absent. Furthermore, the experimental measurements and computational results for the 0.2% offset yield strength stress, and the evolution of hysteresis and of the Bauschinger effect are in good quantitative agreement. © 2006 Elsevier Ltd. All rights reserved.
Bauschinger effect; Computer simulation; Dislocations; Size effects; Thin films
Statistical mechanics in a nutshell
arXiv
23
1998
I give a concise introduction to some essential concepts of statistical mechanics: 1. Probability theory (constrained distributions, concentration theorem, frequency estimation, hypothesis testing); 2. Macroscopic systems in equilibrium (macrostate, thermodynamic variables, entropy, first law, thermodynamic potentials, correlations); 3. Linear response (Kubo formula).
On the mechanics of the actin filament: the linear relationship between stiffness and yield strength allows estimation of the yield strength of thin filament in vivo.
Journal of muscle research and cell motility
25
1
103-5
2004
Comparison of the behaviour of actin filaments either modified with tetramethylrhodamine iodoacetamide or decorated with tetramethylrhodamine-phalloidin or with tropomyosin or with myosin subfragment 1 shows that, in all the cases, yield strength is linearly related to stiffness.
Actin Cytoskeleton; Actin Cytoskeleton: chemistry; Actin Cytoskeleton: physiology; Actins; Actins: chemistry; Actins: physiology; Linear Models; Muscle Contraction; Muscle Contraction: physiology; Myosin Subfragments; Myosin Subfragments: chemistry; Myosin Subfragments: physiology; Phalloidine; Phalloidine: analogs & derivatives; Phalloidine: chemistry; Rhodamines; Rhodamines: chemistry; Tensile Strength; Tropomyosin; Tropomyosin: chemistry; Tropomyosin: physiology
Prandtl’s essentials of fluid mechanics
Prandtl’s essentials of fluid mechanics
xii + 795
2010
10.1007/b97538
Ludwig Prandtl, with his fundamental contributions to hydrodynamics, aerodynamics and gasdynamics, greatly influenced the development of fluid mechanics as a whole and it was his pioneering research in the first half of the 20th century that founded modern fluid mechanics. His book „Führer durch die Strömungslehre” or ‘Essentials of Fluid Mechanics’ appeared in 1942. Even today it is considered one of the most important books in the area. It is based on the 12th German edition with additional material included. All Chapters have been revised and extended, and there are new chapters on fluid mechanical instabilities and turbulence, microflows and biofluid mechanics. Essentials of Fluid Mechanics is aimed at science and engineering students and researchers wishing to obtain an overview of the different branches of fluid mechanics. The book is extensively illustrated throughout and includes problems to aid learning in many chapters.
aerodynamics; fluid mechanics; heat and mass transport; instabilities and turbulance; microfluidics; multiphase flows
Motion planning for concentric tube robots using mechanics-based models
IEEE International Conference on Intelligent Robots and Systems
5153-5159
2011
10.1109/IROS.2011.6048768
Concentric tube robots have the potential to enable new minimally invasive surgical procedures by curving around anatomical obstacles to reach difficult-to-reach sites in body cavities. Planning motions for these devices is challenging in part due to their complex kinematics; concentric tube robots are composed of thin, pre-curved, telescoping tubes that can achieve a variety of shapes via extension and rotation of each of their constituent tubes. We introduce a new motion planner to maneuver these devices to clinical targets while minimizing the probability of colliding with anatomical obstacles. Unlike prior planners for these devices, we more accurately model device shape using mechanics-based models that consider torsional interaction between the tubes. We also account for the effects of uncertainty in actuation and predicted device shape. We integrate these models with a sampling-based approach based on the Rapidly-Exploring Roadmap to guarantee finding optimal plans as computation time is allowed to increase. We demonstrate our motion planner in simulation using a variety of evaluation scenarios including an anatomy-based neurosurgery case that requires maneuvering to a di#cult-to-reach brain tumor at the skull base.
Quantum Mechanics of Many-Electron Systems
Proc. Royal Soc. (London) A
123
April
714-733
1929
10.1098/rspa.1929.0094
A mathematical paper showing how to translate the methods and results of group theory into the language of quantum mechanics. A formula is arrived at which, combined with Hartree's method for determining approximate wave-functions for the different electrons, should provide a powerful way of dealing with complicated atomic systems.
Engineering Damage Mechanics
New York
395
2005
10.1007/b138882
After introductory chapters on Continuum Damage Mechanics and numerical analysis of damage, the remaining chapters focus on a mode of damage – ductile failures; low-cycle fatigue; creep, creep-fatigue and dynamic failures; high-cycle fatigue; and failure of brittle and quasi-brittle materials. Each of these chapters appropriately begins with a section on engineering considerations to set the stage and provides a guide to analysis methods and tools. It is quite remarkable that such a wide range of behaviors are incorporated within a unified presentation. The damage mechanics “apple” has blossomed into a tree with many branches! Since failure is a complex nonlinear process, the predicted behavior can be sensitive to parameter values. Their appropriate identification is key for reliable engineering predictions, as is understanding the sensitivity of predictions to the particular choice of parameter values. The presentation here pays attention to parameter sensitivity as well as to parameter identification. This book provides a comprehensive guide to Engineering Damage Mechanics. It should appeal to all engineers and students of engineering concerned with lifetime prediction and with the failure resistant design of structures, components, and processes.
Ply-Slip During the Forming of Thermoplastic Composite Parts
Journal of Composite Materials
23
6
587-605
1989
10.1177/002199838902300604
A model for the ply-slip deformation behavior of a laminate composite is presented which allows prediction of the stresses, displacements, and strains developed during the forming process. The model takes into account the viscous nature of the matrix and the stress relaxation achievable via ply slippage. The stress response is inherently time dependent and is strongly affected by the forming rate. Results calculated for the isother mal three point bending of a unidirectional lay-up agree well with previous experimental data. An important parameter, the maximum system time constant, is identified and related to the material properties and part geometry. Comparisons with experiments and simulation results for nonisothermal forming are also discussed.
The mechanics of wrinkling
Finishing and Converting Conference
1-15
1996
Wrinkling is a common problem with thin webs of almost any material. This paper shows how all wrinkling is a compressive buckling of the web induced by either CD compression or inplane shear stresses. Common causes of wrinkling are then discussed which include roll(er) misalignment, deflection and diametral variations; constrained expansion, as well as residual stresses of manufacturing. Wrinkle removal via web flattening and web spreading are briefly reviewed.
alignment; baggy web; corrugations; creases; design; foldovers; roller; spreader; tolerances; wrinkles
Adhesion mechanics of the surface force apparatus
Journal of Physics D: Applied Physics
30
12
1710-1719
1999
10.1088/0022-3727/30/12/004
The surface force apparatus (SFA) comprises thin molecularly smooth mica sheets glued to glass cylinders, which are pressed into contact with their axes at right angles. It is frequently used, in conjunction with the Johnson - Kendall - Roberts (JKR) adhesion theory, to extract the surface energy of the contacting sheets. This procedure is open to possible error since the JKR theory is based on the contact of homogeneous, isotropic elastic cylinders. This paper extends the JKR theory to the layered structure of the SFA. Two approaches have been followed: (i) direct calculations for prescribed values of the layer thickness and elastic moduli; (ii) an experimental calibration procedure for an existing apparatus.
Radial basis functions collocation for the bending and free vibration analysis of laminated plates using the Reissner-Mixed Variational Theorem
European Journal of Mechanics - A/Solids
39
104-112
2013
10.1016/j.euromechsol.2012.10.012
In this paper, we combine the Carrera's Unified Formulation CUF (E. Carrera. Theories and Finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Meth. Eng., 10:215–297, 2003) and a radial basis function (RBF) collocation technique for predicting the static deformations and free vibrations behavior of thin and thick cross-ply laminated plates. For the first time, the Reissner-Mixed Variational Theorem is used together with the RBF collocation to achieve a highly accurate technique. The accuracy and efficiency of this collocation technique for static and vibration problems are demonstrated through numerical examples.
Laminated plates; Meshless methods; Vibrations
Is quantitative PCR for the pneumolysin (ply) gene useful for detection of pneumococcal lower respiratory tract infection?
Clinical microbiology and infection : the official publication of the European Society of Clinical Microbiology and Infectious Diseases
15
6
565-70
2009
10.1111/j.1469-0691.2009.02714.x
The pneumolysin (ply) gene is widely used as a target in PCR assays for Streptococcus pneumoniae in respiratory secretions. However, false-positive results with conventional ply-based PCR have been reported. The aim here was to study the performance of a quantitative ply-based PCR for the identification of pneumococcal lower respiratory tract infection (LRTI). In a prospective study, fibreoptic bronchoscopy was performed in 156 hospitalized adult patients with LRTI and 31 controls who underwent bronchoscopy because of suspicion of malignancy. Among the LRTI patients and controls, the quantitative ply-based PCR applied to bronchoalveolar lavage (BAL) fluid was positive at >or=10(3) genome copies/mL in 61% and 71% of the subjects, at >or=10(5) genome copies/mL in 40% and 58% of the subjects, and at >or=10(7) genome copies/mL in 15% and 3.2% of the subjects, respectively. Using BAL fluid culture, blood culture, and/or a urinary antigen test, S. pneumoniae was identified in 19 LRTI patients. As compared with these diagnostic methods used in combination, quantitative ply-based PCR showed sensitivities and specificities of 89% and 43% at a cut-off of 10(3) genome copies/mL, of 84% and 66% at a cut-off of 10(5) genome copies/mL, and of 53% and 90% at a cut-off of 10(7) genome copies/mL, respectively. In conclusion, a high cut-off with the quantitative ply-based PCR was required to reach acceptable specificity. However, as a high cut-off resulted in low sensitivity, quantitative ply-based PCR does not appear to be clinically useful. Quantitative PCR methods for S. pneumoniae using alternative gene targets should be evaluated.
Adult; Aged; Aged, 80 and over; Bacterial Proteins; Bacterial Proteins: genetics; Bronchoalveolar Lavage Fluid; Bronchoalveolar Lavage Fluid: microbiology; Bronchoscopy; Bronchoscopy: methods; Humans; Middle Aged; Pneumococcal Infections; Pneumococcal Infections: diagnosis; Polymerase Chain Reaction; Polymerase Chain Reaction: methods; Prospective Studies; Respiratory Tract Infections; Respiratory Tract Infections: microbiology; Sensitivity and Specificity; Streptococcus pneumoniae; Streptococcus pneumoniae: genetics; Streptolysins; Streptolysins: genetics
Error compensation strategy in milling flexible thin-wall parts
Journal of Materials Processing Technology
162-163
SPEC. ISS.
673-681
2005
10.1016/j.jmatprotec.2005.02.192
Accuracy of machined components is one of the most critical considerations for any manufacturer. One of the challenging difficult areas is the machining of low-rigidity complex parts usually associated with industries such as aerospace. The paper reports on advanced error prediction and compensation strategy specifically focused on force-induced errors in machining of thin-wall structures. The machining error is predicted using a theoretical flexible force-deflection model and compensated for by optimising the tool path prior to machining. The error compensation scheme is simulated using NC verification tools and experimentally validated. The experimental results show that the overall error in the flexible milling can be captured and predicted with very high accuracy using the proposed flexible force-deflection model and a large percentage of it can be eliminated through the proposed error compensation scheme. ?? 2005 Elsevier B.V. All rights reserved.
CAD/CAM; Cutting mechanics; Error compensation; Part deflection
Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates
International Journal of Solids and Structures
34
3
359-378
1997
10.1016/S0020-7683(96)00012-1
Laminate and structural mechanics for the analysis of laminated composite plate structures with piezoelectric actuators and sensors are presented. The theories implement layerwise representations of displacements and electric potential, and can model both the global and local electromechanical response of smart composite laminates. Finite-element formulations are developed for the quasi-static and dynamic analysis of smart composite structures containing piezoelectric layers. Comparisons with an exact solution illustrate the accuracy, robustness and capability of the developed mechanics to capture the global and local response of thin and/or thick laminated piezoelectric plates. Additional correlations and numerical applications demonstrate the unique capabilities of the mechanics in analyzing the static and free-vibration response of composite plates with distributed piezoelectric actuators and sensors.
Mechanics of Composite Strengthening
Fiber Composite Materials
37-75
1964
Influence of fiber and matrix characteristics on mechanics of deformation and fracture of fibrous composite
Statistical-Mechanics of Vortex System in a Thin-Film Superconductor in the Ring Approximation
Theoretical and Mathematical Physics
96
3
1062-&
1993
The statistical mechanics and thermodynamics of a two-dimensional system of vortices in a thin superconducting film are constructed. The long-range interaction of the vortices is taken into account in the ring approximation well known from plasma theory.
bond-orientational order; coulomb-gas; disorder; flux lattices; high-tc superconductors; liquids; magnetic-field; phase-transitions; resistive transition; two-dimensional superconductors
Fault Mechanics
Treatise on Geophysics
6
441-483
2007
10.1016/B978-044452748-6.00111-5
The past 15 years have seen a revolution in fault mechanics. Before the 1990s, the field was limited to the Andersonian fault mechanics, which offered no mechanism for fault propagation and grown. Linear elastic fracture mechanics, which had been applied to calculating the stress fields around faults, also did not offer a mechanism for fault growth. The CTOA model, an elastic-plastic numerical model that allows for inelastic yielding in a volume surrounding the crack tip, is consistent with all observations concerning fault growth. It predicts the linear scaling between fault displacement and length, and the observation that faults propagate by the breakdown of a brittle process zone that widens with fault length. The process zone consists primarily of intergranular dilatant microcracks that are oriented parallel to the maximum principal stress of the fault tip stress field and whose density increases exponentially as the fault is approached. These properties are consistent with theory and laboratory experiments. The theory is also consistent with the observation that fault tip displacement tapers are linear, scale independent, and increase with rock strength. Fault interactions through their stress fields are not understood except for the simple case of subparallel faults. These interactions result in the development of fault populations with well-defined statistical properties. These populations evolve with increasing brittle strain from power law to exponential size distributions and finally to evenly spaced system size faults. Fault rocks and structures are described as a function of depth, from the upper schizosphere through the plastosphere. The strength of faults is shown to be consistent with Byerlee friction, and the weak San Andreas Fault hypothesis is critiqued. ?? 2007 Elsevier B.V. All rights reserved.
Brittle fracture; Earthquakes; Faults; Friction; Rock mechanics; Strength; Structure; Tectonics
Principles of Composite Material Mechanics
Isbn0070234515 9780070234512
205
xxvii, 579 p.
1994
Extensively updated and maintaining the high standard of the popular original, Principles of Composite Material Mechanics, Second Edition reflects many of the recent developments in the mechanics of composite materials. It draws on the decades of teaching and research experience of the author and the course material of the senior undergraduate and graduate level classes he has taught.New and up-to-date information throughout the text brings modern engineering students everything they need to advance their knowledge of the evermore common composite materials. The introduction strengthens the book's emphasis on basic principles of mechanics by adding a review of the basic mechanics of materials equations. New appendices cover the derivations of stress equilibrium equations and the strain-displacement relations from elasticity theory. Additional sections address recent applications of composite mechanics to nanocomposites, composite grid structures, and composite sandwich structures. More detailed discussion of elasticity and finite element models have been included along with results from the recent World Wide Failure Exercise. The author takes a phenomenological approach to illustrate linear viscoelastic behavior of composites. Updated information on the nature of fracture and composite testing includes coverage of the finite element implementation of the Virtual Crack Closure techniqueand new and revised ASTM standard test methods. The author includes updated and expanded material property tables, many more example problems and homework exercises, as well as new reference citings throughout the text.Requiring a solid foundation in materials mechanics, engineering, linear algebra, and differential equations, Principles of Composite Materials Mechanics, Second Edition provides the advanced knowledge in composite materials needed by today's materials scientists and engineers.
Environmental Fluid Mechanics
Applied Mechanics Reviews
55
3
B59
2002
10.1115/1.1470688
Environmental Fluid Mechanics provides comprehensive coverage of a combination of basic fluid principles and their application in a number of different situations-exploring fluid motions on the earth’s surface, underground, and in oceans-detailing the use of physical and numerical models and modern computational approaches for the analysis of environmental processes. Environmental Fluid Mechanics covers novel scaling methods for a variety of environmental issues; equations of motion for boundary layers; hydraulic characteristics of open channel flow; surface and internal wave theory; the advection diffusion equation; sediment and associated contaminant transport in lakes and streams; mixed layer modeling in lakes; remediation; transport processes at the air/water interface; and more.
Contact Mechanics - Needs for Broader Applications
Journal of Physics D-Applied Physics
25
1A
A273-A278
1992
Doi 10.1088/0022-3727/25/1a/041
Contact mechanics is a well established subject, often associated with the work of Boussinesq and Hertz, but larger in scope. This paper discusses new areas where contact mechanics could contribute extensively if a certain number of questions were answered. Some domains just lack data to include in existing models; for instance information on the thermo-mechanical properties of thin coatings is lacking, and an effort in that direction would open up the design of coated machine elements to contact mechanics. Similar deficiencies are noted in fracture mechanics. In other areas, transfer of contact mechanics methods to industrial problems is hindered by changes in material properties under working conditions. Flow stress, toughness, etc vary during most sliding or rolling operations, and contact analyses should include these variations. A strong cooperation between mathematicians, mechanical engineers and material scientists can extend the field of application of contact mechanics in the design of machine elements.
friction
A note on the growth of Kelvin-Helmholtz waves on thin liquid sheets
Journal of Fluid Mechanics
57
04
671
1973
10.1017/S0022112073001941
A photographic study has been made of Kelvin-Helmholtz waves on thin liquid sheets and it has been found that, contrary to two-dimensional theory, wave growth is critically dependent upon sheet velocity and distance from the origin. This is attributed to boundary-layer separation and to subsequent vortex growth.
Dynamical Ensembles in Nonequilibrium Statistical Mechanics
Physical Review Letters
74
14
2694-2697
1995
10.1103/PhysRevLett.74.2694
Ruelle's principle for turbulence leading to what is usually called the Sinai-Ruelle-Bowen (SRB) distribution is applied to the statistical mechanics of many particle systems in nonequilibrium stationary states. A specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid. This presents the first test of the principle on a many particle system far from equilibrium. A possible application to fluid mechanics is also discussed.
Delamination and fracture of thin films
Journal of Research and Development
31
5
585
1987
10.1147/rd.315.0585
The fracture and delamination of thin films is a relatively common occurrence, and prevention of these mechanical failures is essential for the successful manufacture of thin-film devices. Internal elastic stresses are an inherent part of the thin-film deposition process, and are largely responsible for the mechanical failures of thin films. However, it is not the magnitude of the film stress S which governs film fracture or delamination, but the elastic energy U stored in the film. It is the intent of this presentation to show that the mechanical stability of the film and the substrate requires that U be less than a critical value Uc and that Uc is dependent upon the surface energy γ.
Films; Physics; thin
"Relative state" formulation of quantum mechanics
Reviews of Modern Physics
29
3
454-462
1957
10.1103/RevModPhys.29.454
'HE task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the ... \n
A continuum damage model for composite laminates: Part I - Constitutive model
Mechanics of Materials
39
10
897-908
2007
10.1016/j.mechmat.2007.03.005
A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level. © 2007 Elsevier Ltd. All rights reserved.
Composite materials; Continuum damage mechanics; Fracture mechanics
A Course on Damage Mechanics
Springer-Verlag Berlin Heidelberg
1996
10.1007/978-3-642-18255-6
This well-established textbook teaches macroscopic modeling for design, processing, testing, and control of mechanical components in engineering. The first chapter deals with the phenomenology of damage; the second couples damage to strains and covers the three-dimensional situation; the third is devoted to kinetic laws of damage evolution used by the author to unify many models; the fourth gives several methods for predicting crack initiation. Detailed calculations and many exercises help students to apply the powerful techniques to practical problems in engineering. This second, corrected and enlarged edition also includes the damage of interfaces and statistical damage analysis with microdefects.
Tissue mechanics
Tissue Mechanics
1-682
2007
10.1007/978-0-387-49985-7
Tissue Mechanics, Second Edition is about the mechanics of tissues for use at the advanced undergraduate level or above. Tissues transmit mechanical loads just like bridges and building structures. Not only do they transmit loads, but also they adapt their own structures so that the structures will transmit the mechanical loads more effectively, unlike bridges and building structures. The structures of living tissues are continually changing due to growth and response to the tissue environment, including the mechanical environment. The objective of this text is to describe the nature of the composite components of a tissue, the cellular processes that produce these constituents, the assembly of the constituents into a hierarchical structure, and the behavior of the tissues composite structure in the adaptation to its mechanical environment. A tissues mechanical environment is the history of mechanical loading experienced by the tissue in some reference time period, like a day. The most important features of the textbook are its middle level, neither too advanced nor too elementary, its fresh perspective on older material issues, and the inclusion of new research results carefully crafted onto this intermediate base of mechanics. Key Features: An introductory chapter on the structure of tissues and the fascinating unresolved problems concerning how biological tissues are formed and constructed. Detailed illustrations and included (with book/author watermark) on CD for tutorial instructional use Example problems to provide the student with hands-on experience with concepts Extensive appendices and tutorial materials on new developments including expanded treatment of ceramic materials and implants Detailed references for further reading Solutions Manual on CD for Bona Fide Instructors (separate entity; top secret sales code) As in TM, 1E a website (http://tissue-mechanics.com/) that has been established to provide supplemental material for the book. On this website is posted downloadable additional chapters on specific tissues, downloadable PowerPoint presentations of all the book's chapters, corrections to the published volume and additional exercises and examples for the existing chapters.
Ply angle effect on fiber composite wrapped reinforced concrete beam-column connections under combined axial and cyclic loads
Composite Structures
82
532-538
2008
10.1016/j.compstruct.2007.02.004
This paper presents a numerical analysis to investigate the effect of ply angle on the improvement of shear capacity and ductility of beam-column connections strengthened with carbon fiber-reinforced polymer (CFRP) wraps under combined axial and cyclic loads. Three-dimensional nonlinear finite element models for the beam-column connections were developed and simulated with the Marc.Mentat??? 2001 finite element analysis (FEA) software. An experimental study on an FRP-wrapped beam-column connection, which was previously reported in the literature, was utilized to validate the accuracy of the proposed finite element models. The FEA study entailed profiling the behavior of three beam-column connections that were strengthened through the CFRP wrapping with various ply angle configurations. Analysis results indicated that four layers of wrapping placed successively at ??45?? ply angles with respect to the horizontal axis is the most suitable upgrade scheme for improving shear capacity and ductility of beam-column connections under combined axial and cyclic loads. ?? 2007.
Beam-column joints; Composite wrap; Concrete; Ductility; Fibers; Strength
Localization of folds and cracks in thin metal films coated on flexible elastomer foams.
Advanced materials (Deerfield Beach, Fla.)
25
22
3117-21
2013
10.1002/adma.201300587
Thin metal films coated on soft elastomeric foam substrates exhibit enhanced electromechanical performance. The open-cell foam structure conveys highly anisotropic mechanical properties within the top, thin capping elastomer at the surface of the foam. Upon stretching, large strain fields inducing cracks and folds localize above the foam cells, while the surrounding cell ligaments remain almost strain-free, enabling stable electrical conduction in the metallic coating.
Elastomers; Elastomers: chemistry; Electric Conductivity; Gold; Gold: chemistry; Mechanical Processes; Models; Molecular; Molecular Conformation; Polyurethanes; Polyurethanes: chemistry
Mechanics of biomolecules
Journal of the Mechanics and Physics of Solids
50
11
2237-2274
2002
10.1016/S0022-5096(02)00035-2
Over the last few years molecular biomechanics has emerged as a new ?eld in which theo- retical and experimental studies of the mechanics of proteins and nucleic acids have become a focus, and the importance of mechanical forces and motions to the fundamentals of biology and biochemistry has begun to be recognized. In particular, single-molecule biomechanics of DNA extension, bending and twisting; protein domain motion, deformation and unfolding; and the generation of mechanical forces and motions by biomolecular motors has become a new frontier in life sciences. There is an increasing need for a more systematic study of the basic issues involved in molecular biomechanics, and a more active participation of researchers in applied mechanics. Here we review some of the advances in this ?eld over the last few years, explore the connection between mechanics and biochemistry, and discuss the concepts, issues, approaches and challenges, aiming to stimulating a broader interest in developing molecular biomechanics. ? 2002 Elsevier Science Ltd. All rights reserved.
a; b; biological material; c; chemo-mechanical processes; constitutive behavior; mechanical; mechano-chemical transduction; testing
Foundations of statistical mechanics
Reports on Progress in Physics
42
12
1937
1979
10.1088/0034-4885/42/12/002
Developments in the foundations of statistical mechanics during the past ten years or so. The author discusses how statistical concepts enter the treatment of deterministic mechanical systems, with particular reference to trajectory instabilities and to the KAM theorem. Then he deals with large systems: the thermodynamic limit and the theory of infinite systems. Non-equilibrium statistical mechanics is covered but LC relativistic statistical mechanics is not.
Mechanics of high speed projectile perforation
Journal of the Franklin Institute
264
2
117-126
1957
10.1016/0016-0032(57)90892-X
The problem of perforation of thin plates by high speed projectiles is considered from a momentum viewpoint. Equations representing the magnitude and direction of forces, velocity, etc. as a function of penetration distance are derived for the conical projectile under normal impact. Good correlation between the theory and experiment is obtained.
Stresses and Failure Modes in Thin Films and Multilayers
Thin Films
October
47
1996
Thin films and multilayers are widely used in technology, and their mechanical perfor- mance under severe environmental conditions often dictates design. Examples include electronic packages, coatings for thermal, chemical or abrasion protection, and ferroelec- tric actuators. This set of notes addresses both the origins and details of the stresses which develop in thin films and multilayers and the failure modes stemming from these stresses. The notes draw from many sources in the literature but two articles, in particular, are used. An overview article (Evans and Hutchinson, 1995) provides an integrated picture of the subject which goes beyond the scope of the notes. Much of the quantitative mechanics, which will be the focus of the notes, is contained in the article by Hutchinson and Suo (1992). Specific sections from these papers willbe cited and integrated into the notes as part of the reading. These two articles have an extensive list of references, which serve these notes as well. Detailed citations to the literature are not provided in these notes.
Mechanics of composite materials with MATLAB
New York
1
1
9-13
2005
10.1007/3-540-27710-2
The solutions to most of the given problems appear in an appendix at the end of the book.
A probabilistic static fatigue model for transverse cracking in CFRP cross-ply laminates
Composites Science and Technology
69
3-4
469-476
2009
10.1016/j.compscitech.2008.11.023
This paper presents a delayed-fracture model for transverse cracking in CFRP cross-ply laminates under static fatigue loading. First, a delayed-fracture model for a crack in a brittle material was established on the basis of the slow crack growth (SCG) concept in conjunction with a probabilistic fracture model using the three-parameter Weibull distribution. Second, the above probabilistic SCG model was applied to transverse cracking in cross-ply laminates under static fatigue loading. The stress and the length of the unit element in the transverse layers were calculated with the aid of a shear-lag analysis, taking the residual stress into account. The transverse crack density was expressed as a function of applied stress and time with the parameters in the Paris law and the Weibull distribution function specified, in addition to the mechanical and geometrical properties. Unknown parameters were determined from experiment data gathered in static tensile and static fatigue tests. The reproduced transverse crack density at various applied loads agreed well with the experiment results. © 2008 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Fatigue; C. Probabilistic methods; C. Transverse cracking; D. Life prediction
Soil compaction produced by tractor with radial and cross-ply tyres in two tillage regimes
Soil and Tillage Research
101
1-2
44-51
2008
10.1016/j.still.2008.06.001
The aim of this paper was to quantify soil compaction induced by tractor traffic on two tillage regimes: conventional tillage and direct drilling. Traffic was simulated with one pass of a conventional 2WD tractor, using four configurations of cross-ply rear tyres: 18.4–34, 23.1–30, 18.4–38 and 24.5–32, and four configurations of radial tyres 18.4R34, 23.1R 30, 18.4R 38 and 24.5R 32, with two ballast conditions used in each configuration. The experiment was conducted in the east of the Rolling Pampa region, Buenos Aires State, Argentina at 34°25′S, 59°15′W; altitude 22m above sea level. Rut depth after traffic and soil bulk density and cone index in a 0–450-mm profile were measured before and after traffic. Considering topsoil level, in two tillage regimes, all treatments induced significant values of soil compaction as compared to the control plot without traffic. Subsoil compaction increased as total axle load increased and was independent of ground pressure. For the same tyre configuration, radial tyre caused less soil compaction than the cross-ply.
Axle load; Ground contact pressure; Soil compaction; Tractor traffic
An investigation of matrix damage in composite laminates using continuum damage mechanics
Composite Structures
131
565-573
2015
10.1016/j.compstruct.2015.06.012
Transverse and shear damage in the polymer matrix of fiber reinforced composites are often treated independently, while the associated cracks are similar in appearance and effect. Matrix damage is often quantified by its crack density. However, damage also can be presented as a state variable. The definition of damage state variables and their evolution laws are the foundation of continuum damage mechanics, yet experimental data for shear damage evolution is limited. The effect of crack closure on the transverse stiffness of laminates was already incorporated in the damage models. However, the shear modulus sensitivity to crack closure has received little attention due to the complicated constitutive equations. This paper focused on the in-plane shear modulus reduction due to matrix transverse cracks and the evolution of transverse and shear damage. The comparison of existing models with experimental data showed that shear damage is currently not suitably described. Accordingly, a shear damage evolution model was proposed that included the effect of internal traction and crack closure on the in-plane shear modulus. The numerical predictions of the modified shear model resulted in good agreement with experimental data by predicting the same saturation crack density, axial and shear responses.
polymer-matrix composites
Out-of-plane ply wrinkling defects during consolidation over an external radius
Composites Science and Technology
105
151-159
2014
10.1016/j.compscitech.2014.10.007
If carbon fibre layers are prevented from slipping over one another as they consolidate onto a non-trivial geometry, they can be particularly susceptible to wrinkling/buckling instabilities. A one dimensional model for out-of-plane ply wrinkling during consolidation over an external radius is presented. Critical conditions for the appearance of wrinkles provide manufacturing strategies to eliminate such defects. Predicted wrinkle wavelengths and critical wrinkling conditions show good agreement with wrinkle defects observed in a spar demonstrator.
A. Layered structures; B. Defects; C. Modelling; Wrinkling
Computational contact mechanics
Springer
1-518
2006
10.1007/978-3-540-32609-0
This is the second edition of the valuable reference source for numerical simulations of contact mechanics suitable for many fields like civil engineering, car design, aeronautics, metal forming, or biomechanics. Boundary value problems involving contact are of great importance in industrial applications in engineering such as bearings, metal forming processes, rubber seals, drilling problems, crash analysis of cars, rolling contact between car tires and the road, cooling of electronic devices... Other applications are related to biomechanical engineering design where human joints, implants or teeth are of consideration. Due to this variety, contact problems are today combined either with large elastic or inelastic deformations including time dependent responses. Thermal coupling also might have to be considered. Even stability behaviour has to be linked to contact. The topic of computational contact is described in depth providing an up-to-date treatment of different formulations, algorithms and discretisation techniques for contact problems which are established in the geometrically linear and nonlinear range. This book provides the necessary continuum mechanics background which includes the derivation of the contact constraints. Constitutive equations stemming from tribology which are valid at the contact interface are discussed in detail. Discretization schemes for small and finite deformations are discussed in depth. Solid and beam contact is considered as well as contact of unstable systems and thermomechanical contact. The algorithmic side covers a broad range of solution methods. Additionally adaptive discretisation techniques for contact analysis are presented as a modern tool for engineering design simulations. The present text book is written for graduate, Masters and PhD students, but also for engineers in industry, who have to simulate contact problems in practical application and wish to understand the theoretical and algorithmic background of contact treatment in modern finite element systems. For this second edition, illustrative simplified examples and new discretisation schemes as well as adaptive procedures for coupled problems are added. © Springer-Verlag Berlin Heidelberg 2006. All rights are reserved.
Comparison of arterial wall mechanics using ring and cylindrical segments.
The American journal of physiology
244
2
H298-303
1983
Thin rings and intact cylindrical segments of canine carotid and iliac arteries were used to determine wall mechanics. Measurements of force and length were obtained from the ring segments, whereas measurements of pressure and diameter were obtained from the cylindrical segments under conditions of active (147 mM K+) and passive smooth muscle (Ca2+ free and 2 mM ethyleneglycolbis (beta-aminoethylether)-N,N'-tetraacetic acid). These measurements were normalized to values of segment stress and strain. Under passive conditions stress-strain relations for the rings appeared to be stiffer than those obtained using cylindrical segments. Pressure-diameter curves computed using force-length data from the rings were shifted to higher values of diameter compared with values from the intact segments at all pressure levels. Passive mechanics derived from measurements on ring segments yielded poor estimates of mechanics derived from intact segments. Despite this finding, values of active force development from the two sample geometries were similar. No statistically significant differences were found in values of maximum force development expressed in terms of sample cross-sectional area. Some differences in values of active force development at low values of muscle length were found. The latter were probably related to the differences in passive mechanics and the procedure used to normalize muscle length. Reasonable values of active force development can be obtained from ring segments.
Animals; Arteries; Arteries: physiology; Carotid Arteries; Carotid Arteries: physiology; Dogs; Female; Iliac Artery; Iliac Artery: physiology; Male; Muscle, Smooth, Vascular; Muscle, Smooth, Vascular: physiology; Physical Phenomena; Physics; Pressure; Stress, Mechanical
Benchmark solution of imperfect angle-ply laminated rectangular plates in cylindrical bending with surface piezoelectric layers as actuator and sensor
Computers and Structures
82
22
1773-1784
2004
10.1016/j.compstruc.2004.05.011
The static and dynamic responses of simply supported adaptive angle-ply laminates in cylindrical bending are considered. The interlaminar bonding of the host elastic laminate is assumed to be imperfect, described by a spring-layer model, while the bonding between the host elastic laminate and the surface piezoelectric actuator and sensor layers is perfect. The state-space approach, which is directly based on the three-dimensional exact elasticity (piezoelasticity) equations and very effective in analyzing laminated structures, is employed. The numerical results should provide a useful means of comparison in the development of simplified analyses or numerical methods. ?? 2004 Elsevier Ltd. All rights reserved.
Actuator/sensor layer; Adaptive laminate; Angle-ply; Cylindrical bending; Imperfect bonding; Spring-layer model; State-space approach
“ Basics of Fluid Mechanics ”
“ Basics of Fluid Mechanics ”
273-300
2013
The book is organized into several chapters which, as a traditional textbook, deals with a basic introduction to the fluid properties and concepts (under construction). The second chapter deals with Thermodynamics. The third book chapter is a review of mechanics. The next topic is statics. When the Static Chapter was written, this author did not realize that so many new ideas will be inserted into this topic. As traditional texts in this field, ideal flow will be presented with the issues of added mass and added forces (under construction). The classic issue of turbulence (and stability) will be presented. An introduction to multi–phase flow, not a traditional topic, will be presented next (again under construction). The next two chapters will deals with open channel flow and gas dynamics. At this stage, dimensional analysis will be present (again under construction).
Bohmian Mechanics as the Foundation of Quantum Mechanics
Arxiv Preprints
35
1995
In order to arrive at Bohmian mechanics from standard nonrelativistic quantum mechanics one need do almost nothing! One need only complete the usual quantum description in what is really the most obvious way: by simply including the positions of the particles of a quantum system as part of the state description of that system, allowing these positions to evolve in the most natural way. The entire quantum formalism, including the uncertainty principle and quantum randomness, emerges from an analysis of this evolution. This can be expressed succinctly---though in fact not succinctly enough---by declaring that the essential innovation of Bohmian mechanics is the insight that particles move!
Bohmian mechanics
Shear Buckling of Unsymmetrical Cross-Ply Plates
Journal of Composite Materials
3
2
359-363
1969
10.1177/002199836900300213
Recently solutions have been obtained [1, 2, 3] for the bending, vibrations, and buckling of laminated plates in which coupling between bending and stretch ing is important. However, buckling results were limited to unsymmetric angle- ply laminates under biaxial compression. Thus, there are no solutions available for the buckling of coupled laminates subjected to shear loading.This paper is concerned with the stability of unsymmetric cross-ply rectangular plates under uniform shear. These composites consist of an even number of layers all of the same thickness and elastic properties with the orthotropic axes of symmetry in each ply alternately oriented at 0° and 90° to the plate axes. Hinge- support boundary conditions are considered. The effect of coupling is ascertained by comparing coupled solutions to those obtained by neglecting the coupling coefficients in the governing equations. Applicability of the reduced bending stiffness approximation to shear buckling of cross-ply composites is also in vestigated.
The Essential Work of Fracture (EWF) method - Analyzing the Post-Yielding Fracture Mechanics of polymers
Engineering Failure Analysis
16
8
2604-2617
2009
10.1016/j.engfailanal.2009.04.027
The Post-Yielding Fracture Mechanics describe the fracture behaviour of pre-cracked films and thin sheets that show yielding phenomenon at the crack tip during fracture. The Essential Work of Fracture method (EWF) has been used for this type of fracture characterization, determining two parameters: the specific work of fracture, we related with the real fracture process area, and the specific non-essential work of fracture, wp that corresponds with the work done in the outer region of the crack tip. The EWF technique has been successfully employed especially with polymers, allowing the study of the influence of many variables in fracture properties, unavailable using other techniques such us KIC or JIC determination. In this work, the fundamentals of the technique and examples of application are reviewed, presenting a brief summary of the most relevant contributions of our group to the EWF method. © 2009 Elsevier Ltd. All rights reserved.
Energy partition; EWF applications; EWF method; Testing conditions
Modern Quantum Mechanics, Revised Edition
American Journal of Physics
63
1
93
1995
10.1119/1.17781
This classic text sets the standard for the quantum mechanics physics market. It provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts for first year graduate students. The author was a noted theorist in particle theory, and was well ...
Fracture Mechanics
Civil Engineering
376
2005
10.1007/1-4020-3153-X
Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written bij authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity.
Buckling and first ply failure of composite toroidal pressure hull
Computers & Structures
82
23-26
1981-1992
2004
10.1016/j.compstruc.2003.07.009
The paper addresses the static stability of externally pressurised toroidal shells with closed circular and non-circular cross-sections. Results of a numerical study into bifurcation buckling and first ply failure of CFRP filament wound toroids are presented. The influence of boundary conditions, variable wall thickness, laminations stacking and initial geometric imperfections on the load carrying capacity is provided. © 2004 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved.
buckling; circular and elliptical cross-sections; external pressure; toroids
On the forced motions of antisymmetric cross-ply laminated plates
International Journal of Mechanical Sciences
31
7
499-510
1989
10.1016/0020-7403(89)90099-4
Analytical solutions of the classical, first-order and third-order laminate plate theories are used to study the transient response of antisymmetric cross-ply simply supported rectangular plates. The solutions bring out the influence of the transverse shear deformation, the degree of anisotropy and the number of layers on the transient response. The study concludes that shear deformation theories accurately predict the behavior of the composite laminates, while the classical theory underestimates the transverse deflection.
Time-dependent matrix cracking in cross-ply laminates
Composites Science and Technology
39
1-12
1990
10.1016/0266-3538(90)90029-5
The use of fiber-reinforced polymer composites has escalated in recent years, raising numerous questions concerning their long-term durability in both static and transient environments. Time-dependent damage accumulation in cross-ply laminates, specifically in the form of matrix cracking, is discussed. The results of this study show that certain composite materials may display significant time-dependent damage under quasi-static and creep loads even at room temperature.
Extreme hardening of PDMS thin films due to high compressive strain and confined thickness.
Langmuir : the ACS journal of surfaces and colloids
27
13
8470-7
2011
10.1021/la201122e
Polymers confined to small dimensions and that undergo high strains can show remarkable nonlinear mechanics, which must be understood to accurately predict the functioning of nanoscale polymer devices. In this paper we describe the determination of the mechanical properties of ultrathin polydimethylsiloxane (PDMS) films undergoing large strains, using atomic force microscope (AFM) indentation with a spherical tip. The PDMS was molded into extremely thin films of variable thickness and adhered to a hard substrate. We found that for films below 1 μm in thickness the Young's modulus increased with decreasing sample thickness with a power law exponent of 1.35. Furthermore, as the soft PDMS film was indented, significant strain hardening was observed as the indentation depth approached 45% of the sample thickness. To properly quantify the nonlinear mechanical measurements, we utilized a pointwise Hertzian model which assumes only piecewise linearity on the part of the probed material. This analysis revealed three regions within the material. A linear region with a constant Young's modulus was seen for compression up to 45% strain. At strains higher than 45%, a marked increase in Young's modulus was measured. The onset of strain induced stiffening is well modeled by finite element modeling and occurs as stress contours expanding from the probe and the substrate overlap. A third region of mechanical variation occurred at small indentations of less than 10 nm. The pointwise Young's modulus at small indentations was several orders of magnitude higher than that in the linear elasticity region; we studied and ruled out causes responsible for this phenomenon. In total, these effects can cause thin elastomer films to become extremely stiff such that the measured Young's modulus is over a 100-fold higher than the bulk PDMS. Therefore, the mechanics of a polymer can be changed by adjusting the geometry of a material, in addition to changing the material itself. In addition to understanding the mechanics of thin polymer films, this work provides an excellent test of experimental techniques to measure the mechanics of other nonlinear and heterogeneous materials such as biological cells.
Artificial; Atomic Force; Dimethylpolysiloxanes; Dimethylpolysiloxanes: chemistry; Membranes; Microscopy; Particle Size; Surface Properties
Dependence of fracture toughness of composite laminates on interface ply orientations and delamination growth direction
Composites Science and Technology
64
13-14
2139-2152
2004
10.1016/j.compscitech.2004.03.007
A critical review has been performed of the published experimental research concerning delamination onset and growth in composite laminate interfaces of different lay-ups under single-mode loadings. It was found that, depending on the loading mode and interface lay-up, the traditional fracture toughness characterization by unidirectionally reinforced composite tests can lead to marked under- or overestimation of material resistance to crack growth. Empirical models of fracture toughness as a function of delamination front orientation with respect to reinforcement directions of the adjacent laminae have been validated and their applicability range established. © 2004 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites; B. Fracture toughness; C. Delamination; C. Laminates
Strength and Failure Modes of Bonded Single Lap Joints Between Cross-Ply Adherends
Composites
24
6
475-484
1993
10.1016/0010-4361(93)90017-3
Adhesively bonded joints with cross-ply adherends having a 0° or 90° surface layer have been manufactured and tested. The stresses in the joint were determined using a continuum method of analysis and large displacement finite element analysis was also undertaken. A numerical crack simulation was used to determine approximately stress/strain redistribution after initial cracking. Numerical predictions are compared with joint experimental performance and failure modes.
2D and 3D numerical models of transverse cracking in cross-ply laminates
9th French National Colloquium on Composite Materials
56
7
793-796
1996
10.1016/0266-3538(96)00022-x
Two numerical models, 2D and 3D, have been developed in order to study the behaviour of cross-ply laminates during multiplication of transverse cracks. The displacement and stress fields have been evaluated by the finite-element method in an elementary cell which is characteristic of regularly spaced cracks. The longitudinal stiffness reduction has then been deduced as a function of the transverse crack multiplication. In the case of quasi-static tensile tests, the 2D model has been used to estimate the initiation and development of transverse cracking. The different numerical results obtained have been compared with experimental results.
crack development; cross-ply laminates; finite-element analysis; stiffness reduction; transverse cracking
Micromechanical model of 3D cross-ply copper matrix composite reinforced with SiC fibres
Engineering Failure Analysis
16
8
2559-2566
2009
10.1016/j.engfailanal.2009.04.026
A 3D cross-ply micromechanical model is used to analyse the thermomechanical behaviour of copper matrix composite reinforced with SiC fibres, when subjected to cyclic loadings at high temperature. The copper matrix composite is reinforced with 45% fibre volume fraction. A cohesive model is employed to capture the influence of the debonding interface in the composite, during the consolidation and subsequent thermal and mechanical loading. © 2009 Elsevier Ltd. All rights reserved.
Cohesive model; Composite micromechanics; Composites; Copper; Copper matrix composite; Creep; Creep-fatigue interaction; Cross-ply; Cyclic loadings; Debonding; Fibre volume fraction; Finite element analysis; Finite element method; High temperature; High temperature fatigue; Loading; Mechanical loading; Metallic matrix composites; Micromechanical model; Silicon carbide; Thermomechanical behaviour; Three dimensional
Creep Mechanics
Applied Mechanics Reviews
56
5
B69
2003
10.1115/1.1584417
The third edition of "Creep Mechanics" provides a short survey of recent advances in the mathematical modelling of the mechanical behavior of anisotropic solids under creep conditions, including principles, methods, and applications of tensor functions. Some examples for practical use are discussed, as well as experiments by the author to test the validity of the modelling. The monograph offers an overview of other experimental investigations in creep mechanics. Rules for specifying irreducible sets of tensor invariants, scalar coefficients in constitutive and evolutional equations, and tensorial interpolation methods are also explained. The text has been re-examined and improved throughout. © 2008 Springer-Verlag Berlin Heidelberg. All rights are reserved.
Quantum mechanics in the brain.
Nature
440
7084
611
2006
10.1038/440611a
The relation between quantum mechanics and higher brain functions, including con- sciousness, is often discussed, but is far from being understood. Physicists, ignorant of modern neurobiology, are tempted to assume a formal or even dualistic view of the mind–brain problem. Meanwhile, cog- nitive neuroscientists and neurobiologists consider the quantum world to be irrelevant to their concerns and therefore do not attempt to understand its concepts. What can we confidently state about the current relationship between these two fields of scientific inquiry?
The dependence of Transverse Cracking and Delamination on Ply Thickness in Graphite/Epoxy Laminates
Damage in composite materials
118-139
1982
(25/-25/90n)s, n = ½, 1, 2, 3, 4, 6, 8, and (252/-252/902)s T300/934 graphite/epoxy laminate coupons were tested in tension and examined periodically by di-iodobutane (DIB) enhanced X-radiography following progressively larger increments of applied load. The tensile strain required to initiate transverse cracking in the 90-deg ply was found to depend on the thickness of the 90-deg layer. For n ≤ 3 delamination was initiated at the edge of the coupon. The onset of delamination occurred before or after transverse cracking, depending on the laminate construction. For n ≥ 4 delamination at the 25/90 interface was initiated across the entire width of the coupon by the formation of a transverse crack in the 90-deg ply. In some laminate constructions the location of specimen separation during final fracture was associated with the growth and coalescence of edge delaminations under either incrementally increasing or constant strain cyclic loading. Comparisons of experiments to the fracture sequence predictions by stress and energy analysis are made to assess our ability to account for the ply thickness dependence of fracture in these laminates.
a sequential accumulation of; composite laminates; composite materials; damage; delamination; fracture; graphite-epoxy; in the form of; is known to involve; laminate fracture under static; ma-; or fatigue loading; tension testing; the process of composite; trans-; verse cracking; x-radiography
Geological fluid mechanics
Perspectives in Fluid Dynamics: A Collective Introduction to Current Research
125
5
447-506
2003
10.1115/1.1603306
Now available in paperback, this wide-ranging text on modern fluid mechanics research includes sections on modelling the environment, physiology and magnetohydrodynamics. At the same time, the book discusses basic physical phenomena such as turbulence that still present fundamental challenges. Conventional textbooks cannot hope to give graduate students more than an inkling of what topics are currently being researched, or how to make a choice between them. This book aims to rectify matters, at least in part. It consists of eleven chapters that each introduces a different branch of the subject. Though not exhaustive, the coverage is broad: thin-film flows, Saffman-Taylor fingering, flows in arteries and veins, convective and absolute instabilities, turbulence, natural convection, magnetohydrodynamics, solidification, geological fluid mechanics, oceanography and atmospheric dynamics are all introduced and reviewed by established authorities. Thus the book will not only be suitable for graduate-level courses but also for specialists seeking introductions to other areas.
Mechanics of compressive stress evolution during thin film growth
Journal of the Mechanics and Physics of Solids
51
11-12
2127-2148
2003
Based on recent in situ measurements, Chason et al. (2002) proposed that the evolution of compressive stress during thin film growth by vapor deposition is due to an increase in surface chemical potential in the presence of growth flux and the consequent exchange of adatoms between the free surface and the grain boundaries. Based on this hypothesis, we present a model for grain boundary stress evolution during thin film growth. To illustrate the mechanics of the problem, first it is assumed that the local normal stress on the grain boundary is proportional to the local grain boundary opening only. The resulting "linear spring" model captures all essential features of the experimental observations. A more accurate description of the grain boundary stress evolution is presented by modeling the stress field due to the material inserted into the grain boundary as that resulting from a continuous distribution of dislocations along the grain boundary. The adatom flux between the grain boundary and the free surface is assumed to be proportional to the difference in chemical potential between the two. This model successfully explains a wide range of experimental observations, including the development of compressive stress during room temperature growth, effect of growth rate on the kinetics of compressive stress evolution and the continued tensile stress generation during low-temperature growth. (C) 2003 Elsevier Ltd. All rights reserved.
Evolutionary implications of the unusual walking mechanics of the common marmoset (C. jacchus)
American Journal of Physical Anthropology
122
1
28-37
2003
10.1002/ajpa.10214
Several features that appear to differentiate the walking gaits of most primates from those of most other mammals (the prevalence of diagonal-sequence footfalls, high degrees of humeral protraction, and low forelimb vs. hindlimb peak vertical forces) are believed to have evolved in response to requirements of locomotion on thin arboreal supports by early primates that had developed clawless grasping hands and feet. This putative relationship between anatomy, behavior, and ecology is tested here by examining gait mechanics in the common marmoset (Callithrix jacchus), a primate that has sharp claws and reduced pedal grasping, and that spends much of its time clinging on large trunks. Kinematic and kinetic data were collected on three male Callithrix jacchus as they walked across a force platform attached to the ground or to raised horizontal poles. The vast majority of all walking gaits were lateral-sequence. For all steps, the humerus was retracted (<90 degrees relative to a horizontal axis) or held in a neutral (90 degrees ) position at forelimb touchdown. Peak vertical forces on the forelimb were always higher than those on the hindlimb. These three features of the walking gaits of C. jacchus separate it from any other primate studied (including other callitrichids). The walking gaits of C. jacchus are mechanically more similar to those of small, nonprimate mammals. The results of this study support previous models that suggest that the unusual suite of features that typify the walking gaits of most primates are adaptations to the requirements of locomotion on thin arboreal supports. These data, along with data from other primates and marsupials, suggest that primate postcranial and locomotor characteristics are part of a basal adaptation for walking on thin branches.
Biomechanics; Callitrichids; Kinematics; Kinetics; Locomotion; Primate origins
How to use damage mechanics
Nuclear Engineering and Design
80
2
233-245
1984
10.1016/0029-5493(84)90169-9
The background of continuum damage mechanics is first presented in the framework of thermodynamics with some examples of constitutive equations for ductile damage, creep damage and fatigue damage. After the general scheme of structural calculations for macro-crack initiation, through non-coupled or coupled strain damage equations, some examples of “simple applications” are given: fracture limits of metal forming, surface initial damage in fatigue, creep fatigue interaction, and bifurcation of cracks.
Vibration and stability of angle-ply laminated composite plates subjected to in-plane stresses
International Journal of Mechanical Sciences
43
1925-1944
2001
10.1016/S0020-7403(01)00002-9
Natural frequencies and buckling stresses of angle-ply laminated composite plates are analyzed by taking into account the effects of shear deformation, thickness change and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for thick rectangular laminates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported thick laminated plate. In order to assure the accuracy of the present theory, convergence properties of the fundamental natural frequency are examined in detail. Numerical results are compared with those of the published existing theories. The modal displacement and stress distributions in the thickness direction are obtained and plotted in figures. The present global higher-order approximate theories can predict the natural frequencies, buckling stresses and modal stresses of thick multilayered angle-ply composite laminates accurately within small number of unknowns which is not dependent on the number of layers. ?? 2001 Elsevier Science Ltd.
Angle-ply; Buckling; Composite laminate; Higher-order theory; Vibration
Information Theory and Statistical Mechanics
Physical Review
106
4
1-11
1955
10.1103/PhysRev.108.171
Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. it is the least biased estimate possible on the given information; i.e., it is maximally noncommital with regard to the missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics", the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that cound have been made on the basis of the information available. It is concluded that statistical mechancis need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists only of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.
information theory; statistical mechanics
The mechanism for the long-wave instability in thin liquid films
Journal of Fluid Mechanics
217
469
1990
10.1017/S0022112090000805
A physical mechanism for the long-wave instability of thin liquid films is presented. We show that the many diverse systems that exhibit this instability can be classified into two large groups. Each group is studied using the model of a thin liquid film with a deformable top surface flowing down a rigid inclined plane. In the first group, the top surface has an imposed stress, while in the other, an imposed velocity. The proposed mechanism shows how the details of the energy transfer from the basic state to the disturbance are handled differently in each of these cases, and how a common growth mechanism produces the unstable motion of the disturbance.
Can a single-wall carbon nanotube be modeled as a thin shell?
Journal of the Mechanics and Physics of Solids
56
6
2213-2224
2008
10.1016/j.jmps.2008.01.004
Single-wall carbon nanotubes (SWCNT) have been frequently modeled as thin shells, but the shell thickness and Young's modulus reported in literatures display large scattering. The order of error to approximate SWCNTs as thin shells is studied in this paper via an atomistic-based finite-deformation shell theory, which avoids the shell thickness and Young's modulus, but links the tension and bending rigidities directly to the interatomic potential. The ratio of atomic spacing (Δ≈0.14 nm) to the radius of SWCNT, Δ/R, which ranges from zero (for graphene) to 40% [for a small (5,5) armchair SWCNT (R=0.35 nm)], is used to estimate the order of error. For the order of error O[(Δ/R)3], SWCNTs cannot be represented by a conventional thin shell because their constitutive relation involves the coupling between tension and curvature and between bending and strain. For the order of error O[(Δ/R)2], the tension and bending (shear and torsion) rigidities of SWCNTs can be represented by an elastic orthotropic thin shell, but the thickness and elastic modulus cannot. Only for the order of error O(Δ/R), a universal constant shell thickness can be defined and SWCNTs can be modeled as an elastic isotropic thin shell. © 2008 Elsevier Ltd. All rights reserved.
Atomic spacing; Bending (deformation); Elastic moduli; Finite deformation shell theory; Molecular modeling; order of error; orthotropic; Orthotropic thin shells; Rigidity; Shells (structures); Shell thickness; single-wall carbon nanotubes; Single-walled carbon nanotubes (SWCN); Strain rate; thickness; thin shell
Hydrothermal synthesis of ultra-thin LiFePO4 platelets for Li-ion batteries
Journal of Materials Science
46
14
4906-4912
2011
10.1007/s10853-011-5403-1
Ultra-thin LiFePO4 platelets are prepared by a hydrothermal process using tetraethylene glycol as co-solvent. The prepared LiFePO4 platelets have a very thin thickness of about 50–80 nm, which is beneficial for Li ions to fast transfer in the bulk of the electrode. It is found that the as-synthesized LiFePO4 cathode material exhibits a quite high reversible capacity of 137 mAh g−1 at 0.2 C. After carbon coating, the obtained LiFePO4/C composite cathode has the enhanced electronic conductivity, and thus the rate capability has been improved significantly. At 8 and 12 C, the composite has the discharge capacity of 104 and 95 mAh g−1, respectively, which suggests that the ultra-thin LiFePO4 platelets are a promising candidate for the large-scale Li-ion batteries.
Computational Mechanics of the Heart
Journal of Elasticity
61
113-141
2001
10.1023/A:1011084330767
Finite elasticity theory combined with finite element analysis provides the framework for analysing ventricular mechanics during the filling phase of the cardiac cycle, when cardiac cells are not actively contracting. The orthotropic properties of the passive tissue are described here by a “pole–zero” constitutive law, whose parameters are derived in part from a model of the underlying distributions of collagen fibres. These distributions are based on our observations of the fibrous- sheet laminar architecture of myocardial tissue. We illustrate the use of high order (cubic Hermite) basis functions in solving the Galerkin finite element stress equilibrium equations based on this orthotropic constitutive law and for incorporating the observed regional distributions of fibre and sheet orientations. Pressure–volume relations and 3D principal strains predicted by the model are compared with experimental observations. A model of active tissue properties, based on isolated muscle experiments, is also introduced in order to predict transmural distributions of 3D principal strains at the end of the contraction phase of the cardiac cycle. We end by offering a critique of the current model of ventricular mechanics and propose new challenges for future modellers
abbreviations; cardiac mechanics; fe; fem; fibrous-; fibrous- sheet tissue structure; finite elastic deformation; finite element; finite element method; la; left; left atrium; left ventricular end-diastolic pressure; lv; lvedp; orthotropic constitutive relations; ra; right atrium; right ventricle; rv; sheet tissue structure; ventricle
Contact mechanics and interfacial fatigue studies between thin semicrystalline and glassy polymer films
Adhesion
365-386
2005
In order to develop a greater understanding of interfacial interactions between a semicryst. polymer and a glassy polymer, adhesion tests were performed on very thin layers of poly(ethylene oxide) (PEO) sandwiched between two layers of poly(tetra-Me bisphenol A polycarbonate) (TMPC). The tests were designed to provide intimate contact between the surfaces while they were heated above the m.p. of the PEO and cooled back to room temp. A contact mechanics approach, based on the Johnson, Kendall, and Roberts (JKR) theory, was used to det. values of the energy release rate describing the energetic driving force for crack propagation within the interfacial region. The ability to measure crack propagation at large values of the energy release rate was limited by rupture of the silicone elastomer that was used to provide a sufficiently compliant matrix for the adhesion expt. By cycling the tensile stress at relatively low loading levels, we were able to measure fatigue crack propagation at values of the energy release rate that did not result in failure of the elastomer. [on SciFinder (R)]
Base plate mechanics of the barnacle Balanus amphitrite (=Amphibalanus amphitrite).
Biofouling
24
2
109-118
2008
10.1080/08927010701882112
The mechanical properties of barnacle base plates were measured using a punch test apparatus, with the purpose of examining the effect that the base plate flexural rigidity may have on adhesion mechanics. Base plate compliance was measured for 43 Balanus amphitrite (=Amphibalanus amphitrite) barnacles. Compliance measurements were used to determine flexural rigidity (assuming a fixed-edge circular plate approximation) and composite modulus of the base plates. The barnacles were categorized by age and cement type (hard or gummy) for statistical analyses. Barnacles that were 'hard' (> or =70% of the base plate thin, rigid cement) and 'gummy' (>30% of the base plate covered in compliant, tacky cement) showed statistically different composite moduli but did not show a difference in base plate flexural rigidity. The average flexural rigidity for all barnacles was 0.0020 Nm (SEM +/- 0.0003). Flexural rigidity and composite modulus did not differ significantly between 3-month and 14-month-old barnacles. The relatively low flexural rigidity measured for barnacles suggests that a rigid punch approximation is not sufficient to account for the contributions to adhesion mechanics due to flexing of real barnacles during release.
adhesion of plates; balanus amphitrite; barnacle; fouling release; mechanics of adhesion; release coatings
Geometry and mechanics in the opening of chiral seed pods.
Science
333
6050
1726-30
2011
10.1126/science.1203874
We studied the mechanical process of seed pods opening in Bauhinia variegate and found a chirality-creating mechanism, which turns an initially flat pod valve into a helix. We studied configurations of strips cut from pod valve tissue and from composite elastic materials that mimic its structure. The experiments reveal various helical configurations with sharp morphological transitions between them. Using the mathematical framework of "incompatible elasticity," we modeled the pod as a thin strip with a flat intrinsic metric and a saddle-like intrinsic curvature. Our theoretical analysis quantitatively predicts all observed configurations, thus linking the pod's microscopic structure and macroscopic conformation. We suggest that this type of incompatible strip is likely to play a role in the self-assembly of chiral macromolecules and could be used for the engineering of synthetic self-shaping devices.
Bauhinia; Bauhinia: anatomy & histology; Bauhinia: physiology; Biological; Biomimetic Materials; Elasticity; Latex; Mathematical Concepts; Models; Physical Phenomena; Seeds; Seeds: anatomy & histology; Seeds: physiology
Initiation and growth of delamination from the tips of transverse cracks in CFRP cross-ply laminates
Composites Science and Technology
52
309-318
1994
10.1016/0266-3538(94)90166-X
Delamination initiation and growth from the tips of the transverse cracks in toughened-type CFRP (T800H/3631) cross-ply laminates was measured by the replica technique as a function of the applied laminate strain. In addition, loading/unloading tests were performed to obtain the relationship between the measured material damage and Young's modulus reduction. ENF (end-notched flexure) tests were also performed to obtain the mode II interlaminar fracture toughness in order to understand the delamination growth behavior. A simple shear-lag stress analysis was extended to the laminates containing delaminations at the tips of transverse cracks. This stress analysis was used to obtain Young's modulus reduction and the energy release rate associated with the delamination growth. The shear-lag prediction of Young's modulus reduction was compared with experimental data. The total delamination length was predicted as a function of the applied laminate strain by using the energy release rate and the experimentally obtained mode II interlaminar fracture toughness.
cross-ply laminates; delamination; energy; release rate; s modulus reduction; transverse; young
The mechanics of membrane proteins is a signature of biological function
Soft Matter
9
32
7866
2013
10.1039/c3sm50967b
Beyond structure, the mechanics of plasma membrane components is of key importance to biological function. Nanoscale mechanics is however poorly described due to the lack of suitable experimental tools. Here, we combined atomic force microscopy and nanomechanical mapping to analyze the structure and mechanical properties of native eye lens cell membranes. Lens membranes mainly comprise two proteins; aquaporin 0 and connexin, forming respectively thin and gap intercellular junctions that sustain mechanical stress during accommodation. Our results reveal the mechanical heterogeneity of the plasma membrane, allowing examination of the mechanical nanoenvironment of individual proteins and the flexibility of supramolecular assemblies. The remarkable rigidity of gap junctions suggests their role as stable intercellular adhesion complexes ensuring maintenance of thin junctions, which form more flexible supramolecular complexes capable of sustaining pressure differences between cells. Our work proposes the mechanical properties of individual proteins and protein domains directly related to biological function as a novel molecular signature.
Fracture mechanics of rock
Academic Press geology series
548
1987
10.1007/978-94-007-2595-9
The increased attention paid to both experimental rock fracture mechanics and the application of fracture mechanics to the solving of geophysical problems has affected many diverse areas. In this work, the authors have attempted to present a concise treatment of the physics and mathematics of a representative selection of problems from areas such as earthquake mechanics and prediction, hydraulic fracturing, hot dry rock geothermal energy, and dynamic fragmentation.
Nuclear Mechanics and Methods
Methods in Cell Biology
83
07
269-294
2007
10.1016/S0091-679X(07)83011-1
The role of the nucleus in protecting and sequestering the genome is intrinsically mechanical, and disease-causing structural mutants in lamins and other components underscore this function. Various methods to measure nuclear mechanics, isolated or in situ, are outlined here in some detail. ?? 2007 Elsevier Inc. All rights reserved.
Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory: Part II—Buckling and free vibration
Composite Structures
9
4
259-277
1988
10.1016/0263-8223(88)90048-7
Using the higher-order plate theory developed in the first part of this paper, as well as the technique based on the state space concept, the free vibration and buckling problems of rectangular cross-ply laminated plates are analyzed. In this context a variety of boundary conditions is considered and comparisons with the existing literature are made.
Introductory fluid mechanics
Choice: Current Reviews for Academic Libraries
48
8
1517
2011
A review of the book "Introductory Fluid Mechanics," by Joseph Katz is presented.
BOOKS -- Reviews; INTRODUCTORY Fluid Mechanics (Book); KATZ, Joseph; NONFICTION
Quantum mechanics
Il Nuovo Cimento A
50
2
375-376
1967
10.1007/BF02827752
Molecular mechanics (MM) methods are computationally affordable tools for screening chemical libraries of novel compounds for sites of P450 metabolism. One challenge for MM methods has been the absence of a consistent and transferable set of parameters for the heme within the P450 active site. Experimental data indicate that mammalian P450 enzymes vary greatly in the size, architecture, and plasticity of their active sites. Thus, obtaining X-ray-based geometries for the development of accurate MM parameters for the major classes of hepatic P450 remains a daunting task. Our previous work with preliminary gas-phase quantum mechanics (QM)-derived atomic partial charges greatly improved the accuracy of docking studies of raloxifene to CYP3A4. We have therefore developed and tested a consistent set of transferable MM parameters based on gas-phase QM calculations of two model systems of the heme-a truncated (T-HM) and a full (F-HM) for four states of the P450 catalytic cycle. Our results indicate that the use of the atomic partial charges from the F-HM further improves the accuracy of docked predictions for raloxifene to CYP3A4. Different patterns for substrate docking are also observed depending on the choice of heme model and state. Newly parameterized heme models are tested in implicit and explicitly solvated MD simulations in the absence and presence of enzyme structures, for CYP3A4, and appear to be stable on the nanosecond simulation timescale. The new force field for the various heme states may aid the community for simulations of P450 enzymes and other heme-containing enzymes. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011.
Use of material grading for enhanced buckling design of thin-walled composite rings/long cylinders under external pressure
Composite Structures
93
2
351-359
2011
10.1016/j.compstruct.2010.09.007
This paper presents a mathematical model for enhancing the buckling stability of composite, thin-walled rings/long cylinders under external pressure using radial material grading concept. The main structure to be analyzed is built of multi-angle fibrous laminated lay-ups having different volume fractions of the constituent materials within the individual plies. This leads to a piecewise grading of the material in the radial direction. The objective is to maximize the critical buckling pressure while preserving the total structural mass at a constant value equal to that of a baseline design. The fiber volume fractions are included among the standard design variables such as fiber orientation angles and ply thicknesses, which are used by many investigators in the field. The model employs the classical lamination theory, where an analytical solution that accounts for the effective axial and flexural stiffness separately is given. The critical buckling pressure contours subject to the mass equality constraint are given for several types of anisotropic rings/long cylinders showing the functional dependence of the constrained objective function on the selected design variables. It is shown that material grading can have significant contribution to the whole optimization process in achieving the required structural designs with enhanced stability limits. ?? 2010 Elsevier Ltd.
Buckling stability; External hydrostatic pressure; Fibrous composites; Functionally graded material; Laminated rings/cylindrical shells; Structural optimization
A shaft-loaded blister test for elastic response and delamination behavior of thin film–substrate system
Thin Solid Films
424
1
115-119
2003
10.1016/s0040-6090(02)00909-4
The elastic response of a thin film of photoresist deposited on a silicon wafer is studied by using a shaft-loaded blister test method developed recently. Experiment data are compared with an analytical solution. Results demonstrated that under shaft loading, the thin film underwent a pure bending mode at small deformation and gradually transformed to a pure stretching mode at larger deformation. The effect of residual stress on elastic response is also studied. The delamination of thin film from substrate can be successfully measured under displacement control mode by the shaft-loaded blister test.
Delamination; Mechanics of thin film; Shaft-loaded blister test; Thin film
Fatigue damage mechanics of composite-materials 1. Experimental-measurement of damage and post-fatigue properties
Composites Science and Technology
44
2
159-168
1992
10.1016/0266-3538(92)90109-g
A new approach for modelling the post-fatigue strength and stiffness of notched fibre composite laminates has been developed. It is based on the observation of notch tip damage which can be quantified by the extent of the individual failure processes, splitting in the 0-degrees plies and delamination between the 0-degrees ply and off-axis plies. The notch tip damage zone grows stably under tensile cyclic loading in a self-similar manner and the size and shape of this damage zone is dependent on laminate geometry and constituent properties of the fibre, matrix and interface. The post-fatigue strength and stiffness of the laminate can be related uniquely to the split length, which defines the extent of damage growth. In this first paper in a series of four, observation is made and measurements taken of the damage growth mechanisms that make up the damage zone in carbon fibre/epoxy laminates. Radiographs are used to characterise the notch tip damage zone and to establish a qualitative relationship between post-fatigue strength (or stiffness), cyclic stress, damage size and numbers of cycles.
BEHAVIOR; DELAMINATION; MATRIX CRACKING; MODEL; NOTCHES; POST-FATIGUE STRENGTH STIFFNESS; RESIDUAL STRENGTH; SPLITTING
Stress-Strain Behavior of Nano / Micro Thin Film Materials
ARPN Journal of Engineering and Applied Sciences
5
3
72-76
2010
Nano/micro size thin films are being developed at present for various applications as stretchable electronic displays, flexible and foldable solar panels, body conformable smart electronic textiles and fabrics, and other embedded sensor-actuator surfaces. This paper describes the results from an experimental investigation of elastic-plastic deformation behavior of nano/micro thick conducting metal such as gold (Au) on a highly compliant, biocompatible polymer such as polydimethylsiloxane (PDMS). Two layer laminates were fabricated with various nano Au film on micron scale PDMS substrate and tested using a micro-tensile tester. Also, in-situ scanning electron microscope (SEM) tests captured the digital images of Au film under static load to explain the changes in grain structure of the gold film. Stress-strain data for the gold film under large deformation was extracted using a mechanics of material based model, and changes in stiffness values of the Au film were determined. The experimental results validated the Hall-Petch law indicating that the material strength properties have inverse relationship with grain size. Results indicated that the metallic Au films sustained large deformation without rupture and SEM studies indicated that at higher strain levels, grains in the Au film experienced intra- granular fractures.
mechanics layered media; metal polymer; thin films
Failure analysis of curved composite panels based on first-ply and buckling failures
Procedia Engineering
10
1591-1596
2011
10.1016/j.proeng.2011.04.266
Curved panels are used extensively in several branches of engineering and in particular in marine and aerospace engineering working mostly under compressive loads. Failure of these components by buckling or excessive stress is an important design consideration. In the present study the effect of fiber orientation is studied on the failure load of a laminated curved panel subject to uniaxial compression. The failure modes are specified as first-ply failure and buckling with the failure load defined as the minimum of these two loads. The panel is taken as a symmetrically laminated angle-ply plate and the failure load is determined for different aspect ratios, panel thicknesses and boundary conditions (simply supported and clamped panels). The failure load is maximized for a set of selected stacking sequences by determining the best ply angle for each stacking sequence giving the highest failure load. ?? 2011 Published by Elsevier Ltd.
Buckling; Composite panels; Curved panel; First-ply failure; Optimal design
A continuum damage model for composite laminates: Part I – Constitutive model
Mechanics of Materials
39
10
897-908
2007
10.1016/j.mechmat.2007.03.005
A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level.
composite materials; continuum damage mechanics; fracture mechanics
Thin Film Cracking Modulated by Underlayer Creep
Experimental Mechanics
43
3
269-279
2003
10.1177/00144851030433006
In devices that integrate dissimilar materials in small dimensions, crack extension in one material often accompanies inelastic deformation in another. In this paper we analyze a channel crack advancing in an elastic film, while an underlayer creeps. The film is subject to a tensile stress. As the underlayer creeps, the stress field in the film relaxes in the crack wake, and intensifies around the crack tip. In a blanket film, the crack can attain a steady velocity, set by two rate processes: subcritical decohesion at the crack tip, and creep in the underlayer. In a thin-film microbridge over a viscous stripe, the crack cannot grow when the bridge is short, and can grow at a steady velocity when the bridge is long. We use a two-dimensional shear lag model to approximate the three-dimensional fracture process, and an extended finite element method to simulate the moving crack with an invariant, relatively coarse mesh. On the basis of the theoretical findings, we propose new experiments to measure fracture toughness and creep laws in small structures. As a byproduct, an analytical formula is found for the growth rate per temperature cycle of a channel crack in a brittle film, induced by ratcheting plastic deformation in a metal underlayer.
crack; creep; ratcheting; thin film
Multi-scale modeling in damage mechanics of composite materials
Journal of Materials Science
41
20
6800-6812
2006
10.1007/s10853-006-0210-9
This paper addresses the multi-scale modeling aspects of damage in composite materials. The multiplicity of the scales of the operating mechanisms is discussed and clarified by taking examples of damage in a unidirectional ceramic matrix composite and in a cross ply polymer matrix composite laminate. Two multi-scale modeling strategies-the hierarchical and the synergistic-are reviewed in the context of deformational response. Finally, the "big picture" as it relates to the cost-effective manufacturing of composite structures intended for long-term performance is outlined and desired future direction in multi-scale modeling is discussed.
Multi-scale modeling in damage mechanics of composite materials
Special section: Advances in Multi-Scale Modelling of Composite Material Systems and Components; Guest Editor: Peter W. R. Beaumont
41
20
6800-6812
2006
This paper addresses the multi-scale modeling aspects of damage in composite materials. The multiplicity of the scales of the operating mechanisms is discussed and clarified by taking examples of damage in a unidirectional ceramic matrix composite and in a cross ply polymer matrix composite laminate. Two multi-scale modeling strategies - the hierarchical and the synergistic - are reviewed in the context of deformational response. Finally, the "big picture" as it relates to the cost-effective manufacturing of composite structures intended for long-term performance is outlined and desired future direction in multi-scale modeling is discussed. Springer Science+Business Media, Inc. 2006.
Ceramic matrix composites; Composite materials; Composite micromechanics; Cost effectiveness; Deformation; Hierarchical systems; Mathematical models
Effect of composite type and its configuration on buckling strength of thin laminated composite plates
Latin American Journal of Solids and Structures
3
279-299
2006
For civil engineering applications, a plate which is strong enough against buckling is al- ways desirable. In the market there are number of composites available which differ from each other in various aspects of engineering properties. In the present study, an effort has been made to identify better configuration of given composite to achieve higher buckling strength for laminated anti-symmetric cross and angle-ply simply supported rectangular orthotropic plates subjected to uniaxial compressive loads. The study has further been extended with number of available composites to find the more effective type of composite against buckling for given configuration of laminated plates. For this purpose, a brief formulation, available in the literature, for the estimation of buckling load for orthotropic laminated composite plates has been presented. Based on this formulation a computer program is developed and using this program various parametric studies are conducted to achieve the above objectives.
Mechanics of active salt diapirism
Tectonophysics
228
3-4
275-312
1993
10.1016/0040-1951(93)90345-K
An active diapir forcefully intrudes its overburden, driven by diapir pressure that overcomes the resistance of the overburden strength. Possible causes for the driving pressure are differential loading of the source layer and a density contrast with the overburden. Possible resisting forces derive from the mass of the roof block and resistance to the faulting and folding that accommodate the intrusion. For a typical density contrast between salt and a sedimentary overburden, a simple force balance demonstrates that the diapir height must be more than two-thirds to three-quarters the thickness of the surrounding overburden to initiate substantial active diapirism. Narrow diapirs must be even taller. Physical and numerical modeling show that typical structures of active diapirism are a central crestal graben flanked by relatively unstrained flaps that rotate upward and outward. Curved reverse faults can separate the flaps from the regional overburden. Normal faults in the crestal graben propagate downward, with new faults created farther outward as the roof arches over the rising diapir. Thin, wide roofs develop multiple grabens separating a relatively flat roof from the rotating flaps. In cases leading to emergence, the piercing diapir evolves from a pointed crest to a progressively rounded and widening crest as the flaps rotate outward. The numerical models show that overburden flexure contributes to early formation of active diapir structures, but piercement does not continue to emergence unless the diapir is very wide or tall relative to the overburden thickness. Active diapirism becomes progressively more difficult for diapir crests ranging from a rectangle, a round-cornered rectangle, a semicircle, to a triangle with a pointed crest.
Muscle mechanics
Journal of Biomechanics
40
July 2007
S2
2007
10.1016/S0021-9290(07)70002-7
Muscles are not straightforward linear tension generators but behave in quite unexpected ways. This lecture looks at how muscles perform: their mechanical properties and how they behave when they are generating tension.
Engineering Fluid Mechanics
Applied Mechanics Reviews
54
5
B89
2001
10.1115/1.1399677
A fluid is a substance, which deforms when subjected to a force. A fluid can offer no permanent resistance to any force causing change of shape. Fluid flow under their own weight and take the shape of any solid body with which they are in contact. Fluids may be divided into liquids and gases. Liquids occupy definite volumes. Gases will expand to occupy any containing vessel.
Capillary buckling of a thin film adhering to a sphere
Journal of the Mechanics and Physics of Solids
61
2
450-471
2013
10.1016/j.jmps.2012.09.016
We present a combined theoretical and experimental study of the buckling of a thin film wrapped around a sphere under the action of capillary forces. A rigid sphere is coated with a wetting liquid, and then wrapped by a thin film having an approximately cylindrical shape. The equilibrium of the film is governed by the competing effects of elasticity and capillarity: elasticity tends to keep the film developable while capillarity tends to curve it in both directions so as to maximize the area of contact with the sphere. In the experiments, the region of contact between the film and the sphere has cylindrical symmetry when the sphere radius is small, but destabilizes to a non-symmetric, wrinkled configuration when the radius is larger than a critical value. We combine the Donnell equations for near-cylindrical shells to include a unilateral constraint with the impenetrable sphere, and the capillary forces acting along a moving edge. A non-linear solution describing the axisymmetric configuration of the film is derived. A linear stability analysis is then presented, which successfully captures the wrinkling instability, the symmetry of the unstable mode, the instability threshold and the critical wavelength. The motion of the free boundary at the edge of the region of contact, which has an effect on the instability, is treated without any approximation. ?? 2012 Elsevier Ltd. All rights reserved.
Adhesion and adhesives; Buckling; Contact mechanics; Elastic material; Stability and bifurcation
Quantum mechanics demystified
Book
412
2005
10.1036/0071455469
Fun format makes this complex subject easy to grasp solutions to typical problems that are explained in full detail. It is perfect for self-study or class supplement. It is great for quick review or help prepare for the Physics qualifying exam. Learn quantum mechanics at warp speed! Now anyone can master the basics of quantum mechanics - without formal training, unlimited time, or a genius IQ. In "Quantum Mechanics Demystified", physicist (and student-savvy author) David McMahon provides an effective and illuminating way to learn the essentials of quantum mechanics.With "Quantum Mechanics Demystified", you master the subject one step at a time - at your own speed. This unique self-teaching guide is filled with solved examples throughout, and offers problems to try at the end of each chapter to pinpoint weaknesses. A final exam serves to reinforce concepts covered in the entire book. This fast and entertaining self-teaching course makes it much easier to - master serious quantum mechanics in easy-to-follow steps.This book cuts through the jargon and learn how to do quantum mechanics using worked examples. It helps reinforce learning and pinpoint weaknesses with questions at the end of each chapter and a comprehensive final exam. Learn about Schrodinger's equation, one dimensional scattering, Hilbert space, and the density operator. Find extensive explanations of spin and angular momentum, vector spaces, matrix mechanics, the harmonic oscillator, and the hydrogen atom. Perform better on qualifying or placement exams. Take a 'final exam' and grade it yourself! Clear enough for beginners, but challenging enough for those who already know something about advanced physics, "Quantum Mechanics Demystified" is the best self-teaching tool you can find!
Mechanics of carbon nanotubes
Applied Mechanics Reviews
55
6
495
2002
10.1115/1.1490129
Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young’s modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references.
Mechanics of hydrogenated amorphous carbon deposits from electron-beam-induced deposition of a paraffin precursor
Journal of Applied Physics
98
1
1-7
2005
10.1063/1.1940138
Many experiments on the mechanics of nanostructures require the creation of rigid clamps at specific locations. In this work, electron-beam-induced deposition (EBID) has been used to deposit carbon films that are similar to those that have recently been used for clamping nanostructures. The film deposition rate was accelerated by placing a paraffin source of hydrocarbon near the area where the EBID deposits were made. High-resolution transmission electron microscopy, electron-energy-loss spectroscopy, Raman spectroscopy, secondary-ion-mass spectrometry, and nanoindentation were used to characterize the chemical composition and the mechanics of the carbonaceous deposits. The typical EBID deposit was found to be hydrogenated amorphous carbon (a-C:H) having more sp(2)- than sp(3)-bonded carbon. Nanoindentation tests revealed a hardness of similar to 4 GPa and an elastic modulus of 30-60 GPa, depending on the accelerating voltage. This reflects a relatively soft film, which is built out of precursor molecular ions impacting the growing surface layer with low energies. The use of such deposits as clamps for tensile tests of poly(acrylonitrile)-based carbon nanofibers loaded between opposing atomic force microscope cantilevers is presented as an exam le application (c) 2005 American Institute of Physics.
A well-posed finite-strain model for thin elastic sheets with bending stiffness
Mathematics and Mechanics of Solids
18
1
103-112
2012
10.1177/1081286512441105
An accurate, well-posed two-dimensional model incorporating stretching and bending effects, suitable for analyzing the wrinkling pattern in stretched sheets, is derived from three-dimensional nonlinear elasticity theory.
finite elasticity; thin plates; wrinkling
Active control of laminated composite truncated conical shells using vertically and obliquely reinforced 1-3 piezoelectric composites
European Journal of Mechanics, A/Solids
32
1-12
2012
10.1016/j.euromechsol.2011.08.003
This paper deals with the analysis of active control of vibration of thin laminated composite truncated circular conical shells using vertically and obliquely reinforced 1-3 piezoelectric composite (PZC) materials as the constraining layer of the active constrained layer damping (ACLD) treatment. A finite element model of smart truncated conical laminated shells integrated with the patches of such ACLD treatment has been developed to demonstrate the performance of these patches on enhancing the damping characteristics of thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated truncated conical shells. Velocity feedback control loop has been implemented to activate the patches. The effect of variation of semi-cone angle on the performance of the patches for controlling first few modes of the truncated conical laminated shells has been demonstrated. Emphasis has also been placed on exploring the effect of variation of piezoelectric fiber orientation angle in the constraining layer on the control authority of the ACLD patches. ?? 2011 Elsevier Masson SAS. All rights reserved.
1-3 Piezocomposite; Active control; Conical shells; Smart structures
The foundations of fracture mechanics
Engineering Fracture Mechanics
16
497-515
1982
10.1016/0013-7944(82)90129-1
Fracture is a process characterized by localized deformation that is leading to material separation. With one exception (fracture of thin plates) this localized deformatiin and the ensuing separation is a result of the non-continuum character of solid matter. The solid should therefore be modelled as an aggregate of cells, each one containing one nucleus for the dominating microseparation mechanism, rather than as a continuum. By starting from a discussion of this approach and gradually introducing simplifications, approximations and restrictions of problem types, currently practiced methods in fracture mechanics are examined. The conclusion is that the foundations of these methods are very weak. Some suggestions are made about very simple engineering methods and about directions of future research work.
Crack Mechanisms and Crack Interaction in Thin Films
and no.: Technical report ME-TR-1
2012
The report contains a description of the theory for through- surface channeling crack in thin film systems. Key topics and mecha- nisms are described including channeling criteria, crack interaction and elastic mismatch in the system. A case of radial cracks spreading from a Rockwell indenter is used to describe how the theory can be used to determine fracture toughness and residual stresses in a thin film.
channeling cracks; crack interaction; crack spacing; elastic mismatch; fracture mechanics; indentation fracture toughness; Rockwell indentation.; steady- state cracking; Thin films
On the internal structure and mechanics of large strike-slip fault zones: Field observations of the Carboneras fault in southeastern Spain
Tectonophysics
367
3-4
235-251
2003
10.1016/S0040-1951(03)00134-3
Deciphering the internal structure of large fault zones is fundamental if a proper understanding is to be gained of their mechanical, hydrological and seismological properties. To this end, new detailed mapping and microstructural observations of the excellently exposed Carboneras fault zone in southeastern Spain have been used to elucidate both the internal arrangement of fault products and their likely mechanical properties. The fault is a 40 km offset strike-slip fault, which constitutes part of the Africa-Iberia plate boundary. The zone of faulting is ∼ 1 km in width not including the associated damage zone surrounding the fault. It is composed of continuous strands of phyllosilicate-rich fault gouge that bound lenses of variably broken-up protolith. This arrangement provides a number of fluid flow and fluid sealing possibilities within the fault zone. The gouge strands exhibit distributed deformation and are inferred to have strain hardening and/or velocity hardening characteristics. Also included in the fault zone are blocks of dolomite that contain thin (< 1 cm thick) fault planes inferred to have been produced by strain weakening/velocity weakening behaviour. These fault planes have a predominantly R1 Riedel shear orientation and are arranged in an en echelon pattern. A conceptual model of this type of wide fault zone is proposed which contrasts with previous narrow fault zone models. The observed structural and inferred mechanical characteristics of the Carboneras fault zone are compared to seismological observations of the San Andreas fault around Parkfield, CA. Similarities suggest that the Carboneras fault structure may be a useful analogue for this portion of the San Andreas fault at depth. © 2003 Elsevier Science B.V. All rights reserved.
Earthquakes; Faults; Mechanics; Structure
Human antibodies to PhtD, PcpA, and Ply reduce adherence to human lung epithelial cells and murine nasopharyngeal colonization by Streptococcus pneumoniae.
Infection and immunity
82
12
5069-75
2014
10.1128/IAI.02124-14
Streptococcus pneumoniae adherence to human epithelial cells (HECs) is the first step in pathogenesis leading to infections. We sought to determine the role of human antibodies against S. pneumoniae protein vaccine candidates PhtD, PcpA, and Ply in preventing adherence to lung HECs in vitro and mouse nasopharyngeal (NP) colonization in vivo. Human anti-PhtD, -PcpA, and -Ply antibodies were purified and Fab fragments generated. Fabs were used to test inhibition of adherence of TIGR4 and nonencapsulated strain RX1 to A549 lung HECs. The roles of individual proteins in adherence were tested using isogenic mutants of strain TIGR4. Anti-PhtD, -PcpA, and -Ply human antibodies were assessed for their ability to inhibit NP colonization in vivo by passive transfer of human antibody in a murine model. Human antibodies generated against PhtD and PcpA caused a decrease in adherence to A549 cells (P < 0.05). Anti-PhtD but not anti-PcpA antibodies showed a protective role against mouse NP colonization. To our surprise, anti-Ply antibodies also caused a significant (P < 0.05) reduction in S. pneumoniae colonization. Our results support the potential of PhtD, PcpA, and Ply protein vaccine candidates as alternatives to conjugate vaccines to prevent non-serotype-specific S. pneumoniae colonization and invasive infection.
Animals; Antibodies, Bacterial; Antibodies, Bacterial: immunology; Antigens, Bacterial; Antigens, Bacterial: immunology; Bacterial Adhesion; Bacterial Proteins; Bacterial Proteins: immunology; Carrier Proteins; Carrier Proteins: immunology; Carrier State; Carrier State: prevention & control; Cell Line; Disease Models, Animal; Epithelial Cells; Epithelial Cells: microbiology; Female; Humans; Immunization, Passive; Mice, Inbred C57BL; Nasopharynx; Nasopharynx: microbiology; Pneumococcal Infections; Pneumococcal Infections: prevention & control; Streptococcus pneumoniae; Streptococcus pneumoniae: immunology; Streptococcus pneumoniae: physiology; Streptolysins; Streptolysins: immunology
Mechanics of solid materials
Canadian Journal of Civil Engineering
19
1
197-197
1992
10.1139/l92-025
Elasticity, plasticity, damage mechanics and cracking are all phenomena that determine the resistance of solids to deformation and fracture. The authors of this book discuss a modern method of mathematically modeling the behavior of macroscopic volume elements. The first three chapters review physical mechanisms at the microstructural level, thermodynamics of irreversible processes, mechanics of continuous media, and the classification of the behavior of solids. The rest of the book is devoted to the modeling of different types of material behavior. In each case the authors present characteristic data for numerous materials, and discuss the physics underlying the phenomena together with methods for the numerical analysis of the resulting equations.
Three-dimensional solutions for the thermal buckling and sensitivity derivatives of temperature-sensitive multilayered angle-ply plates
Journal of Applied Mechanics-Transactions of the ASME
59
4
848-856
1992
10.1115/1.2894052
Analytic three-dimensional thermoelasticity solutions are presented for the thermal buckling of multilayered angle-ply composite plates with temperature-dependent thermoelastic properties. Both the critical temperatures and the sensitivity derivatives are computed. The sensitivity derivatives measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the plate. The plates are assumed to have rectangular geometry and an antisymmetric lamination with respect to the middle plane. The temperature is assumed to be independent of the surface coordinates, but has an arbitrary symmetric variation through the thickness of the plate. The prebuckling deformations are accounted for. Numerical results are presented, for plates subjected to uniform temperature increase, showing the effects of temperature-dependent material properties on the prebuckling stresses, critical temperatures, and their sensitivity derivatives.
Complex coordinates and quantum mechanics
Reviews of Modern Physics
38
1
36-40
1966
10.1103/RevModPhys.38.36
By introducing complex canonical coordinates, classical and quantum mechanics may be embedded in the same formulation. In such a way, the connection between Poisson brackets and commutators, canonical transformations and unitary transformations, etc., become apparent. This formulation is also particularly suitable for discussing the classical limit of quantum mechanics and for quantum-statistical mechanics.
Modelling and analysis of multi-ply torispheres draped from woven carbon fabric
Computers & Structures
76
1-9
2000
DOI: 10.1016/S0045-7949(99)00150-9
This paper provides details about an algorithm predicting orientation of fibres in woven fabric being draped onto domes with torispherical geometry. Two positions of the drape focal point are examined, i.e. one positioned at the apex and the second one moved away from the apex. The algorithms' predictions of fibre orientation compare well with the measured values. The wall thickness variation and near net-shape of initial cloth could also be obtained using the described algorithm. Two eighteen-ply and two fifty-ply torispheres were manufactured and collapsed under static external pressure. The collapse pressures were in the range of 6-25 MPa. Comparison of numerically predicted Last Ply Failure pressures with the experimental results is good. References to other work where further details can be found are also provided in this paper.
Woven fabric
Ply level failure prediction of carbon fibre reinforced laminated composite panels subjected to low velocity drop-weight impact using adaptive meshing techniques
Acta Astronautica
102
169-177
2014
10.1016/j.actaastro.2014.05.024
This work is concerned with physical testing and numerical simulations of flat and round nose drop-weight impact of carbon fibre-reinforced laminate composite panels to predict ply level failure. Majority of the existing studies on impact of composites by spherical nose impactors are experimental, computational models are simplified, and based on classical laminated plate theories where contributions of through-thickness stresses are neglected. Present work considers flat nose impact and contributions from through-thickness stresses and is mainly simulation based. A computational model was developed in ABAQUS™ software using adaptive meshing techniques. Simulation produced (2D model) stresses were numerically integrated using MATALB™ code to predict through-thickness (3D) stresses. Through-the-thickness stresses were then utilised in advanced failure criteria coded in MATLAB™ software to predict ply level failures. Simulation produced results demonstrate that the computational model can efficiently and effectively predict ply-by-ply failure status of relatively thick laminates. © 2014 Elsevier Inc. All rights reserved.
A. Carbon fibre; Adaptive meshing; B. Impact behaviour; C. Computational modelling; D. Mechanical testing
Acoustic structural health monitoring of composite materials : Damage identification and evaluation in cross ply laminates using acoustic emission and ultrasonics
Composites Science and Technology
72
10
1127-1133
2012
10.1016/j.compscitech.2011.10.011
The characterisation of the damage state of composite structures is often performed using the acoustic behaviour of the composite system. This behaviour is expected to change significantly as the damage is accumulating in the composite. It is indisputable that different damage mechanisms are activated within the composite laminate during loading scenario. These "damage entities" are acting in different space and time scales within the service life of the structure and may be interdependent. It has been argued that different damage mechanisms attribute distinct acoustic behaviour to the composite system. Loading of cross-ply laminates in particular leads to the accumulation of distinct damage mechanisms, such as matrix cracking, delamination between successive plies and fibre rupture at the final stage of loading. As highlighted in this work, the acoustic emission activity is directly linked to the structural health state of the laminate. At the same time, significant changes on the wave propagation characteristics are reported and correlated to damage accumulation in the composite laminate. In the case of cross ply laminates, experimental tests and numerical simulations indicate that, typical to the presence of transverse cracking and/or delamination, is the increase of the pulse velocity and the transmission efficiency of a propagated ultrasonic wave, an indication that the intact longitudinal plies act as wave guides, as the transverse ply deteriorates. Further to transverse cracking and delamination, the accumulation of longitudinal fibre breaks becomes dominant causing the catastrophic failure of the composite and is expected to be directly linked to the acoustic behaviour of the composite, as the stiffness loss results to the velocity decrease of the propagated wave. In view of the above, the scope of the current work is to assess the efficiency of acoustic emission and ultrasonic transmission as a combined methodology for the assessment of the introduced damage and furthermore as a structural health monitoring tool. ?? 2011 Elsevier Ltd.
A. Laminate; B. Delamination; C. Transverse cracking; D. Acoustic emission; D. Ultrasonics
Advanced Soil Mechanics
Eos, Transactions American Geophysical Union
66
42
714
1985
10.1029/EO066i042p00714-02
Advanced Soil Mechanics provides a general review of grain-size distribution, nature of water in clay, consistency of cohesive soils, weight - volume relationships and soil classification systems. It also covers the fundamental concepts of elasticity, equations of equilibrium and compatibility as they relate to the determination of stress and displacement in a soil medium. Relationships based on the theory of elasticity are presented to show how to estimate the stress and displacement in a soil mass due to various types of loading. The book sets out, in a logical and sequential manner, novel or refined procedures as they relate to hydraulic conductivity of granular and cohesive soils and flow through porous media, consolidation, shear strength and settlement of foundations. Advanced Soil Mechanics is an upper undergraduate and beginning graduate level textbook for students of civil engineering, engineering mechanics and soil mechanics, as well as professionals working in these fields. Each chapter concludes with a list of references for further in-depth review or research and further study problems are included at the end of the book.
Dynamic aeroelastic response and active control of composite thin-walled beam structures in compressible flow
Journal of Sound and Vibration
330
21
4998-5013
2011
10.1016/j.jsv.2011.05.026
The dynamic aeroelastic response and its active control of composite beam structures in compressible flow and exposed to gust and explosive type loads are examined. Modeling of the structures is based on a refined composite thin-walled beam theory and incorporate a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, and rotatory inertia. The unsteady compressible aerodynamic loads for arbitrary small motion in the time domain are derived based on the concept of indicial functions. The sliding mode control (SMC) and linear-quadratic Gaussian (LQG) control methodology with sliding mode observer are used for the purpose of control. The beam structures are restricted to circumferentially asymmetric lay-up construction and the influence of ply angle, flight speed, and external excitations on the response and its active control are specifically investigated. A number of conclusions are outlined at the end. ?? 2011 Elsevier Ltd. All rights reserved.
Experimental and analytical characterization of transverse cracking behavior in carbon/bismaleimide cross-ply laminates under mechanical fatigue loading
Composites Part B: Engineering
33
471-478
2002
10.1016/S1359-8368(02)00028-8
Transverse cracking behavior in high temperature bismaleimide-based carbon fiber reinforced plastics (CFRP) laminates under fatigue loading was observed. Three types of cross-ply laminate, [0/902/0], [02/903/02] and [02/904/02], were tested to study the effect of ply thickness. Damage observation was conducted using two methods. Optical microscopy and soft X-ray radiography were used for edge and internal damage observation, respectively. Variational approach was used to derive the energy release rate associated with transverse cracking. Multiplication of transverse cracks was modeled based on modified Paris-law approach. ?? 2002 Elsevier Science Ltd. All rights reserved.
A. Laminates; A. Thermosetting resin; B. Fatigue; B. Transverse cracking
Spectroscopic and mechanical evaluation of thin film commonly used for banding congenital portosystemic shunts in dogs.
Veterinary surgery : VS
42
4
478-87
2013
10.1111/j.1532-950X.2013.12010.x
OBJECTIVES: To (1) determine whether different types of thin film used to occlude congenital portosystemic shunts are cellophane, and (2) evaluate the influence of saline immersion and sterilization on the tensile properties of cellophane.\n\nSTUDY DESIGN: Ex vivo spectroscopic evaluation and mechanical testing.\n\nSAMPLE POPULATION: Rectangular strips of thin film from 4 sources.\n\nMETHODS: Samples were evaluated with Fourier Transform Infrared Spectroscopy and microscopy with a polarizing lens. Samples consistent with cellophane were divided into 5 sterilization groups: non-sterile, autoclave, gamma irradiation, hydrogen peroxide and ethylene oxide. Samples were tested while dry or after saline solution immersion. Tensile properties were compared using ANOVA, unpaired t-tests, Mann-Whitney U-tests and Fisher's exact tests. P < 0.05 was considered significant.\n\nRESULTS: One thin film was consistent with cellophane and it could be differentiated from the other thin films by visible striations. Cellophane was strongest when strips were oriented parallel with its fiber direction and saline immersion reduced its strength by 48% (P < .001). All sterilization methods except autoclave significantly weakened wet cellophane (ethylene oxide [P < .001], gamma irradiation [P < .001], and hydrogen peroxide [P < .001]).\n\nCONCLUSIONS: Thin film from most sources was not consistent with cellophane. Autoclave sterilization is the best way to preserve the strength of wet cellophane.
Animals; Cellophane; Cellophane: chemistry; Dog Diseases; Dog Diseases: surgery; Dogs; Mechanics; Osmotic Fragility; Portal System; Portal System: pathology; Spectroscopy, Fourier Transform Infrared; Sterilization; Surface Properties; Tensile Strength; Vascular Malformations; Vascular Malformations: surgery; Vascular Malformations: veterinary
Popular Mechanics
1956
88
1956
0032-4558
Popular Mechanics inspires, instructs and influences readers to help them master the modern world. Whether it’s practical DIY home-improvement tips, gadgets and digital technology, information on the newest cars or the latest breakthroughs in science -- PM is the ultimate guide to our high-tech lifestyle.
Impact behavior of cross-ply laminated composite plates under low velocities
Composite Structures
51
3
237-244
2001
10.1016/S0263-8223(00)00134-3
The behavior of different E-glass/epoxy laminated composite plates has been experimentally studied under impact of aluminum projectile at low velocities (0.53-3.1 m/s). The results were obtained using a drop weight impact machine and presented for three different cross-ply laminates [02/906/02], [03/904/03] and [04/902/04]. The time history of the impact process such as the acceleration impactor, the projectile displacement and the target circular plate deflection due to an impact force acting at the center has been measured. The effects of the projectile velocities and lamination sequences on composite plates behavior have been discussed. Applications of the theoretical model based on Hertzian contact law were used as an efficient guide for the experimental results validation. ?? 2001 Elsevier Science Ltd. All rights reserved.
Contact law; Drop weight; E-glass/epoxy; Impact; Laminated plates; Low velocity
FLEXURAL STIFFNESS OF MULTI-PLY PAPERBOARD
Fibre Science and Technology
13
3
213-223
1980
An equation for calculating the flexural stiffness of multi-ply paperboard has been derived from classical lamination theory. Calculations using the equation are simpler to perform than those following the methods previously proposed in the literature as no reference to a neutral surface is necessary. The application of the equation was tested on both homogeneous boards and three-ply boards.
PAPERBOARDS
Solutions to intra-ply shear locking in finite element analyses of fibre reinforced materials
Composites Part A: Applied Science and Manufacturing
39
7
1167-1176
2008
10.1016/j.compositesa.2008.03.014
Intra-ply shear locking results in unrealistic fibre stresses and spurious wrinkling in composite forming simulations. Three remedies were investigated: aligning the mesh, applying reduced integration and using multi-field elements. Several triangular and quadrilateral elements were tested on their capability to avoid locking in a two-dimensional bias extension simulation. The resulting locking-free elements were tested in a realistic three-dimensional drape simulation of a biaxial fabric as well. The new triangular multi-field element seems to be the best locking-free element for unaligned meshes. It has a semi-quadratic in-plane and a linear out-of-plane displacement field. This combination improves the accuracy of the element and avoids contact problems in 3D simulations. ?? 2008 Elsevier Ltd. All rights reserved.
A. Fabrics/textiles; C. Finite element analysis; E. Forming; Intra-ply shear locking
A novel approach for the investigation of mesoscopic contact mechanics
Thin Solid Films
428
1-2
111-114
2003
10.1016/S0040-6090(02)01231-2
We present a novel experimental technique devoted to the investigation of contact mechanics on mesoscopic scale. It consists of an atomic force microscope (AFM) equipped with custom-designed probes with integrated flat micrometric tips. Samples are normally compressed by the flat tips and load-displacement curves are acquired. The latter allow to investigate the mechanical response under a multi-asperity regime not accessible by conventional AFM. Preliminary results are reported for the contact mechanics of nanostructured carbon-based films having a self-affine fractal morphology. © 2002 Elsevier Science B.V. All rights reserved.
Atomic force microscopy; Carbon; Clusters; Contact mechanics
Statistical Mechanics of Nonequilibrium Liquids
Simulation
1
314
2008
10.1017/CBO9780511535307
In recent years the interaction between dynamical systems theory and non-equilibrium statistical mechanics has been enormous. The discovery of fluctuation theorems as a fundamental structure common to almost all non-equilibrium systems, and the connections with the free energy calculation methods of Jarzynski and Crooks, have excited both theorists and experimentalists. This graduate level book charts the development and theoretical analysis of molecular dynamics as applied to equilibrium and non-equilibrium systems. Designed for both researchers in the field and graduate students of physics, it connects molecular dynamics simulation with the mathematical theory to understand non-equilibrium steady states. It also provides a link between the atomic, nano, and macro worlds. The book ends with an introduction to the use of non-equilibrium statistical mechanics to justify a thermodynamic treatment of non-equilibrium steady states, and gives a direction to further avenues of exploration.
Wavy-ply sandwich with composite skins and crushable core for ductility and energy absorption
Composite Structures
116
1
364-376
2014
10.1016/j.compstruct.2014.05.020
Conventional composite materials offer high specific stiffness and strength, but suffer from low failure strains and failure without warning. This work proposes a new design for sandwich structures with symmetrically-wavy composite skins and a crushable foam core, aiming to achieve large strains (due to unfolding of the skins) and energy absorption (due to crushing of the foam core) under tensile loading. The structure is designed by a combination of analytical modelling and finite element simulations, and the concept is demonstrated experimentally. When loaded under quasi-static tension, wavy-ply sandwich specimens with carbon-epoxy skins and optimised geometry exhibited an average failure strain of 8.6%, a specific energy dissipated of 9.4. kJ/kg, and ultimate strength of 1570. MPa. The scope for further developing the wavy-ply sandwich concept and potential applications requiring large deformations and energy absorption are discussed. © 2014 Elsevier Ltd.
Finite element analysis; Large deformations; Mechanical testing; Non-linear behaviour; Sandwich structures
Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells
Composite Structures
59
3
313-340
2003
10.1016/S0263-8223(02)00245-3
Closed-form formulations of 2D higher-order shear deformation theories for the thermo-mechanical analysis of simply supported doubly curved cross-ply laminated shells are presented. Formulation includes the Sander's theory for doubly curved shells. Two of the higher-order shear deformation theories account for the effects of both transverse shear strains/stresses and the transverse normal strain/stress, while the third includes only the effects of the transverse shear deformation. In these developments a realistic parabolic distribution of transverse shear strains through the shell thickness is assumed. The temperature variation considered in the formulation is uniform or sinusoidal over the surface and linearly varying through the thickness. Numerical results are presented for thermal and mechanical load cases in laminated composite and sandwich shallow shells. The closed-form solutions presented herein for laminated composite plate or shells are compared with the available 3D elasticity solutions for mechanical loading and it is believed that solutions for thermal loading will serve as bench mark in future. ?? 2003 Elsevier Science Ltd. All rights reserved.
Closed-form solutions; Cross-ply laminates; Higher-order theory; Shear deformation; Thermo-mechanical
A theory of thin films of martensitic materials with applications to microactuators
Journal of the Mechanics and Physics of Solids
47
3
531-576
1999
10.1016/s0022-5096(98)00043-x
A direct derivation is given of a theory for single crystal thin films, starting from three-dimensional nonlinear elasticity theory augmented by a term for interfacial energy. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a frame-indifferent Cosserat membrane theory with one Cosserat vector field. The theory is applied to multi-well energy functions appropriate to martensitic materials. It is found that, unlike in bulk materials, which generally only support finely twinned austenite/martensite interfaces as energy minimizing states, the thin film theory predicts the existence of exact, untwinned austenite/martensite interfaces. These are used to construct some simple energy minimizing deformations-"tents" and "tunnels"-that could possibly be the basis of simple large-deformation microactuators. Explicit results are given for martensitic materials in the systems NiMnGa, NiTi, NiTiCu, and NiAl. A certain alloy of precise composition Ni30.5Ti49.5Cu20.0 is predicted to support a four-sided "tent" on an (001) film, which furthermore is predicted to collapse to the substrate upon heating. A formal derivation is given of higher order theories, which yields two additional Cosserat vectors and an explicit form of the bending energy. The derivation indicates an approach to plate-shell-thin film theories that is rather different from the ones usually followed. (C) 1999 Elsevier Science Ltd. All rights reserved.
behavior; deformation; elasticity; electron-microscopy; microactuator; model; neutron-scattering; phase; phase transformation; shape memory effect; strain; thin films; titanium; transformation; variational calculus
Understanding Bohmian mechanics: A dialogue
American Journal of Physics
72
9
1220-1226
2004
10.1119/1.1748054
This paper is an introduction to the ideas of Bohmian mechanics, an interpretation of quantum mechanics in which the observer plays no fundamental role. Bohmian mechanics describes, instead of probabilities of measurement results, objective microscopic events. In recent years, Bohmian mechanics has attracted increasing attention by researchers. The form of a dialogue allows me to address questions about the Bohmian view that often arise.
Combined influences of shear deformation, rotary inertia and heterogeneity on the frequencies of cross-ply laminated orthotropic cylindrical shells
Composites Part B: Engineering
66
500-510
2014
10.1016/j.compositesb.2014.06.015
The non-dimensional frequencies for symmetric and anti-symmetric cross-ply laminated heterogeneous composite circular cylindrical shells are analyzed by taking into account the effects of first-order deformations such as transverse shear deformations and rotary inertia. By using the Donnell-type shell theory, a set of fundamental dynamic equations of laminated circular cylindrical shells made of heterogeneous orthotropic materials is derived through Hamilton's principle. The basic equations are reduced to the six-order algebraic equation. One of the lowest positive roots of the algebraic equation represents the fundamental frequency. Attention is focused on the case of cross-ply laminated heterogeneous orthotropic cylindrical shells, from which solution for homogenous and heterogeneous orthotropic monolayer cylindrical shells follows based on classical shell theory (CST) and shear deformation theory (SDT), as a special case. Moreover, further detailed numerical results dealing with non-dimensional frequencies and corresponding mode shapes of laminated heterogeneous cylindrical shells having symmetric or anti-symmetric cross-ply lay-up are discussed. Furthermore, some comparisons are made to show the reliability and accuracy of the study. © 2014 Elsevier Ltd. All rights reserved.
A. Lamina/ply; B. Anisotropy; B. Vibration; C. Analytical modeling
Surface acoustic wave characterization of a thin, rough polymer film
Thin Solid Films
517
8
2697-2701
2009
10.1016/j.tsf.2008.11.140
Laser generated surface acoustic waves (SAW) in a heterodyne diffraction scheme is a powerful technique for elastic characterization of thin films and it is frequently used on samples of high optical quality. We show that the method can also be effectively used in difficult conditions, on rough samples. Measurements are presented on a 3 μm thick film of polymer, spin-coated on steel, and on the same sample after addition of an aluminum coating. The experimental data are interpreted using a model assuming a stack of perfect layers. The analyses show good consistency within the SAW results for both configurations, and consistency with nano-indentation results, cross-validating both approaches. © 2008.
Elastic properties of thin films; Heterodyne diffraction; Laser ultrasonics; Mechanics of thin, visco-elastic polymer and glass; Nano-indentation; Protective layers; Surface acoustic wave spectroscopy
In vitro expression of Streptococcus pneumoniae ply gene in human monocytes and pneumocytes.
European journal of medical research
20
1
52
2015
10.1186/s40001-015-0142-4
BACKGROUND: Streptococcus pneumoniae is one major cause of pneumonia in human and contains various virulence factors that contribute to pathogenesis of pneumococcal disease. This study investigated the role of pneumolysin, Ply, in facilitating S. pneumoniae invasion into the host blood stream.\n\nMETHODS: S. pneumoniae strains were isolated from clinical blood and sputum samples and confirmed by PCR. Expression of ply gene was assessed by infecting human monocytes and pneumocytes.\n\nRESULTS: A total of 23 strains of S. pneumoniae isolated from blood (n = 11) and sputum (n = 12) along with S. pneumoniae ATCC49619 were used to infect human monocyte (THP-1) and Type II pneumocyte (A549) cell lines. All clinical strains of S. pneumoniae showed higher expression of ply mRNA than the American Type Culture Collection (ATCC) strain. Among the clinical strains, blood isolates showed higher expression of ply genes than sputum isolates, i.e., 2(1.5)- to 2(1.6)-folds in THP-1 and 2(0.4)- to 2(4.9)-folds in A549 cell lines.\n\nCONCLUSIONS: The data from the current study demonstrated that ply gene of blood- and sputum-derived S. pneumoniae is differentially expressed in two different cell lines. Under survival pressure, ply is highly expressed in these two cell lines for blood-derived S. pneumoniae, indicating that ply gene may facilitate S. pneumoniae invasion into the host blood system.
Mechanics of Stiff Thin Films of Controlled Wavy Geometry on Compliant Substrates for Stretchable Electronics
Semiconductor Nanomaterials for Flexible Technologies: From Photovoltaics and Electronics to Sensors and Energy Storage
275-291
2010
10.1016/B978-1-4377-7823-6.00010-6
This chapter reviews two alternative approaches, including both experimental and theoretical studies, which overcome some or all of the limitations and thus have the potential for extensive applications in stretchable electronics and other emerging technologies. It reviews two conceptually different, but related, approaches to achieve reversible, elastic response to large strain deformations in inorganic films that can be used for electronics. It shows that these methods can be scaled to active devices, circuits, and full-integrated systems. Further optimization of the approaches and development of new application possibilities appear to represent promising directions for future work. There are two main approaches to achieve stretchability in electronics. One design uses isolated, rigid islands, which are fabricated with semiconductor components on top and linked by stretchable, interconnects of conducting materials. Another different, but complementary method is to directly produce stretchable electronic devices based on well-defined sinusoidal distributions of surface relief through non-linear buckling processes. © 2010 Copyright Elsevier Inc. All rights reserved.
Mechanics of Distension of Dog Veins and Other Very Thin-Walled Tubular Structures
Circulation Research
27
6
1069-1081
2014
10.1161/01.RES.27.6.1069
We present first phenomenological characterizations of the pressure-volume relationships (a) in veins excised from dogs under anesthesia and (b) in thinwalled latex tubes. We measured their cross-sectional areas and perimeters from cinefluorographic enlargements during distension. From flattened to circular cross sections, the perimeter of latex tubes remained constant while the area increased exclusively by bending of the walls. Compliance was large in this regime. After circular cross sections were reached, further increases in area were associated with increments in perimeter and there was stretching of the wall. Compliance declined sharply. Veins did not show a distinct two-regime behavior but a combination of bending and stretching which extended the region of large compliance to values of transmural pressure of physiological interest. Using classical theory of elasticity, we propose mathematical relationships describing the proportionality between the pressure and the curvature of the wall during the regime where bending is the primary controlling mechanism. We mechanized these relationships on an analog computer and correlated the solutions with the physical experiments. We conclude that no modulus of elasticity, alone, can relate the pressure and the volume when bending is predominant. In this regime the significant quantity is the modulus of flexural rigidity.
Statistical mechanics of pluripotency
Cell
154
3
484-489
2013
10.1016/j.cell.2013.07.024
Recent reports using single-cell profiling have indicated a remarkably dynamic view of pluripotent stem cell identity. Here, we argue that the pluripotent state is not well defined at the single-cell level but rather is a statistical property of stem cell populations, amenable to analysis using the tools of statistical mechanics and information theory. ?? 2013 Elsevier Inc.
A discontinuous elastic interface transfer model of thin film nanoindentation
Experimental Mechanics
50
6
793-801
2010
10.1007/s11340-009-9309-7
A new model of thin film indentation that accounted for an apparent discontinuity in elastic strain transfer at the film/substrate interface was developed. Finite element analysis suggested that numerical values of strain were not directly continuous across the interface; the values in the film were higher when a soft film was deposited on a hard substrate. The new model was constructed based on this discontinuity; whereby, separate weighting factors were applied to account for the influence of the substrate in strain developed in the film and vice-versa. By comparing the model to experimental data from thirteen different amorphous thin film materials on a silicon substrate, constants in each weighting factor were found to have physical significance in being numerically similar to the bulk scale Poisson's ratios of the materials involved. When employing these material properties in the new model it was found to provide an improved match to the experimental data over the existing Doerner and Nix and Gao models. Finally, the model was found to be capable of assessing the Young's modulus of thin films that do not exhibit a flat region as long as the bulk Poisson's ratio is known. Society for Experimental Mechanics 2009.
Elastic moduli of laminated anisotropic composites
Experimental Mechanics
5
6
177-185
1965
10.1007/BF02328424
Elastic moduli of laminated anisotropic composites, specifically glass-filament-reinforced resin cylindrical pressure vessels and cross-ply and angle-ply plates
Entanglement and the foundations of statistical mechanics
Nature Physics
2
11
754-758
2006
10.1038/nphys444
Statistical mechanics is one of the most successful areas of physics. Yet, almost 150 years since its inception, its foundations and basic postulates are still the subject of debate. Here we suggest that the main postulate of statistical mechanics, the equal a priori probability postulate, should be abandoned as misleading and unnecessary. We argue that it should be replaced by a general canonical principle, whose physical content is fundamentally different from the postulate it replaces: it refers to individual states, rather than to ensemble or time averages. Furthermore, whereas the original postulate is an unprovable assumption, the principle we propose is mathematically proven. The key element in this proof is the quantum entanglement between the system and its environment. Our approach separates the issue of finding the canonical state from finding out how close a system is to it, allowing us to go even beyond the usual boltzmannian situation.
The Mechanics and Thermodynamics of Continua
AIAA Journal
48
11
2719-2719
2010
10.2514/1.52158
The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasizes the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behavior. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics, and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.
A general approach forcing convexity of ply angle optimization in composite laminates
Structural optimization
16
1982
201-211
1998
10.1007/BF01202831
This paper deals with optimization of laminated composite structures\nin which the ply angles are taken as design variables. One of the\nmajor problems when using ply-angles as design variables, is the\nlack of convexity of the objective function and thus the existence\nof local optima, which implies that usual gradient based optimization\nprocedures may not be effective. Therefore, a new general approach\nthat avoids the abovementioned problems of nonconvexity when ply-angles\nare used as design variables is proposed. The methodology is based\nupon the fact that the design space for an optimization problem formulated\nin lamination parameters [introduced by Tsai and Pagano (1968)] is\nproven to be convex, because the laminate stiffnesses are expressed\nlinearly in terms of the lamination parameters. However, lamination\nparameters have at least two major shortcomings: as yet, for the\ngeneral case involving membrane-bending coupling, the constraints\nbetween the lamination parameters are not completely defined; also,\nfor a prescribed set of lamination parameters physically realizable\ncomposite laminates (e.g. laminates with equal thickness plies) may\nnot exist. The approach here, uses both lamination parameters and\nply-angles and thereby uses the advantages of both and eliminates\nthe shortcomings of both.\n\nIn order to illustrate this approach, several stiffness optimization\nexamples are provided.
Modeling friction effects on the ballistic impact behavior of a single-ply high-strength fabric
International Journal of Impact Engineering
31
8
996-1012
2005
10.1016/j.ijimpeng.2004.06.008
It has been shown through experiments that interfacial friction affects the energy absorption of fabrics subjected to ballistic impact. However, how the friction plays a role is not well understood. In this paper, a commercially available finite element analysis code, LS-DYNA, is used to model the ballistic impact of a square patch of single-ply plain-woven fabric. Three types of boundary conditions are applied on the fabric: four edges clamped, two edges clamped, and four edges free. The friction between yarns at their crossovers and the friction between projectile and fabric are taken into account. Effects of the friction during the phase prior to yarn failure are parametrically studied. Simulation results show that at a given time, the fabric with high friction absorbs more energy than the fabric with no friction. For the boundary condition with four edges free, friction contributes to increasing the fabric energy absorption mainly through the mechanism of frictional sliding dissipated energy. For the boundary conditions with two or four edges clamped, the energy dissipated through frictional sliding only accounts for a very small portion of the total absorbed energy; however, both the yarn strain energy and the yarn kinetic energy are increased when there is friction. Friction has an indirect effect on the fabric energy absorption by influencing the number of yarns that become involved. Simulation results also indicate that the boundary conditions significantly affect the fabric deformation, stress distribution, and time history of energy absorption. ?? 2004 Elsevier Ltd. All rights reserved.
Ballistic impact; Energy absorption; Fabric; Finite element analysis; Friction
High yield four-point bend thin film adhesion testing techniques
Engineering Fracture Mechanics
78
12
2390-2398
2011
10.1016/j.engfracmech.2011.05.010
Novel four-point bend specimen geometries are proposed for improved test yield over standard four-point bend specimens when measuring high-strength and ultra-thin film structures. The fracture energies of both a Cu/SiN dielectric diffusion barrier interface and a high-k/metal gate (HfO2/Pt–Ti metal bilayer) interface are reported. Four novel specimen types were evaluated and result in significantly increased test yield as compared to the standard four-point bend specimens. The modified four-point bend specimens were fabricated by altering the crystallographic orientation, width, and thickness of the beams which make up the specimen. The mechanics of the four-point bend test are discussed for each different specimen type. The increased test yield is explained in terms of the stresses which develop in the specimen during testing, the phase angle of loading experienced for each specimen type, and the anisotropic fracture properties of single crystal silicon.
Adhesion; Delamination; Four-point bend; Thin films
Mechanics and strength of materials
Mechanics and Strength of Materials
1-529
2006
10.1007/3-540-30813-X
This reference offers a clear, comprehensive presentation of the fundamentals of mechanics and strength of materials. It provides both the theory and applications of mechanics of materials on an intermediate theoretical level, ranging from the mechanical properties of materials through the effects of axial load, torsion, bending, and transverse shear to stresses and strains in bars and continuum mechanics. The book is designed for graduate and advanced undergraduate students in materials science courses in Mechanical, Civil, and Aerospace Engineering departments, and as a reference tool by postgraduates and researchers in the fields of solid mechanics.
Bone mechanics
Clinical Biomechanics
5
1
53-54
1990
10.1016/0268-0033(90)90036-6
This informative volume summarizes what is known about bone mechanics. It describes the methods used to acquire that knowledge and suggests the nature of future research on this topic. This easy-to-read book keeps mathematical notation simple and minimal and presents data in summary form. Bone Mechanics is concerned with the mechanical behavior and functional stress adaptation of whole bones as structural elements, the mechanical behavior and functional adaptation of bone tissue as material, and the physiological significance of the mechanical properties of bone and the biological response of bone to applied stress. Orthopaedic surgeons, dentists, anatomists, biologists, biomedical engineers and physiologists are among those who will find this volume to be of interest.
Analytical solution for response of ferroelectric thin film to infrared radiation
Acta Mechanica Solida Sinica
23
2
135-146
2010
10.1016/S0894-9166(10)60015-8
ABSTRACT\nMicro-bolometer pixel is an essential element in the infrared focal plane array (IRFPA) of infrared detectors. Its response to infrared radiation is analyzed in this paper. The pixel structure is modeled as a composite laminate thin plate whose sides are measured with the thickness from 0.1-1 μm. Its middle ply is a ferroelectric thin film. Its top surface is covered with a gold or platinum infrared absorber, while the bottom surface is deposited with platinum or lanthanum-nickel. Meanwhile both surfaces are a pair of electrodes. The top surface receives infrared radiation pulses successively. For the very tiny micro bolometer pixel, it is assumed that the infrared radiation is uniformly distributed on the plate. Furthermore, as the ratio of the side length to the thickness of the plate is dramatically large, it is assumed that heat transfer only takes place across the thickness of the plate. The thermal-electric-mechanical coupling governing equations are solved in a form of Fourier series. Results of the displacement, temperature variation and electric output signals of the micro bolometer pixel structure under infrared radiation are obtained, analyzed and compared with experimental data.
composite laminate plate; ferroelectric thin film; infrared radiation; micro-bolometer pixel structure
Mechanics of engineering materials
Engineering Structures
19
393
1997
10.1016/S0141-0296(97)86702-8
Assuming little or no prior knowledge, Peter Benham develops the theory of the subject from first principles, and covers all topics of strain analysis.
A continuum damage model for linear viscoelastic composite materials
Mechanics of Materials
35
3-6
463-480
2003
10.1016/S0167-6636(02)00265-X
This paper presents a constitutive model for linear viscoelastic orthotropic solids containing a fixed level of distributed cracks. The model is formulated in a continuum damage mechanics framework using internal variables taken as second rank tensors. Use is made of the correspondence principle for linear viscoelastic solids to define a pseudo strain energy function in the Laplace domain. This function is then expressed as a polynomial in transformed strain and tensorial damage variables using the integrity bases restricted by the initial orthotropic symmetry of the material. The constitutive relationships derived in the Laplace domain are then converted to the time domain by using the inverse Laplace transform. The model is applied to the specific case of cross-ply laminates with transverse matrix cracks. The material coefficient functions appearing in the model are determined by a numerical (finite element) method for one cross-ply laminate configuration at one damage level. Predictions of the viscoelastic response are then made for the same laminate at other damage levels and for other cross-ply laminate configurations at different damage levels. These predictions agree well with independently determined time variations of properties by an analytic method (Kumar and Talreja, 2001, Linear viscoelastic behavior of matrix cracked cross-ply laminates. Mechanics of Materials 33 (3), 139–154) as well as with the numerically calculated values. Extension of the model to incorporate effects of transient temperature, physical aging and moisture is outlined.
composite materials; constitutive modeling; continuum damage mechanics; correspondence principle; damage; internal variables; pseudo strain energy function; viscoelasticity
Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations
Computational Mechanics
24
334-347
1999
10.1007/s004660050456
In this paper, the conventional moving least squares interpolation scheme is generalized, to incorporate the information concerning the derivative of the field variable into the interpolation scheme. By using this generalized moving least squares interpolation, along with the MLPG (Meshless Local Petrov-Galerkin) paradigm, a new numerical approach is proposed to deal with 4th order problems of thin beams. Through numerical examples, convergence tests are performed; and problems of thin beams under various loading and boundary conditions are analyzed by the proposed method, and the numerical results are compared with analytical solutions.
Mechanics of fatigue crack growth in a bonding interface
Engineering Fracture Mechanics
89
52-64
2012
10.1016/j.engfracmech.2012.04.009
Experimental investigations have shown that cracks in a bonding interface such as adhesives or brazings under cyclic loading behave fundamentally different from cracks in homogeneous metals. In particular the slope of da/. dN-vs.-??. K-curves is much steeper and the threshold value higher than in homogeneous metals. In the present paper, the general case of a fatigue crack located in a thin layer of elastic-plastic material embedded in an elastic surrounding is considered analytically. Since the layer is thin compared to the size of the plastic zone, linear-elastic fracture mechanics is not applicable. Therefore Paris' law is formulated in terms of CTOD. It was found that a non-linear shielding mechanism reduces CTOD of a crack in the layer compared to a crack in bulk material under the same stress intensity. The shielding decreases with increasing stress intensity factor. This effect leads to the steep da/. dN curves. Based on the hypothesis of a linear damage accumulation in the active plastic zone, an analytical formula is derived to estimate the fatigue crack growth rate as well as the threshold values of cracks in thin interlayers. The predictions agree well with the experimental data. ?? 2012 Elsevier Ltd.
Adhesive; Analytical model; Bonding interface; Brazing; Constraint; Crack growth threshold; Elastic-plastic; Fatigue crack propagation; Thin layer
Fundamentals of airplane flight mechanics
Fundamentals of Airplane Flight Mechanics
1-298
2007
10.1007/978-3-540-46573-7
Flight mechanics is the application of Newton's laws to the study\nof vehicle trajectories (performance), stability, and aerodynamic\ncontrol. This volume details the derivation of analytical solutions\nof airplane flight mechanics problems associated with flight in a\nvertical plane. It covers trajectory analysis, stability, and control.\nIn addition, the volume presents algorithms for calculating lift,\ndrag, pitching moment, and stability derivatives. Throughout, a subsonic\nbusiness jet is used as an example for the calculations presented\nin the book.
About the impact behavior of woven-ply carbon fiber-reinforced thermoplastic- and thermosetting-composites: A comparative study
Composite Structures
101
9-21
2013
10.1016/j.compstruct.2013.01.025
This study is aimed at comparing the response of TS-based (epoxy) and TP-based (PPS or PEEK) laminates subjected to low velocity impacts. C-scan inspections showed that impact led to diamond-shaped damage resulting from different failure mechanisms: fiber breakages in warp and weft directions, more or less inter-laminar and intra-ply damage, and extensive delamination in C/PEEK and C/epoxy laminates. The permanent indentation can be ascribed to specific mechanisms which mainly depend on many factors including the ultimate out-of-plane shear strength, and the interlaminar fracture toughness in modes I-II-III. In TP-based laminates, the matrix plasticization seems to play an important role in matrix-rich areas by locally promoting permanent deformations. Fiber-bridging also prevents the plies from opening in mode I, and slows down the propagation of interlaminar and intralaminar cracks in modes II-III. Both mechanisms seem to reduce the extension of damages, in particular, the subsequent delamination for a given impact energy. In epoxy-based laminates, the debris of broken fibers and matrix get stuck in the cracks and the adjacent layers, and create a sort of blocking system that prevents the cracks and delamination from closing after impact. ?? 2013 Elsevier Ltd.
Impact behavior; Mechanical testing; Polymer-matrix composites; Woven fabrics
Structure of carboxyl-acid-terminated self-assembled monolayers from molecular dynamics simulations and hybrid quantum mechanics-molecular mechanics vibrational normal-mode analysis
Journal of Physical Chemistry C
116
770-782
2012
10.1021/jp208443u
Self-assembled monolayers (SAMs) are excellent models for studying interfacial reactions and various properties of thin films. Carboxylic acid-terminated SAMs (CATSAMs) are of special interest because their surface properties are highly pH-dependent. To elucidate the complicated pH-dependent structural properties of CATSAMs, we combine force-field molecular dynamics simulations with hybrid quantum mechanics-molecular mechanics (QM/MM) calculations of vibrational frequencies. These studies show that at low pH the carboxylic acids behave similarly to bulk carboxylic acids, hydrogen bonding mainly to the aqueous phase. With increasing pH, intralayer hydrogen bonds and monolayer disorder increase. The computed QM/MM vibrational data show that the observed range of carbonyl frequencies is due to inherent condensed phase properties of the CATSAMs such as fluctuating hydrogen bond environment and steric interactions. The results reported herein underscore the role H-bonding and steric congestion play in pH-dependent structural properties of CATSAMs.
Thermo-mechanical fatigue behavior of a cross-ply SCS-6/Ti-15-3 metal-matrix composite
Composites Science and Technology
50
1
49-57
1994
10.1016/0266-3538(94)90125-2
The thermo-mechanical fatigue behavior of a cross-ply laminate of a silicon-carbide-fiber-reinforced titanium-matrix composite, SCS-6/Ti-15-3, has been investigated. Two sets of tests involving in-phase and out-of-phase thermal-mechanical fatigue from 149 to 427°C at different stress levels, which were below and above the static first ply failure strength of the laminate, were conducted. Fatigue damage originated at the fiber/matrix interface of 90° fibers, and progressed as transverse cracking in the matrix. However, final damage modes were dependent on stress level and test conditions. Furthermore, fatigue lives were also found to be dependent on test conditions at a given stress level.
damage mechanisms; fatigue; metal-matrix composites; silicon carbide fibers; thermomechanical fatigue; titanium matrix
Further assessment of a generalized plate model: Stress analysis of angle-ply laminates
International Journal of Solids and Structures
40
16
4125-4133
2003
10.1016/S0020-7683(03)00203-8
This study is a continuation of the investigation presented in reference (International Journal of Mechanical Sciences 44 (2002) 287) and deals with an assessment of the stress analysis performance of the generalised shear deformable theory presented in (Acta Mechanica 123 (1997c) 163) when dealing with angle-ply laminated beams. One of the main conclusions is that the existing elasticity solutions for simply supported laminates cannot anymore be considered as safe means in checking and testing the effectiveness of other, conventional shear deformable theories, at least as far as angle-ply laminates are concerned. ?? 2003 Published by Elsevier Science Ltd.
Laminates; Plate; Stress
Effects of weld profile and undercut on fatigue crack propagation life of thin-walled cruciform joint
Thin-Walled Structures
39
261-285
2001
10.1016/S0263-8231(00)00061-6
Fatigue may occur in undercarriages and support systems of trailers, haymakers, graders and swing-ploughs made up of thin-walled tubular sections with wall thicknesses less than 4 mm. Little research has been done on the fatigue of thin-walled tubular sections below 4 mm thickness. The weld profile and weld undercut may affect the fatigue crack propagation life of welded joints especially for thin-walled sections. Numerical analysis of 2-dimensional non-load carrying thin-walled cruciform joints was performed to determine the effect of weld profile and weld undercut on fatigue crack propagation life under cyclic tensile loading. The cruciform joints analyzed are made up of 3 mm thick plates, joined by fillet welds. The Boundary Element Analysis System Software (BEASY) is used, which uses fracture mechanics theory to carry out crack propagation analysis. The weld profiles and weld undercuts were measured from welded connections in thin-walled fillet welded sections. The measured weld profiles and undercut were used in the analysis. The results are compared with those of a similar study to determine the comparative reduction in fatigue crack propagation life between thin-walled cruciform joints (T = 3 mm) and thicker walled cruciform joints (T = 20 mm). This paper provides an understanding of the impact which weld toe undercut has on the fatigue crack propagation life of thin-walled cruciform joints. The presence of undercuts may reduce the benefits of the thickness effect in thin-walled joints of thicknesses less than 4 mm.
61-3-990-54944; 61-3-990-54972; au; boundary element method; corresponding author; crack propagation; edu; e-mail address; eng; fatigue; fax; fracture mechanics; joints; l; monash; tel; thin-; walled sections; welded connections; welds; x; zhao; zxl
The fatigue damage mechanics of notched carbon-fiber peek laminates
Composites
23
5
305-311
1992
10.1016/0010-4361(92)90329-s
A model is presented for the strength, post-fatigue residual strength and damage propagation in notched, cross-ply carbon fibre/polyetheretherketone (PEEK) laminates. Fracture mechanics principles are used to predict quasi-static damage growth, and the application of a Paris law permits extension to fatigue damage. Strength is predicted by applying a failure criterion based on the tensile stress distribution in the 0-degrees plies, as modified by damage (either quasi-static or fatigue). The volume dependence of strength is included by using a simple Weibull distribution. The parameters of the model are determined from independent experiments. Good agreement with experimental results is obtained. Comparisons are made with previous results from carbon fibre/epoxy laminates. The behaviour of the carbon fibre/PEEK is similar, although the extent of delamination and matrix cracking is reduced owing to the higher inherent toughness of the matrix.
CARBON; COMPOSITE MATERIALS; COMPOSITE-MATERIALS; DAMAGE PROPAGATION; EPOXY MATRIX; FATIGUE; FATIGUE STRENGTH; FIBERS; GROWTH; MODELING; NOTCHED CROSS-PLY LAMINATES; PEEK MATRIX; RESIDUAL STRENGTH; STRENGTH
Quantum-well states in copper thin films
Nature
398
6723
132-134
1999
10.1038/18178
A standard exercise in elementary quantum mechanics is to describe the properties of an electron confined in a potential well. The solutions of Schrodinger's equation are electron standing waves-or 'quantum-well' states-characterized by the quantum number n, the number of half-wavelengths that span the well. Quantum-well states can be experimentally realized in a thin film, which confines the motion of the electrons in the direction normal to the film: for layered semiconductor quantum wells, the aforementioned quantization condition provides (with the inclusion of boundary phases) a good description of the quantum-well states. The presence of such states in layered metallic nanostructures is believed to underlie many intriguing phenomena, such as the oscillatory magnetic coupling of two ferromagnetic layers across a non-magnetic layer(1,2) and giant magnetoresistance(3). But our understanding of the properties of the quantum-well states in metallic structures is still limited. Here we report photoemission experiments that reveal the spatial variation of the quantum-well wavefunction within a thin copper film. Our results confirm an earlier proposal(4) that the amplitude of electron waves confined in a metallic thin film is modulated by an envelope function (of longer wavelength), which plays a key role in determining the energetics of the quantum-well states.
Magnetoresistance; superlattices
Stimuli-responsive buckling mechanics of polymer films
Journal of Polymer Science Part B: Polymer Physics
52
22
1441-1461
2014
10.1002/polb.23590
Thin polymer films may undergo a wide variety of elastic instabilities that include global buckling modes, wrinkling and creasing of surfaces, and snapping transitions. Traditionally, these deformations have usually been avoided as they often represent a means of mechanical failure. However, a new trend has emerged in recent years in which buckling mechanics can be harnessed to endow materials with beneficial functions. For many such applications, it is desirable that such deformations happen reversibly and in response to well-defined signals or changes in their environment. While significant progress has been made on understanding and exploiting each type of deformation in its own right, here we focus on recent advances in the control and application of stimuli-responsive mechanical instabilities.
creasing; crumpling; films; folding; global buckling; snapping; stimuli-sensitive polymers; swelling; wrinkling
Fracture mechanics of a new blister test with stable crack growth
Acta Metallurgica Et Materialia
43
11
4109-4115
1995
10.1016/0956-7151(95)00108-8
A new blister test is proposed to measure the specific work of adhesion W between a thin flexible film on a rigid substrate. In contrast to the conventional blister loaded by constant fluid pressure which leads to catastrophic crack propagation, the new test is driven by an internal expansion of a fixed mass of working gas which leads tostable crack growth. The new technique is demonstrated by measuring W of an interface with a commercial sticky tape serving as the thin film and aluminium as the rigid substrate. ?? 1995 Acta Metallurgica Inc. All rights reserved.
Mechanics of the F-actin cytoskeleton
Journal of Biomechanics
43
1
9-14
2010
10.1016/j.jbiomech.2009.09.003
Dynamic regulation of the filamentous actin (F-actin) cytoskeleton is critical to numerous physical cellular processes, including cell adhesion, migration and division. Each of these processes require precise regulation of cell shape and mechanical force generation which, to a large degree, is regulated by the dynamic mechanical behaviors of a diverse assortment of F-actin networks and bundles. In this review, we review the current understanding of the mechanics of F-actin networks and identify areas of further research needed to establish physical models. We first review our understanding of the mechanical behaviors of F-actin networks reconstituted in vitro, with a focus on the nonlinear mechanical response and behavior of "active" F-actin networks. We then explore the types of mechanical response measured of cytoskeletal F-actin networks and bundles formed in living cells and identify how these measurements correspond to those performed on reconstituted F-actin networks formed in vitro. Together, these approaches identify the challenges and opportunities in the study of living cytoskeletal matter. ?? 2009 Elsevier Ltd. All rights reserved.
Cell mechanics; Cell migration; F-actin cytoskeleton; Rheology
Elastic growth in thin geometries
Origins of Life: Self-Organization and/or Biological Evolution?
79-94
2009
10.1051/orvie/2009007
Generation of shapes in biological tissues is a complex multiscale phenomenon. Biochemical details of cell proliferation, death and mobility can be incorporated within a continuum mechanical framework by specifying locally the amplitude and direction of growth. For tissues exhibiting an elastic behavior, equilibrium shapes of growing bodies can be evaluated through the minimization of an appropriate energy. This model is applied to thin shells and plates, a geometry relevant to nuts and pollen grains but also leaves, petals and algae.
bone; gradient; mechanics; model; morphogenesis; pattern-formation; plants; sheets; skin; tissues
Measurements of Piezoelectric Coefficient d33 of Lead Zirconate Titanate Thin Films Using a Mini Force Hammer
Journal of Vibration and Acoustics
135
1
11003
2013
10.1115/1.4006881
Lead zirconate titanate (PbZrxTi1-xO3, or PZT) is a piezoelectric material widely used as sensors and actuators. For microactuators, PZT often appears in the form of thin films to maintain proper aspect ratios. One major challenge encountered is accurate measurement of piezoelectric coefficients of PZT thin films. In this paper, we present a simple, low-cost, and effective method to measure piezoelectric coefficient d33 of PZT thin films through use of basic principles in mechanics of vibration. A small impact hammer with a tiny tip acts perpendicularly to the PZT thin-film surface to generate an impulsive force. In the meantime, a load cell at the hammer tip measures the impulsive force and a charge amplifier measures the responding charge of the PZT thin film. Then the piezoelectric coefficient d33 is obtained from the measured force and charge based on piezoelectricity and a finite element modeling. We also conduct a thorough parametric study to understand the sensitivity of this method on various parameters, such as substrate material, boundary conditions, specimen size, specimen thickness, thickness ratio, and PZT thin-film material. Two rounds of experiments are conducted to demonstrate the feasibility and accuracy of this new method. The first experiment is to measure d33 of a PZT disk resonator whose d33 is known. Experimental results show that d33 measured via this method is as accurate as that from the manufacturer's specifications within its tolerance. The second experiment is to measure d33 of PZT thin films deposited on silicon substrates. With the measured d33, we predict the displacement of PZT thin-film membrane microactuators. In the meantime, the actuator displacement is measured via a laser Doppler vibrometer. The predicted and measured displacements agree very well validating the accuracy of this new method.
Discrete ply modelling of open hole tensile tests
Composite Structures
113
1
369-381
2014
10.1016/j.compstruct.2014.03.031
The Discrete Ply Modelling (DPM) method, previously applied with success to out-of-plane loading such as impact or pull-through, is used to model open hole tensile tests. According to the literature, this kind of test is relevant to assess the efficiency of a modelling strategy. Four different stacking sequences are tested and the failure scenario and patterns are well predicted. The main advantages of DPM are the very small number of parameters required and the robustness of the models. The main drawback is the computation cost. © 2014 Elsevier Ltd.
Discrete modelling; Failure; Laminate; Open-hole tensile test
Derivation of the Schrödinger Equation from Newtonian Mechanics
Physical Review
150
4
1079-1085
1966
10.1103/PhysRev.150.1079
The hypothesis leads in a natural way to the , but the VOLUME 150, NUMBER 4 of the from
stochastic quantization
Three-dimensional thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates using finite layer method
Composite Structures
92
1
31-38
2010
http://dx.doi.org/10.1016/j.compstruct.2009.06.010
Finite layer method is the most efficient numerical method for 3D analysis of simply supported rectangular plates. Using this method, the 3D analysis is transformed into one dimensional analysis by virtue of the orthogonal properties of trigonometric interpolation functions. In the present study, the finite layer method is extended to the thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates, which may be combined with some symmetrical cross-plies. Full coupling between the thermal, electrical and mechanical fields is taken into consideration. Pre-buckling state is assumed to be steady, and initial thermal stresses are computed accordingly. The geometrical stiffness matrix is then formed, and the critical temperature and buckling mode are obtained. Numerical examples are presented to verify the proposed method. The critical temperature is determined for both the adiabatic and isothermal buckling processes. The thermal buckling behaviours of some piezoelectric laminates and the effects of the thermo-electro-mechanical coupling are investigated.
Antisymmetric angle-ply; Finite layer method; Piezoelectric laminates; Thermal buckling; Thermal, electric and mechanical coupling; Three dimensional analysis
A ply drop-off element for analysis of tapered laminated composites
Composite Structures
39
l
123-144
1997
10.1016/S0263-8223(97)00132-3
A novel ply drop-off element has been developed for the analysis of tapered laminated composites. The element has the capability to accommodate the drop-off within the element. Therefore, drop-off need not lie along the nodal lines. As a result, drop-off location is independent of the mesh division. This facilitates the use of a coarse mesh at the ply drop location even when the stagger distance is very small. This element can be used in the global model without increasing the size of the global structural matrices. The stiffness matrix is developed by superimposing the stiffness matrices of all layers. Since the size of the dropped layer is different from the size of the element a special integration technique has been adopted for developing the stiffness matrices of dropped layers. In addition, a degenerated 1D drop-off element has been discussed. The 1D element can be used when the lateral dimension of the plate is high in comparison to longitudinal dimension. The validation of the proposed drop-off element has been carried out with the help of numerical examples.
Novel mucosal vaccines generated by genetic conjugation of heterologous proteins to pneumolysin (PLY) from Streptococcus pneumoniae
Vaccine
28
18
3231-3237
2010
10.1016/j.vaccine.2010.02.014
Induction of immunity at mucosal surfaces is thought to be an essential feature in the protection of the host against the many pathogens that gain access through these surfaces. Here we describe how strong local and systemic immune responses can be generated when proteins are genetically conjugated to pneumolysin (PLY) from Streptococcus pneumoniae. Using green fluorescent protein (eGFP) and PsaA from S. pneumoniae, we have shown that genetic fusion (eGFPPLY and PsaAPLY) is essential to ensure high levels of antigen specific IgG and IgA in the serum and at mucosal surfaces. This form of vaccination is highly effective with antigen specific antibodies detected after a single dose of nanogram quantities of the conjugated proteins. In addition, generation of a non-toxic variant (eGFP??6PLY) indicated that while the toxic activity of PLY was not essential for adjuvanticity, it contributed to the magnitude of the response generated. Whilst vaccination with the PsaAPLY fusion proteins did not protect the animals from challenge, these studies confirm the utility of pneumolysin to act as a novel mucosal adjuvant to substantially increase the local and systemic humoral response to genetically fused protein antigens. ?? 2010 Elsevier Ltd. All rights reserved.
Mucosal adjuvant; Non-toxic; Pneumolysin
Dynamic simulation of crack initiation and propagation in cross-ply laminates by DEM
Composites Science and Technology
71
11
1410-1418
2011
DOI 10.1016/j.compscitech.2011.05.014
A representative element of the cross-ply laminate was modeled by the discrete element method (DEM) to analyze the stresses distribution. The DEM modeling results were compared with those from alternative approaches to validate the DEM model. The transverse cracking and interfacial delamination in [0 degrees(1)/90 degrees(3)](s) and [90 degrees(n)/0 degrees(1)](s) cross-ply laminates under transverse loading were analyzed by comparing crack densities as well as stiffness reduction with those from experiments and other numerical methods. It was found that the proposed DEM model can simultaneously capture the transverse cracking and delamination phenomenon, and can predict the variation of crack density and stiffness reduction accurately. (C) 2011 Elsevier Ltd. All rights reserved.
cohesive-zone model; damage; delamination; dem; discrete element method; fiber-reinforced composite; finite-element; formulation; fracture; free-edge; laminate; mixed-mode delamination; multiscale modeling; transverse cracking
Charge distribution on thin semiconducting silicon nanowires
Computer Methods in Applied Mechanics and Engineering
197
41-42
3366-3377
2008
10.1016/j.cma.2008.02.007
The subject of this paper is the calculation of charge distribution on and inside thin semiconducting silicon nanowires in electrostatic problems, by a coupled finite and boundary element method (FEM/BEM). A hybrid semi-classical (Laplace/Poisson) model is employed and a line model (with finite thickness) for a silicon nanowire of circular cross-section is proposed here. This model overcomes the prob-lem of dealing with nearly singular matrices that occur when the standard BEM is applied to very thin features (objects or gaps). This new approach is also very efficient. Numerical results are presented for selected examples.
boundary element method; charge distribution; finite element method; semiconducting silicon nanowires
A fractional model of continuum mechanics
Journal of Elasticity
107
June 2011
105-123
2012
10.1007/s10659-011-9346-1
Although there has been renewed interest in the use of fractional models in many application areas, in reality fractional analysis has a long and distinguished history and can be traced back to the likes of Leibniz (Letter to L'Hospital, 1695), Liouville (J. A parts per thousand c. Polytech. 13:71, 1832), and Riemann (Gesammelte Werke, p. 62, 1876). Recent publications (Podlubny in Math. Sci. Eng. 198, 1999; Sabatier et al. in Advances in fractional calculus: theoretical developments and applications in physics and engineering, Springer, Berlin, 2007; Das in Functional fractional calculus for system identification and controls, Springer, Berlin, 2007) demonstrate that fractional derivative models have found widespread applications in science and engineering. Late fundamental considerations have led to the introduction of fractional calculus in continuum mechanics in an attempt to develop non-local constitutive relations (Lazopoulos in Mech. Res. Commun. 33:753-757, 2006). Attempts have also been made to model microscopic forces using fractional derivatives (Vazquez in Nonlinear waves: classical and quantum aspects, pp. 129-133, 2004). Our approach in this paper differs from previous theoretical work, in that we develop a general framework directly from the classical continuum mechanics, by defining the laws of motion and the stresses using fractional derivatives. The timeliness and relevance of this work is justified by the surge in interest in applications of fractional order models to biological, physical and economic systems. The aim of the present paper is to lay the foundations for a new non-local model of continuum mechanics based on fractional order derivatives which we will refer to as the fractional model of continuum mechanics. Following the theoretical development, we apply this framework to two one-dimensional model problems: the deformation of an infinite bar subjected to a self-equilibrated load distribution, and the propagation of longitudinal waves in a thin finite bar.
Continuum mechanics; Deformable media; Fractional calculus
Maximal Velocity Sprint Mechanics
Track Coach
179
2007
Sprinting is a complex task that places a high neuromuscular demand on the performer and requires high levels of coordinated movement and appropriate sequencing of muscle activations to perform at peak levels. This paper will examine maximal velocity sprint mechanics with particular focus on the primary factors affecting performance, the mechanics associated with those factors, and the causal relationships that occur as a result of optimal sprinting mechanics. Although it is understood that maximum velocity sprinting mechanics cannot be taken out of the context of either the acceleration that preceded it or the biomotor abilities of a given athlete, the following discussion will focus solely on maximal velocity mechanics for the sake of simplicity.
The large deviation approach to statistical mechanics
Physics Reports
478
1-3
1-69
2009
10.1016/j.physrep.2009.05.002
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations. ?? 2009 Elsevier B.V. All rights reserved.
Transverse Cracking in a Cross-ply Composite Laminate - Detection in Acoustic Emission and Source Characterization
Journal of Composite Materials
40
1
37-69
2005
10.1177/0021998305053507
Transverse cracking detection in a uniaxially loaded symmetric cross-ply hybrid composite laminate is studied using modal-based acoustic emission (MAE) method. Transverse cracking in the hybrid laminate is identified in conjunction with the finite element analysis and acoustic emission (AE) testing on unidirectional carbon/epoxy specimens. Higher wave modes are involved in various damage events in both types of specimens. Wave attenuation in the hybrid laminate is observed to be much stronger than in the unidirectional carbon/epoxy specimen, resulting in fewer AE events detected. A material failure kinetics-based characterization of the transverse cracking process is proposed. Results of dynamic response analysis of the hybrid laminate show good agreement with the AE experiment data. © 2006 SAGE Publications.
acoustic emission; attenuation; composite laminate; source characterization; transverse cracking
Numerical calculation of bending fatigue life of thin-rim spur gears
Engineering Fracture Mechanics
71
647-656
2004
10.1016/S0013-7944(03)00024-9
Mechanical elements subjected to cyclic loading have to be designed against fatigue. The aim of this paper is to examine the bending fatigue life of thin-rim spur gears of truck gearboxes. The gear service life is divided into the initiation phase of the damage accumulation and the crack growth, respectively. The analysis of thin-rim gear fatigue life has been performed using the finite element method and the boundary element method. The continuum mechanics based approach is used for the prediction of the fatigue process initiation phase, where the basic fatigue parameters of the materials are taken into account. The remaining life of gear with an initial crack is evaluated using the linear-elastic fracture mechanics. © 2003 Elsevier Ltd. All rights reserved.
Bending fatigue; Crack initiation; Fatigue crack growth; Life prediction; Mechanical elements; Numerical modelling; Thin-rim gears
Introduction to rock mechanics
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts
101-140
1989
10.1016/0148-9062(81)90521-0
Introduces a new approach to rock mechanics called ``block theory,'' which formalizes procedures for selecting proper shapes and orientations for excavations in hard jointed rock. Applies block theory to rock slopes and underground excavations, and covers the Q theory of rock classification, the empirical criterion of joint shear strength, rock bolting, properties of weak rocks, statistical frequency of jointing, an empirical criterion of rock strength, and design of underground supports. Contains many new problems with worked-out solutions.
Mode Dependent Toughness and the Delamination of Compressed Thin Films
Journal of the Mechanics and Physics of Solids
48
2315-2332
2000
10.1016/S0022-5096(00)00007-7
We consider the buckle-driven delamination of compressed thin films. For a wide class of patterns of delamination, it is shown that the loading on the delamination front progressively goes from mode I to mode II during growth of the blister. As a result, the mode dependence of the film/substrate interface excludes widespread delamination. This explains the observations of blisters of finite extent, which are otherwise difficult to interpret. We also study a model of interfacial fracture with friction. It reveals that a severe mode dependence can be induced by interfacial friction. This permits us to account for the mode dependence using only simple ingredients: friction and linear elasticity.
a; b; c; delamination; friction; plates; stability and bifurcations
Gamification: Using Game Mechanics to Enhance eLearning
eLearn
2011
9
3
2011
10.1145/2025356.2031772
Is gamification just another empty buzzword, or can the principles that game designers employ to engage players really be applied to the design of eLearning software? What exactly is gamification? And, can the theories of gamification be applied to a variety of projects regardless of scope and budget? This article will address specific ways that game mechanics can be applied to your eLearning projects.
Microcapsule mechanics: From stability to function
Advances in Colloid and Interface Science
207
1
65-80
2014
10.1016/j.cis.2013.11.016
Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties for functional aspects. At first, assembly strategies are presented that allow control over the decisive geometrical parameters, diameter and wall thickness, which both influence the capsule's mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified. Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences. ?? 2013 Elsevier B.V.
Drug delivery; Layer-by-layer; Mechanical characterization; Microcapsules; Shell theory
Curvature elasticity of thin films
Advances in Physics
48
4
395-448
1999
10.1080/000187399243428
A tutorial review of the theory of curvature elasticity of thin films is presented with an emphasis on the physical origins of the bending energy. We begin with a discussion of surface curvature and focus on the role of special surfaces of curvature to show how such surfaces can be defined to eliminate either the coupling of the compressibility and bending terms (neutral surface) or the saddle-splay (Gaussian curvature) modulus. Next, we consider phenomenological models for curvature elasticity and discuss the coupling of the curvature degrees of freedom with other properties of the system such as the packing area and the number of molecules at the interface. The pressure distribution in the film is related to the bending moduli. We then connect the elastic moduli to the physical properties of both solid and liquid thin films with a detailed discussion of the role of solid elasticity (including defects), electrostatic interactions (applicable to polar head groups and chain packing (using a block copolymer model of amphiphilic molecules). Finally, we demonstrate the effects of fluctuations and inhomogeneities in these systems in a discussion of the role of thermal undulations in renormalizing the bending moduli and of mixtures of amphiphiles of different chain lengths in fluid films. The article is concluded with a brief review of experimental characterizations of curvature elasticity in self-assembling systems.
Amplitude and counts per event analysis of the acoustic emission generated by the transverse cracking of cross-ply CFRP
Composites Science and Technology
36
1
27-43
1989
10.1016/0266-3538(89)90014-6
Acoustic emission methods have been used to study the multiple fracture process of carbon fibre/epoxy cross-ply laminates with the objective of making valid assignments for the failure of the transverse layer, so as to facilitate the establishment of a satisfactory statistical description of that mode of damage. Several materials were introduced in order to confer some generality to the study. The paper gives indications of the different features that have been deduced from consideration of the amplitude or counts per event distributions in close relationship with direct observations by X-radiography.
Non-relativistic Quantum Mechanics
Philosophy of Physics
275-416
2007
xiii \nxiii \nIntroduction \nJeremy Butterfield and John Earman \nxxiii \nList of Contributors \nPart A \n1 \nOn Symplectic Reduction in Classical Mechanics \nJeremy Butterfield \n133 \nThe Representation of Time and Change in Mechanics \nGordon Belot \n229 \nClassical Relativity Theory \n275 \nMichael Dickson \n417 \nBetween Classical and Quantum \nN. P. Landsman \n555 \nQuantum Information and Computing \nJeffrey Bub \n661 \nThe Conceptual Basis of Quantum Field Theory \nGerard `t Hooft \n731 \nAlgebraic Quantum Field Theory \nHans Halvorson (with an Appendix by Michael M¨ \nuger) \nIndex to Part A and Part B \nDavid B. Malamet \nNon-Relativistic Quantum Mechanics \nI-1David B. Malamet \nNon-Relativistic Quantum Mechanics
Quantum Mechanics; Physics; Textbook
Thermal stresses and deflections of cross-ply laminated plates using refined plate theories
Journal of thermal stress
October 2014
37-41
1991
10.1080/01495739108927077
Exact analytical solutions of refined plate theories are developed to study the thermal stresses and deflections of cross-ply rectangular plates. The state-space approach in conjunction with the Levy method is used to solve exactly the governing equations of the theories under various boundary conditions. Numerical results of the higher-order theory of Reddy for thermal stresses and deflections are compared with those obtained using the classical and first-order plate theories.
On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics
Acta Mechanica
162
1-4
99-110
2003
DOI 10.1007/s00707-002-1007-9
In this paper, we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work is the development of an efficient direct numerical collocation method. The paper also includes two examples taken from fracture mechanics and acoustics: a single crack in a linear isotropic elastic medium, and diffraction of a plane acoustic wave by a thin rigid screen.
Effective ply and constituent elastic properties for cracked laminates
Composites Part B: Engineering
43
5
2143-2151
2012
10.1016/j.compositesb.2012.02.034
Symmetric laminates with cracked plies were studied utilizing finite element unit cell models. The laminate unit cell models were developed based on periodicity which assumes uniformly spaced cracks. A volume-averaging scheme was developed for evaluating the volume-averaged stresses, strains and effective residual properties in the cracked plies. Sensitivities of residual properties to several material parameters were examined. The predictions of the finite element model were found to be in good agreement with published experimental results. Finally, an approach is described for computing the effective fiber and matrix properties, from the effective lamina properties, as required for progressive failure analysis using multicontinuum theory. It was found that, even though the fibers are undamaged, their effective continuum properties in the transverse direction must be degraded to achieve constituent properties that coincide with the damage mode and the residual effective ply properties. ?? 2012 Elsevier Ltd. All rights reserved.
A. Lamina/ply; B. Transverse cracking; C. Finite element analysis (FEA); Residual properties
Ply drop-off effects in CFRP/honeycomb sandwich panels—theory
Composites Science and Technology
56
4
407-422
1996
10.1016/0266-3538(95)00145-X
This paper introduces a simple method for engineering analysis of ply drop-off induced local bending effects in CFRP/honeycomb sandwich panels. The model constituent parts are the base-line face laminate of a CFRP/sandwich panel, a dropped sub-laminate, a supporting honeycomb core material, and an adhesive/resin layer interfacing the laminates. The interaction between the core material and the face laminates is modelled using a two-parameter elastic foundation model. Two examples are evaluated, and it is shown that the elastic response is strongly influenced by the presence of a supporting core material. The results of a brief parametric study are presented, and it is demonstrated that the ply drop-off problem is influenced significantly by the out-of-plane stiffness of the honeycomb core, by the bending stiffness of the base-line face laminate and finally by the bending stiffness of the dropped sub-laminate. The paper is concluded by a discussion of design aspects. © 1996 Elsevier Science Limited.
Relational quantum mechanics
International Journal of Theoretical Physics
35
8
1637-1678
1996
10.1007/BF02302261
I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the "measurement problem") could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion is the notion of observer-independent state of a system (or observer-independent values of physical quantities). I reformulate the problem of the "interpretation of quantum mechanics" as the problem of deriving the formalism from a few simple physical postulates. I consider a reformulation of quantum mechanics in terms of information theory. All systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other; nevertheless, the theory is complete.
Parametric and non-parametric probabilistic approaches in the mechanics of thin-walled composite curved beams
Thin-Walled Structures
90
95-106
2015
10.1016/j.tws.2014.12.018
In this paper we perform a quantification of the uncertainty propagation of the dynamics of slender initially curved structures constructed with fiber reinforced composite materials. Depending on the manufacturing process, composite materials may have deviations with respect to the expected response, often called nominal response in a deterministic sense. The manufacturing aspects lead to uncertainty in the structural response associated with constituent proportions, material and/or geometric parameters among others. Another aspect of uncertainty that can be sensitive in composite structures is the mathematical model that represents the mechanics of the structural member, that is: the assumptions and type of hypotheses invoked reflect the most relevant aspects of the physics of a structure, however in some circumstances these hypotheses are not enough, and cannot represent properly the mechanics of the structure. Uncertainties should be considered in a structural system in order to improve the predictability of a given modeling scheme. There are two approaches to evaluate the propagation of uncertainties in structural models: the parametric probabilistic approach and the non-parametric probabilistic approach. In the parametric, one quantifies the uncertainty of given parameters (such as variation of the angles of fiber reinforcement and material constituents) by associating random variables to them. In the non-parametric, the propagation of uncertainty is quantified by considering uncertain the matrices of the whole system. In this study a shear deformable model of composite curved thin-walled beams is employed as the mean or expected model. The probabilistic model is constructed by adopting random variables for the uncertain entities (parameters or matrices) of the model. The probability density functions of the random entities are derived appealing to the maximum entropy principle under given constraints. Once the probabilistic model is discretized in the context of the finite element method, the Monte Carlo method is employed to perform the simulations. Then the statistics of the simulations is evaluated and the parametric and non-parametric approaches are compared.
Composite curved beams; Dynamics; Flexible structures; Uncertainties quantification
Progressive Fracture of Fiber Composite Thin Shell Structures under Internal Pressure and Axial Loads
International Journal of Damage Mechanics
7
4 PG - 332
-350
1998
Graphite/epoxy composite thin shell cylindrical structures were simulated to investigate damage and fracture progression due to internal pressure and axial loading. Defective and defect-free structures (thin cylinders) were examined.
Mapping right ventricular myocardial mechanics using 3D cine DENSE cardiovascular magnetic resonance.
Journal of Cardiovascular Magnetic Resonance
14
1
4
2012
10.1186/1532-429X-14-4
BACKGROUND: The mechanics of the right ventricle (RV) are not well understood as studies of the RV have been limited. This is, in part, due to the RV's thin wall, asymmetric geometry and irregular motion. However, the RV plays an important role in cardiovascular function. This study aims to describe the complex mechanics of the healthy RV using three dimensional (3D) cine displacement encoding with stimulated echoes (DENSE) cardiovascular magnetic resonance (CMR). METHODS: Whole heart 3D cine DENSE data were acquired from five healthy volunteers. Tailored post-processing algorithms for RV mid-wall tissue tracking and strain estimation are presented. A method for sub-dividing the RV into four regions according to anatomical land marks is proposed, and the temporal evolution of strain was assessed in these regions. RESULTS: The 3D cine DENSE tissue tracking methods successfully capture the motion and deformation of the RV at a high spatial resolution in all volunteers. The regional Lagrangian peak surface strain and time to peak values correspond with previous studies using myocardial tagging, DENSE and strain encoded CMR. The inflow region consistently displays lower peak strains than the apical and outflow regions, and the time to peak strains suggest RV mechanical activation in the following order: inflow, outflow, mid, then apex. CONCLUSIONS: Model-free techniques have been developed to study the myocardial mechanics of the RV at a high spatial resolution using 3D cine DENSE CMR. The consistency of the regional RV strain patterns across healthy subjects is encouraging and the techniques may have clinical utility in assessing disrupted RV mechanics in the diseased heart.
Adult; Algorithms; Anatomic Landmarks; Biomechanics; Cine; Computer-Assisted; Heart Ventricles; Heart Ventricles: anatomy & histology; Humans; Image Processing; Imaging; Magnetic Resonance Imaging; Mechanical; Middle Aged; Myocardial Contraction; Predictive Value of Tests; Reference Values; Right; South Africa; Stress; Three-Dimensional; Time Factors; Ventricular Function; Young Adult
An experimental study of the effect of ply orientation on ballistic impact performance of multi-ply fabric panels
Textile Research Journal
0040517514566110-
2015
10.1177/0040517514566110
This paper presents a comprehensive experimental study of the effect of ply orientation on the ballistic performance of the multi-ply fabric panels. The fabric panels used in the experiments were constructed by laying plies of plain-woven fabrics in a selection of orientations. Particular attention was paid to the stacking sequence of fabrics with different laying angles. Ballistic impact tests were carried out on such angled fabric panels. The results showed significant improvement in energy-absorbing capacity of the angled multi-ply panel over the conventional aligned panel where all fabric plies are laid in the same orientation. The impact energy absorption by these angled fabric panels showed a 14% increase over the aligned counterpart, depending on the number of the plies. Optimizing the stacking sequence of the angled plies caused a 15% increase in impact energy absorption. For the panels with a large number of plies, such as the eight-ply panels, the effective panel construction can be determined according to the performance of the sub-level ply group.
Notch insensitive fracture in nanoscale thin films
Applied Physics Letters
94
25
2009-2011
2009
10.1063/1.3157276
To study the effect of stress concentration at the nanoscale, we performed fracture experiments on single edge notched thin film specimens inside the transmission electron microscope. Even at about 4 GPa stress at the notch tip, the specimens failed far away from the notch at places with no apparent stress concentration. The in situ electron microscopy showed evidence of little or no plastic deformation at the notch tip. We propose that the apparent notch insensitivity arises from the breakdown of the classical fracture mechanics at the nanoscale, where materials fail by reaching a uniform rupture stress and not due to stress concentration.
Mechanics and modeling of plant cell growth
Trends in Plant Science
14
9
467-478
2009
10.1016/j.tplants.2009.07.006
Cellular expansive growth is one of the foundations of morphogenesis. In plant and fungal cells, expansive growth is ultimately determined by manipulating the mechanics of the cell wall. Therefore, theoretical and biophysical descriptions of cellular growth processes focus on mathematical models of cell wall biomechanical responses to tensile stresses, produced by the turgor pressure. To capture and explain the biological processes they describe, mathematical models need quantitative information on relevant biophysical parameters, geometry and cellular structure. The increased use of mechanical modeling approaches in plant and fungal cell biology emphasizes the need for the concerted development of both disciplines and underlines the obligation of biologists to understand basic biophysical principles. ?? 2009 Elsevier Ltd. All rights reserved.
Spatial resolution of wrinkle patterns in thin elastic sheets at finite strain
Journal of the Mechanics and Physics of Solids
62
1
163-180
2014
10.1016/j.jmps.2013.09.024
Koiter's nonlinear plate theory is used to simulate the wrinkling patterns observed in stretched thin elastic sheets. The phenomenon considered is associated with wrinkle patterns distributed over the interior of the sheet, in regions where the stretching and bending energies are of the same order of magnitude. Numerical solutions to several equilibrium boundary-value problems are obtained by the method of dynamic relaxation based on a dissipative dynamical system and compared with existing experimental, numerical, and analytical results. © 2013 Elsevier Ltd. All rights reserved.
Nonlinear elasticity; Thin elastic sheets; Wrinkling
Elementary Principles in Statistical Mechanics
Nature
66
1708
291-292
1902
10.1038/066291a0
Developed with special ref. to the rational foundation of thermodynamics
Mechanics of noncoplanar mesh design for stretchable electronic circuits
Journal of Applied Physics
105
12
123516
2009
10.1063/1.3148245
A noncoplanar mesh design that enables electronic systems to achieve large, reversible levels stretchability (>100%) is studied theoretically and experimentally. The design uses semiconductor device islands and buckled thin interconnects on elastometric substrates. A mechanics model is established to understand the underlying physics and to guide the design of such systems. The predicted buckle amplitude agrees well with experiments within 5.5% error without any parameter fitting. The results also give the maximum strains in the interconnects and the islands, as well as the overall system stretchability and compressibility. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3148245]
buckling; compressibility; integrated circuit design; integrated circuit interconnections; internal stresses; island structure
Soil Mechanics
Soil Mechanics and Foundation Engineering
365
June
576
1969
10.1098/rsta.2007.0009
We study in this Letter the neutrinoless double beta decay nuclear matrix elements (NMEs) in the framework of the interacting shell model. We analyze them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NMEs predicted by different nuclear models. In addition, it gives back the protagonist role in this process to the pairing interaction, the one which is responsible for the very existence of double beta decay emitters. We show that low seniority approximations, comparable to those implicit in the quasiparticle RPA in a spherical basis, tend to overestimate the NMEs in several decays.
Delamination of tapered composite structures
Engineering Fracture Mechanics
34
1
43-54
1989
10.1016/0013-7944(89)90241-5
he delamination of tapered composite laminates with multiple internal ply drop steps is investigated. Both experimental testing of glass-epoxy coupon specimens and finite element modeling of the tapered region are conducted. The average stress concept is applied to out-of-plane stresses from a thr~-dimensional finite element model. ~lamination failure criteria are then used to predict strength based on ply failure and interply resin failure. Strength predictions based on interply resin failure using a stress averaging distance of one ply thickness are found to correlate well with the experimental results. Delamination in the tapered laminates is due to interlaminar shear failure of the interply resin surrounding the last ply drop step.
Transverse cracking and Poisson's ratio reduction in cross-ply carbon fibre-reinforced polymers
Journal of Materials Science
34
5513-5517
1999
10.1023/A:1004716612960
Gradual damage development in carbon fibre-reinforced polymers (CFRP)\nand its effect on the mechanical properties have been important subjects\nof investigation for many years. Most authors have studied transverse\nmatrix cracking in cross-ply lay-ups and used the longitudinal Young's\nmodulus as an indicator of the extent of damage development. Reductions\nof typically only a few percent have been found at saturation crack\nspacing. Some authors have studied the effect of matrix cracking\non Poisson's ratio. The results show large reductions, but few data\nare available on the evolution of Poisson's ratio throughout the\nprocess of gradual matrix cracking and on the influence of the 0°/90°\nply thickness ratio. Moreover, none of the available models seems\nto accurately predict the quantitative evolution of Poisson's ratio.\nIn this work the degradation of the longitudinal and the transverse\nproperties of a number of cross-ply CFRP laminates due to transverse\nmatrix cracking under longitudinal tension was studied. The longitudinal\nYoung's modulus appeared to be less sensitive to damage development,\nin contrast to Poisson's ratio which exhibited significant reductions\nin all lay-ups. A micromechanical model, based on the shear lag theory,\nwas developed to predict the evolution of Poisson's ratio and the\neffect of the 0°/90° ply thickness ratio. The correlation between\nexperiment and theory was very satisfactory.
Local strain re-distribution and stiffness degradation in cross-ply polymer composites under tension
Acta Materialia
53
12
3335-3343
2005
10.1016/j.actamat.2005.03.045
Individual aramid Kevlar® 49 fibers were embedded into the 0° ply of transparent cross-ply glass fiber reinforced polymer (GFRP) laminates and used as Raman sensors for the monitoring of the local strain field due to matrix cracking under quasi-static loading. The sensors were placed near the 0/90 interface, and the resulting strain within the 0° ply and its dependence on the geometry of the specimen due to 90° cracking were recorded. The decay of the strain magnification with the distance from the crack front, the residual strain and the axial modulus of elasticity reduction were derived from the strain distributions at each separate level of loading. The results obtained were compared with shear-lag calculations as well as numerical and analytical models. © 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
damage; modeling; non-destructive testing; polymer matrix composites; raman spectroscopy
On the Classical Limit of Quantum Mechanics
Arxiv Preprints
15
2001
http://dx.doi.org/10.1063/1.463909
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of the many results on the h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing real objects in an observer-independent way.
Bohmian mechanics
Real-time simulation of thin shells
Computer Graphics Forum
26
3
349-354
2007
10.1111/j.1467-8659.2007.01057.x
This paper proposes a real-time simulation technique for thin shells undergoing large deformation. Shells are thin objects such as leaves and papers that can be abstracted as 2D structures. Development of a satisfactory physical model that runs in real-time but produces visually convincing animation of thin shells has been remaining a challenge in computer graphics. Rather than resorting to shell theory which involves the most complex formulations in continuum mechanics, we adopt the energy functions from the discrete shells proposed by Grinspun et al. [GHDS03]. For real-time integration of the governing equation, we develop a modal warping technique for shells. This new simulation framework results from making extensions to the original modal warping technique [CK05] which was developed for the simulation of 3D solids. We report experimental results, which show that the proposed method runs in real-time even for large meshes, and that it can simulate large bending and/or twisting deformations with acceptable realism.
Simple and efficient interlaminar stress analysis of composite laminates with internal ply-drop
Composite Structures
84
73-86
2008
10.1016/j.compstruct.2007.06.004
A stress function-based variational method is developed to investigate the interlaminar stresses near the dropped plies. The present method is based on expanding stress functions in terms of harmonic series to the out-of-plane direction. The stresses satisfying the traction free boundary conditions of tapered laminates are obtained by the complementary strain energy principle. Stress concentrations near the dropped plies are predicted well as the number of initially assumed out-of-plane stress functions is increased. The proposed method is relatively simple and efficient in the prediction of interlaminar stresses near the dropped plies. Therefore, it is expected that the proposed method can be used in the parametric study of the preliminary design stage of tapered composite laminates. ?? 2007 Elsevier Ltd. All rights reserved.
Delamination fraction; Interlaminar stress; Internal ply-drop; Stress concentration; Stress function
Floquet wave ultrasonic method for determination of single ply moduli in multidirectional composites
Journal of the Acoustical Society of America
112
3
916-924
2002
10.1121/1.1498854
An inversion method based on Floquet wave velocity in a periodic medium has been introduced to determine the single ply elastic moduli of a multi-ply composite. The stability of this algorithm is demonstrated by numerical simulation. The applicability of the plane wave approximation to the velocity measurement in the double-through-transmission self-reference method has been analyzed using a time-domain beam model. It shows that the finite width of the transmitter affects only the amplitudes of the signals and has almost no effect on the time delay. Using this method, the ply moduli for a multiply composite have been experimentally determined. While the paper focuses on elastic constant reconstruction from phase velocity measurements by the self-reference double-through-transmission method, the reconstruction methodology is also applicable to assessment of data collected by other methods. (C) 2002 Acoustical Society of America.
ANISOTROPIC MATERIALS; ELASTIC-CONSTANTS; MEDIA; SOLIDS; VELOCITY-MEASUREMENTS
The effect of thermo-oxidation on matrix cracking of cross-ply [0/90] S composite laminates
Composites Part A: Applied Science and Manufacturing
44
114-121
2013
10.1016/j.compositesa.2012.08.013
The present article focuses on the effects of thermo-oxidation on matrix cracking in cross-ply [0/90] S composite laminates. IM7/977-2 carbon/epoxy samples were firstly aged at 150 ??C under 1.7 bars of oxygen for 24 h, 48 h and 96 h, respectively. Quasi-static tensile tests were then carried out on un-aged and aged samples. The number of matrix cracks was counted during the tensile tests in order to establish the evolution of the crack density as a function of the applied stress and a numerical model was employed to evaluate the critical energy release rate of un-aged and aged laminates. A reduction of the critical energy release rate of aged samples was measured compared to un-aged sample. Scanning Electron Microscopy (SEM) observations were carried out by replicas of the sample surfaces in order to identify a possible relationship between the thermo-oxidation induced damage at the local scale and the onset of matrix cracking at ply scale. ?? 2012 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Environmental degradation; C. Numerical analysis; D. Mechanical testing
New solutions for surface tension driven spreading of a thin film
International Journal of Non-Linear Mechanics
40
4
523-529
2005
10.1016/j.ijnonlinmec.2004.07.017
The standard fourth-order non-linear PDE modelling the flow of thin\nfluid film subject to surface tension is studied. The\n\nLie group method is used to reduce the model equation from a fourth-order\nPDE to a fourth-order ODE. Analytical solutions\n\nare obtained for certain cases. Where analytical progress cannot be\nmade, we determine numerical solutions.
lie group method; surface tension; thin film; travelling waves
Influence of Ply Orientation on Delamination in Composite Laminates
Journal of Composite Materials
32
21
1933-1947
1998
10.1177/002199839803202103
An experimental investigation in interlaminar fracture behavior and toughness of multi-directional composite laminates was conducted. ENF-like specimens were used for three-point-bending tests first to determine the crack-jumping behavior in various laminates. It was found that a delamination crack could propagate only along the 0/0 interface. Based on the result of this investigation, an experimental method to determine Mode II dominated interlaminar toughness was proposed and used to obtain interlaminar toughness of 0/0 interfaces in AS4/3501-6 composite material with 0 = 30{degrees}, 45{degrees}, 60{degrees}, and 90{degrees}. It was found that the critical strain energy release rate decreases as the off-axis angle 0 increases.
Failure Criteria in Fibre-Reinforced-Polymer Composites
Failure Criteria in Fibre-Reinforced-Polymer Composites
140-156
2004
10.1016/B978-008044475-8/50007-X
This chapter describes the stress-based Grant–Sanders method developed at British Aerospace for the prediction of failure in composite laminates. The method is based on a ply-by-ply analysis with discrete failure criteria. The only interactions considered being shear-tension for matrix failure and shear-compression for fiber failure. It has been applied to a number of examples to produce envelopes of initial and final failure and stress/strain curves. Hence, each failure prediction is accompanied by a prediction of the mode and location of failure. Nonlinear stiffnesses are accommodated by inputting curves of secant modulus versus strain. British Aerospace Defense has never used the ply-discount technique; however the shear and transverse tension stiffnesses have been taken to reduce gradually as strain increases above a threshold value. The chapter explains a recently developed procedure for the interaction of the matrix-dominated nonlinearities, which has been incorporated into the model. The use of discrete failure criteria gives an abrupt appearance, with sharp corners, to many of the predicted failure envelopes in contrast to the elliptical shapes produced by techniques based on tensor polynominals. It describes the lamina properties and the details of the laminates analyzed. Classical thin-laminate theory is used to determine the loading induced into each individual ply by the current level of applied loading. These ply loadings are then resolved into ply axes. An updated version of the Grant–Sanders method, based on stress criteria, has been used with the conventional notation for loading parallel and perpendicular to the fiber direction. Values of material and interactive constants used in this work, other than those supplied by the organizers, are also presented.
composite laminates; discrete criteria; grant; non-linear; sanders method; strength prediction
Compressive strength of composite laminates with terminated internal plies
Composites Part A: Applied Science and Manufacturing
36
6
798-805
2005
10.1016/j.compositesa.2004.10.024
Composite laminates are commonly tapered by terminating internal prepreg plies, creating geometrical defects which can induce failure. In this study, experiments have been conducted on tapered laminates loaded in axial compression. Failures by microbuckling or delamination were observed to nucleate near the dropped plies. The results indicate that existing models of microbuckling give adequate predictions of strength in specimens with mild geometric defects, while a new model given here for delamination provides satisfactory predictions of strength for more severe defects. © 2004 Elsevier Ltd. All rights reserved.
A. Laminates; B. Delamination; B. Microstructure; C. Micro-mechanics
Quantum Mechanics in Chemistry
Zeitschrift für Physikalische Chemie
205
Part_1
135-135
1998
10.1524/zpch.1998.205.Part_1.135
Written for beginning graduate students and advanced undergraduates, this unique text combines both introductory and modern quantum chemistry in a single volume. Unlike similar texts, which concentrate on quantum physics and provide only brief examples of chemical applications, Quantum Mechanics in Chemistry focuses on the topics a chemist needs to know. It provides an introduction to the fundamentals of quantum mechanics as they apply to chemistry, then moves on to the more modern aspects of the field, which are very important in industry and are not emphasized in any other text. It also includes introductions to molecular spectroscopy, chemical dynamics, and computational chemistry as applied to electronic structures. The authors' websites offer text-related computer programs and a large number of exercises, problems, and solutions to further enhance the flexibility and utility value of the text for students, instructors, and professionals in the field. The publisher's website is linked to the authors' websites: see Appendix H for WWW addresses.
A micro-mechanics model of dentin mechanical properties
Biomaterials
25
20
5081-5090
2004
10.1016/j.biomaterials.2003.12.042
Application of a micro-mechanics cell model to dentin composites for determination of their effective mechanical properties is discussed in this paper. The dilute micro-mechanics model for fibre-reinforced composites is utilized and the corresponding cell model is chosen to consist of a circular hollow cylinder filled with liquid or gas phase, which is surrounded by two circular cylindrical shells, a thin shell and a matrix phase. Each layer of cylindrical shell is here considered as a composite consisting of collagen fibrils, with mineralized hydroxyapatite, loosely connected to their neighbours, and water (or gas in the case of dry dentin composite). Determination of the effective material properties of such a three phase composite is discussed. Using the cell model the effect of porosity, thickness of each cylindrical shell, and mineral content on material properties is analysed. Results obtained from nano-indentation observations are compared with numerical predictions of the analytical model. ?? 2004 Elsevier Ltd. All rights reserved.
Collagen; Constitutive modelling; Dentine; Mechanical properties
Mechanics of wire rope
Wire Journal International
36
56-63
2003
10.1007/978-1-4612-1970-5
This presentation on the mechanics of wire rope will be divided into two parts: a theory for the static and dynamic response of wire rope, and practical examples in the form of consulting problems with which I have been associated.
Deformation behavior of thin, compliant layers under tensile loading conditions
Journal of Polymer Science Part B: Polymer Physics
42
22
4023-4043
2004
10.1002/polb.20258
In this article, a connection is made between the behavior of thin layers of Newtonian liquids under tensile loading conditions and the behavior of highly deformable elastic or viscoelastic solids, which are more commonly used as adhesives. The behavior of Newtonian liquids is understood in the most quantitative detail and serves as a starting point for understanding the origins of fingering and cavitation instabilities that appear when the tensile deformation rates applied to these layers are sufficiently large. Similar instabilities appear in solid systems and can be attributed to common features of the stress distribution for incompressible liquids and solids. A unifying treatment is presented that can be used to understand the overall deformation behavior and adhesive performance of a wide variety of solid and liquid systems that are typically applied as thin layers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4023–4043, 2004
Adhesion; Interfaces; Microdeformation; Rheology; Viscoelastic properties
Experimental and numerical investigation of fatigue of thin tensile specimen
International Journal of Fatigue
44
116-130
2012
10.1016/j.ijfatigue.2012.05.013
This paper presents the results of experimental and numerical investigation on fatigue of thin 304 stainless steel tensile specimens. In order to achieve the experimental aspects of this investigation a Micro Fatigue Test Rig (MFTR) was designed and developed to evaluate fatigue life and failure mechanism of tensile specimen. A 3D finite element model was also developed to investigate the fatigue damage of thin tensile specimen and to account for the effects of topological randomness of material microstructure on fatigue lives. The topology of the material grain structure was modeled using randomly generated 3D Voronoi tessellations corresponding to the measured grain size. Continuum damage mechanics was used to model the progressive material degradation. The damage parameters were obtained from the experimentally obtained S–N curve. A 3D mesh partitioning procedure was developed to consider both crack initiation and propagation stages considering the predominant transgranular, non-planar crack growth observed in the experiments. The stress–life results obtained from the fatigue damage model are in good agreement with the experimental data. The progression of damage and the proportion of life spent in crack initiation obtained from the model are consistent with empirical observations. The fatigue damage model was used to assess the influence of microstructure randomness accompanied by material inhomogeneity and internal voids on fatigue life dispersion.
Continuum damage mechanics; Fatigue; Finite element modeling; Thin sheet
Thermal effects on the response of cross-ply laminated shallow shells
International Journal of Solids and Structures
29
5
653-667
1992
10.1016/0020-7683(92)90059-3
The static response of cross-ply laminated shallow shells subjected\nto thermal loadings is investigated. An exact analytical solution\nusing the state space approach is presented in conjunction with the\nLévy method, for doubly curved, cylindrical and spherical shells\nunder various boundary conditions. Numerical results of the higher-order\ntheory of Reddy and Liu (1985, 1987) for center deflection of cross-ply\nlaminated shallow shells are compared with those obtained using classical\nand first-order shell theories. © 1991.
Theory of stress transfer in a 0°—90°—0° cross-ply laminate containing a parallel array of transverse cracks
Journal of the Mechanics and Physics of Solids
40
1
27-68
1992
10.1016/0022-5096(92)90226-R
Two new analytical methods have been developed that can predict the stress transfer between the 0 and 90° plies in a 0°—90°—0° cross-ply laminate containing transverse cracks. Account is taken of thermal residual stresses arising from a mismatch in thermal expansion coefficients of the 0 and 90° plies. The first method is based on a 2-D model which assumes that generalised plane strain conditions prevail. The theoretical approach retains all relevant stress and displacement components, and satisfies exactly the equilibrium equations, the interface conditions, and other boundary conditions involving stresses. The stress—strain—temperature relations are satisfied either exactly or in an average sense. The 2-D representation can be used to predict the stress and displacement fields for a laminate containing parallel transverse cracks. In this paper the solutions are used to estimate the dependence of the longitudinal values of Young's modulus, Poisson's ratio, and thermal expansion coefficient on the density of transverse cracks. The second analytical method extends the 2-D model so that it can apply to 3-D problems which arise, for example, when edge effects or orthogonal cracking are to be taken into account. For the special case of very large laminate widths the 2- and 3-D models predict results which are very close to each other for both glass fibre/epoxy and carbon fibre/epoxy laminates. It is shown how the 3-D model can be used to predict the transverse Young's modulus and thermal expansion coefficient. Theoretical predictions of the dependence of Poisson's ratio on transverse crack density indicate that experimental measurements can be sensitive to the strain measurement technique used, and to specimen width when using a transverse extensometer. Theoretical predictions, for glass fibre/epoxy and carbon fibre/epoxy laminates, of the dependence of Young's modulus and Poisson's ratio on the crack density are compared with some experimental results.
Quantum Mechanics Without State Vectors
arXiv.org
14-May
1-28
2014
10.1103/PhysRevA.90.042102
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical state, even in entangled states nothing that is done in one isolated system can instantaneously effect the physical state of a distant isolated system. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semi-group. Here new transformation properties are studied for general symmetry transformations forming groups, rather than semi-groups. Ar- guments are given that such symmetries should act on the density matrix as in ordinary quantum mechanics, but loopholes are found for all of these arguments
density matrix; quantum mechanics; state vectors
Damage mechanisms induced by cyclic ply-stresses in carbon-epoxy laminates: Environmental effects
International Journal of Fatigue
28
1202-1216
2006
10.1016/j.ijfatigue.2006.02.014
This paper aims to identify and to describe the damage mechanisms of CFRP composite laminates subjected to thermal cycling. Thermal cycling tests are performed in different atmospheres, more or less oxidative (air or oxygen) or neutral (nitrogen). Microscopic observations and weight measurements of cross-ply laminates samples, put in light a significant oxidation of the matrix when tests are carried out in oxidative environment. In such thermal loading, there exists a coupling between two degradation processes: oxidation and fatigue, which dramatically accelerates the damage build-up. In a second part of this paper, the results of some iso- and cyclic-thermal tests, on virgin or damaged specimens, are analysed in order to emphasise the coupling between the degradation mechanisms. ?? 2006 Elsevier Ltd. All rights reserved.
Durability; Fatigue; Matrix cracking; Oxidation; Thermo-mechanical properties
Mechanics of Generalized Continua
Advanced Structured Materials
7
3-19
2011
10.1007/978-3-642-19219-7
In a period of forty years the author has had the opportunity to work, or to entertain friendly connections, with many actors of the scene of generalized continuum mechanics (GCM). This training and knowledge here is used to the benefit of the readers as an overview of this scene with the aim to delineate further avenues of development within the framework of the trilateral seminar held in Wittenberg (2010). Starting essentially with Pierre Duhem and the Cosserat brothers, this specialized, albeit vast, field of continuum mechanics has developed by successive abandonments of the working hypotheses at the basis of standard continuum mechanics, that mechanics masterly devised by Euler and Cauchy and some of their successors in the 19th century (Piola, Kirchhoff, etc.). In the present survey we briefly analyze successive steps such as the introduction of nonsymmetric stresses, couple stresses, internal degrees of freedom and microstructure, the introduction of strain gradient theories, and material inhomogeneities with a length scale, nonlocality of the weak and strong types, the loss of Euclidean geometry to describe the material manifold, and finally the loss of classical differentiability of basic operations as can occur in a deformable fractal material object. © Springer-Verlag Berlin Heidelberg 2011.
Couple stress; Generalized continua; Micromorphic bodies; Micropolar materials; Non-Euclidean manifold; Nonlocality; Nonsymmetric stress; Strain-gradient materials
Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory
Composite Structures
48
4
231-244
2000
10.1016/S0263-8223(99)00110-5
Natural frequencies and buckling stresses of cross-ply laminated composite plates are analyzed by taking into account the effects of shear deformation, thickness change and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for thick rectangular laminates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported thick laminated plate. In order to assure the accuracy of the present theory, convergence properties of the lowest natural frequency and buckling stress are examined in detail. Numerical results are compared with those of the published existing theories and FEM solutions. The modal displacement and stress distributions in the thickness direction are obtained and plotted in figures. It is noticed that the present global higher-order approximate theories can predict the natural frequencies, buckling stresses and stresses of thick multilayered composite laminates as accurately as three-dimensional solutions.
Buckling stresses; Global higher-order plate thoery; Laminated composite plates; Natural frequencies
Boundary vortices for thin ferromagnetic films
Archive for Rational Mechanics and Analysis
174
2
267-300
2004
10.1007/s00205-004-0329-2
We consider a simplified version of the micromagnetic energy for ferromagnetic samples in the shape of thin films. We study (a) stationary, stable critical points, and (b) solutions of the corresponding Landau-Lifshitz equation under a stability condition. We determine the asymptotic behaviour of solutions of these variational problems in the thin film limit. A characteristic property of the limit is the development of Ginzburg-Landau-type vortices at the boundary.
3D constitutive model of anisotropic damage for unidirectional ply based on physical failure mechanisms
Computational Materials Science
50
2
479-486
2010
10.1016/j.commatsci.2010.09.008
A 3D anisotropic continuum damage model is developed for the computational analysis of the elastic-brittle behaviour of fibre-reinforced composite. The damage model is based on a set of phenomenological failure criteria for fibre-reinforced composite, which can distinguish the matrix and fibre failure under tensile and compressive loading. The homogenized continuum theory is adopted for the anisotropic elastic damage constitutive model. The damage modes occurring in the longitudinal and transverse directions of a ply are represented by a damage vector. The elastic damage model is implemented in a computational finite element framework, which is capable of predicting initial failure, subsequent progressive damage up to final collapse. Crack band model and viscous regularization are applied to depress the convergence difficulties associated with strain softening behaviours. To verify the accuracy of the damage model, numerical analyses of open-hole laminates with different lay-up configurations under tension and compression were performed. The numerical predictions were compared with the experimental results, and satisfactory agreement was obtained. ?? 2010 Elsevier B.V. All rights reserved.
Anisotropic damage; Crack band model; Fibre-reinforced composite; Finite element method; Viscous regulation
All-PP composites (PURE®) with unidirectional and cross-ply lay-ups: Dynamic mechanical thermal analysis
Express Polymer Letters
1
8
519-526
2007
10.3144/expresspolymlett.2007.74
All polypropylene (all-PP) composite laminates with unidirectional (UD) and cross-ply (CP) lay-ups were produced by hot consolidation from oriented coextruded PP tapes (PURE (R)). The consolidation of the tapes, wound on a steel plate, occurred in autoclave vacuum bag molding. The set processing conditions resulted in all-PP laminates of high rigidity as the PP copolymer surface layers of the tapes were molten and thus forming the matrix, while their PP homopolymer core remained unaffected and thus fulfilled its role as reinforcement. Specimens cut off from the laminates were subjected to dynamic mechanical thermal analysis (DMTA) in a broad temperature range (T = -50...120 degrees C) at various frequencies (f = 10(-2)...10(1)). For the DMTA results the time-temperature superposition principle was adopted and master curves in the form of storage modulus vs. frequency (f = 10(-9)...10(20)) and loss factor vs. frequency were created.
All-polypropylene composite; Polymer composites; Polypropylene; PURE®; Thermal properties
The Buckling of a Swollen Thin Gel Layer Bound to a Compliant Substrate
Journal of Applied Mechanics
75
5
051002
2008
10.1115/1.2936922
Gels are used to design bilayered structures with high residual stresses. The swelling of a thin layer on a compliant substrate leads to compressive stresses. The post-buckling of this layer is investigated experimentally; the wavelengths and amplitudes of the resulting modes are measured. A simplified model with a self-avoiding rod on a Winkler foundation is in semi-quantitative agreement with experiments and reproduces the observed cusp-like folds.
Vectors, Tensors and the Basic Equations of Fluid Mechanics (R. Aris)
SIAM Review
5
165-165
1963
10.1137/1005051
Introductory text for engineers, physicists, and applied mathematicians applies mathematics of Cartesian and general tensors to physical field theories, demonstrating them chiefly in terms of the theory of fluid mechanics. Many exercises throughout the text. Index. Preface. Appendixes.
Controlled nerve growth factor release from multi-ply alginate/chitosan-based nerve conduits
European Journal of Pharmaceutics and Biopharmaceutics
69
2
563-572
2008
10.1016/j.ejpb.2008.01.014
The delivery kinetics of growth factors has been suggested to play an important role in the regeneration of peripheral nerves following axotomy. In this context, we designed a nerve conduit (NC) with adjustable release kinetics of nerve growth factor (NGF). A multi-ply system was designed where NC consisting of a polyelectrolyte alginate/chitosan complex was coated with layers of poly(lactide-co-glycolide) (PLGA) to control the release of embedded NGF. Prior to assessing the in vitro NGF release from NC, various release test media, with and without stabilizers for NGF, were evaluated to ensure adequate quantification of NGF by ELISA. Citrate (pH 5.0) and acetate (pH 5.5) buffered saline solutions containing 0.05% Tween 20 yielded the most reliable results for ELISA active NGF. The in vitro release experiments revealed that the best results in terms of reproducibility and release control were achieved when the NGF was embedded between two PLGA layers and the ends of the NC tightly sealed by the PLGA coatings. The release kinetics could be efficiently adjusted by accommodating NGF at different radial locations within the NC. A sustained release of bioactive NGF in the low nanogram per day range was obtained for at least 15 days. In conclusion, the developed multi-ply NGF loaded NC is considered a suitable candidate for future implantation studies to gain insight into the relationship between local growth factor availability and nerve regeneration. © 2008 Elsevier B.V. All rights reserved.
Nerve conduit; Nerve regeneration; NGF; Release kinetics
Encyclopedia of Computational Mechanics
Encyclopedia of Computational Mechanics
1
Figure 1
2244
2004
10.1002/0470091355
Over the past four decades computational methods in applied mechanics have developed into valuable tools that are widely used across both industry and academia. The applications are numerous ranging through aerospace and civil engineering structures, geotechnics, flow problems, automotive engineering,geo-environmental modeling, biomechanics, electromagnetism, metal forming and numerous other fields. Edited and written by a team of world-renowned authorities, The Encyclopedia of Computational Mechanics provides the most comprehensive collection of knowledge about the theory and practice of computational mechanics. Offering an in-depth, practical source of information, this landmark reference provides a firm foundation for the reader’s research and practice in developing designs and in understanding, assessing and managing numerical analysis systems.
Thin shell and surface crack finite elements for simulation of combined failure modes
Computer Methods in Applied Mechanics and Engineering
194
21-24
2619-2640
2005
10.1016/j.cma.2004.07.049
In this study we present a new approach to analyse cracked shell structures subjected to large geometric changes. It is based on a combination of a rectangular assumed natural deviatoric strain thin shell finite element and an improved linespring finite element. Plasticity is accounted for using stress resultants. A power law hardening model is used for shell and linespring material. A co-rotational formulation is employed to represent nonlinear geometry effects. With this, one can carry out nonlinear fracture mechanics assessments in structures that show instabilities due buckling (local/global), ovalisation and large rigid body motion. By numerical examples it is shown how geometric instabilities and fracture compete as governing failure mode.
Assumed strain thin shell finite element; Co-rotated formulation; Large rotations; Linespring finite element; Nonlinear fracture mechanics; Plasticity
Fracture Mechanics of Concrete
Sadhana
27
4
411-412
2002
10.1007/BF02706990
applications of fracture mechanics to concrete, fock, and other quasi-brittle materials
Coupling multi-physics models to cardiac mechanics
Progress in Biophysics and Molecular Biology
104
1-3
77-88
2011
10.1016/j.pbiomolbio.2009.11.001
We outline and review the mathematical framework for representing mechanical deformation and contraction of the cardiac ventricles, and how this behaviour integrates with other processes crucial for understanding and modelling heart function. Building on general conservation principles of space, mass and momentum, we introduce an arbitrary Eulerian-Lagrangian framework governing the behaviour of both fluid and solid components. Exploiting the natural alignment of cardiac mechanical properties with the tissue microstructure, finite deformation measures and myocardial constitutive relations are referred to embedded structural axes. Coupling approaches for solving this large deformation mechanics framework with three dimensional fluid flow, coronary hemodynamics and electrical activation are described. We also discuss the potential of cardiac mechanics modelling for clinical applications. © 2009.
Cardiac mechanics; Large deformation mechanics; Multi-physics modelling
Biofluid mechanics.
Biomedizinische Technik. Biomedical engineering
43
4
94-99
1998
10.1515/bmte.1998.43.4.94
The flow behavior of biological fluids in living organisms plays a crucial role in determining the state of the tissue through which they flow. Biofluid mechanics, the study of the fundamentals of biological fluid flow, has been recognized to be extremely important for the understanding of how changes in the flow behavior within living tissue maybe affect both the fluid and the tissue. Fluids in living tissue include blood, water, air and bodily fluids of animals, as well as the fluids in plants. The movement and balance of forces in resting fluids and fluids in motion are among the basic subjects for research. Biofluid mechanics is a field whose importance to the field of bioengineering has increased over the last two decades as pharmaceuticals, biomaterials and non-invasive diagnostic and surgical procedures create changes in the fluid mechanics of biofluids. Biofluid mechanics is a complex field including one of the most important areas of study--blood flow and cardiovascular diseases.
Wind-generated waves in thin liquid films with soluble contaminant
Journal of Fluid Mechanics
45
527
1971
10.1017/S002211207100017X
In the presence of an air stream, a uniform liquid film on a horizontal flat plate may be unstable to small disturbances, and waves may arise. In this paper the hydrodynamic stability of thin liquid films is examined both experimentally and theoretically. The experiments concern water films thinner than those which have been examined in the past. It is found that, when the film thickness is sufficiently small, a previously unknown type of instability occurs. The theoretical analysis explains this surprising phenomenon. Due to interaction of the mean airflow and small disturbances of the liquid-air interface, normal and tangential stress perturbations are produced at the liquid surface. It is shown that small wave-like disturbances become unstable when the joint influence of the component of normal stress in phase with the wave elevation and the component of tangential stress in phase with the wave slope is sufficient to overcome the ‘stiffness’ of the liquid surface due to gravity and surface tension. It is found that the destabilizing role of the tangential stress component is dominant for very thin films, and that instability may occur whatever the velocity of the air stream, provided the film is made sufficiently thin.
On the optimization of tapered composite laminates in preliminary structural design
Proceedings of the ICCM17 conference
2009
Ply drop-offs represent preferred initiation sites for delaminations in tapered laminates. This paper presents an optimization tool, based on fracture mechanics, for the preliminary design of tapered composite laminates. The reliability and robustness of this optimization procedure is demonstrated via comparisons with finite element analysis.
delamination; fracture mechanics; optimization; ply drop-off
Fractal property of matrix cracking in GFRP cross-ply laminates
JSME International Journal, Series A: Mechanics and Material Engineering
38
4
446-452
1995
Matrix cracking is the most important damage mechanism in FRP structures because it causes stiffness degradation of structures and becomes the origin of delaminations. In this study, therefore, with specimens of stacking sequence [0/904]s, tension tests were conducted and in situ observations of the matrix cracking in the 90° plys were made by a replica method. As a result, the distribution of the matrix crack positions was experimentally proven to be a fractal distribution of D = 0.45 and was constant at any loading levels. Using this fractal distribution, the stiffness degradation was evaluated based on an imaginary crack density. Based on these results, the fractal distribution of the initial defect size was modeled and experimentally proven to be a fractal distribution of D = 1.6. The model was applied successfully to predict variations of crack density with increasing applied load using damage mechanics.
A detailed analysis of adhesion mechanics between a compliant elastic coating and a spherical probe
Journal of physics. D, applied physics
37
20
2886-2895
2004
10.1088/0022-3727/37/20/016
As length scales decrease, adhesive forces become increasingly important. These adhesive forces contribute to the normal load in experiments conducted on thin layered systems using micro-probe instruments such as the surface force apparatus (SFA) and the atomic force microscope (AFM). Adhesion between these thin-layer systems was analysed by Sridhar et al (1997 J. Phys. D: Appl. Phys. 30 1710) for the SFA geometry and Johnson and Sridhar (2001 J. Phys. D: Appl. Phys. 34 683) for AFM using a numerical SJF (Sridhar–Johnson–Fleck) version of the JKR (Johnson–Kendal–Roberts) theory. In this paper, adhesion mechanics between a compliant elastic coating and a spherical probe is investigated using the SJF model in detail. When the substrate is rigid, the non-dimensional pull-off force may differ from the JKR value of -0.5 by as much as 90%. Computations of the contact size at zero load and pull-off force are presented for a range of values of adhesion energy. Finally, empirical relations for the contact load and contact compliance as a function of contact radius were obtained from the numerical data for practical layer-substrate material systems.
What is Bohmian Mechanics
International Journal of Theoretical Physics
43
15
2001
10.1023/B:IJTP.0000048817.79384.2a
Bohmian mechanics is a quantum theory with a clear ontology. To make clear what we mean by this, we shall proceed by recalling first what are the problems of quantum mechanics. We shall then briefly sketch the basics of Bohmian mechanics and indicate how Bohmian mechanics solves these problems and clarifies the status and the role of of the quantum formalism.
1; about; basic problem; bohmian; interpretation quantum mechanics; mechanics; not clear; pilot wave theories; quantum mechanics; quantum theory; what quantum; what quantum mechanics
Fluid Mechanics
Angewandte Chemie International Edition
40
6
9823
2001
10.1002/1521-3773(20010316)40:6<9823::AID-ANIE9823>3.3.CO;2-C
Just one part. In the fall of 2009, Elsevier approached me about possibly taking over as the lead author of this textbook. After some consider- ation and receipt of encouragement from faculty colleagues here at the University of Michigan and beyond, I agreed. The ensuing revision effort then tenaciously pulled all the slack out of my life for the next 18 months. Unfortunately, I did not have the honor or pleasure of meeting or knowing either prior author, and have therefore missed the opportunity to receive their advice and guid- ance. Thus, the revisions made for this 5th Edition of Fluid Mechanics have been driven primarily by my experience teaching and interacting with undergraduate and grad- uate students during the last two decades.
Cracking of thin films bonded to elastic-plastic substrates
Journal of the Mechanics and Physics of Solids
44
9
1411-1428
1996
10.1016/0022-5096(96)00042-7
Thin bonded films have many applications. In information storage and processing systems, for example, conducting, semiconducting and insulating films are used in integrated circuits, and thin magnetic films are used in disk storage systems. In many cases, thin bonded films an in a state of residual tension, which can lead to film cracking. Because cracking can alter desired film properties, methods for predicting it are needed. The geometry considered in this work is one in which cracks or flaws oriented normal to the film-substrate interface propagate (or ''channel'') across the film. It is assumed that the film is brittle and the substrate is ductile. Plane strain fracture analyses are used to investigate the channel cracking of elastic thin films in residual tension in the presence of yielding in the substrate material. Although crack channeling induces yielding in the substrate, channel crack extension in the brittle film occurs under small scale yielding conditions. The case of an elastic film bonded to an elastic substrate has been considered in earlier work, and is used as the basis for the current study. A numerical model is used to extend the results from the fully elastic problem so that plastic yielding of the substrate is allowed. Results are presented for an elastic-perfectly plastic substrate and for substrates exhibiting strain hardening. A simple shear lag model of the problem without hardening in the substrate is discussed, which gives reasonable predictions for the dependence of dimensionless fracture quantities on the normalized loading over a wide range of material mismatches. In addition, a method is presented by which shear lag modeling can be extended to cases in which the substrate exhibits strain hardening. Copyright (C) 1996 Elsevier Science Ltd
Lecture Notes in Statistical Mechanics and Mesoscopics
arXiv preprint
121
2011
arXiv:quant-ph/0605180v4
These are the lecture notes for quantum and statistical mechanics courses that are given by DC at Ben-Gurion University. They are complementary to "Lecture Notes in Quantum Mechanics" [arXiv: quant-ph/0605180]. Some additional topics are covered, including: introduction to master equations; non-equilibrium processes; fluctuation theorems; linear response theory; adiabatic transport; the Kubo formalism; and the scattering approach to mesoscopics.
Carbon nanomembranes (CNMs) supported by polymer: mechanics and gas permeation.
Advanced materials (Deerfield Beach, Fla.)
26
21
3421-6
2014
10.1002/adma.201304536
Gas permeation characteristics of carbon nanomembranes (CNMs) from self-assembled monolayers are reported for the first time. The assembly of CNMs onto polydimethylsiloxane (PDMS) support membranes allows mechanical measurements under compression as well as determination of gas permeation characteristics. The results suggest that molecular-sized channels in CNMs dominate the permeation properties of the 1 nm thin CNMs.
Fatigue-crack growth properties of thin-walled superelastic austenitic Nitinol tube for endovascular stents
Journal of biomedical materials research. Part A
81A
3
685-691
2007
10.1002/jbm.a.31100
Over the past 10 years, the supereleastic nickel– titanium alloy Nitinol has found widespread application in the manufacture of small-scale biomedical devices, such as self-expanding endovascular stents. Although conventional stress/strain-life (S/N) analyses are invariably used as the primary method for design against fatigue loading and for predicting safe lifetimes, fracture mechanics-based meth- odologies provide a vital means of assessing the quantita- tive effect of defects on such lifetimes. Unfortunately, frac- ture mechanics studies on fatigue in Nitinol are scarce, and most results do not pertain to the (thin-walled tube) product forms that are typically used in the manufacture of endovascular stents. In the current work, we document the basic fatigue-crack growth properties of flattened thin- walled (?400 mm thick) Nitinol tubing in a 378C air envi- ronment. Crack-growth behavior is characterized over a wide range of growth rates (?6 orders of magnitude) and load ratios, that is, as a function of the alternating and maximum stress intensities, at 50 Hz. Limited experiments at both 5 and 50 Hz were also performed in 378C air and simulated body fluid to determine whether the cyclic fre- quency affects the fatigue behavior. Fatigue-crack growth- rate properties in such thin-walled Nitinol tube are found to be quite distinct from limited published data on other (mainly bulk) product forms of Nitinol, for example, bar and strip, both in terms of the relative fatigue thresholds and the variation in steady-state growth rates
crack growth; fatigue; fre-; load ratio effects; nitinol; quency effects; stents
Theory and Modeling of thin film flows
Encyclopedia of Surface and Colloid Science
5283-5297
2002
10.1081/E-ESCS-120000885
Thin liquid films are ubiquitous in nature and technology so an understanding of their mechanics is important in many applications. A typical thin film flow consists of an expanse of liquid partially bounded by a solid substrate with a (free) surface where the liquid is exposed to another fluid (usually a gas and most often air in applications). Typically, the thickness, H, in one direction is much smaller than the characteristic length scale, L, in the other directions and the flow takes place predominantly in the direction of one of the longer dimensions under the action of an external forcing (e.g., gravity, surface tension gradients, a rotating substrate). A simple and obvious example is the flow of a (thin) raindrop down a windowpane under the action of gravity. Typically, the flow velocity in directions perpendicular to the substrate (i.e., the window-pane) is much smaller than the main flow velocity along the windowpane. The most correct approach to modeling such flows is via the macroscopic momentum equation (e.g., the Stokes or Navier Stokes equations in the case of a Newtonian liquid) and this approach invariably involves detailed numerical computation e.g., Refs.1, 2. The approach taken here will be to exploit the existence of the small aspect ratio (? H/L) to expand the momentum equations in a perturbation series in powers of ?. In doing so we will be developing a so-called thin film or long wave approximation3 with the advantage that analytic solutions will often be possible and where this is not feasible, the reduced numerical problem will be greatly simplified.4 The approximation has much in common with classical lubrication theory5, 6 and is thus also referred to as the lubrication approximation. The success of this approximation is well documented in the literature and a feature of this success is its robustness9 and a tendency for it to deliver good results (in agreement with experiment) in parameter regimes on the outer limits of the expected range of validity or beyond. From a mathematical point of view, a typical complication associated with thin film flows is the fact that the free surface of the liquid is initially unknown and must be determined as part of the solution. In many practical thin film models surface tension plays a significant role.10 Even when formally small, surface tension often has a significant smoothing effect preventing the formation of shocks (sharp jumps in the film thickness). Mathematical models will be given here for flows on flat and curved surfaces including other effects such as gravity, compositional changes, and substrate energetics. Application areas include flow behavior of paints and other surface coatings, chemical, and nuclear reactor design, agrochemical applications, as well as several biofluid applications including thin films on the cornea and in the lungs. Asymptotic derivations of lubrication theory for 2-D problems with a free surface are given by Benney3 without surface tension and by Atherton and Homsy7 where surface tension is included. The thin film approximation can also be applied to non-Newtonian flows and there are many examples in the literature, e.g., Ref.8. This article is organized as follows: In The Idea Behind The Thin Film Approximation we discuss a particular (simple) problem to show how the thin film approximation is applied. Then we will discuss variations on the standard problem and more complicated situations. We then sketch a number of relevant examples in Examples Using Thin Film Models before making some closing remarks.
Measurement in fluid mechanics
Choice: Current Reviews for Academic Libraries
43
9
1633
2006
10.2277/ 0521815185
Reviews the book "Measurement in Fluid Mechanics," by Stavros Tavoularis.
BOOKS -- Reviews; MEASUREMENT in Fluid Mechanics (Book); NONFICTION; TAVOULARIS, Stavros
Orbital Mechanics for Engineering Students
Orbital Mechanics for Engineering Students
367-404
2014
10.1016/B978-0-08-097747-8.00007-4
Up to now, we have mostly referenced the motion of orbiting objects to a nonrotating coordinate system fixed to the center of attraction (e.g., the center of the earth). This platform served as an inertial frame of reference, in which Newton's second law can be written as Fnet=maabsolute.
Angular acceleration of comoving frame; Angular velocity of comoving frame; Clohessy–Wiltshire equations; Clohessy–Wiltshire matrices; LVLH frame; r-bar; Relative acceleration in the comoving frame; Relative acceleration in the inertial frame; Two-impulse rendezvous
Introductory Quantum Mechanics
Science
90
2340
420-422
1939
10.1126/science.90.2340.420-a
Careful and detailed explanations of challenging concepts, and comprehensive and up-to-date coverage in this best-selling quantum mechanics book, continue to set the standard in physics education. In this new edition, a new chapter on the revolutionary topic of of quantum computing (not currently covered in any other book at this level) and thorough updates to the rest of the book bring it up to date. For anyone interested physics or quantum mechanics.
A model to predict the through-thickness distribution of heat generation in cross-ply carbon-fiber composites subjected to alternating magnetic fields
Composites Science and Technology
55
119-130
1995
10.1016/0266-3538(95)80024-7
A theory of local and global mechanisms of heat generation and distribution in carbon-fiber-based composites subjected to an alternating magnetic field has been proposed. A model is developed which predicts the strength and distribution of thermal generation through the thickness of carbon-fiber-based laminated composites. Earlier work established the distribution of point voltages in the plane of the laminate which exist in the form of potential differences between fibers in adjacent plies in a cross-ply or angle-ply laminate system. In the present work, a capacitive layer microstructure is formulated which models the actual fiber-reinforced-polymer microstructure from a square-packing assumption to a series of conductive parallel plates. From this capacitive layer analogy, an effective parameter of heating, γ, is defined which establishes the distribution of heating through the thickness. Extreme gradients in this thermal source can exist with peaks occurring at the interfaces of ply/ply orientation changes. An optimization study establishes the effect of various micro- and macrostructural parameters on the parameter γ. Several parametric studies are performed on a computer algorithm which calculates γ to further analyze these effects.
alternating magnetic field; carbon-fiber composites; heat generation
A methodology for determining mechanical properties of freestanding thin films and MEMS materials
Journal of the Mechanics and Physics of Solids
51
1
47-67
2003
10.1016/s0022-5096(02)00062-5
We have developed a novel chip-level membrane deflection experiment particularly suited for the investigation of sub-micron thin films and microelectro-mechanical systems. The experiment consists of loading a fixed-fixed membrane with a line load applied at the middle of the span using a nanoindenter. A Mirau microscope interferometer is positioned below the membrane to observe its response in real time. This is accomplished through a micromachined wafer containing a window that exposes the bottom surface of the specimen. A combined atomic force microscope/nanoindenter incorporates the interferometer to allow continuous monitoring of the membrane deflection during both loading and unloading. As the nanoindenter engages and deflects the sample downward, fringes are formed and acquired by means of a CCD camera. Digital monochromatic images are obtained and stored at periodic intervals of time to map the strain field. Stresses and strains are computed independently without recourse to mathematical assumptions or numerical calibrations. Additionally, no restrictions on the material behavior are imposed in the interpretation of the data. In fact, inelastic mechanisms including strain gradient plasticity, piezo and shape memory effects can be characterized by this technique. The test methodology, data acquisition and reduction are illustrated by investigating the response of 1-mum thick gold membranes. A Young's modulus of 53 GPa, a yield stress of 55 MPa and a residual stress of 12 MPa are consistently measured. The post-yield behavior leading to fracture exhibits typical statistical variations associated to plasticity and microcrack initiation. (C) 2002 Elsevier Science Ltd. All rights reserved.
creep; gold; mechanical properties; MEMS materials; micro-tensile test; modulus; polysilicon; stress; thin films
Quantitative damage detection in cross-ply laminates using Lamb wave method
Composites Science and Technology
63
10
1473-1479
2003
10.1016/S0266-3538(03)00163-5
This paper investigates the effects of transverse cracking and delamination on the S 0 mode velocity in GFRP and CFRP cross-ply laminates. We found experimentally that both the stiffness and the velocity decreased as the transverse crack density increased. In contrast, the stiffness decreased but the velocity increased as the delamination length increased. We analytically deduced the relationship between the velocity and the crack density from a combination of a shear-lag analysis and the classical plate theory. We also confirmed that the Lamb wave propagated through the 0?? layers in the delaminated regions, and formulized the relationship between the velocity and the delamination length. The predicted crack density and delamination length using the measured velocity were in good agreement with the experimental results. This method is simple and promising for structural health monitoring of composite structures. ?? 2003 Elsevier Science Ltd. All rights reserved.
A. Polymer matrix-composites (PMCs); C. Delamination; C. Transverse cracking; D. Non-destructive testing; D. Ultrasonics
High strain rate properties of balanced angle-ply graphite/epoxy composites
Composites Part B: Engineering
34
4
339-346
2003
10.1016/S1359-8368(03)00003-9
The vast differences in strength, ultimate strain and modulus during high strain rate deformation of materials have been a very long-standing subject of engineering interest. The present study is carried out in order to understand the effect of fiber orientations on compressive dynamic properties of balanced angle-ply IM7/8551-7 graphite/epoxy composites using the Split Hopkinson Pressure Bar at varying strain rates, ranging from 500 to 1500s-1. The ultimate stress-strain behavior with respect to change in strain rates for various fiber orientations has been studied in depth. Additionally, optical microscopic images of fracture surfaces show that delamination caused by edge effects is the prominent mechanism of failure. This research provides important data and understanding of composite material structures in high strain rate applications. ?? 2003 Elsevier Science Ltd. All rights reserved.
A. Polymer-matrix composites; B. Impact behavior; D. Optical microscopy; Split Hopkinson Pressure Bar
The micro-mechanics of cortical shell removal in the human vertebral body
Computer Methods in Applied Mechanics and Engineering
196
3025-3032
2007
10.1016/j.cma.2006.06.017
An improved understanding of the biomechanical role of the vertebral cortical shell with respect to the trabecular bone may improve diagnosis of osteoporosis and provide insight into the effects of disease, aging, and drug treatments. In this study, we present results from finite element simulations of removal of the shell from the vertebral body and the associated mechanical effects in terms of overall change in vertebral structural stiffness and of the tissue-level stresses. Specimen-specific micro-mechanical finite element models of thirteen vertebrae were generated from micro-CT scans with 60-??m voxel size. An algorithm was developed to automatically isolate the thin (and discontinuous) shell and the images were converted into finite element models by mapping each image voxel into a finite element. After removal of the endplates, compressive loading conditions were applied and linear elastic analyses were run for three cases - with and without the shell, and shell-only models. The models contained up to 13.6 million elements and were solved using a maximum of 144 CPUs in parallel, 300 GB memory, and a custom code with a parallel mesh partitioner and algebraic multigrid solver. Results indicated that the shell was on average, 0.38 ?? 0.06 mm thick, accounted for 21-39% of the overall bone mass, but accounted for 38-68% of the overall vertebral stiffness. Examination of the tissue-level stresses indicated that this disproportionately large mechanical effect of shell removal was due in part to unloading of the remaining peripheral trabeculae adjacent to the shell. Stress paths were also preferentially within vertically-aligned bone: the cortical shell and vertically-aligned trabeculae. Taken together, these results demonstrate two important roles of the thin vertebral cortical shell: it can carry significant load by virtue of representing a large proportion of the vertically-aligned bone tissue within the vertebra, and, as a shell, it also maximizes the load carrying capacity of the trabecular centrum, particularly around the periphery. ?? 2007 Elsevier B.V. All rights reserved.
Cortical shell; Finite element analysis; Micro-mechanics; Spine biomechanics; Trabecular bone; Vertebral body
Investigation of Buckling Deformation of Thin Plate Welded Structures
Proceeding of 21st International Society of Ocean and Polar Engineering
125-31
2011
Buckling produced during the assembly process is the most critical mode of welding deformation for the thin plate welded structures. In this study, the behavior of buckling deformation has been investigated utilizing computational welding mechanics. The computational approach consists of two steps; a 3D Thermal-Elastic-Plastic FEA to evaluate inherent deformation, and an elastic analysis based on the Inherent Strain/Deformation Method. Based on the computational results, the phenomenon of buckling deformation can be clearly explained. Using the same method, the line heating process is simulated to control and reduce the welding-induced buckling deformation. Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE).
buckling deformation; elastic analysis; fea; inherent deformation; large deformation theory; thin plate welded structure
An Introduction to Mechanics
Physical Review
65
564
2014
10.1103/PhysRevLett.65.247
Height-height correlations for self-affine surfaces with finite horizontal cutoffs are generally modeled by exponential forms. Three mathematically acceptable, alternate forms for the height-height correlation function are investigated, to explore their impact on the analysis of diffuse x-ray-reflectivity data. The appropriateness of these functions to actual physical samples is explored through comparison with x-ray-reflectivity and scanning-tunneling-microscopy data recorded on known self-affine surfaces.
Axi-symmetric contact on thin compliant coatings
Journal of the Mechanics and Physics of Solids
1981
10.1016/0022-5096(81)90018-1
presents a theory for the indentation of a soft thin coating by a rigid body. The coating is assumed to be bonded to a rigid substrate and to behave linearly elastically. A simplifying approximation enables the stresses within the coating, averaged through its thickness, to be determined for particular indenter profiles. The results are shown to be sensitive to the thickness and compressibility of the coating material. Unlike much previous work, the results can be expressed analytically for certain indenter profiles and have been substantiated by experiment. The theory has many useful applications, in particular for situations where the layer acts as a protective coating and for the accurate, in situ and non-destructive measurement of the elastic modulus of the coating material.
Equilibrium mechanics of monolayered epithelium
Journal of Theoretical Biology
260
3
333-339
2009
10.1016/j.jtbi.2009.06.021
In order to fully understand the epithelial mechanics it is essential to integrate different levels of epithelial organization. In this work, we propose a theoretical approach for connecting the macroscopic mechanical properties of a monolayered epithelium to the mechanical properties at the cellular level. The analysis is based on the established mechanical models-at the macroscopic scale the epithelium is described within the mechanics of thin layers, while the cellular level is modeled in terms of the cellular surface (cortical) tension and the intercellular adhesion. The macroscopic elastic energy of the epithelium is linked to the energy of an average epithelial cell. The epithelial equilibrium state is determined by energy minimization and the macroscopic elastic moduli are calculated from deformations around the equilibrium. The results indicate that the epithelial equilibrium state is defined by the ratio between the adhesion strength and the cellular surface tension. The lower and the upper bounds for this ratio are estimated. If the ratio is small, the epithelium is cuboidal, if it is large, the epithelium becomes columnar. Importantly, it is found that the cellular cortical tension and the intercellular adhesion alone cannot produce the flattened squamous epithelium. Any difference in the surface tension between the apical and basal cellular sides bends the epithelium towards the side with the larger surface tension. Interestingly, the analysis shows that the epithelial area expansivity modulus and the shear modulus depend only on the cellular surface tension and not on the intercellular adhesion. The results are presented in a general analytical form, and are thus applicable to a variety of monolayered epithelia, without relying on the specifics of numerical finite-element methods. In addition, by using the standard theoretical tools for multi-laminar systems, the results can be applied to epithelia consisting of layers with different mechanical properties. © 2009 Elsevier Ltd. All rights reserved.
Adhesion; Bending; Cellular mechanics; Cellular surface tension; Columnar epithelium; Cuboidal epithelium; Squamous epithelium
A comparative analysis of numerical approaches to the mechanics of elastic sheets
Journal of the Mechanics and Physics of Solids
79
92-107
2015
10.1016/j.jmps.2015.04.009
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrink- ling. Determining the location, structure, and evolution of wrinkles in these problems has important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently pro- posed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solu- tions are compared to analytic predictions of the ground state, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches produce local minima that are highly sensitive to initial im- perfections, relying on a priori knowledge of the equilibriumwrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial im- perfections and can generate low-energy solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand.
Dynamic relaxation; Finite element method; Thin elastic sheets; Wrinkling
Fluid Mechanics of Planktonic Microorganisms
Annual Review of Fluid Mechanics
44
1
373-400
2012
10.1146/annurev-fluid-120710-101156
The diversity of the morphologies, propulsion mechanisms, flow environments, and behaviors of planktonic microorganisms has long provided inspiration for fluid physicists, with further intrigue provided by the counterintuitive hydrodynamics of their viscous world. ... \n
Spontaneous instability of soft thin films on curved substrates due to van der Waals interaction
Journal of the Mechanics and Physics of Solids
59
3
610-624
2011
10.1016/j.jmps.2010.12.009
The linear bifurcation theory is used to investigate the stability of soft thin films bonded to curved substrates. It is found that such a film can spontaneously lose its stability due to van der Waals or electrostatic interaction when its thickness reduces to the order of microns or nanometers. We first present the generic method for analyzing the surface stability of a thin film interacting with the substrate and then discuss several important geometric configurations with either a positive or negative mean curvature. The critical conditions for the onset of spontaneous instability in these representative examples are established analytically. Besides the surface energy and Poisson's ratio of the thin film, the curvature of the substrate is demonstrated to have a significant influence on the wrinkling behavior of the film. The results suggest that one may fabricate nanopatterns or enhance the surface stability of soft thin films on curved solid surfaces by modulating the mechanical properties of the films and/or such geometrical properties as film thickness and substrate curvature. This study can also help to understand various phenomena associated with surface instability.
Soft matter; Surface effect; Surface instability; Thin film; Van der Waals force
Mechanics of Unsaturated Geomaterials
Mechanics of Unsaturated Geomaterials
1-28
2013
10.1002/9781118616871
This chapter contains sections titled: Introduction Stress states Thermo-hydro-mechanical behavior of unsaturated soils Effective stress in unsaturated soils A coupled THM constitutive framework for unsaturated soils Conclusion Bibliography
Modelling and testing of the snap-through process of bi-stable cross-ply composites
Composite Structures
120
41-52
2015
10.1016/j.compstruct.2014.09.064
Bi-stable response of cross-ply composites is modelled when snap processes are trigged by a vertical force and the laminate is supported at four points. The model is based on the Rayleigh–Ritz technique. Non-linear von Kármán strains, non-uniform curvatures and uniform through-the-thickness normal strain are included in the analysis. The analysis has been carried out step by step, by small increments of the applied load. Experiments in four [0/90]T carbon/epoxy laminates have been carried out for comparison in a test configuration that fulfils the requirements of the model. The multi-event snap-through and intermediate equilibrium positions have been experimentally observed and recorded. The initial snap-through and snap-back load–displacement curves have been experimentally determined and compared to those corresponding to the proposed model.
Bi-stable composites; Cross-ply; Mechanical testing; Rayleigh–Ritz; Snap process
Free edge stress analysis of general cross-ply composite laminates under extension and thermal loading
Composite Structures
60
91-103
2003
10.1016/S0263-8223(02)00290-8
An elasticity formulation for finite general cross-ply (symmetric and unsymmetric) laminates subjected to extension and/or a layerwise temperature distribution is developed. It is shown that the edge-effect problem of such laminates is actually a quasi-threedimensional problem and its stress analysis can be restricted to a generic two-dimensional cross-section of the laminates. A layerwise theory is used to investigate analytically the interlaminar stresses near the free edges of general cross-ply composite laminates. The results obtained from this theory are compared with those available in the literature. It is found that the theory can predict very accurately the stresses in the interior region and near the free edges of composite laminates. ?? 2002 Elsevier Science Ltd. All rights reserved.
Composite laminates; Elasticity formulation; Extension; Free edge stresses; Layerwise theory; Thermal loading
The onset of delamination at stress-free edges in angle-ply laminates—analysis of two criteria
Composites Science and Technology
61
0-5
2001
10.1016/S0266-3538(00)00105-6
Prediction of delamination onset in View the MathML source angle-ply carbon-fiber/epoxy-resin laminates is proposed by means of two approaches. Both are based on a preliminary analysis of the boundary effects. In the first, more classical, case, an ‘average stress’ criterion retaining only the interface shear component of the stress field is used. Layer-thickness influence is taken into account to estimate the averaging length. The second case takes advantage of the stress concentrations caused by singularities to put to work an incremental Griffith-like criterion. Initiation is considered to be a locally unstable process. It requires us to account for the existence of surface flaws to explain the influence of layer thickness on the critical delamination stress
1; 10 y 20 y; 30; æ; and; b; been performed for di; c; ects; erent lay-ups; failure criterion; fracture; interface; introduction ð boundary e; laminate; laminates; s specimens have; tension tests on angle-ply
Study of induced ultrasonic deviation for the detection and identification of ply waviness in carbon fibre reinforced polymer
NDT & E International
56
1-9
2013
10.1016/j.ndteint.2013.02.001
Ply waviness is a major defect, which can appear in certain composite materials such as CFRP. Attenuation and ultrasound velocity measurements allow the detection, but not the identification, of ply waviness. In the present study it is shown that in order to identify this ply waviness, it is important to take the deviation of the ultrasonic beam into account. Two different methods allowing such deviations to be detected are proposed. On the one hand, the deviation produces an asymmetrical behaviour in the responses obtained at oblique incidence angles. This phenomenon is revealed through the study of incidence angle ranges, which can normally be superimposed. On the other hand, the double scanning technique allows the deviation of the energy maxima of the transmitted acoustic field to be determined. In both cases, the study of induced deviation reveals that it is sensitive to the presence of ply waviness. These methods have been experimentally validated and their potential use, depending on the thickness of the component, is discussed.
CFRP; Double scanning; NDT; Ply waviness; Ultrasonic deviation
Applied Soil Mechanics: with ABAQUS Applications. Sam
Applied Soil Mechanics: With ABAQUS Applications
398
2007
10.1002/9780470168097
A simplified approach to applying the Finite Element Method to geotechnical problems Predicting soil behavior by constitutive equations that are based on experimental findings and embodied in numerical methods, such as the finite element method, is a significant aspect of soil mechanics. Engineers are able to solve a wide range of geotechnical engineering problems, especially inherently complex ones that resist traditional analysis. Applied Soil Mechanics with ABAQUS® Applications provides civil engineering students and practitioners with a simple, basic introduction to applying the finite element method to soil mechanics problems. Accessible to someone with little background in soil mechanics and finite element analysis, Applied Soil Mechanics with ABAQUS® Applications explains the basic concepts of soil mechanics and then prepares the reader for solving geotechnical engineering problems using both traditional engineering solutions and the more versatile, finite element solutions. Topics covered include: Properties of Soil Elasticity and Plasticity Stresses in Soil Consolidation Shear Strength of Soil Shallow Foundations Lateral Earth Pressure and Retaining Walls Piles and Pile Groups Seepage Taking a unique approach, the author describes the general soil mechanics for each topic, shows traditional applications of these principles with longhand solutions, and then presents finite element solutions for the same applications, comparing both. The book is prepared with ABAQUS® software applications to enable a range of readers to experiment firsthand with the principles described in the book (the software application files are available under "student resources" at www.wiley.com/college/helwany). By presenting both the traditional solutions alongside the FEM solutions, Applied Soil Mechanics with ABAQUS® Applications is an ideal introduction to traditional soil mechanics and a guide to alternative solutions and emergent methods. Dr. Helwany also has an online course based on the book available at www.geomilwaukee.com.
Degenerative mechanics of the lumbar spine
Spine Journal
4
6 SUPPL.
202-208
2004
10.1016/j.spinee.2004.07.013
This paper reviews both the normal biomechanical behavior of the lumbar motion segment and changes in that behavior with disc degeneration. Each level of the spine consists of a disc anteriorly and two facet joints posteriorly. A complex ligamentous structure also contributes to the mechanics of the spine. Degenerative changes include intervertebral disc (nuclear) degeneration, facet joint osteoarthritis, vertebral body degeneration, and ligament degeneration. The goal of this review is to discuss the effect of disc degeneration on the biomechanical behavior of the spine, specifically the load-bearing and kinematic behavior after degeneration. ?? 2004 Elsevier Inc. All rights reserved.
Degeneration; Kinematics; Load bearing; Lumbar; Mechanics
Depth-sensing indentation modeling for determination of Elastic modulus of thin films
Mechanics of Materials
42
2
166-174
2010
10.1016/j.mechmat.2009.11.016
There are various methods to address the problem of determining the hardness of thin films when the substrate is involved in the deformation process produced during conventional indentation tests. For the determination of the elastic modulus using depth-sensing indentation methods, the problem is more complex due to the deformation of the equipment that comes in addition to the effect of the substrate. In the paper we discuss the use of Oliver and Pharr’s method to take into account the deformation of the equipment for the measurement of the elastic modulus of TiCN thin films. For micro-indentation tests we proposed a new model to precise the effect of the substrate. The elastic moduli that are calculated are in very good agreement to those found in literature. For nano-indentation tests it is necessary to correct the data to take into account the shape of the indenter tip. We show that this correction, proposed at the origin for massive materials, is not able to explain the discrepancies between the calculated values and those coming from the literature for the elastic modulus of thin films.
Analytical solutions using a higher-order refined theory for the static analysis of antisymmetric angle-ply composite and sandwich plates
Composite Structures
64
3-4
405-417
2004
10.1016/j.compstruct.2003.09.042
Analytical formulations and solutions to the static analysis of simply supported anti-symmetric angle-ply composite and sandwich plates hitherto not reported in the literature based on a higher-order refined theory already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations, which account for the effect of transverse shear deformation and a non-linear variation of in-plane displacements with respect to the thickness coordinate. The transverse displacement is assumed to be constant throughout the thickness. The equations of equilibrium are obtained using principle of minimum potential energy. Solutions are obtained in closed form using Navier's technique by solving the boundary value problem. Accuracy of the theoretical formulations and the solution method is first ascertained by comparing the results with that already reported in the literature. After establishing the accuracy of the solutions, numerical results with real properties are presented for the multilayer antisymmetric angle-ply composite and sandwich plates, which will serve as a benchmark for future investigations.
Analytical solutions; Angle-ply plates; Higher-order theory; Shear deformation; Static analysis
The role of mechanics during brain development.
Journal of the mechanics and physics of solids
72
75-92
2014
10.1016/j.jmps.2014.07.010
Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated to neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms of cortical folding. Here we identify the role of the key anatomic players during the folding process: cortical thickness, stiffness, and growth. To establish estimates for the critical time, pressure, and the wavelength at the onset of folding, we derive an analytical model using the Föppl-von-Kármán theory. Analytical modeling provides a quick first insight into the critical conditions at the onset of folding, yet it fails to predict the evolution of complex instability patterns in the post-critical regime. To predict realistic surface morphologies, we establish a computational model using the continuum theory of finite growth. Computational modeling not only confirms our analytical estimates, but is also capable of predicting the formation of complex surface morphologies with asymmetric patterns and secondary folds. Taken together, our analytical and computational models explain why larger mammalian brains tend to be more convoluted than smaller brains. Both models provide mechanistic interpretations of the classical malformations of lissencephaly and polymicrogyria. Understanding the process of cortical folding in the mammalian brain has direct implications on the diagnostics of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.
Brain development; Cortical folding; Growth; Instabilities; Thin films
Modeling interlamellar interactions in angle-ply biologic laminates for annulus fibrosus tissue engineering
Biomechanics and Modeling in Mechanobiology
10
973-984
2011
10.1007/s10237-011-0288-0
Mechanical function of the annulus fibrosus of the intervertebral disc is dictated by the composition and microstructure of its highly ordered extracellular matrix. Recent work on engineered angle-ply laminates formed from mesenchymal stem cell (MSC)-seeded nanofibrous scaffolds indicates that the organization of collagen fibers into planes of alternating alignment may play an important role in annulus fibrosus tissue function. Specifically, these engineered tissues can resist tensile deformation through shearing of the interlamellar matrix as layers of collagen differentially reorient under load. In the present work, a hyperelastic constitutive model was developed to describe the role of interlamellar shearing in reinforcing the tensile response of biologic laminates, and was applied to experimental results from engineered annulus constructs formed from MSC-seeded nanofibrous scaffolds. By applying the constitutive model to uniaxial tensile stress-strain data for bilayers with three different fiber orientations, material parameters were generated that characterize the contributions of extrafibrillar matrix, fibers, and interlamellar shearing interactions. By 10 weeks of in vitro culture, interlamellar shearing accounted for nearly 50% of the total stress associated with uniaxial extension in the anatomic range of ply angle. The model successfully captured changes in function with extracellular matrix deposition through variations in the magnitude of model parameters with culture duration. This work illustrates the value of engineered tissues as tools to further our understanding of structure-function relations in native tissues and as a test-bed for the development of constitutive models to describe them.
Hyperelastic model; Intervertebral disc; Mesenchymal stem cells; Nanofibers; Structure-function
Interaction of combined loads on the lateral stability of thin-walled composite beams
Engineering Structures
32
11
3516-3527
2010
10.1016/j.engstruct.2010.07.020
Based on a seven-degree-of-freedom shear deformable beam model, analytical solutions are derived for the lateral stability analysis of cross-ply laminated thin-walled beams subjected to combined axial and bending loads. The model includes shear deformability in a full form, i.e. shear flexibility due to both bending and nonuniform warping is considered. The theory is formulated in the context of large displacements and rotations, considering moderate bending rotations and large twist. Composite is assumed to be made of symmetric balanced laminates and especially orthotropic laminates. The closed-form analytic expressions obtained in this paper are valid for simply supported bisymmetric beams. These fundamental solutions explicitly identify the influence of geometric nonlinear effects due to the prebuckling deformation. The numerical results are compared with the bifurcation loads of the postbuckling response. In addition, the effects of the variation of load height parameter and fiber angle orientation are investigated. © 2010 Elsevier Ltd.
Buckling; Composite material; Postbuckling; Prebuckling deformation; Shear flexibility; Thin-walled beams
Canonical transformations in quantum mechanics
Annals of Physics
331
70-96
2013
10.1016/j.aop.2012.12.006
This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when passing to a new coordinate system, observables and states transform as in classical mechanics, i.e., by composing them with a transformation of coordinates. Then the developed formalism of coordinate transformations is transferred to a standard formulation of quantum mechanics. In addition, the developed theory is illustrated on examples of particular classes of quantum canonical transformations. © 2012 Elsevier Inc.
Canonical transformations; Deformation quantization; Moyal product; Phase space; Quantum mechanics
Mechanics of materials: top-down approaches to fracture
Acta Materialia
48
1
125-135
2000
10.1016/s1359-6454(99)00291-8
The utility and robustness of the mechanics of materials is illustrated through a review of several recent applications to fracture phenomena, including adhesive failures, the role of plasticity in enhancing toughness in films and multilayers, and crack growth resistance in ductile structural alloys. The commonalty among the approaches rests in a reliance on experiments to provide calibration of the failure process at the smallest scale.
Fracture and fracture toughness; Mechanical properties; Mechanics of materials; Plastic properties
A pressure vessel fracture mechanics study of the aluminum beverage can
Engineering Fracture Mechanics
65
5
525-539
2000
10.1016/S0013-7944(99)00144-7
Two fracture mechanics studies were conducted using two different aluminum beverage containers (wall thicknesses of 0.0044 in. [0.112 mm] and 0.0039 in. [0.099 mm]). The first study involved a 1.25 in. (31.75 mm) wide center-cracked panel specimen to measure the axial fracture resistance of the containers. Factors contributing to beverage container fracture resistance are discussed, including the thickness and rolling direction orientation. Due to the extremely thin nature of these containers, a reduced specimen thickness leads to a reduced fracture resistance. This resistance is also seen to increase as the orientation to the material rolling direction becomes perpendicular. The second study was a full-scale, leak-before-break rupture test. Each container had a crack of a known length and depth machined in the exterior wall. The stress intensity factor of these cracks upon failure gives excellent correlation to the center-cracked panel specimens as well as to other models for predicting pressure vessel rupture.
Aluminum beverage container; Fracture mechanics; Leak-before-break; Pressure vessel; Product performance; Thin wall
Soil Mechanics and Foundations
Soil Mechanics and Foundations
697-699
2010
10.1061/(ASCE)HE.1943-5584
The semaphorin family contains secreted and transmembrane signaling proteins that function in the nervous, immune, and cardiovascular systems. Chick collapsin-1 is a repellent for specific growth cones. Two other secreted members of the semaphorin family, collapsin-2 and -3, are structurally similar to collapsin-1 but have different biological activities. Semaphorins contain a 500 amino acid family signature semaphorin domain. We show in this study that (1) the semaphorin domain of collapsin-1 is both necessary and sufficient for biological activity, (2) the semaphorin domain contains a 70 amino acid region that specifies the biological activity of the three family members, and (3) the positively charged carboxy terminus potentiates activity without affecting specificity. We propose that semaphorins interact with their receptors through two independent binding sites: one that mediates the biological response and one that potentiates it.
Fractals In Fluid Mechanics
Annual Review of Fluid Mechanics
20
1
5-16
1988
10.1146/annurev.fluid.20.1.5
Definition of a fractal distribution, perimeter relations, probability, relation to time series, chaos, strange attractors, turbulence, scale invariance.
Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up
Composites Engineering
4
4
429-444
1994
10.1016/S0961-9526(09)80016-6
A refined formulation of an approach suitable for three-dimensional vibration analyses of homogeneous and cross-ply laminated cylinders and cylindrical panels (Soldatos and Hadjigeorgiou, 1990, J. Sound. Vibr. 137, 369–384) is presented. Based on a recursive rather than a successive approximation formula, the present refined formulation always makes use of a 6 × 6 frequency determinant, regardless of the number of layers of the laminated shell or panel considered. Upon comparing its results with corresponding numerical results available in the literature, the effectiveness of the approach in producing the exact frequencies of vibration is checked. Moreover, further detailed numerical results dealing with flexural vibration frequencies and corresponding mode shapes of laminated cylinders and cylindrical panels having symmetric or regular antisymmetric cross-ply lay-up are presented, studied and discussed.
Shear strain distribution in PRF and PUR bonded 3-ply wood sheets by means of electronic laser speckle interferometry
Wood Science and Technology
40
5
351-357
2006
10.1007/s00226-005-0051-8
The distribution of shear strain across a 3-ply wood sheet bonded with PRF and PUR, respectively, was measured by means of electronic laser speckle interferometry. Owing to the higher shear modulus of PRF compared to PUR, shear strains were more evenly distributed in PRF bonded specimens than in PUR bonded specimens. However, considering the different shear moduli of earlywood and latewood bands in the core layer of the 3-ply sheet, it is concluded that shear stress is distributed more evenly along PUR bond lines compared to PRF bond lines. Since it is less prone to stress concentrations, PUR should provide more durable adhesive connections than stiff adhesives such as PRF.
The mechanics behind plant development
New Phytologist
185
2
369-385
2010
10.1111/j.1469-8137.2009.03100.x
Morphogenesis in living organisms relies on the integration of both biochemical and mechanical signals. During the last decade, attention has been mainly focused on the role of biochemical signals in patterning and morphogenesis, leaving the contribution of mechanics largely unexplored. Fortunately, the development of new tools and approaches has made it possible to re-examine these processes. In plants, shape is defined by two local variables: growth rate and growth direction. At the level of the cell, these variables depend on both the cell wall and turgor pressure. Multidisciplinary approaches have been used to understand how these cellular processes are integrated in the growing tissues. These include quantitative live imaging to measure growth rate and direction in tissues with cellular resolution. In parallel, stress patterns have been artificially modified and their impact on strain and cell behavior been analysed. Importantly, computational models based on analogies with continuum mechanics systems have been useful in interpreting the results. In this review, we will discuss these issues focusing on the shoot apical meristem, a population of stem cells that is responsible for the initiation of the aerial organs of the plant.
Effect of transverse cracks on the elastic properties of high temperature angle-ply laminated composites
Computational Materials Science
37
4
470-475
2006
http://dx.doi.org/10.1016/j.commatsci.2005.11.006
The development of transverse cracks can be detrimental to the stiffness and dimensional stability of composite laminates. In this investigation, a modified shear lag analysis, taking into account the concept of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in high temperature angle-ply laminated composites. The results present well the effect of high temperature and the fibre orientation of the outer layers on the degradation of mechanical properties of the angle-ply polymer composite laminates.
Angle-ply laminates; High-temperature properties; Polymer–matrix composites; Shear-lag model; Transverse cracks
Application of fracture mechanics to crack growth in rubber-cord laminates
Rubber chemistry and technology
74
3
509-524
2001
The use of a fracture mechanics approach based on the strain energy release rate to assess failure due to the growth of fatigue cracks in rubber—cord laminated structures is discussed. The mechanics of crack propagation is considered for cracking either between the plies or around individual cords, and also for crack initiation and growth near cord ends. Energy release rates can be calculated approximately for each of these cases and enable the laminate results to be related to the independently measured crack growth characteristics of the rubber. Experimental energy release rate determinations, from compliance changes produced by propagating model inter-ply cracks by cutting, provide a check on the accuracy of the calculated energies. The approach identifies material properties relevant to laminate failure and indicates the effects of loading, design and construction parameters on the rate and nature of failure.
Fiducial marks as measures of thin film crack arrest toughness
Engineering Fracture Mechanics
69
13
1511-1515
2002
10.1016/S0013-7944(02)00003-6
Carbon fiducial marks are formed during thin film local delamination processes induced either by indentation. forming circular blisters, or by residual stress relief through telephone cord blister formations. Hydrocarbons are sucked into the crack tip during the delamination processes, outlining the crack tip opening angle, which can be used to back calculate thin film adhesion using elastic or plastic analyses presented in the paper. ?? 2002 Published by Elsevier Science Ltd.
Adhesion; Crack arrest; Crack tip opening angle; Delamination; Fiducial marks; Fracture; Thin films
Mechanics of the pleural space: fundamental concepts.
Lung
165
5
249-267
1987
10.1007/BF02714442
The transmission of forces from the respiratory muscles to the lung across the extremely thin pleural space has been poorly understood because of the difficulty of accurately measuring pleural liquid and pleural surface pressure (lung static recoil or transpulmonary pressure). Recent results using relatively noninvasive techniques have indicated that the vertical gradient in pleural liquid pressure is not hydrostatic, that pleural liquid pressure is closely related to lung recoil, and that there exists a very thin but continuous pleural liquid layer. These findings contradict concepts based on hydrostatic equilibrium and on the distinction between pleural liquid and pleural surface pressure due to pleural contact. Pleural liquid pressure is not in hydrostatic equilibrium because the difference between the vertical gradient in pleural liquid pressure and the effect of gravity is always balanced by a pressure loss due to a viscous flow within the pleural space. Fluid lubrication of the pleural surfaces is the primary function of the pleural space. The mechanical interaction between the lung and the chest wall is coupled to the dynamics of liquid within the pleural space, which is viewed as a flow-through system. Homeostasis is achieved in such a system by the adjustment of the viscous flow within the pleural space and the outflow absorption rate by lymphatics to the microvascular filtration rate across pleural capillaries.
Micromechanics-based predictive model for compressively loaded angle-ply composite laminates
Aiaa Journal
38
12
2299-2304
2000
Doi 10.2514/2.899
A micromechanics-based analysis to predict damage initiation in compressively loaded symmetric angle-ply laminates is described. The finite element method in conjunction with the commercial code Abaqus is used to solve the governing system of equations. The results obtained for the predictions are compared against a set of experimental results previously made available for AS4/3402 symmetric angle-ply laminates. A unified model that captures damage initiation and that describes failure mode transition as a function of ply angle is reported. The prediction of the model is found to compare favorably against the experimental data.
behavior; failure; fiber composites; interphase; matrix; strength
Some observations on the large deflection bending of rectangular antisymmetric cross-ply plates
Composite Structures
18
1
77-91
1991
http://dx.doi.org/10.1016/0263-8223(91)90015-Q
Large deflection bending analysis of antisymmetric rectangular cross-ply plates based on Von-Karman plate theory is investigated in this paper, with one-term approximation for the in-plane and transverse displacements, under sinusoidal loading. The presence of bending-stretching coupling in such plates results in an additional square nonlinear term which makes the solution (for example, displacements) load direction dependent, unlike isotropic, orthotropic, symmetric, square antisymmetric cross-ply and symmetric and antisymmetric angle-ply plates. The effect of this term on large deflection response, based on the Rayleigh-Ritz method is presented for various configurations and modular ratios of such plates. It is shown that the presence of this square term could alter the very nature of nonlinearity i.e. hardening or softening for certain values of the load parameter.
Instability of a biaxially stressed thin film on a substrate due to material diffusion over its free surface
Journal of the Mechanics and Physics of Solids
41
7
1245-1264
1993
10.1016/0022-5096(93)90092-T
J. Mech. Phvs. Solids Vol. 41, No. 7, pp. 12451264, 1993. 00225096 93 6.00+0.00 Printed in Great Britain. 1993 Pergamon Press Ltd INSTABILITY OF A BIAXIALLY STRESSED THIN FILM ON A SUBSTRATE DUE TO MATERIAL DIFFUSION OVER ITS FREE SURFACE LB ...
Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics
Reports on Progress in Physics
61
9
1267-1324
1998
10.1088/0034-4885/61/9/002
Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics are reviewed with the aim of providing an insight into different processes which may affect the behaviour of ferroelectric devices, such as ferroelectric memories and micro-electro-mechanical systems. Taking into consideration recent advances in this field, topics such as polarization switching, polarization fatigue, effects of defects, depletion layers, and depolarization fields on hysteresis loop behaviour, and contributions of domain-wall displacement to dielectric and piezoelectric properties are discussed. An introduction into dielectric, pyroelectric, piezoelectric and elastic properties of ferroelectric materials, symmetry considerations, coupling of electro-mechanical and thermal properties, and definitions of relevant ferroelectric phenomena are provided.
A thermodynamics based damage mechanics constitutive model for low cycle fatigue analysis of microelectronics solder joints incorporating size effects
International Journal of Solids and Structures
42
13
3744-3772
2005
10.1016/j.ijsolstr.2004.11.022
Below certain length scales and in the presence of a non-uniform plastic strain field the mechanical behavior of many metals and its alloys is substantially different from that in bulk specimens. In particular, an increase in resistance with decreasing size has been observed in Pb/Sn eutectic solder alloys which are extensively used in microelectronics packaging interconnects. Due to the high homologous temperature, the Pb/Sn solder exhibits creep–fatigue interaction and significant time, temperature, stress and rate dependent material characteristics. The simultaneous consideration of all the above mentioned factors makes constitutive modeling an extremely difficult task. In this paper, a viscoplastic constitutive model unified with a thermodynamics based damage evolution model is embedded into a couple stress framework in order to simulate low cycle fatigue response coupled to size effects. The model is implemented into commercial finite element code ABAQUS. The microbending experiment on thin nickel foils is used to validate the model. Analyses are performed on a thin layer solder joint in bending under cyclic loading conditions.
constitutive modeling; damage mechanics; finite element analysis; low cycle fatigue; solder; strain gradient plasticity
Crack branching in cross-ply composites: an experimental study
Composite Structures
53
3
333-344
2001
10.1016/S0263-8223(01)00017-4
The objective of this research is to discuss experimental data regarding a type of failure called crack branching. The specimens tested are layered glass/epoxy and graphite/epoxy cross-ply composites, manufactured with an initial interlayer crack. Experiments were carried out under static conditions. A designed two-level two-variable experiment based on an 8x8 Hadamard matrix was performed in order to identify the key parameters of the phenomenon. Moreover, a smoothing technique (smoothing by running median of 3 repeated) was used to interpret the crack growth rate in terms of branching angles. The results indicate that there is a critical branching angle (39-40°). When the crack branches with an angle greater than this critical value, the crack growth rate increases with the branching angle. Moreover, the branching angle increases when the initial delamination decreases, for branching angles greater than the critical value. The position through the thickness does not seem to significantly affect the branching angle. © 2001 Elsevier Science Ltd. All rights reserved
branching; cross-ply; delamination; double cantilever beam; epoxy; glass; graphite; kinking; mixed mode bending; smoothing
Stochastic failure modelling of unidirectional composite ply failure
Reliability Engineering & System Safety
108
1-9
2012
DOI 10.1016/j.ress.2012.05.006
Stochastic failure envelopes are generated through parallelised Monte Carlo Simulation of a physically based failure criteria for unidirectional carbon fibre/epoxy matrix composite plies. Two examples are presented to demonstrate the consequence on failure prediction of both statistical interaction of failure modes and uncertainty in global misalignment. Global variance-based Sobol sensitivity indices are computed to decompose the observed variance within the stochastic failure envelopes into contributions from physical input parameters. The paper highlights a selection of the potential advantages stochastic methodologies offer over the traditional deterministic approach. (C) 2012 Elsevier Ltd. All rights reserved.
criteria; design; emphasis; envelopes; fiber-reinforced composites; matrix cracking; monte carlo simulation; predictive capabilities; sensitivity analysis; stochastic failure envelope; strength; uncertainty; unidirectional carbon fibre-reinforced composites
Contact Mechanics and Friction
Media
55-70
2010
10.1007/978-3-642-10803-7
This application-oriented book introduces the associations between contact mechanics and friction and with it offers a deeper understanding of tribology. It deals with the associated phenomena of contact, adhesion, capillary forces, friction, lubrication, and wear from one consistent viewpoint. The author goes into (1) methods of rough estimation of tribological quantities, (2) methods for analytical calculations which attempt to minimize the necessary complexity, (3) the crossover into numerical simulation methods. With these methods the author conveys a consistent view of tribological processes in various scales of magnitude (from nanotribology to earthquake research). Also, system dynamic aspects of tribological systems, such as squeal and its suppression as well as other types of instabilities and spatial patterns are investigated. This book contains problems and worked solutions for individual chapters in which the reader can apply the theory to practical situations and deepen the understanding of the material.
Plastic Micromechanical Response of 2D Cross Ply Magnesium Matrix Composites
Procedia Engineering
81
October
1354-1359
2014
10.1016/j.proeng.2014.10.156
2D cross ply magnesium matrix composites were fabricated by melt magnesium infiltration in carbon fiber preform. Carbon fiber uni-directional fabric was used to prepare the carbon fiber preform by alternatively placing fabric in orthogonal way layer by layer. Preform was strengthened by stitching in the perpendicular direction to the fabric layers. The micromechanical model was generated based on the real microstructue of 2D cross ply magnesium matrix composites. The plastic response of 2D cross ply magnesium matrix composites was predicted based on the constructed micromechanical model by applying tensile load in different direction with respect to the fabric direction. Effects of layer mode and packing mode on the plastic response were investigated by numerical simulation. The results showed that composites were strengthened maximally along the fabric direction. Layering mode of fabric played important role on the plastic response of composite. The best layer mode for maximum properties improvement was that perpendicular layer and parallel layer should be used alternatively. The simulated results were verified through corresponding experiments.
abaqus; finite element; magnesium matrix composite; micromechanical model
Tensile fracture and failure behavior of thermoplastic starch with unidirectional and cross-ply flax fiber reinforcements
Macromolecular Materials and Engineering
288
9
699-707
2003
10.1002/mame.200300040
Thermoplastic starch (MaterBi®) based composites containing flax fibers in unidirectional and crossed-ply arrangements were produced by hot pressing using the film stacking method. The flax content was varied in three steps, viz. 20, 40 and 60 wt.-%. Static tensile mechanical properties (stiffness and strength) of the composites were determined on dumbbell specimens. During their loading the acoustic emission (AE) was recorded. Burst type AE signal characteristics (amplitude, width) were traced to the failure mechanisms and supported by fractographic inspection. The mechanical response and failure mode of the composites strongly depended on the flax content and the flax fiber lay-up. It was established that the tensile strength increases until 40 wt.-% flax fiber content but stays almost constant above this value. In the case of 40 wt.-% unidirectional fiber reinforcement, the tensile strength of the composite was 3 times greater than that of the pure starch matrix. The flax fiber reinforcement increased the tensile modulus of the pure starch by several orders of amplitude.
Acoustic emission; Biocomposites; Failure; Flax fiber; Thermoplastic starch
Analysis of thin piezoelectric solids by the boundary element method
Computer Methods in Applied Mechanics and Engineering
191
21–22
2297-2315
2002
http://dx.doi.org/10.1016/S0045-7825(01)00410-8
The piezoelectric boundary integral equation (BIE) formulation is applied to analyze thin piezoelectric solids, such as thin piezoelectric films and coatings, using the boundary element method (BEM). The nearly singular integrals existing in the piezoelectric BIE as applied to thin piezoelectric solids are addressed for the 2-D case. An efficient analytical method to deal with the nearly singular integrals in the piezoelectric BIE is developed to accurately compute these integrals in the piezoelectric BEM, no matter how close the source point is to the element of integration. Promising BEM results with only a small number of elements are obtained for thin films and coatings with the thickness-to-length ratio as small as 10−6, which is sufficient for modeling many thin piezoelectric films as used in smart materials and micro-electro-mechanical systems.
Boundary element method; Boundary integral equation; Nearly singular integrals; Piezoelectric films
The fluid mechanics of solidification
Journal of Fluid Mechanics
212
209
1990
10.1017/S0022112090001938
Intense fluid motions can be generated by the solidification of a binary liquid. This review paper describes systematically some of the concepts involved in the fluid mechanics of solidification . It also presents quantitative calculations for the fluid motion, the rate of ...
Mechanics of flight
Physics Education
10
5
385-389
2002
10.1088/0031-9120/10/5/009
Mechanics of Flight is an ideal introduction to the principles of flight. The eleventh edition has been updated to conform to current teaching practices and technical knowledge. Written in a clear jargon-free style, the book contains simple numerical examples. The book commences with a summary of the relevant aspects of mechanics, and goes on to cover topics such as air and airflow, aerofoils, thrust, level flight, gliding, landing, performance, manoeuvres and stability and control. Important aspects of these topics are illustrated by a description of a trial flight in a light aircraft. The book also deals with flight at transonic and supersonic speeds, and finally orbital flight and spacecraft.
Introduction to Modern Statistical Mechanics
Physics Today
41
12
114
1988
10.1063/1.2811680
read the last chapter for introduction to non-equilibrium statistical mechanics
Constraints in quantum mechanics
Annals of Physics
25
6
586-591
1982
10.1103/PhysRevA.25.2893
The motion of a particle bounded to a plane curve C is discussed in detail from the point of view of quantum mechanics, considering a sequence of increasingly stronger potentials which limit the motion of the particle to an infinitely thin neighbourhood of C. This procedure gives a well defined result provided that one takes some simple precautions (explained in the text) in the choice of the constraining potentials. The result obtained in this way presents an interesting property which has no classical analogue: in its motion along the curve the particle 'sees' a longitudinal potential which is a function of the curvature. The consequences of this result, as well as some further information about more complex situations, are presented using the simplest language and a minimum of mathematical sophistication in order to render this paper legible and useful to both teachers and students.
On the mechanics of mother-of-pearl: A key feature in the material hierarchical structure
Journal of the Mechanics and Physics of Solids
55
2
306-337
2007
10.1016/j.jmps.2006.07.007
Mother-of-pearl, also known as nacre, is the iridescent material which forms the inner layer of seashells from gastropods and bivalves. It is mostly made of microscopic ceramic tablets densely packed and bonded together by a thin layer of biopolymer. The hierarchical microstructure of this biological material is the result of millions of years of evolution, and it is so well organized that its strength and toughness are far superior to the ceramic it is made of. In this work the structure of nacre is described over several length scales. The tablets were found to have wavy surfaces, which were observed and quantified using various experimental techniques. Tensile and shear tests performed on small samples revealed that nacre can withstand relatively large inelastic strains and exhibits strain hardening. In this article we argue that the inelastic mechanism responsible for this behavior is sliding of the tablets on one another accompanied by transverse expansion in the direction perpendicular to the tablet planes. Three dimensional representative volume elements, based on the identified nacre microstructure and incorporating cohesive elements with a constitutive response consistent with the interface material and nanoscale features were numerically analyzed. The simulations revealed that even in the absence of nanoscale hardening mechanism at the interfaces, the microscale waviness of the tablets could generate strain hardening, thereby spreading the inelastic deformation and suppressing damage localization leading to material instability. The formation of large regions of inelastic deformations around cracks and defects in nacre are believed to be an important contribution to its toughness. In addition, it was shown that the tablet junctions (vertical junctions between tablets) strengthen the microstructure but do not contribute to the overall material hardening. Statistical variations within the microstructure were found to be beneficial to hardening and to the overall mechanical stability of nacre. These results provide new insights into the microstructural features that make nacre tough and damage tolerant. Based on these findings, some design guidelines for composites mimicking nacre are proposed. © 2006 Elsevier Ltd. All rights reserved.
Biological material; Finite elements; Mechanical testing; Microstructures; Strengthening and mechanisms
Statistical Mechanics. — A Set of Lectures
Zeitschrift für Physikalische Chemie
95
4-6
323-324
1975
10.1524/zpch.1975.95.4-6.323a
Physics, rather than mathematics, is the focus in this classic graduate lecture note volume on statistical mechanics and the physics of condensed matter. This book provides a concise introduction to basic concepts and a clear presentation of difficult topics, while challenging the student to reflect upon as yet unanswered questions.
Nanomechanics of biocompatible hollow thin-shell polymer microspheres.
Langmuir : the ACS journal of surfaces and colloids
25
13
7514-22
2009
10.1021/la900317d
The nanomechanical properties of biocompatible thin-shell hollow polymer microspheres with approximately constant ratio of shell thickness to microsphere diameter were measured by nanocompression tests in aqueous conditions. These microspheres encapsulate an inert gas and are used as ultrasound contrast agents by releasing free microbubbles in the presence of an ultrasound field as a result of free gas leakage from the shell. The tests were performed using an atomic force microscope (AFM) employing the force-distance curve technique. An optical microscope, on which the AFM was mounted, was used to guide the positioning of tipless cantilevers on top of individual microspheres. We performed a systematic study using several cantilevers with spring constants varying from 0.08 to 2.3 N/m on a population of microspheres with diameters from about 2 to 6 microm. The use of several cantilevers with various spring constants allowed a systematic study of the mechanical properties of the microsphere thin shell at different regimes of force and deformation. Using thin-shell mechanics theory for small deformations, the Young's modulus of the thin wall material was estimated and was shown to exhibit a strong size effect: it increased as the shell became thinner. The Young's modulus of thicker microsphere shells converged to the expected value for the macroscopic bulk material. For high applied forces, the force-deformation profiles showed a reversible and/or irreversible nonlinear behavior including "steps" and "jumps" which were attributed to mechanical instabilities such as buckling events.
Mechanics of crawling cells
Medical Engineering and Physics
27
9
743-753
2005
10.1016/j.medengphy.2005.04.021
Crawling of keratocytes derived from aquatic vertebrates represents a very useful model system for the investigation of cell locomotion because of its ease of handling and the clear structural separation of a thin cytoplasmic layer, the lamella, from the cell body containing the nucleus and other organelles. Spreading of spherical keratocytes results in fried egg shaped cells, which on withdrawing their lamella at one side become polarized and start moving. Hydrostatic pressure, tension at the cortex, traction forces exerted on the adhesion sites and inside the cells along filamentous structures are required to gain a certain shape. Traction forces have been made visible using scanning acoustic microscopy. This method also allowed for the demonstration of cytoplasmic fluxes inside a moving keratocyte and changes of forces while a migrating cell is changing its direction of locomotion. The pros and cons for actin polymerization at the leading front providing the driving force for crawling are discussed on the basis of structural and experimental results: Do they stringently identify polymerization of actin as the only driving machinery. Such a mechanism not only should explain the advancement of the leading edge but also the movement of the whole cell, i.e. the material flux taking place from the cell body to the periphery. Even if the lamella periphery itself may be motile by actin turnover this scheme may represent an oversimplification if applied to the whole cell. Considering the complexity of a whole cell simplifying model systems may not lead to adequate descriptions of the mechanisms as they occur within cells with a highly complex structure, although the model might be consistent and sufficient to describe, i.e. crawling in general. ?? 2005 IPEM. Published by Elsevier Ltd. All rights reserved.
Acoustic microscopy; Cell elasticity; Forces; Keratocytes; Locomotion
Glass: Mechanics and Technology
Glass: Mechanics and Technology
1-366
2007
10.1002/9783527617029
The prelims comprise: * Half-title page * Related Titles * Title page * Copyright page * Contents * Foreword * Preface * Symbols and Definitions (units in parentheses) * Physical Constants * Abbreviations
Morphogenesis of thin hyperelastic plates: A constitutive theory of biological growth in the Föppl–von Kármán limit
Journal of the Mechanics and Physics of Solids
57
3
458-471
2009
10.1016/j.jmps.2008.11.011
The shape of plants and other living organisms is a crucial element of their biological functioning. Morphogenesis is the result of complex growth processes involving biological, chemical and physical factors at different temporal and spatial scales. This study aims at describing stresses and strains induced by the production and reorganization of the material. The mechanical properties of soft tissues are modeled within the framework of continuum mechanics in finite elasticity. The kinematical description is based on the multiplicative decomposition of the deformation gradient tensor into an elastic and a growth term. Using this formalism, the authors have studied the growth of thin hyperelastic samples. Under appropriate assumptions, the dimensionality of the problem can be reduced, and the behavior of the plate is described by a two-dimensional surface. The results of this theory demonstrate that the corresponding equilibrium equations are of the Föppl–von Kármán type where growth acts as a source of mean and Gaussian curvatures. Finally, the cockling of paper and the rippling of a grass blade are considered as two examples of growth-induced pattern formation.
Buckling; Finite deflections; Growth; Hyperelasticity; Plates
Buckling of symmetric cross-ply square plates with various boundary conditions
Composite Structures
68
381-389
2005
10.1016/j.compstruct.2004.04.003
The buckling analysis of cross-ply laminated square plates subjected to three types of in-plane forces and various edge boundary conditions is presented on the basis of a unified five-degree-of-freedom shear deformable plate theory. The employment of the appropriate "shear deformation shape functions" in the theory leads to certain shear deformable plate theories developed previously, also, fulfills the requirement of the continuity conditions among the layers. The governing equations of buckling behaviour of completely simply supported cross-ply laminated plates are solved analytically. For the plates with different combinations of free, clamped and simply supported boundary conditions at their edges, the Ritz method is applied by assuming the displacement components as the double series of simple algebraic polynomials. The numerical results obtained on the basis of various plate theories for uniaxial, biaxial compression and compression-tension types of loading and different length-to-thickness ratios are presented and compared with the ones available in the literature. ?? 2004 Elsevier Ltd. All rights reserved.
Buckling; Cross-ply plates; Ritz method; Shear deformable plate theory
Mechanical Similarities Between Alternate Osteons and Cross-Ply Laminates
Journal of Biomechanics
9
2
65-71
1976
Fully calcified osteon samples with alternating lamellae were prepared from longitudinal sections of human femoral shafts according to the technique described by Ascenzi and Bonucci. Osteons of this type reveal an alternation of dark and bright lamellae under the polarizing microscope. The samples were loaded by tension in a direction parallel with their longitudinal axis using a specially designed microwave extensimeter based on cavity and pulse techniques. All the samples were tested wet at a temperature of ca. 20C. The stress-strain curves recorded from each osteon show a change in slope or knee at low stresses. A useful model for understanding this phenomenon is furnished by the mechanical properties of that type of fiber-reinforced plastic material called cross-ply laminate. The comparison of the data obtained from this material with those furnished by an electron microscope investigation carried out on the loaded osteons suggests that the change in slope at low stresses is due to failure of the interfibrillar cementing substance in those lamellae having fiber bundles oriented perpendicularly to the loading direction and to yielding of the canaliculi previously filled with osteocyte processes. The physiological implications of these results are discussed.
Biological; Biomechanics; Bone and Bones; Bone and Bones: physiology; Bone and Bones: ultrastructure; Humans; Mechanical; Models; Plastics; Stress
A variational model for fracture and debonding of thin films under in-plane loadings
Journal of the Mechanics and Physics of Solids
70
1
320-348
2014
10.1016/j.jmps.2014.05.020
We study fracture and debonding of a thin stiff film bonded to a rigid substrate through a thin compliant layer, introducing a two-dimensional variational fracture model in brittle elasticity. Fractures are naturally distinguished between transverse cracks in the film (curves in 2D) and debonded surfaces (2D planar regions). In order to study the mechanical response of such systems under increasing loads, we formulate a dimension-reduced, rate-independent, irreversible evolution law accounting for both transverse fracture and debonding. We propose a numerical implementation based on a regularized formulation of the fracture problem via a gradient damage functional, and provide an illustration of its capabilities exploring complex crack patterns, showing a qualitative comparison with geometrically involved real life examples. Moreover, we justify the underlying dimension-reduced model in the setting of scalar-valued displacement fields by a rigorous asymptotic analysis using Γ-convergence, starting from the three-dimensional variational fracture (free-discontinuity) problem under precise scaling hypotheses on material and geometric parameters. © 2014 Elsevier Ltd.
Asymptotic analysis; Dimension reduction; Fracture mechanics; Thin films; Variational mechanics
Energy methods for modelling damage in laminates
Journal of Composite Materials
47
20-21
2613-2640
2012
10.1177/0021998312468188
The paper represents the author's contribution to the Third World-Wide Failure Exercise, which is aimed at benchmarking current models of damage, matrix cracking, initiation of delamination and their interaction with fibre failure. The approach used for the development of damage in laminates is based on an energy methodology that requires knowledge of the dependence of thermo-elastic constants on damage. The various models, developed by the author, are applied to the majority of the Third World-Wide Failure Exercise Test Cases, which included thin and thick cross ply and quasi-isotropic laminates, loading and unloading of an angle ply laminate, bending of a general laminate, and cracking under thermal loadings. Methods used to predict ply properties from those of the fibres and matrix are also described. Crack density in the 90 degree plies was modelled using a ply refinement technique. Detailed discussion is made on a number of relevant issues (initiating defect size and shape, fibre strength, ply saturation, off-axis ply cracking, delamination, mixed mode ply cracking) and their likely effects on design.
Re-Appraisal of Terzaghi’S Soil Mechanics
invited Special Lecture at the International Society of Soil Mechanics and Geotechnical Engineering Conference
August
1-14
2001
... RE - APPRAISAL OF TERZAGHI'S SOIL MECHANICS . ... below) to develop an alternative to the normal soil mechanics theory taught by Coulomb, Rankine, Mohr and Terzaghi . ... This Lecture will re - appraise the normal soil mechanics theory by contrasting it with the alternative theory ... \n
Translation of an engineered nanofibrous disc-like angle-ply structure for intervertebral disc replacement in a small animal model
Acta Biomaterialia
10
6
2473-2481
2014
10.1016/j.actbio.2014.02.024
Intervertebral disc degeneration has been implicated in the etiology of low back pain; however, the current surgical strategies for treating symptomatic disc disease are limited. A variety of materials have been developed to replace disc components, including the nucleus pulposus (NP), the annulus fibrosus (AF) and their combination into disc-like engineered constructs. We have previously shown that layers of electrospun poly(ε-caprolactone) scaffold, mimicking the hierarchical organization of the native AF, can achieve functional parity with native tissue. Likewise, we have combined these structures with cell-seeded hydrogels (as an NP replacement) to form disc-like angle-ply structures (DAPS). The objective of this study was to develop a model for the evaluation of DAPS in vivo. Through a series of studies, we developed a surgical approach to replace the rat caudal disc with an acellular DAPS and then stabilized the motion segment via external fixation. We then optimized cell infiltration into DAPS by including sacrificial poly(ethylene oxide) layers interspersed throughout the angle-ply structure. Our findings illustrate that DAPS are stable in the caudal spine, are infiltrated by cells from the peri-implant space and that infiltration is expedited by providing additional routes for cell migration. These findings establish a new in vivo platform in which to evaluate and optimize the design of functional disc replacements. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Electrospinning; External fixation; Intervertebral disc; Surgical model; Tissue engineering
Numerical methods in rock mechanics
International Journal of Rock Mechanics and Mining Sciences
39
4
409-427
2002
10.1016/S1365-1609(02)00065-5
The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures built on and in rock masses, and hence for supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating coupling between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized, Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference list, 'significant' references are asterisked and 'very significant' references are doubly asterisked. ?? 2002 Elsevier Science Ltd. All rights reserved.
Coupled processes; Design; Numerical modelling; Outstanding issues; Review; Rock mechanics
Statistical Mechanics, A Short Treatise
European Journal of Mechanics - B/Fluids
19
3
459
2000
10.1016/S0997-7546(00)00119-9
This clear book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works. The author emphasises the relation between microscopic reversibility and macroscopic irreversibility, explaining fundamental concepts in detail.
Metal Forming and Impact Mechanics
Metal Forming and Impact Mechanics
225-247
1985
10.1016/B978-0-08-031679-6.50021-7
A comparison is made between the experimental results, approximate theoretical predictions and empirical relations for the static and dynamic progressive buckling of thin-walled tubes having circular or square cross-sections. Satisfactory agreement is achieved between theoretical predictions and experimental results when the effective crushing distance is considered and provided that the influence of material strain rate sensitivity is retained in the dynamic crushing case.
Computational modeling of ligament mechanics.
Critical reviews in biomedical engineering
29
3
303-371
2001
10.1615/CritRevBiomedEng.v29.i3.20
This article provides a critical review of past and current techniques for the computational modeling of ligaments and tendons. A brief overview of relevant concepts from the fields of continuum mechanics and finite element analysis is provided. The structure and function of ligaments and tendons are reviewed in detail, with emphasis on the relationship of microstructural tissue features to the continuum mechanical hehavior. Experimental techniques for the material characterization of biological soft tissues are discussed. Past and current efforts related to the constitutive modeling of ligaments and tendons are classified by the particular technique and dimensionality. Applications of one-dimensional and three-dimensional constitutive models in the representation of the mechanical behavior of joints are presented. Future research directions are identified.
constitutive modeling; finite element; ligament; soft tissue mechanics
A decomposition of the strain energy release rate associated with the initiation of transverse cracking, longitudinal cracking and delamination in cross-ply laminates
Composite Structures
84
2
186-197
2008
10.1016/j.compstruct.2007.12.004
An energy criterion is proposed to study the damage evolution in a composite cross-ply laminate. This criterion is based on the computation of the partial strain energy release rate associated with each damage mechanism (transverse cracking, longitudinal cracking and delamination) and mode (I, II or III). Several decompositions of the complementary strain energy are put forward. Each component part of this decomposition is related to a specific damage mechanism and loading mode. The related criterion can predict and describe the initiation and propagation of the different damage mechanisms. © 2008 Elsevier Ltd. All rights reserved.
Delamination; Failure criterion; Longitudinal cracking; Transverse cracking
Statistical mechanics of dislocation systems
Scripta Materialia
54
723-727
2006
10.1016/j.scriptamat.2005.11.031
This paper discusses a number of issues related to the development of a physical theory of crystal plasticity based on the statistical mechanics modeling of the underlying dislocation system. © 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Dislocation dynamics; Dislocation theory; Plastic deformation; Statistical mechanics
Statistical Mechanics: A Selective Review of Two Central Issues
Reviews of modern physics
71
2
36
2000
10.1103/RevModPhys.71.S346
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These phenomena are emergent collective properties not discernible in the behavior of individual atoms. They are given precise and elegant mathematical formulations when the ratio between macroscopic and microscopic scales becomes very large.
Classical Mechanics
Nature
278
September
131
1980
10.1038/278075a0
This is the English version of a friendly graduate course on Classical Mechanics, containing about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. For the Spanish version, see physics/9906066
Modified Stoney Equation for Patterned Thin Film Electrodes on Substrates in the Presence of Interfacial Sliding
Journal of Applied Mechanics
79
3
031018
2012
10.1115/1.4005900
Mechanical stresses and failure are believed to be a major cause for the limited cycle life of lithium-ion batteries employing high capacity Si electrodes. Recent experiments have shown that patterned Si thin film electrodes on substrate exhibit improved cycling stability and substantial sliding at the film/substrate interface. To facilitate experimental studies of stress evolution in such systems, we have developed a modified Stoney equation which accounts for the effect of interfacial sliding on the relationship between curvature and stress in patterned thin films on substrate. [DOI: 10.1115/1.4005900]
ANODES; BATTERIES; CURVATURE; LITHIATION; NANOWIRES; patterned thin films; rechargeable batteries; SILICON; silicon anodes; Stoney equation
Students’ preconceptions in introductory mechanics
American Journal of Physics
50
1
66
1982
10.1119/1.12989
Data from written tests and videotaped problem‐solving interviews show that many physics students have a stable, alternative view of the relationship between force and acceleration. This ’’conceptual primitive’’ is misunderstood at the qualitative level in addition to any difficulties that might occur with mathematical formulation. The misconception is highly resistant to change and is remarkably similar to one discussed by Galileo, as shown by comparison of his writings with transcripts from student interviews. The source of this qualitative misunderstanding can be traced to a deep‐seated preconception that makes a full understanding of Newton’s first and second laws very difficult. In such cases learning becomes a process in which new concepts must displace or be remolded from stable concepts that the student has constructed over many years.
A BRIGHT FUTURE – SINGLE PLY THERMOPLASTIC POLYOLEFIN ROOFING
Society of Plastics Engineers Annual Technical Conference
1509-1515
2009
Single ply thermoplastic polyolefin (TPO) has been the fastest growing commercial roofing membrane in the last decade due to its superior weatherability, heat-welded seam integrity, energy savings, and safe and easy installation. In 2008, TPO installed roofing systems exceeded EPDM and became the largest single ply roofing market segment. This paper discusses the heat-welded seaming, fire retardancy and UV stability of TPO roofing.
Fire Retardancy; Heat Welding; Single Ply Roofing; TPO; UV Weathering
Analysis of Thin Beams and Cables Using the Absolute Nodal Co--ordinate Formulation
Nonlinear Dynamics
45
1
109-130
2006
10.1007/s11071-006-1856-1
The purpose of this paper is to present formulations for beam elements\nbased on the absolute nodal co-ordinate formulation that can be effectively\nand efficiently used in the case of thin structural applications.\nThe numerically stiff behaviour resulting from shear terms in existing\nabsolute nodal co-ordinate formulation beam elements that employ\nthe continuum mechanics approach to formulate the elastic forces\nand the resulting locking phenomenon make these elements less attractive\nfor slender stiff structures. In this investigation, additional shape\nfunctions are introduced for an existing spatial absolute nodal co-ordinate\nformulation beam element in order to obtain higher accuracy when\nthe continuum mechanics approach is used to formulate the elastic\nforces. For thin structures where bending stiffness can be important\nin some applications, a lower order cable element is introduced and\nthe performance of this cable element is evaluated by comparing it\nwith existing formulations using several examples. Cables that experience\nlow tension or catenary systems where bending stiffness has an effect\non the wave propagation are examples in which the low order cable\nelement can be used. The cable element, which does not have torsional\nstiffness, can be effectively used in many problems such as in the\nformulation of the sliding joints in applications such as the spatial\npantograph/catenary systems. The numerical study presented in this\npaper shows that the use of existing implicit time integration methods\nenables the simulation of multibody systems with a moderate number\nof thin and stiff finite elements in reasonable CPU time.
On the effect of prestrain and residual stress in thin biological membranes
Journal of the Mechanics and Physics of Solids
61
9
1955-1969
2013
10.1016/j.jmps.2013.04.005
Understanding the difference between ex vivo and in vivo measurements is critical to interpret the load carrying mechanisms of living biological systems. For the past four decades, the ex vivo stiffness of thin biological membranes has been characterized using uniaxial and biaxial tests with remarkably consistent stiffness parameters, even across different species. Recently, the in vivo stiffness was characterized using combined imaging techniques and inverse finite element analyses. Surprisingly, ex vivo and in vivo stiffness values differed by up to three orders of magnitude. Here, for the first time, we explain this tremendous discrepancy using the concept of prestrain. We illustrate the mathematical modeling of prestrain in nonlinear continuum mechanics through the multiplicative decomposition of the total elastic deformation into prestrain-induced and load-induced parts. Using in vivo measured membrane kinematics and associated pressure recordings, we perform an inverse finite element analysis for different prestrain levels and show that the resulting membrane stiffness may indeed differ by four orders of magnitude depending on the prestrain level. Our study motivates the hypothesis that prestrain is important to position thin biological membranes in vivo into their optimal operating range, right at the transition point of the stiffening regime. Understanding the effect of prestrain has direct clinical implications in regenerative medicine, medical device design, and tissue engineering of replacement constructs for thin biological membranes. ?? 2013 Elsevier Ltd.
Finite element method; Mitral leaflet; Parameter identification; Prestrain; Residual stress
Proposed extension of the SINTAP/FITNET thin wall option based on a simple method for reference load determination
Engineering Fracture Mechanics
76
1
74-87
2009
10.1016/j.engfracmech.2008.06.029
A “correct” limit or yield load is an essential element of flaw assessment procedures of the R6 or SINTAP/FITNET type. In this paper the authors propose a definition of this quantity which is based on the SINTAP option 3 failure assessment function. This “reference load” can be determined for any component geometry by finite element analysis. The method is applied to two kinds of thin walled structures (notched plates and curved stiffened panels) and the results demonstrate that the approach is a suitable extension of the existing thin wall module.
Equilibrium depth and spacing of cracks in a tensile residual stressed thin film deposited on a brittle substrate
Engineering Fracture Mechanics
69
5
589-596
2002
10.1016/S0013-7944(01)00098-4
The depth and spacing of cracks in a tensile residual stressed thin film bonded on a brittle substrate are analyzed thermodynamically using the minimum energy theorem on the basis that the film has the same mechanical properties as the substrate. The results show that the cracks penetrate into the substrate. Simple and approximate relationships between three dimensionless parameters, i.e., the normalized crack depth and spacing, and the cracking resistance number, are derived, which determine the fracture behavior of the film. ?? 2002 Elsevier Science Ltd. All rights reserved.
Crack; Critical thickness; Thin films
Brinkmann Model and Double Penalization Method for the Flow Around a Porous Thin Layer
Journal of Mathematical Fluid Mechanics
10
1
126-158
2006
10.1007/s00021-006-0221-y
in this paper we study a penalization method used to compute the flow\nof a viscous fluid around a thin layer of porous material. Using\na BKW method, we perform an asymptotic expansion of the solution\nwhen a little parameter, measuring the thickness of the thin layer\nand the inverse of the penalization coefficient, tends to zero. We\ncompare then this numerical method with a Brinkman model for the\nflow around a porous thin layer.
bkw method; navier-stokes equations; penalization; porous ma-
Behavior of Composite Laminates After First-Ply-Failure
Composite Structures
3
187-200
1985
http://dx.doi.org/10.1016/0263-8223(85)90043-1
The optimum use of composite laminates involves predicting both first- ply-failure (FPF) and the subsequent behavior of the laminate. Several theories have been proposed to model the behavior of a ply after it fails. Three of these theories are examined here. They include modeling the lamina behavior as elastic-perfectly plastic; as a strain hardening material, as a material which unloads through a negative tangent modulus. These three methods are used to predict the ultimate strength of various laminates. Results are compared to experimental results. Although none of these approaches is totally accurate, the elastic- perfectly plastic model seems to give the best results.
Assessment of third order smeared and zigzag theories for buckling and vibration of flat angle-ply hybrid piezoelectric panels
Composite Structures
90
3
346-362
2009
http://dx.doi.org/10.1016/j.compstruct.2009.03.019
A recently developed improved third order theory (ITOT) for angle-ply hybrid piezoelectric plates in cylindrical bending is extended to include geometric non-linearity in the Von Karman sense. The transverse deflection is approximated non-uniformly to explicitly account for the transverse strain due to temperature and electric potential. The coupled non-linear equations of motion and the boundary conditions are derived using the extended Hamilton's principle. The non-linear theory is used to obtain the buckling and free vibration response of symmetrically laminated hybrid angle-ply panels under inplane electro-thermomechanical loading. This theory and the third order zigzag theory with additional layerwise terms for inplane displacements are assessed in direct comparison with the exact 2D piezothermoelasticity solutions for forced harmonic response, buckling and free vibration response under initial inplane electro-thermomechanical loading. The comparison establishes the accuracy of the results of the zigzag theory and its superiority over the ITOT for the dynamic and buckling response of angle-ply hybrid panels. © 2009 Elsevier Ltd. All rights reserved.
Angle-ply; Buckling; Forced vibration; Hybrid panel; Non-linear
Experimental and finite element analysis of fracture criterion in general yielding fracture mechanics
Sadhana
27
December
631-642
2002
Efforts made over the last three decades to understand the fracture behaviour of structural materials in elastic and elasto-plastic fracture mechanics are numerous, whereas investigations related to fracture behaviour of materials in thin sheets or general yielding fracture regimes are limited in number. Engineering simulative tests are being used to characterize formability and drawability of sheet metals. However, these tests do not assure consistency in quality of sheet metal products. The prevention of failure in stressed structural components currently requires fracture mechanics based design parameters like critical load, critical crack-tip opening displacement or fracture toughness. The present attempt would aim to fulfill this gap and generate more information thereby increased understanding on fracture behaviour of sheet metals. In the present investigation, using a recently developed technique for determining fracture criteria in sheet metals, results are generated on critical CTOD and fracture toughness. Finite element analysis was performed to support the results on various fracture parameters. The differences are within 1 to 4%. At the end it is concluded that magnitude of critical CTOD and/or critical load can be used as a fracture criterion for thin sheets.
crack-tip opening displacement; extra deep-drawn steel sheets; fracture criterion; fracture mechanics; general yielding
Fracture mechanics based fatigue life prediction for welded joints of square tubes
Thin-Walled Structures
21
2
107-120
1995
10.1016/0263-8231(94)00028-X
Square tubes of mild and low alloy steels are extensively used in vehicle structures and offshore platforms. Despite this fact the fatigue behaviour of welded nodes of these tubes is not sufficiently known, especially in thin sections. The paper presents the results of fatigue life predictions based on fracture mechanics, in non-load carrying T and also load carrying cruciform joints. The fatigue life prediction models include crack initiation and crack propagation. The stress intensity factor formulations were obtained using the weight function solution for semi-elliptical surface cracks with the stresses computed using a three-dimensional finite element program. The prediction results are compared with experimental results and a good agreement was obtained. The tube material was mild steel St 37 (DIN 17100). The loading modes were in-plane three point bending and canti-lever bending or tension.
Bending (deformation); Carbon steel; Crack initiation; Crack propagation; Fatigue of materials; Finite element method; Fracture mechanics; Loads (forces); Stresses; Stress intensity factors; Welds
A damage meso-mechanical approach to fatigue failure prediction of cross-ply laminate composites
International Journal of Fatigue
24
429-435
2002
10.1016/S0142-1123(01)00098-6
This paper focuses on the description and prediction of local fatigue damage development in fiber-reinforced cross-ply laminate composites. The transverse laminae and longitudinal laminae are homogenized and simulated by subcritical and critical effective laminae; and for each of them a meso-damage factor is introduced to represent the change of its in-situ elastic modulus. Based on the meso-damage theory, the redistributed local stresses in each lamina at the moment of crack saturation, or at the characteristic damage stage (CDS) are evaluated with measurable parameters of the laminate. This theory is therefore able to predict the CDS life and the stage II fatigue life of a cross-ply laminate. Experimental results of glass fiber/epoxy resin composite laminates are presented and found to be in agreement with the theoretical prediction. ?? 2002 Elsevier Science Ltd. All rights reserved.
Composite; Effective lamina; Laminate; Local damage; Meso scale
Fracture behavior in CFRP cross-ply laminates with initially cut fibers
Composites Part A: Applied Science and Manufacturing
40
6-7
938-947
2009
10.1016/j.compositesa.2009.04.023
This study qualitatively investigates the effects of initially cut fibers (slits) on fracture behavior in carbon fiber reinforced plastic (CFRP) cross-ply laminates, which had alternate or identical slit angle ±θ in the 0° plies. Damage progress during tensile tests was observed for several geometries of cutting. We also numerically evaluated fracture behavior in laminates with slits by a layer-wise finite-element model with cohesive elements. The simulated damage patterns included matrix cracks along the slits, splits in the 0° layer from the slit tips, and transverse cracks in the 90° layer. Delamination was also generated at the crossing point of ply cracks due to the large shear stress, and then extended to form the triangular region bounded by the slits and splits. The predicted damage extension to the final failure agreed with the observations. A numerical study demonstrated that the damage near the slits produced a stress field similar to that of a penetrating notch. © 2009 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Delamination; B. Stress concentrations; C. Finite element analysis (FEA)
Hybrid Quantum Mechanics/Molecular Mechanics Approaches
Modern Methods and Algorithms of Quantum Chemistry
285-305
2000
An overview is provided of the range of approaches to hybrid QM/MM (quantum mechanics/molecular mechanics) calculations. The factors considered include the choice of QM and MM methods, the construction of the total QM/MM energy ex- pression, the nature of the QM/MM coupling, and the treatment of bonds between QM and MM regions. The practical issues associated with handling the increased conformational complexity of macromolecular systems, and the construction of QM/MM codes are discussed.
On the investigation of the biaxial fatigue behaviour of unidirectional composites
Composites Part B: Engineering
54
1
200-208
2013
10.1016/j.compositesb.2013.05.014
The paper illustrates the preliminary activity of an extensive research program oriented to investigate the multiaxial fatigue behaviour of unidirectional composite laminates, with particular attention to the analysis of the damage mechanisms and their correlation with the local multiaxial stress state to be used then as the basis for the development of multiaxial fatigue criterion. The definition of an effective experimental procedure for multiaxial fatigue testing is carefully discussed in terms of specimen geometry, specimen manufacturing and local stress state. Once identified in the thin-walled tubular specimens under tension-torsion loading the best test configuration for the aims of the research, the results of comparative fatigue tests investigating the influence of the tubes geometry (wall thickness to diameter ratio) on the transverse fatigue response are presented. In the final part of the paper the effects of an increasing shear stress component (σ6) on the transverse (σ2) fatigue strength and damage evolution in UD glass-epoxy tubes are illustrated. © 2013 Elsevier Ltd. All rights reserved.
A. Lamina/ply; B. Fatigue; C. Damage mechanics; D. Mechanical testing Multiaxial fatigue
Ultrasonic ply-by-ply detection of matrix cracks in laminated composites
Journal of Nondestructive Evaluation
25
1
39-51
2006
DOI 10.1007/s10921-006-0001-x
In the design of cryogenic fuel tanks for the next generation Reusable Launch Vehicles (RLVs), permeability of cryogenic fuels across the thickness of the tank is a critical issue. In this context, the detection of matrix cracks and their connectivity takes on an unprecedented significance. In this work we develop an ultrasonic backscattering technique for the detection of matrix cracks in each of the plies of a damaged graphite/epoxy laminated composite.
acoustic-backscattering; laminated composites; matrix cracking; nondestructive testing; polymer-matrix composites; transverse cracks; ultrasonics
Soil mechanics: breaking ground.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
365
December
2985-3002
2007
10.1098/rsta.2007.0009
In soil mechanics, student's models are classified as simple models that teach us unexplained elements of behaviour; an example is the Cam clay constitutive models of critical state soil mechanics (CSSM). 'Engineer's models' are models that elaborate the theory to fit more behavioural trends; this is usually done by adding fitting parameters to the student's models. Can currently unexplained behavioural trends of soil be explained without adding fitting parameters to CSSM models, by developing alternative student's models based on modern theories?Here I apply an alternative theory to CSSM, called 'breakage mechanics', and develop a simple student's model for sand. Its unique and distinctive feature is the use of an energy balance equation that connects grain size reduction to consumption of energy, which enables us to predict how grain size distribution (gsd) evolves-an unprecedented capability in constitutive modelling. With only four parameters, the model is physically clarifying what CSSM cannot for sand: the dependency of yielding and critical state on the initial gsd and void ratio.
Numerical analysis of intralaminar failure mechanisms in composite structures. Part I: FE implementation
Composite Structures
93
2
1039-1046
2011
10.1016/j.compstruct.2010.06.028
This paper presents a three-dimensional continuum damage mechanics-based material model which was implemented in an implicit finite element code to simulate the progressive intralaminar degradation of fibre reinforced laminates. The damage model is based on ply failure mechanisms and uses seven damage variables assigned to tensile, compressive and shear damage at a ply level. Non-linear behaviour and irreversibility were taken into account and modelled. Some issues on the numerical implementation of the damage model are discussed and solutions proposed. Applications of the methodology are presented in Part II [1].
Damage mechanics; Finite element analysis (FEA); Modelling; Non-linear behaviour
Numerical simulation of laser-induced thin film delamination
Thin Solid Films
516
6
971-981
2008
DOI: 10.1016/j.tsf.2007.06.066
Laser-induced thin film spallation has been developed to be one of the most powerful tools for quantitative measurement of thin film interfacial adhesion. High-energy laser pulse absorption generates stress pulse that can be used to delaminate a thin film-substrate interface. Interfacial strength is obtained from the measured surface motion of the thin film using elastic wave mechanics. Due to the short duration of the stress pulses, the dynamic interfacial debonding process usually happens within nanosecond duration, thus the interfacial strength measurement pertains to the intrinsic adhesion of the interface. In this paper, we performed detailed numerical simulations on various aspects of this experimental technique. Combining with experimental observations, the simulation results provide explanations of various phenomena and insights on the fundamental mechanisms of the laser-induced interface debonding process.
Laser-induced stress waves
Numerical simulations of large deformation of thin shell structures using meshfree methods
Computational Mechanics
25
2-3
102-116
2000
10.1007/s004660050463
In this paper, meshfree simulations of large deformation of thin shell structures is presented. It has been shown that the window function based meshfree interpolants can be used to construct highly smoothed (high order "manifold") shape functions for three-dimensional (3-D) meshfree discretization/interpolation, which can be used to simulate large deformation of thin shell structures while avoiding ill-conditioning as well as stiffening in numerical computations. The main advantage of such 3-D meshfree continuum approach is its simplicity in both formulation and implementation as compared to shell theory approach, or degenerated continuum approach. Moreover, it is believed that the accuracy of the computation may increase because of using 3-D exact formulation. Possible mechanism to relieve shear/volumetric locking due to the meshfree interpolation is discussed. Several examples have been computed by using a meshfree, explicit, total Lagrangian formulation. Towards to developing a self-contact algorithm, a novel meshfree contact algorithm is proposed in the end.
Collagen: Structure and mechanics
Collagen: Structure and Mechanics
1-506
2008
10.1007/978-0-387-73906-9
Collagen type I is the most abundant protein in mammals. It confers mechanical stability, strength and toughness to a range of tissues from tendons and ligaments, to skin, cornea, bone and dentin. These tissues have quite different mechanical requirements, some need to be elastic or to storemechanical energy and others need to be stiff and tough. This shows the versatility of collagen as a building material. While in some cases (bone and dentin) the stiffness is increased by the inclusion ofmineral, the mechanical properties are, in general, adapted by amodifi- cation of the hierarchical structure rather than by a different chemical composition. The basic building block of collagen-rich tissues is the collagen fibril, a fiberwith 50 to a few hundred nanometer thickness. These fibrils are then assembled to a variety of more complex structures with very differentmechanical properties. As a general introduction to the book, the hierarchical structure and the mechanical properties of some collagen-rich tissues are briefly discussed. In addition, this chapter gives elementary definitions of some basic mechanical quantities needed throughout the book, such as stress, strain, stiffness, strength and toughness.
Advances in Applied Mechanics Volume 29
Advances in Applied Mechanics
29
63-191
1991
10.1016/S0065-2156(08)70164-9
This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.
Interfacial mechanics of push-out tests: Theory and experiments
Composites Part A: Applied Science and Manufacturing
32
3-4
575-584
2001
10.1016/S1359-835X(00)00051-8
The thermo-mechanical characterization of interfaces in composite systems (PMC/MMC/IMC/CMC) is one of the challenging problems in composite mechanics and engineering. Each system has its own distinguishing features; however, in MMCs and IMCs the study is rendered more complex due to the evolving chemical species (both temporally and spatially), and the multi-axial state of residual stresses. Before MMCs or IMCs can be used in actual applications, the role of interfaces in not only the strengthening but also toughening mechanisms needs to be clearly understood. For evaluating the interfacial mechanical properties of interfaces, thin slice push-out test has emerged as the de-facto standard. Though, conceptually the testing procedure is simple, interpretation of the test results is not. It is essential to conduct very careful experiments, make precise meso- and macroscopic chemical/structural/mechanical observations and perform a thorough theoretical/numerical simulation before the test data can be used in a quantitative manner. In this paper, a comprehensive analysis of the push-out test is presented based on the theoretical/numerical and experimental research work of the authors' group during the past few years. In this work, thin slice push-out tests were conducted primarily on Titanium Matrix Composites at various test temperatures (room and elevated) with different processing conditions (temperature and time). Different composite systems with Titanium based matrices (Ti-6Al-4V, Timetal 21S, Ti-15Nb-3Al) uniaxially reinforced with Silicon Carbide fibers (SCS-6) were chosen for the study. Effect of the evolution of interfacial chemistry and architecture (in matrix, coating and reaction zone) on both shear strength ??s and frictional strength ??f were studied. A novel finite element analysis based on nonlinear finite element method was implemented, in which not only the initiation but propagation of interfacial cracks are simulated. In the analysis, both shear stress and fracture energy based criteria are used to model the initiation of (closed) cracks. Quantitative values of ??s, ??f, GI and GII are then extracted based on the experimental data and the numerical simulation. A critical review of stress and energy based interface-modeling approaches and their applicability to various boundary value problems are made.
b; c; finite element analysis; interface failure; residual stress
Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives
Journal of Physics A: Mathematical and General
39
33
10323-10354
2006
10.1088/0305-4470/39/33/005
Mechanics of fluid membranes may be described in terms of the concepts of mechanical deformations and stresses or in terms of mechanical free-energy functions. In this paper, each of the two descriptions is developed by viewing a membrane from two perspectives: a microscopic perspective, in which the membrane appears as a thin layer of finite thickness and with highly inhomogeneous material and force distributions in its transverse direction, and an effective, two-dimensional perspective, in which the membrane is treated as an infinitely thin surface, with effective material and mechanical properties. A connection between these two perspectives is then established. Moreover, the functional dependence of the variation in the mechanical free energy of the membrane on its mechanical deformations is first studied in the microscopic perspective. The result is then used to examine to what extent different, effective mechanical stresses and forces can be derived from a given, effective functional of the mechanical free energy.
Snap-Through of Unsymmetric Cross-Ply Laminates Using Piezoceramic Actuators
Journal of Intelligent Materials Systems and Structures
14
12
795-814
2003
10.1177/104538903039261
The paper discusses the concept of using a piezoceramic actuator bonded to one side of a two-layer unsymmetric cross ply [0/90]T laminate to provide the moments necessary to snap the laminate from one stable equilibrium shape to another. The results presented are considered an alternative to existing morphing concepts wherein actuators are used to elastically warp structures into a shape other than their natural and unique equilibrium shape. These existing concepts require the continuous application of power to maintain the warped shape. With the concept discussed here, the actuators are used only to change from one equilibrium shape to another, so continuous power is not needed. The paper discusses several phases of modeling, including bonding the actuator to the laminate and applying voltage to the actuator to effect the shape change, and experimental work. Two models are developed, a simple model and a more refined one. Both are based on the Rayleigh–Ritz technique and the use of energy and variational methods. The experimental phase of the study is discussed, particularly the measurement of the voltage level needed to snap the laminate. The voltage measurements are compared with predictions and the agreement between measurements and the predictions of the refined model are reasonable, both qualitatively and quantitatively. Suggestions for future activities are presented.
bistable composites; mfc tm actuator; morphing; rayleigh; ritz technique
Information theory and statistical mechanics
Physical review
106
4
620-630
1957
10.1103/PhysRev.106.620
Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available. It is conCluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists only of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.
Carbon composites based on multi-axial multi-ply stitched preforms. Part 4. Mechanical properties of composites and damage observation
Composites Part A: Applied Science and Manufacturing
36
9
1207-1221
2005
10.1016/j.compositesa.2005.02.004
Multi-axial multi-ply fabric (MMF) or non-crimp stitched carbon fabric (NCF) reinforced epoxy composites, produced by the resin transfer moulding process are described. The mechanical properties of the composites - tensile, in-plane shear and out-of-plane shear - are measured in a number of orientations relative to the stitching direction for different NCF based laminates: quadriaxial, biaxial ??45 and 0/90??, as well as unidirectional. As expected, the quadriaxial laminates show a quasi-isotropic behaviour while biaxial laminates show an an-isotropic behaviour. The mechanical properties of the biaxial ??45?? laminates are similar to the 0/90?? laminates in the corresponding directions. The in-plane shear properties of the materials are strongly dependent on the amount of reinforcement in the +45 and -45?? direction relative to the loading direction. Absence of a significant difference in stiffness between experimental results and classical laminate theory predictions reveals that stitching has minor effects on the stiffness of this material. Tensile tests on 0/90?? laminates were accompanied by acoustic emission registration. The results were correlated with X-ray and C-Scan damage observation. Early (at 0.3% applied strain for load in fibre direction) initiation of damage has been detected. Damage sites are correlated with the resin-rich zones created by the stitching. ?? 2005 Elsevier Ltd. All rights reserved.
A. Fabrics/textiles; A. Laminates; B. Mechanical properties; D. Mechanical testing; D. Non-destructive testing
Bulge Testing Transparent Thin Films with Moire Deflectometry
Experimental Mechanics
50
2
217-225
2010
10.1007/s11340-009-9291-0
The problem that is addressed here is the measurement of the mechanical properties of very thin, transparent films using bulge tests. All existing techniques make use of reflection from the film surface, but they can be difficult or impossible to apply to very thin, transparent films. Consequentyly, a novel approach based on the formation of a lens structure and using transmitted light is developed. IN this technique, the focal length of the lens structure formed by the bulged film and the pressurizing medium is determined by moire deflectometry with a corrected governing equation. The resulting curvature of the bulge film is used in the stress analysis of the bulge-test. By combining circular and rectangular configurations, the Young's modulus and Poisson's ratio of a 3 um PET film were 4.65 +/- 0.11 GPa and 0.34 +/- 0.01 respectively. Consistent residual stresses were obtained from both configurations.
bulge test; lens structure; Micro-opto-electro-mechanical systems (MOEMS); Moire deflectometry; Poisson's ratio; radius of curvature; Young's modulus
Contact mechanics
International Journal of Solids and Structures
37
1-2
29-43
2000
10.1016/S0020-7683(99)00075-X
Contact problems are central to Solid Mechanics, because contact is the principal method of applying loads to a deformable body and the resulting stress concentration is often the most critical point in the body. Contact is characterized by unilateral inequalities, describing the physical impossibility of tensile contact tractions (except under special circumstances) and of material interpenetration. Additional inequalities and/or non-linearities are introduced when friction laws are taken into account. These complex boundary conditions can lead to problems with existence and uniqueness of quasi-static solution and to lack of convergence of numerical algorithms. In frictional problems, there can also be lack of stability, leading to stick–slip motion and frictional vibrations. If the material is non-linear, the solution of contact problems is greatly complicated, but recent work has shown that indentation of a power-law material by a power law punch is self-similar, even in the presence of friction, so that the complete history of loading in such cases can be described by the (usually numerical) solution of a single problem. Real contacting surfaces are rough, leading to the concentration of contact in a cluster of microscopic actual contact areas. This affects the conduction of heat and electricity across the interface as well as the mechanical contact process. Adequate description of such systems requires a random process or statistical treatment and recent results suggest that surfaces possess fractal properties that can be used to obtain a more efficient mathematical characterization. Contact problems are very sensitive to minor profile changes in the contacting bodies and hence are also affected by thermoelastic distortion. Important applications include cases where non-uniform temperatures are associated with frictional heating or the conduction of heat across a non-uniform interface. The resulting coupled thermomechanical problem can be unstable, leading to a rich range of physical phenomena. Other recent developments are also briefly surveyed, including examples of anisotropic materials, elastodynamic problems and fretting fatigue.
Mechanics of Machines
Applied Mechanics Reviews
57
2
B11
2004
10.1115/1.1704624
Mechanics of Machines covers the basic concepts of gears, gear trains, the mechanics of rigid bodies, and graphical and analytical kinematic analyses of planar mechanisms.
A cohesive approach to thin-shell fracture and fragmentation
Computer Methods in Applied Mechanics and Engineering
194
21-24 SPEC. ISS.
2604-2618
2005
10.1016/j.cma.2004.07.048
We develop a finite-element method for the simulation of dynamic fracture and fragmentation of thin-shells. The shell is spatially discretized with subdivision shell elements and the fracture along the element edges is modeled with a cohesive law. In order to follow the propagation and branching of cracks, subdivision shell elements are pre-fractured ab initio and the crack opening is constrained prior to crack nucleation. This approach allows for shell fracture in an in-plane tearing mode, a shearing mode, or a bending of hinge mode. The good performance of the method is demonstrated through the simulation of petalling failure experiments in aluminum plates. ?? 2005 Elsevier B.V. All rights reserved.
Cohesive fracture; Finite elements; Petalling failure; Shells; Subdivision shape functions
Influence of glass fibre/epoxy resin interface on static mechanical properties of unidirectional composites and on fatigue performance of cross ply composites
Composites Part A: Applied Science and Manufacturing
29
5-6
701-705
1998
10.1016/S1359-835X(97)00106-1
In this study the influence of the interface of differently sized glass fibres on the mechanical properties of glass fibre/epoxy resin composites is investigated. It is of essential importance that all other parameters are kept constant so that the behaviour differences can only be attributed to interfacial phenomena. The results of micromechanical and macromechanical tests of unidirectional laminates characterize the fibre/matrix adhesioh. In the second part of this study the tensile fatigue performance of cross ply laminates with two different sizings in the 0” and 90” layers is investigated. The best fatigue performance is determined for composites with a good nbre/ matrix interaction in both layers.
a; b; fibres; interface; interphase; resin; tbermosetting
Plastic ratcheting induced cracks in thin film structures
Journal of the Mechanics and Physics of Solids
50
1079-1098
2002
10.1016/S0022-5096(01)00113-2
In the microelectronic and photonic industries, temperature cycling has long been used as a reliability test to qualify integrated materials structures of small feature sizes. The test is time consuming, and is a bottleneck for innovation. Tremendous needs exist to understand various failure modes in the integrated structures caused by cyclic temperatures. This paper presents a systematic study of a failure mechanism recently discovered by the authors. In a thin film structure comprising both ductile and brittle materials, the thermal expansion mismatch can cause the ductile material to plastically yield in every temperature cycle. Under certain circumstances, the plastic deformation ratchets, namely, accumulates in the same direction as the temperature cycles. The ratcheting deformation in the ductile material may build up stress in the brittle materials, leading to cracking. The paper introduces an analogy between ratcheting and viscous flow. An analytical model is developed, which explains the experimental observations, and allows one to design the structure to avert this failure mode. Design rules with increasing levels of sophistication are described. Concepts presented here are generic to related phenomena in thin film structures.
cracking; plasticity; ratcheting; temperature cycling; thin ÿlms
Petroleum Related Rock Mechanics
Marine Environmental Research
71
5
357-68
2011
10.1016/0148-9062(93)92632-Z
Subsurface sediments from a pockmark area in South-Western Barents Sea have been earlier found to contain elevated levels of petroleum-related polycyclic aromatic hydrocarbons. This work describes a comprehensive analysis of various biomarkers, including the highly source-specific hopanes, in a 4.5m long gravity core from the same area, together with subsurface sediment samples from other areas in the region without pockmarks present ("background samples"). A clear difference between the pockmark gravity core and the background sediment cores was found, both with regard to genesis and the level of transformation of organic matter. A number of indicator parameters, such as methylphenanthrene index (MPI-1), point towards a significantly higher maturity of hydrocarbons in the pockmark core throughout its length as compared to the other sampled locations. Higher contents of microbial hopanoids (hopenes) may indicate the former presence of petroleum. These findings confirm the hypothesis of a natural hydrocarbon source in the deeper strata present in the studied location with pockmarks.
Effect of ulnar ostectomy on intra-articular pressure mapping and contact mechanics of the congruent and incongruent canine elbow ex vivo
Veterinary Surgery
43
339-346
2014
10.1111/j.1532-950X.2014.12137.x
OBJECTIVE: To determine (1) the effect of elbow incongruity on contact mechanics and (2) the effect of treatment of this incongruity with 1 of 2 ulnar ostectomies in the canine elbow. STUDY DESIGN: Ex vivo biomechanical study. SAMPLE POPULATION: Unpaired cadaveric canine forelimbs (n = 17). METHODS: In a servohydraulic testing frame, thin-film pressure sensors were placed into the lateral and medial compartments of the elbow. Specimens were tested in 135° of elbow joint flexion at 200 N of cyclic axial force, followed by a 20 seconds hold. Intra-articular contact area (CA), mean contact pressure (mCP) and peak contact pressure (pCP) were measured in each compartment. After radial shortening, testing was repeated and limbs randomized into proximal ulnar ostectomy with IM pin (PUO) or sequential distal ulnar ostectomy (DUO), interosseous ligament release (DUO-L), and ulnar attachment of the abductor pollicis longus muscle and interosseous membrane release (DUO-ML). Paired t-tests were used to compare each treatment to baseline values. Differences between treatment groups were evaluated with a mixed model with random effect to adjust for the clustering of limbs within dog. P < .05 was considered significant. RESULTS: Radial shortening resulted in shift of mCP and pCP from the lateral to the medial compartment. The PUO group resulted in normalization of medial compartment mCP and decrease of pCP, whereas in the DUO group return to baseline was achieved only after DUO-ML. CONCLUSION: PUO is effective in unloading medial compartment pCP in an incongruent joint.
The past, present, and future of fracture mechanics
Engineering Fracture Mechanics
69
5
533-553
2002
10.1016/S0013-7944(01)00101-1
The science of fracture mechanics was born and came to maturity in the 20th century. Its literature is now vast. Perhaps the most successful application of fracture mechanics is to fatigue. However, this short paper is limited to a core topic of fracture, the initiation and propagation of fracture under monotonic loading at low strain rates. As the author was invited to present this paper on the occasion of his 65th birthday, it is a somewhat personal view of the development and future of fracture mechanics, but it is hoped that it will interest many, especially the young researchers at the beginning of their careers. ?? 2002 Elsevier Science Ltd. All rights reserved.
Substrate curvature due to thin film mismatch strain in the nonlinear deformation range
Journal of the Mechanics and Physics of Solids
48
6
1159-1174
2000
10.1016/S0022-5096(99)00070-8
The physical system considered is a thin film bonded to the surface of an initially flat circular substrate, in the case when a residual stress exists due to an incompatible mismatch strain in the film. The magnitude of the mismatch strain is often inferred from a measurement of the curvature it induces in the substrate. This discussion is focused on the limit of the linear range of the relationship between the mismatch strain and the substrate curvature, on the degree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and on the bifurcation of deformation mode from axial symmetry to asymmetry with increasing mismatch strain. Results are obtained on the basis of both simple models and more detailed finite element simulations.
buckling; ections; finite de; layered material; lms; stability and bifurcation; thin
Nanomechanical Architectures—Mechanics-Driven Fabrication Based on Crystalline Membranes
MRS Bulletin
34
March
190-195
2009
10.1557/mrs2009.51
Bending of thin sheets or ribbons is a ubiquitous phenomenon that impacts our daily lives, from the household thermostat to sensors in airbags. At nanometer-scale thicknesses, the mechanics responsible for bending and other distortions in sheets can be employed to create a nanofabrication approach leading to novel nanostructures. The process and resulting structures have been aptly referred to as nanomechanical architecture. In this article, we review recent progress in atomistic simulations that not only have helped to reveal the physical mechanisms underlying this nanofabrication approach, but also have made predictions of new nanostructures that can be created. The simulations demonstrate the importance of the atomic structure of the crystalline membrane and of the intrinsic surface stress in governing membrane bending behavior at the nanoscale and making the behavior fundamentally distinct from that at the macroscale. Molecular dynamics simulations of the bending of patterned graphene (a single-atomic layer film) suggest a new method for synthesizing carbon nanotubes with unprecedented control over their size and chirality.
Modelling of the mechanical behaviour of woven-fabric CFRP laminates up to failure
Composites Science and Technology
61
221-230
2001
10.1016/S0266-3538(00)00199-8
In order to model the mechanical behaviour of woven composite materials up to failure, we have adapted models developed for unidirectional plies and based on damage mechanics. The model used to describe the degradations is non-linear with progressive damage and inelastic strains. The behaviour of woven plies in the warp and fill directions is elastic and brittle. The progressive loss of rigidity (shear modulus) is described by a damage variable, the development of which depends on the shear load but also on the in-plane tension load. The inelastic strains concern only shear strains. The identification of the model was done by means of two tensile tests. A program that makes it possible to simulate the woven laminate behaviour was carried out. Validation tests, which compare numerical results and experimental results, have shown the relevance of the model. These tests show a lesser sensitivity of woven-ply laminates to delamination phenomena with respect to unidirectional plies. In the case of woven-ply laminates, the only inelastic damageable model of the ply should be sufficient to describe the behaviour of any laminate.
a; b; c; damage mechanics; fracture; laminates; mechanical properties; textile composites
Finite element model for NCF composite reinforcement preforming: Importance of inter-ply sliding
Composites Part A: Applied Science and Manufacturing
43
12
2269-2277
2012
10.1016/j.compositesa.2012.08.005
A semi-discrete model is proposed for the simulation of non-crimp fabric reinforcement preforming. This approach is based on experimental observations of in-plane shear deformations of the reinforcement, out-of-plane bending and inter-ply sliding during the non-crimp fabric preforming. The experiment highlights strong sliding between the two plies of the non-crimp fabric during forming. The two plies of fibers composing the reinforcement are modeled by two layers of shell elements; the stitches are modeled by bar elements. The relationship between bar and shell elements is managed with a specific contact and anisotropic friction law associated to sliding threshold. This meso-macroscopic approach allows the simulation of industrial part forming in a reasonable computational time. The model shows a good prediction of deformations during the forming on a hemispherical shape. In particular sliding between the two fiber layers of the NCF obtained by the simulation is in good agreement with that measured during the preforming experiment. ?? 2012 Elsevier Ltd. All rights reserved.
A. Fabrics/textiles; C. Finite element analysis (FEA); E. Forming; Non-crimp fabric (NCF)
An approximate analysis of the collapse of thin cylindrical shells under axial loading
Quarterly Journal of Mechanics and Applied Mathematics
13
1
10-15
1960
10.1093/qjmam/13.1.10
An approximate theory for the process is derived, leading to a solution of the type P = Ct1.5√D, where P is the collapse load, t the shell thickness, D the shell diameter, and C a constant for any given material. Good agreement is exhibited between this relationship and experimental results
Delamination growth from face sheet seams in cross-ply titanium/graphite hybrid laminates
Composites Science and Technology
61
2
261-269
2001
10.1016/S0266-3538(00)00206-2
A test program was conducted to study the fatigue delamination behavior of titanium/graphite hybrid laminates (TiGr) with seams in the titanium face sheets. Tension fatigue experiments were conducted at −18°C, 21°C (room temperature), 93°C, and at 177°C on cross-ply, [Ti/0/90/02]s, titanium/graphite hybrid laminates (TiGr). The delamination growth rate obeyed a power-law function of the applied strain energy release rate range. The prefactor on the power-law function showed a strong dependence on temperature. In addition, experiments were performed on laminates with ±30° plies. The primary damage mode in this lay-up was edge delamination of the interior plies. Analysis of the [Ti/0/90/±θ]s family of laminates indicated that for angles greater than 10°, edge delamination would be the dominant damage mode in coupon specimens.
Factors influencing the learning of classical mechanics
American Journal of Physics
48
1980
1074
1980
10.1119/1.12290
The study in this paper investigates the combined effect of certain variables on student achievement in classical mechanics.....
Mechanics of fossil vertebrates
Journal of the Geological Society, London
146
1
41-52
1989
All the principal branches of mechanics have been used in studies of fossil vertebrates, including kinematics, statics, solid dynamics, strength of materials, hydrostatics and hydrodynamics. They have been applied to problems concerning jaws, posture, running, swimming, flight and blood circulatio
fossil vertebrates; hydrodynamics; hydrostatics; kinematics; solid dynamics; statics; strength
Convergence of strain energy release rate components for Edge-Delaminated composite laminates
Engineering Fracture Mechanics
30
3
383-396
1988
10.1016/0013-7944(88)90196-8
Strain energy release rates for edge-delaminated composite laminates were obtained using quasi three-dimensional finite element analysis. The problem of edge-delamination at the −3590 interfaces of an eight ply [0/±35/90]s composite laminate subjected to uniform axial strain was studied. A quasi three-dimensional finite element analysis was used to calculate the total and individual components of the strain energy release rate. The individual components did not show convergence as the delamination tip elements were made smaller. In contrast, the total strain energy release rate, G, converged and remained unchanged as the delamination tip elements were made smaller and agreed with the total G calculated using a closed-form equation derived from the rule of mixtures and classical laminated plate theory. The studies of the near-field solutions for a delamination at an interface between two dissimilar isotropic or orthotropic plates showed that the imaginary part of the singularity is the cause of the nonconvergent behavior of the individual components. To evaluate the accuracy of the results, an eight ply [0/±35/r/90]s laminate with the delamination modeled in a thin resin layer, similar to the resin layer that exists between the −35 and 90 plies, was analysed. Because the delamination exists in a homogeneous isotropic material, the oscillatory component of the singularity vanishes. The strain energy release rates remained unchanged as the delamination tip elements were made smaller. Comparison of the strain energy release rates for the ‘bare’ interface laminate, i.e. one without the resin layer, and for the laminate with the resin showed that the ‘bare’ interface models are a very good approximation for the resin case if the delamination tip elements were one-quarter to one-half of the ply thickness.
ON THE EXTENDED THEORY OF MECHANICS OF TWISTED YARNS.
Journal of the Textile Machinery Society of Japan
25
3
68-72
1979
10.1080/09636416908629980
The theory of mechanics of twisted homogeneous filament yarns is extended in terms of fiber angles to the yarn axis. Firstly, the axial strain of an element in a yarn is generally considered in the three dimensional analysis. The axial stress of the element is then examined in terms of each element angle to the axis. From these analyses on, the yarn stress can be discussed as a function of the filament angles to the yarn axis as well as the distribution function for the angles and the filament stress according to the strain. Secondly, in order to confirm the possibility that a yarn stress-strain curve can be computed by knowing the distribution for the angles, some simple mathematical models are applied as general disfunctions for the filament angles in a yarn. The theory and computer programs developed was used not only to compute but also to predict the stress-strain curve of each particular structure of homogeneous filament yarns such as the single, the ply, or even the cabled yarn. Numerical and graphical outputs of estimated yarn stresses has been obtained by the input of some experimental data and assumed values.
Analysis of damage mode transition in a cross-ply laminate under uniaxial loading
Composite Structures
55
1
115-126
2002
10.1016/S0263-8223(01)00133-7
The aim of this work is to study the transition from one damage mode to another. The three damage mechanisms usually observed in [0m/90n]s long fibre cross-ply laminates with organic matrix are transverse cracking, which appears first, longitudinal cracking and/or delamination. The proposed analytical model is meant to describe the development of transverse cracks and to predict the order of initiation of subsequent damage modes; it relies on the strain energy release rate associated with each damage mechanism.
critical damage density; damage mode transition; delamination; longitudinal cracking; strain energy release rate; transverse cracking
Thermal buckling behavior of cross-ply hybrid composite laminates with inclined crack
Composites Science and Technology
66
15
2965-2970
2006
10.1016/j.compscitech.2006.02.009
Thermal buckling analysis of symmetric and antisymmetric cross-ply laminated hybrid composite plates with an inclined crack subjected to a uniform temperature rise are presented in this paper. The first-order shear deformation theory in conjunction with variational energy method is employed in the mathematical formulation. The eight-node Lagrangian finite element technique is used for obtaining the thermal buckling temperatures of hybrid composite laminates. The effects of crack size and lay-up sequences on the thermal buckling temperatures for symmetric and antisymmetric plates are investigated. The results are shown in graphical form for various boundary conditions.
Finite element method; Hybrid composite plates; Thermal buckling
Dynamic quantized fracture mechanics
International Journal of Fracture
140
1-4
159-168
2006
10.1007/s10704-006-0098-z
A new quantum action-based theory, Dynamic Quantized Fracture Mechanics (DQFM), is presented that modifies continuum-based dynamic fracture mechanics. The crack propagation is assumed as quantized in both space and time. The static limit case corresponds to Quantized Fracture Mechanics (QFM), that we have recently developed to predict the strength of nanostructures.
Dynamic fracture; Finite fracture; Impacts; Nanostructures; Nanotubes; Quantized fracture; Strength
Estimation of Adhesion Hysteresis at Polymer/Oxide Interfaces Using Rolling Contact Mechanics
Langmuir
14
11
3090-3100
1998
10.1021/la971061m
The rolling of a cylinder on a flat plate can be viewed as the propagation of two cracks-one closing at the advancing edge and the other opening at the trailing edge. The difference of adhesion in these two regions, i.e. the adhesion hysteresis, depends on the nonequilibrium interfacial processes in an elastic system. This rolling contact geometry was used to study the effects of dispersion forces and specific interactions on interfacial adhesion hysteresis. In order to accomplish this objective, hemicylindrical elastomers of polydimethylsiloxane (PDMS)-both unmodified and plasma oxidized-were rolled on thin PDMS films bonded to silicon wafers. Plasma oxidation generates a silica-like surface on PDMS elastomer, which interacts with PDMS molecules via hydrogen-bonding forces. The adhesion hysteresis in the latter case is large and depends significantly on the molecular weight of the grafted polymer, whereas the hysteresis is rather negligible for purely dispersive systems. These results are interpreted in terms of the orientation and relaxation of polymer chains, which has its origin in the Lake-Thomas effect.
3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported
Composite Structures
69
1
77-87
2005
10.1016/j.compstruct.2004.05.015
On the basis of the three-dimensional theory of elasticity, a semi-analytical method, which combines the state space approach with the technique of differential quadrature, is developed for free vibration of a cross-ply laminated composite rectangular plate. The plate is assumed to be simply supported at one pair of opposite edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at these two edges. The technique of differential quadrature is then incorporated into the state equation, which enables one to obtain a general solution for orthotropic laminates with arbitrary boundary conditions at the other pair of opposite edges. The method is verified by comparing the present results with the exact elasticity solution for a simply supported plate. Further numerical calculations are carried out and effects of some parameters on natural frequency are discussed. © 2004 Elsevier Ltd. All rights reserved.
Cross-ply laminated rectangular plates; Differential quadrature; Free vibration; Three-dimensional theory of elasticity
Progressive failure modeling in notched cross-ply fibrous composites
Applied Composite Materials
8
1
63-74
2001
10.1023/a:1008909000755
This study models and simulates progressive failure initiating from a notch tip of a laminated fibrous composite specimen subjected to tensile in-plane loading. The micro/macro-level approach is used. The micro-level analysis uses the 3-D unit-cell model while macro-level analysis uses the finite element analysis technique. A cross-ply laminate with double-edge notches was studied to investigate delamination, fiber splitting, and transverse matrix cracking in the specimen. Numerical results are compared to previous experimental work.
Computer simulation; Damage and failure; Delamination; Failure (mechanical); Fiber reinforced materials; Fiber splitting; Fibrous composite; Finite element method; Mathematical models; Microlevel analysis; Micromechanics; Tensile in plane loading; Transverse matrix cracking
Characterisation of the sliding friction response of peel-ply textured surfaces
Composites Part A: Applied Science and Manufacturing
63
123-132
2014
10.1016/j.compositesa.2014.04.004
The present paper reports on effects of texture, contamination by aircraft operating fluids, and contact pressure on the sliding friction response of polymer surfaces. This study provides essential data necessary for the design of friction-based energy absorption devices. Their functionality is ought to integrate into structural elements of aircraft fuselages made from carbon fibre reinforced plastics. The paper specifically addresses epoxy resin surfaces of continuous fibre reinforced composite material currently applied in aircraft industry. Peel-ply was utilised to achieve the characteristic surface texture. A pin-on-flat type test apparatus was designed and used to determine the friction coefficient as a function of the initial surface texture, the contamination by five different aircraft operating fluids, as well as the contact pressure. The sliding friction results obtained in this study indicate a significant influence of both, the surface texture and the state of contamination. © 2014 Elsevier B.V. All rights reserved.
A. Prepreg; B. Physical properties; D. Physical methods of analysis; Sliding friction
The mechanics of marine sediment gravity flows
Margin Sedimentation
Continental Margin Sedimentation
2007
10.1002/9781444304398.ch6
Summary Sediment gravity flows, particularly those in the marine environment, are dynamically interesting because of the non-linear interaction of mixing, sediment entrainment/suspension and water-column stratification. Turbidity currents, which are strongly controlled by mixing at their fronts, are the best understood mode of sediment gravity flows. The type of mixing not only controls flow and deposition near the front, but also changes the dynamics of turbidity currents flowing in self-formed channels. Debris flows, on the other hand, mix little with ambient fluid. In fact, they have been shown to hydroplane, i.e. glide on a thin film of water. Hydroplaning enables marine debris flows to runout much farther than their subaerial equivalents. Some sediment gravity flows require external energy, from sources such as surface waves. When these flows are considered as stratification-limited turbidity currents, models are able to predict observed downslope sediment fluxes. Most marine sediment gravity flows are supercritical and thus controlled by sediment supply to the water column. Therefore, the genesis of the flows is the key to their understanding and prediction. Virtually every subaqueous failure produces a turbidity current, but they engage only a small percentage of the initially failed material. Wave-induced resuspension can produce and sustain sediment gravity flows. Flooding rivers can also do this, but the complex interactions of settling and turbulence need to be better understood and measured to quantify this effect and document its occurrence. Ultimately, only integrative numerical models can connect these related phenomena, and supply realistic predictions of the marine record.
debris flows; fluid mud; gravity flows; hydroplaning; sur-; turbidity currents
Categorical Quantum Mechanics
Handbook of Quantum Logic and Quantum Structures
261-323
2009
10.1016/B978-0-444-52869-8.50010-4
This invited chapter in the Handbook of Quantum Logic and Quantum Structures consists of two parts: 1. A substantially updated version of quant-ph/0402130 by the same authors, which initiated the area of categorical quantum mechanics, but had not yet been published in full length; 2. An overview of the progress which has been made since then in this area.
A microbeam bending method for studying stress-strain relations for metal thin films on silicon substrates
Journal of the Mechanics and Physics of Solids
53
3
619-638
2005
10.1016/j.jmps.2004.08.007
We have developed a microbeam bending technique for determining elastic-plastic, stress-strain relations for thin metal films on silicon substrates. The method is similar to previous microbeam bending techniques, except that triangular silicon microbeams are used in place of rectangular beams. The triangular beam has the advantage that the entire film on the top surface of the beam is subjected to a uniform state of plane strain as the beam is deflected, unlike the standard rectangular geometry where the bending is concentrated at the support. To extract the average stress-strain relations for the film, we present a method of analysis that requires computation of the neutral plane for bending, which changes as the film deforms plastically. This method can be used to determine the elastic-plastic properties of thin metal films on silicon substrates up to strains of about 1%. Utilizing this technique, both yielding and strain hardening of Cu thin films on silicon substrates have been investigated. Copper films with dual crystallographic textures and different grain sizes, as well as others with strong ???1 1 1??? textures have been studied. Three strongly textured ???1 1 1??? films were studied to examine the effect of film thickness on the deformation properties of the film. These films show very high rates of work hardening, and an increase in the yield stress and work hardening rate with decreasing film thickness, consistent with current dislocation models. ?? 2004 Elsevier Ltd. All rights reserved.
MEMS; Plasticity; Small-scale yielding; Strain hardening; Thin films
From continuum mechanics to fracture mechanics: The strong discontinuity approach
Engineering Fracture Mechanics
69
2
113-136
2001
10.1016/S0013-7944(01)00060-1
The paper deals with the strong discontinuity approach and shows the links with the decohesive fracture mechanics provided by that approach. On the basis of 1D continuum damage models it is shown that, by introducing some few ingredients like the strong discontinuity kinematics, discrete constitutive models (traction vs. displacement jumps) are automatically induced. For the general 2D-3D cases it is shown that the weak discontinuity concept is an additional ingredient, necessary in order to fulfill the strong discontinuity conditions, which allows to establish additional links with the fracture process zone concept. Also classical fracture mechanics properties as the fracture energy are related to the continuum model properties in a straightforward manner. ?? 2001 Elsevier Science Ltd. All rights reserved.
Damage; Fracture; Localization; Strong discontinuities
Vehicle Crash Mechanics
Applied Mechanics Reviews
56
5
B68
2003
10.1115/1.1584416
Governed by strict regulations and the intricate balance of complex interactions among variables, the application of mechanics to vehicle crashworthiness is not a simple task. It demands a solid understanding of the fundamentals, careful analysis, and practical knowledge of the tools and techniques of that analysis. Vehicle Crash Mechanics sets forth the basic principles of engineering mechanics and applies them to the issue of crashworthiness. The author studies the three primary elements of crashworthiness: vehicle, occupant, and restraint. He illustrates their dynamic interactions through analytical models, experimental methods, and test data from actual crash tests. Parallel development of the analysis of actual test results and the interpretation of mathematical models related to the test provides insight into the parameters and interactions that influence the results. Detailed case studies present real-world crash tests, accidents, and the effectiveness of air bag and crash sensing systems. Design analysis formulas and two- and three-dimensional charts help in visualizing the complex interactions of the design variables. Vehicle crashworthiness is a complex, multifaceted area of study. Vehicle Crash Mechanics clarifies its complexities. The book builds a solid foundation and presents up-to-date techniques needed to meet the ultimate goal of crashworthiness analysis and experimentation: to satisfy and perhaps exceed the safety requirements mandated by law.
Damage mechanics constitutive model for Pb/Sn solder joints incorporating nonlinear kinematic hardening and rate dependent effects using a return mapping integration algorithm
Mechanics of Materials
38
7
585-598
2006
10.1016/j.mechmat.2005.11.008
A thermodynamics-based damage mechanics rate dependent constitutive model is used to simulate experiments conducted on thin layer eutectic Pb/Sn solder joints. As compared to previous implementations of the model here we correct the difficulties introduced by the slow convergency rate of the Owen and Hinton (Owen, D.R.J., Hinton, E., 1980. Finite Element in Plasticity. Pineridge Press Limited, Swansea, UK) integration scheme. To this end, we time-integrated the model with a classical return mapping algorithm where rate dependency, nonlinear kinematic hardening of the Armstrong–Frederick type and damage effects are simultaneously coupled. The model is implemented into the commercial finite element code ABAQUS via its user material subroutine capability and validated against experimental results. We simulated monotonic shear, cyclic shear and fatigue shear experiments performed on homemade thin layer solder joints. The simulation results are in good agreement with the experiments and the model accurately describes the true behavior of Pb/Sn solder alloys. As a direct advantage of the new model implementation this can be used for axisymmetric and 3D simulations as opposed to the plain strain-only capability in the Owen and Hinton (Owen, D.R.J., Hinton, E., 1980. Finite Element in Plasticity. Pineridge Press Limited, Swansea, UK) integration scheme.
constitutive modeling; damage mechanics; integration scheme; microelectronics packaging; rate dependence; solder joints
Experimental damage mechanics of microelectronic solder joints under fatigue loading
Mechanics of Materials
36
11
1111-1121
2004
10.1016/j.mechmat.2003.10.002
Fatigue damage is a progressive process of material degradation. The objective of this study is to experimentally qualify the damage mechanism in solder joints in electronic packaging under thermal fatigue loading. Another objective of this paper is to show that damage mechanism under thermal cycling and mechanical cycling are very different. Elastic modulus degradation under thermal cycling, which is considered as a physically detectable quantity of material degradation, was measured by Nano-indenter. It was compared with tendency of inelastic strain accumulation of solder joints in Ball Grid Array package under thermal cycling, which was measured by Moir e interferometry. Fatigue damage evolution in solder joints with traditional load-drop criterion was also investigated by shear strain hysteresis loops from strain-controlled cyclic shear testing of thin layer solder joints. Load-drop behavior was compared with elastic modulus degradation of solder joints under thermal cycling. Following conventional Coffin–Manson approach, S–N curve was obtained from isothermal fatigue testing with load-drop criterion. Coffin–Manson curves obtained from strain-controlled mechanical tests were used to predict fatigue life of solder joints. In this paper it is shown that this approach underestimates the fatigue life by an order of magnitude. Results obtained in this project indicate that thermal fatigue and isothermal mechanical fatigue are completely different damage mechanism for microstructurally evolving materials.
MODELING of SINGLE PLY THERMOPLASTIC POLYOLEFIN ROOFING
Society of Plastics Engineers Annual Technical Conference
2020-2024
2013
A finite element simulation is developed to model the stress distribution of heat seamed Single Ply thermoplastic polyolefin (TPO) composite under FM wind uplift test conditions. Separate models are developed for the TPO layers, reinforcement layer, and lap-joint geometry in order to obtain an integrated TPO composite model. TPO membrane material and attachment parameters are evaluated for wind uplift enhancement. Good correlation is observed between model prediction and real wind uplift test results.
Foundations of Mechanics
American Journal of Physics
36
280
1968
10.1119/1.1974504
Preface to the Second Edition Since the first edition of this book appeared in 1967, there has been a great deal of activity in the field of symplectic geometry and Hamiltonian systems. In addition to the recent textbooks of Arnold, Arnold-Avez, Godbillon, Guillemin-Sternberg, Siegel-Moser, and Souriau, there have been many research articles published. Two good collections are "Symposia Mathematica," vol. XIV, and "Géométrie Symplectique el Physique Mathématique," CNRS, Colloque Internationaux, no. 237. There are also important survey articles, such as Weinstein 1977b. The text and bibliography contain many of the important new references we are aware of. We have continued to find the classic works, especially Whittaker 1959, invaluable. The basic audience for the book remains the same: mathematicians, physicists, and engineers interested in geometrical methods in mechanics, assuming a background in calculus, linear algebra, some classical analysis, and point set topology. We include most of the basic results in manifold theory, as well as some key facts from point set topology and Lie group theory. Other things used without proof are clearly noted. We have updated the material on symmetry groups and qualitative theory, added new sections on the rigid body, topology and mechanics, and quantization, and other topics, and have made numerous corrections and additions. In fact, some of the results in this edition are new. We have made two major changes in notation: we now use f for pull-back (the first edition used fsub), in accordance with standard usage, and have adopted the "Bourbaki" convention for wedge product. The latter eliminates many annoying factors of 2. A. N. Kolmogorov's address at the 1954 International Congress of Mathematicians marked an important historical point in the development of the theory, and is reproduced as an appendix. The work of Kolmogorov, Arnold, and Moser and its application to Laplace's question of stability of the solar system remains one of the goals of the exposition. For complete details of all tbe theorems needed in this direction, outside references will have to be consulted, such as Siegel-Moser 1971 and Moser 1973a. We are pleased to acknowledge valuable assistance from Paul Chernoff, Wlodek Tulczyjew, Morris Hirsh, Alan Weinstein, and our invaluable assistant authors, Richard Cushman and Tudor Ratiu, who all contributed some of their original material for incorporation into the text. Also, we are grateful to Ethan Akin, Kentaro Mikami, Judy Arms, Harold Naparst, Michael Buchner, Ed Nelson, Robert Cahn, Sheldon Newhouse, Emil Chorosoff, George Oster, André Deprit, Jean-Paul Penot, Bob Devaney, Joel Robbin, Hans Duistermaat, Clark Robinson, John Guckenheimer, David Rod, Martin Gutzwiller, William Satzer, Richard Hansen, Dieter Schmidt, Morris Kirsch, Mike Shub, Michael Hoffman, Steve Smale, Andrei Iacob, Rich Spencer, Robert Jantzen, Mike Spivak, Therese Langer, Dan Sunday, Ken Meyer, Floris Takens, and Randy Wohl for contributions, remarks, and corrections which we have included in this edition. Further, we express our gratitude to Chris Shaw, who made exceptional efforts to transfom our sketches into the graphics which illustrate the text, to Peter Coha for his assistance in organizing the Museum and Bibliography, and to Ruthie Cephas, Jody Hilbun, Marnie McElhiney, Ruth (Bionic Fingers) Suzuki, and Ikuko Workman for their superb typing job. Theoretical mechanics is an ever-expanding subject. We will appreciate comments from readers regarding new results and shortcomings in this edition. RALPH ABRAHAM JERROLD E. MARSDEN
Mechanics of Robotic Manipulation
Technology
266
2001
"Manipulation" refers to a variety of physical changes made to the world around us. Mechanics of Robotic Manipulation addresses one form of robotic manipulation, moving objects, and the various processes involvedgrasping, carrying, pushing, dropping, throwing, and so on. Unlike most books on the subject, it focuses on manipulation rather than manipulators. This attention to processes rather than devices allows a more fundamental approach, leading to results that apply to a broad range of devices, not just robotic arms.The book draws both on classical mechanics and on classical planning, which introduces the element of imperfect information. The book does not propose a specific solution to the problem of manipulation, but rather outlines a path of inquiry.
Influence of rock properties and environmental conditions on thin spray-on liner adhesive bond
International Journal of Rock Mechanics and Mining Sciences
48
7
1196-1198
2011
10.1016/j.ijrmms.2011.06.006
International Journal of Rock Mechanics and Mining Sciences, 48 + (2011) 1196-1198. doi:10.1016/j.ijrmms.2011.06.006
Classical and Quantum Mechanics via Lie algebras
Quantum
502
2008
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
A study of the behaviour of a thin sheet of moving liquid
Journal of Fluid Mechanics
10
02
297
1961
10.1017/S002211206100024X
An investigation has been carried out on the behaviour of a thin sheet of liquid in connexion with the new method of lacquer application known as ‘curtain coating ’. A method is described for measuring the velocity of the sheet and an equation deduced for calculating this for a liquid of any viscosity. The minimum liquid flow rate required to maintain a stable sheet is discussed, and some effects of the impingement of the sheet on a rapidly moving surface are described.
Numerical homogenization of cracking processes in thin fibre-epoxy layers
European Journal of Mechanics, A/Solids
29
2
119-131
2010
10.1016/j.euromechsol.2009.09.006
Discrete microscale fracture processes in thin fibre-epoxy layers are connected to a mesoscale traction-separation law through a numerical homogenization framework. The microscale fracture processes are studied with the finite element method, where cracking within the epoxy and debonding between fibres and epoxy is simulated by placing interface elements furnished with a mixed-mode interface damage model in between the continuum elements modelling the fibres and epoxy. It is demonstrated how the effective traction-separation response and the corresponding microscale fracture patterns under mesoscale tensile conditions depend on the sample size, the fibre volume fraction and the presence of imperfections. © 2009 Elsevier Masson SAS. All rights reserved.
Discrete fractal fracture mechanics
Engineering Fracture Mechanics
75
5
1127-1142
2008
10.1016/j.engfracmech.2007.04.020
A modification of the classical theory of brittle fracture of solids is offered by relating discrete nature of crack propagation to the fractal geometry of the crack. The new model incorporates all previously considered theories of fracture processes, in particular the Griffith [Griffith AA. The phenomenon of rupture and flow in solids. Philos Trans Roy Soc Lond 1921;A221:163–398] theory, its contemporary extension known as LEFM and the most recently developed Quantized Fracture Mechanics (QFM) by Pugno and Ruoff [Pugno N, Ruoff RS. Quantized fracture mechanics. Philos Mag 2004;84(27):2829–45]. Using an equivalent smooth blunt crack for a given fractal crack, we find that assuming that radius of curvature of the blunt crack is a material property, the crack roughens while propagating. In other words, fractal dimension at the crack tip is a monotonically increasing function of the nominal crack length, i.e., the presence of the Mirror–Mist–Hackle phenomenon is analytically demonstrated.
crack roughening; Crack roughening; discrete fracture; Discrete fracture; fractal fracture mechanics; Fractal fracture mechanics; quantized fracture; Quantized fracture
Stresses in a Multilayer Thin Film/Substrate System Subjected to Nonuniform Temperature
Journal of Applied Mechanics
75
2
21022
2008
10.1115/1.2755178
Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to uniform film stress and system curvature states over the entire system of a single thin film on a substrate. By considering a circular multilayer thin film/substrate system subjected to nonuniform temperature distributions, we derive relations between the stresses in each film and temperature, and between the system curvatures and temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part, which reflects the effect of temperature of other points on the location of scrutiny. We also derive relations between the film stresses in each film and the system curvatures, which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. The interfacial shear tractions between the films and between the film and substrate are proportional to the gradient of the first curvature invariant, and can also be inferred experimentally.
multilayers; substrates; thermal stresses; thin films
Mechanics of microtubules
Journal of Biomechanics
43
1
23-30
2010
10.1016/j.jbiomech.2009.09.005
Microtubules are rigid cytoskeletal filaments, and their mechanics affect cell morphology and cellular processes. For instance, microtubules for the support structures for extended morphologies, such as axons and cilia. Further, microtubules act as tension rods to pull apart chromosomes during cellular division. Unlike other cytoskeletal filaments (e.g., actin) that work as large networks, microtubules work individually or in small groups, so their individual mechanical properties are quite important to their cellular function. In this review, we explore the past work on the mechanics of individual microtubules, which have been studied for over a quarter of a century. We also present some prospective on future endeavors to determine the molecular mechanisms that control microtubule rigidity.
Cytoskeletal network; Flexibility; Flexural rigidity; Microtubule bundle
Elementary fluid mechanics
Journal of the Franklin Institute
244
6
495
1947
10.1016/0016-0032(47)90483-3
ELEMENTARY FLUID MECHANICS BY JOHN K. VENNARD Assistant Professor of Fluid Mechanics New York University NEW YORK JOHN WILEY SONS, INC. LONDON CHAPMAN HALL, LIMITED 1940 COPYRIGHT, 1940, BY JOHN K. VENNARD All Rights Reserved This book or any part thereof must not be reproduced in any form without the written permission of the publisher. PRINTED IN U. S. A. PRESS OP BRAONWORTH A CO.. INC. BRIDGEPORT. CONN. ELEMENTARY FLUID MECHANICS PREFACE Fluid mechanics is the study under all possible conditions of rest and motion. Its approaches analytical, rational, and mathematical rather than empirical it concerns itself with those basic principles which lead to the solution of numerous diversified problems, and it seeks results which are widely applicable to similar fluid situations and not limited to isolated special cases. Fluid mechanics recognizes no arbitrary boundaries between fields of engineering knowledge but attempts to solve all fluid problems, irrespective of their occurrence or of the characteristics of the fluids involved. This textbook is intended primarily for the beginner who knows the principles of mathematics and mechanics but has had no previous experience with fluid phenomena. The abilities of the average beginner and the tremendous scope of fluid mechanics appear to be in conflict, and the former obviously determine limits beyond which it is not feasible to go these practical limits represent the boundaries of the subject which I have chosen to call elementary fluid mechanics. The apparent conflict between scope of subject and beginner f s ability is only along mathematical lines, however, and the physical ideas of fluid mechanics are well within the reach of the beginner in the field. Holding to the belief that physical concepts are the sine qua non of mechanics, I have sacrificed mathematical rigor and detail in developing physical pictures and in many cases have stated general laws only without numerous exceptions and limitations in order to convey basic ideas such oversimplification is necessary in introducing a new subject to the beginner. Like other courses in mechanics, fluid mechanics must include disciplinary features as well as factual information the beginner must follow theoretical developments, develop imagination in visualizing physical phenomena, and be forced to think his way through problems of theory and application. The text attempts to attain these objectives in the following ways omission of subsidiary conclusions is designed to encourage the student to come to some conclusions by himself application of bare principles to specific problems should develop ingenuity illustrative problems are included to assist in overcoming numerical difficulties and many numerical problems for vi PREFACE the student to solve are intended not only to develop ingenuity but to show practical applications as well. Presentation of the subject begins with a discussion of fundamentals, physical properties and fluid statics. Frictionless flow is then discussed to bring out the applications of the principles of conservation of mass and energy, and of impulse-momentum law, to fluid motion. The principles of similarity and dimensional analysis are next taken up so that these principles may be used as tools in later developments. Frictional processes are discussed in a semi-quantitative fashion, and the text proceeds to pipe and open-channel flow. A chapter is devoted to the principles and apparatus for fluid measurements, and the text ends with an elementary treatment of flow about immersed objects...
On discontinuous plastic states, with special reference to localized necking in thin sheets
Journal of the Mechanics and Physics of Solids
1
1
19-30
1952
10.1016/0022-5096(52)90003-3
Permissible discontinuities of stress, velocity, and surface slope are investigated in a plastic-rigid sheet deformed in its plane. One such discontinuity of velocity is shown to be the mathematical idealization of localized necking; the necessary restrictions on the stress-state and rate of workhardening are obtained for any yield function and plastic potential. The results are illustrated by an examination of the modes of necking in notched tension strips. The constraint factors at the yield point are obtained for notches with wedge-shaped or circular roots.
Advances in Biofilm Mechanics
Biofilm Highlights
5
111-140
2011
10.1007/978-3-642-19940-0
A knowledge of the mechanical properties of bacterial biofilms is required to more fully understand how a biofilm will physically respond, and adapt, to the physical forces, such as those caused by fluid flow or particle or bubble impingement, acting upon it. This is particularly important since biofilms are problematic in a wide diversity of scenarios and spatial and temporal scales and many control strategies designed to remove biofilms include a mechanical component such as fluid flow, particle or bubble impingement or a physical contact with the surface generated by scraping or brushing. Knowing when, and how, a biofilm might fail (through adhesive or cohesive failure) will allow better prediction of accumulation and biomass detachment, key processes required in the understanding of the structure and function of biofilm systems. However, the measurements of mechanical properties are challenging. Biofilms are living systems and they readily desiccate if removed from the liquid medium, it is not clear how quickly their mechanical properties might change when removed from their indigenous environment into a testing environment. They are also very thin and are inherently attached to a surface. They cannot be formed into standard test coupons such as plastics or solids, and cannot readily be poured or placed into conventional viscometers or rheometers, such as liquids and gels. Measured parameters such as the elastic and shear modulus, adhesive strength or tensile strength are sparse but are increasingly appearing in the literature. There is a large range of reported values for these properties, although there is general agreement that biofilms are viscoelastic. Biofilms have been assessed with various experimental methods depending on the desired characteristic and available equipment. The aforementioned challenges and lack of standard methods or equipment for testing attached biofilms have led to the development of many creative methods to tease out aspects of biofilm mechanical properties. In this paper, we review some of the more common techniques and highlight some recent results.
On the mechanical behaviour of thin perforated plates and their application in silicon condenser microphones
Sensors and Actuators A: Physical
54
1-3
499-504
1996
10.1109/SENSOR.1995.721732
In this paper an alternative approach to the modelling of plates with a large number of holes is presented. By means of plate theory, it is shown that perforated plates can be modelled by conventional orthotropic plates with modified elastic properties. The modification of the ... \n
mechanics; plate
The effect of strain rate on the interlaminar shear strength of a carbon/epoxy cross-ply laminate: comparison between experiment and numerical prediction
Composites science and technology
59
749-758
1999
10.1016/S0266-3538(98)00117-1
A previously developed design of single-lap interlaminar shear specimen suitable for tests under impact rates of loading is reexamined and used to determine the interlaminar shear strength of a cross-ply carbon/epoxy material with important applications in the aircraft industry. The test has been modelled dynamically with an explicit-finite element code. The results of this analysis have been used to examine the state of stress just prior to failure and, in terms of a quadratic stress-interaction failure criterion, to predict the onset of delamination. The numerical predictions are compared with the behaviour observed experimentally. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.
c; carbon; delamination; epoxy; ilss; impact; numerical modelling
Molecular mechanics simulation of the diamond nucleation and growth on silicon (001) and (111) surfaces
Thin Solid Films
317
6-9
1998
10.1016/S0040-6090(97)00652-4
The nucleations and growths of diamond on silicon (001) and (111) surfaces according to the models previously proposed by us have been simulated in molecular mechanics optimizations for a series of cluster models. These simulations may provide clear mechanisms of the diamond nucleation and growth on such surfaces and further demonstrate that it may be feasible to grow large, single-crystal diamond film. (C) 1998 Published by Elsevier Science S.A.
diamond film; heteroepitaxy; interface structure; modelling; silicon surfaces
Thermal and Mechanical Cracking in Bis ( triisopropylsilylethnyl ) Pentacene Thin Films
Journal of Polymer Science Part B: Polymer Physics
44
3631-3641
2006
10.1002/polb
Bis(triisopropylsilylethnyl) pentacene (TIPS pentacene) was synthesized to increase its solubility in common liquid solvents and, at the same time, enhance the p–p stacking between neighboring acenes in the crystallized state in comparison with unmodified pentacene. Hot-stage microscopy experiments revealed that during heating voids develop along the long axis of the TIPS pentacene films {along the [210] direction/parallel to the (120) planes} and crystals overlap along the short axis {along the [120] direction/parallel to the (210) planes}. From molecular mechanics simulations, the predominant twin boundaries of (120) and commonly observed crack- ing planes of (120), (120), and (210) had relatively low surface energies in comparison with planes with similar Miller indices. Organic thin-film transistors with TIPS pen- tacene as the active layer were fabricated, and the mobility values decreased from 0.4–1.0 cm2/V s before cracking to ?0.2 cm2/V s after cracking. To maintain the high charge carrier mobility of TIPS pentacene devices, these cracks should be avoided.
annealing; charge transport; ductors; functionalized pentacene; organic semicon-; organic thin-film transistors; structure-property relations; surface energy
Comparison of Tensile and Bulge Tests for Thin-Film Silicon Nitride
Experimental Mechanics
44
49-54
2004
10.1177/0014485104039749
The mechanical properties of thin-film, low-pressure chemical vapor\ndeposited silicon nitride were measured in uniaxial tension and by\na bulge test method suitable for wafer-level testing. This research\ncompares the two approaches and presents additional data on silicon\nnitride. The common property from the two test methods is the Young's\nmodulus. Tensile tests performed at the Johns Hopkins University\nprovided a value of 2575 GPa. Bulge tests conducted by Exponent,\nInc., an engineering and scientific consulting firm, yielded a value\nof 2581 GPa. It is concluded that this bulge test is a valid wafer-level\ntest method. These tensile results, when added to earlier results,\nyield the following properties for low-stress silicon nitride: Young's\nmodulus =2555 GPa, Poisson ratio=0.230.02, and fracture strength=5.870.62\nGPa.
bulge tests; poisson ratio; --silicon nitride; s modulus; strength; tensile tests; young
Capability Assessment of Finite Element Software in Predicting the Last Ply Failure of Composite Laminates
Procedia Engineering
41
Iris
1647-1653
2012
10.1016/j.proeng.2012.07.363
Finite element programming using language such as FORTRAN, C++ and MATLAB has been the common and traditional tool to perform the progressive failure analysis of composite structures. This procedure requires high programming skills and strong mathematical understanding. This paper for the first time assesses the capability of a commercially available finite element analysis (FEA) software, ANSYS, to perform the Last Ply Failure (LPF) analysis of a laminated composite plate. The analysis is carried out by employing Maximum Stress and Tsai-Wu failure criteria. It is modelled and performed using ANSYS software which has a feature that supports the failure criteria and analysis procedure. The feature allows determination of maximum strength on individual layers in a composite laminate, thus provide an easier way to predict the failure progression. Based on analysis, the ultimate failure load and failure curves (LPF) are determined. The failure curves are compared and discussed with respect to previous experimental and FEA (both LPF and FPF) works. The results show that the LPF curves are very close to experiment that exhibits average errors as low as 16%. Finally, it can be concluded that the ANSYS software is applicable in predicting an accurate composite laminate LPF.
ansys; ANSYS; fea; FEA; laminated composite; Laminated composite; lpf; LPF
Effect of Substrate Temperature on the Preparation of Cu2ZnSnSe4 Thin Films
Applied Mechanics and Materials
130-134
895-899
2011
10.4028/www.scientific.net/AMM.130-134.895
The Cu2ZnSnSe4 (CZTSe) thin films were prepared by co-electroplating Cu-Zn-Sn precursors followed by selenization at different substrate temperatures. The effect of substrate temperatures on the morphologies and structures of CZTSe films were characterized using scanning electron microscopy (SEM), energy dispersive spectrometer (EDS), X-ray diffraction (XRD) and Raman scattering spectrum respectively. The results revealed that the impurity phases in CZTSe thin films such as CuSe and SnSe disappeared when the substrate temperatures were increased. The surface morphologies of CZTSe thin films were also strongly dependent on the substrate temperature treatment in the selenization process though the selenium temperature was kept at 340℃ .
Cu2ZnSnSe4; Electrodeposition; Selenization; Substrate temperature; Thin films
The mechanics of tidal streams
arxiv.org
22
November
23
2010
10.1111/j.1365-2966.2011.18270.x
We present an analysis of the mechanics of thin streams, which are formed following the tidal disruption of cold, low-mass clusters in the potential of a massive host galaxy. The analysis makes extensive use of action-angle variables, in which the physics of stream formation and evolution is expressed in a particularly simple form. We demonstrate the formation of streams by considering examples in both spherical and flattened potentials, and we find that the action-space structures formed in each take on a consistent and characteristic shape. We demonstrate that tidal streams formed in realistic galaxy potentials are poorly represented by single orbits, contrary to what is often assumed. We further demonstrate that attempting to constrain the parameters of the Galactic potential by fitting orbits to such streams can lead to significant systematic error. However, we show that it is possible to predict accurately the track of streams from simple models of the action-space distribution of the disrupted cluster.
Cosmology and Extragalactic Astrophysics; Galaxy Astrophysics
An exact derivation of the thin plate equation
Journal of Elasticity
22
2-3
121-133
1989
10.1007/BF00041107
It is shown that, when the traditional assumptions of thin plate theory are taken as exact methematical hypotheses, the desired field and boundary equations can be obtained by mere integration over the thickness of the corresponding equations for a three-dimensional cylindrical body made of a homogeneous, linearly elastictransversely isotropic, constrained material, yet avoiding some inconsistencies usually to be found in textbooks of structural mechanics.
Engineering
Adhesion of arbitrary-shaped thin-film microstructures
Microelectronics Reliability
47
12
2014-2024
2007
10.1016/j.microrel.2007.04.011
We develop, implement in a finite element environment, and experimentally validate an approach to model adhesion of a class of arbitrary-shaped thin-film microstructures commonly used in microsystems technology. The modeling approach adopts principles of three-dimensional linear elastic fracture mechanics and extends them to thin-film plate-like microstructures. A companion experimental effort is carried out to measure adhesion energy of polysilicon microcantilevers using interferometry, and then to study the adhesion behavior of a suite of circular and square plates. The finite element approach is validated by comparison with relevant analytical results. It is then applied to the circular and square plate microstructures and good agreement between measurements and predictions is obtained.
Spatially controlled hydrogel mechanics to modulate stem cell interactions
Soft Matter
6
1
136
2010
10.1039/b916933d
Local control of the stem cell microenvironment with biomaterial design is of critical importance for tissue engineering. Matrix mechanics is one aspect of biomaterial design that has received considerable attention recently due to the effect of mechanics on stem cell proliferation, morphology, and differentiation. In order to investigate the effect of locally controlled mechanics on human mesenchymal stem cells (hMSCs), a sequentially crosslinked hyaluronic acid hydrogel system was developed that permits spatial patterning of mechanics (distinct patterns and gradients). Methacrylated hyaluronic acid was synthesized to allow for crosslinking via both Michael-type addition using a dithiol and radical polymerization using light. By varying the initial methacrylate consumption through addition crosslinking, restricting UV light to specified regions, and varying UV exposure time, a wide range of mechanics (from 3 kPa to 100 kPa) was possible in both uniform and patterned hydrogels. hMSCs exhibited increased spreading and proliferation on stiffer gels compared to cells cultured on softer gels. Furthermore, cells grown on gels with patterned mechanics exhibited spreading and proliferation behavior that correlated with the local mechanics. This method to spatially control matrix mechanics represents a novel hydrogel system to tune the stem cell microenvironment.
Information Theory and Statistical Mechanics
Statistical Physics
181-218
1963
10.1109/TSSC.1968.300117
Lectures from Information and Statistical Mechanics session of Brandeis University Summer Institute Lectures in Theoretical Physics
Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections
Composite Structures
65
3-4
329-337
2004
10.1016/j.compstruct.2003.11.008
State-space approach is employed to investigate the bending and free vibration of simply supported angle-ply piezoelectric laminates in cylindrical bending. The bond between any two adjacent layers is assumed either perfect or imperfect, which is uniformly described by a general spring-layer model. The analysis is completely based on the exact piezoelasticity equations, and hence the presented numerical results can serve as benchmarks for future investigations. ?? 2003 Elsevier Ltd. All rights reserved.
Angle-ply piezoelectric laminate; Cylindrical bending; Interfacial imperfection; Spring-layer model; State-space approach
Vibration of angle-ply symmetric laminated composite plates with edges elastically restrained
Composite Structures
74
294-302
2006
10.1016/j.compstruct.2006.07.012
This paper presents a discussion about the results of the article on the vibration of angle-ply symmetric laminated composite rectangular plates with edges elastically restrained, by Ashour (Vibration of angle-ply symmetric laminated composite plates with edges elastically restrained. Compos Struct [in press]). The same problem is treated but with the application of the Ritz method with orthogonal polynomials as coordinate functions. The existence of some inconsistencies in Ashour [in press] is demonstrated. New numerical results for the described plates are included. ?? 2006 Elsevier Ltd. All rights reserved.
Composite material; Elastically restrained edges; Vibration analysis
How do sock ply changes affect residual-limb fluid volume in people with transtibial amputation?
The Journal of Rehabilitation Research and Development
49
2
241
2012
10.1682/JRRD.2011.02.0022
The purpose of this research was to investigate the influence of sock addition and removal on residual-limb fluid volume in people using prosthetic limbs. We used bioimpedance analysis to measure residual-limb extracellular fluid volume on 28 transtibial amputee subjects during 30 min test sessions. Upon addition of a one-ply polyester sock, residual-limb fluid volume changes ranged from -4.0% to 0.8% (mean -0.9 +/- 1.3%) of the initial limb fluid volume. Changes for sock removal ranged from -1.2% to 2.8% (mean 0.5 +/- 0.8%). Subjects who reduced in fluid volume with both addition and removal of a sock and subjects with high positive ratios between the fluid-volume loss upon sock addition and gain upon sock removal (high add/remove [AR] ratios) tended to have arterial disease, were obese, and were smokers. Subjects with low positive AR ratios, subjects who increased in fluid volume both with sock addition and removal, and a single subject who increased in fluid volume with sock addition and decreased with sock removal tended to be nonsmokers and either individuals in good health without complications or individuals without arterial problems. Results are relevant for the anticipation of limb volume changes during prosthetic fitting and toward the design of adjustable-socket technologies.
abbreviations; abi; accommodation; add; amputee; ankle brachial index; ar; bioimpedance; fluid; interface stress; prosthesis; residual-limb volume; socket fitting; sock ply; transtibial; volume
Experimental and numerical study of oblique transverse cracking in cross-ply laminates under tension
Composites Part A: Applied Science and Manufacturing
67
140-148
2014
10.1016/j.compositesa.2014.08.004
Abstract The first damage mode in cross-ply laminates under tension is broadly accepted as transverse cracks normal to the loading direction in the 90° layers, but there is not the same agreement about the second damage mode. While most of the analytical and experimental results are based on delamination induced by transverse cracking, another type of damage, oblique cracks within the 90° layers, has also been observed as the second damage mode in [0/904]s laminates. To understand the cause of this phenomenon, FE analyses considering damage development at the interfaces were performed. The obtained results indicate that the main reason for the oblique cracking damage mode is the higher toughness of the material in mode-II compared with mode-I: when the value of shear toughness is close to the opening toughness, the second damage mode in cross-ply laminates under tensile loading is delamination induced by transverse cracks, however, if the difference between the two values is large, oblique cracks in the 90° layers are likely to appear. In the specific tested and analysed laminate, if the mode II toughness is double the mode I toughness, oblique cracking occurs but if the values of mode I and mode II toughness are close, delamination is the second damage mode.
Matrix crack evolution in SiC fiber/glass matrix cross-ply laminates
Composites Part A: Applied Science and Manufacturing
30
4
593-597
1999
10.1016/S1359-835X(98)00155-9
Matrix crack evolution was studied for SiC fiber-reinforced glass-matrix cross-ply laminates. A novel in situ SEM (scanning electron microscope) observation was conducted to measure the fiber/matrix debonding and sliding in 0?? plies using specimens with parallel microlines printed on the surfaces. Interfacial debondings were found to grow intermittently as the applied stress increased. The debonding length distribution depends on the number of 90?? plies as well as the type of damage modes. An analytical model for the matrix crack evolution was proposed using the energy balance calculation based on Kuo and Chou (Kuo WS, Chou TW. Multiple cracking of unidirectional and cross-ply ceramic matrix composites. J Am Ceram Soc 1995;78(3):745-755), with the modification of including the effects of damage mode interaction as well as Poisson contraction in the debonded regions. The predicted evolution agrees well with the experimental one.
glass matrix composites; matrix crack evolution; micro-line
Lamb wave evaluation and localization of transverse cracks in cross-ply laminates
Journal of Materials Science
38
8
1765-1771
2003
10.1023/A:1023288012638
This paper investigates the effect of transverse cracks on the S0 mode velocity in GFRP and CFRP cross-ply laminates, and proposes a new AE source location method that considers the change in the S0 mode velocity due to the transverse cracks.We found experimentally that the stiffness and the velocity decreased as the transverse crack density increased. Analytical predictions deduced from the combination of the complete parabolic shear-lag analysis, the classical plate theory and the laminated plate theory are in good agreement with the experimental results. Utilizing this relationship between the velocity and the mechanical damage, we located AE sources of transverse cracks in cross-ply laminates with the calculated in situ velocity.We were able to show that highly accurate source location requires the reduction of the in situ value of the velocity. The present method is simple but quantitative and useful in health-monitoring for detecting and localizing the damage in composite structures.
Fluid Mechanics
Image Rochester NY
6
1
539
2005
10.1007/b138775
Mjog god kennslubok. Agaet fyrir byrjendur sem og lengra komna
Thermal buckling of laminated cross-ply oval cylindrical shells
Composite Structures
65
217-229
2004
10.1016/j.compstruct.2003.10.018
Thermal buckling behavior of laminated cross-ply oval cylindrical shells is analyzed using finite element approach. The formulation is based on higher-order theory that accounts for the transverse shear and transverse normal deformations, and incorporates realistic through the thickness approximations of the in-plane displacements. The strain-displacement relations are accurately introduced in the formulation. The contributions of work done by initial membrane state of thermal stress due to the higher-order function arising from the assumed displacement models are also included. The governing equations are obtained using the principle of minimum potential energy. The combined influence of higher-order shear deformation, shell geometry, ovality, and lay-up on the critical temperature parameter of laminated oval cylindrical shells is examined. ?? 2003 Elsevier Ltd. All rights reserved.
Critical temperature; Cross-ply; Finite element; Higher-order; Laminated shell; Non-circular; Oval cross-section; Thermal buckling
Mechanics analysis of thin-walled box continuous girder with variable cross-sections in considering effect of large deflection and shear lag
Frontiers of Architecture and Civil Engineering in China
3
4
352-356
2009
10.1007/s11709-009-0057-7
In order to study the mechanics behavior of a thin-walled box continuous girder with variable cross-sections, using potential variation theories, considering the effect of shear lag of flange's stress and the nonlinear geometry of vertical displacement, and evolving five generalized displacements with the spline function, the large deflection problem of the thin-walled box continuous girder with variable cross-section was transformed to a nonlinear algebraic equation, which was solved using the Newton-Raphon iterative method. The results of the calculation show that different shear lag warp functions to the cantilever, top and bottom plate should be taken to analyze the mechanics behavior of the thin-walled box continuous girder reliably. The thin-walled box continuous girder with variable cross-sections has more reasonable stress state and is more adaptable for the longitudinal change of internal forces than that with equal cross-sections. The effect of large deflection on the stress and displacement of the thin-walled box continuous girder with variable cross-sections depends on the values of the load. © Higher Education Press and Springer-Verlag 2009.
Quantum mechanics: to be or not to be local.
Nature
446
7138
866-867
2007
10.1038/446866a
The experimental violation of mathematical relations known as Bell's inequalities sounded the death-knell of Einstein's idea of 'local realism' in quantum mechanics. But which concept, locality or realism, is the problem?
Mechanics of a thin walled collapsible microtube.
Annals of biomedical engineering
17
3
203-17
1989
The purpose of this study is to measure the transmural pressure-cross sectional area relation of micro tubes (240 microns diameter) and to compare the measured perfusion pressure-flow relation with the pressure-flow relation calculated from the experimental pressure-cross sectional area relation. The microtubes are made by dipping a glass mould in a latex solution and glueing their outside ends to the inside of glass pipettes. The pressure-cross sectional area relation is determined both with a microplethysmograph (pressure-volume relation) and the microscope (pressure-diameter relations). Heparinized blood is used to include the rheological properties of blood as a perfusion medium. Static pressure-flow relations are obtained with a constant velocity piston pump for two values of external pressure (0 and 10 kPa) and with two downstream resistor settings (0 and 380 kPa cm-3 sec). The calculated pressure-flow relations using length and the experimental pressure-cross sectional area relation, Poiseuille's law, and accounting for the diameter- and shear-dependent viscosity compared well with the relations obtained from the experiments. It is also found that the pressure-flow relation shows an apparent zero flow pressure axis intercept (the extrapolation of the pressure-flow relation to the pressure axis), which can therefore be explained on the basis of the shape of the pressure-area relations.
Hemodynamics; Mathematical Computing; Microcirculation; Microcirculation: physiology; Models, Cardiovascular; Models, Structural; Regional Blood Flow; Rheology
Mechanics of head injuries
Lancet
242
6267
438-441
1943
10.1016/S0140-6736(00)87453-X
The assumption that there is a mechanics of head injuries implies that, when the head recieves a blow, the behaviour of the skull and brain during and immediately after the blow is determined by the physical properties of the skull and brain and by Newton's laws of motion. The most important physical properties of brain are...
Fracture Mechanics Lecture Notes
Architectural Engineering
132
1-8
2009
10.1061/(ASCE)0733-9399(2006)132:11(1151)
Fracture mechanics is a vast and growing field. A search of the Cornell Library in winter 2006 uncovered over 181 entries containing fracture mechanics in the subject heading and 10,000 entries in a relevance keyword search. This book is written for students who want to prepare to be able to read some of this vast literature and for those who want to apply fracture mechanics to real world problems. It is assumed the reader is familiar with the theory of linear elasticity, vector calculus, linear algebra and indicial notation. As much as possible I proceed in a linear fashion, but the reader may find that some backtracking is needed. These notes are used in a one semester course at Cornell. There are many approaches to teaching fracture. Here the emphasis is on mechanics models for crack tip fields and energy flows with discussion of how these results affect observed fracture behavior. A brief discussion of computational fracture methods is given along with additional practical aspects such as fracture toughness testing and fracture criteria. The notes do not contain much on the understanding of material behavior or on fracture at the micromechanical level. Both the mechanics and the materials sides of fracture should be studied in order to obtain a balanced and more complete picture of the field. These notes grow out of my experience teaching fracture at Cornell and taking fracture mechanics in graduate school at Caltech with Ares Rosakis. Textbooks consulted include Hutchinsons notes on nonlinear fracture 1, Lawns book on the fracture of brittle materials 2, Suresh on fatigue 3 and texts by Janssen 4, Anderson 5, Sanford 6 and Hellan 7. Topics that could be added include interface fracture, better coverage of computational methods, viscoelastic fracture and more discussion of the physical aspects of fracture. Topics that I hope to work on but have yet to start include: computational cohesive zone, fatigue crack growth model and fracture of plates and shells.
A Reexamination of Residual Stresses in Thin Films and of the Validity of Stoney's Estimate
Journal of Electronic Packaging
122
3
267-273
2000
10.1115/1.1287930
The residual stresses in thin films are explained using elementary mechanics. In particular, the range of validity of the well-known Stoney's formula is examined using a strength of materials approach. An improved formula is obtained. The results of these analyses can also be used to compute energy release rates for cracks in thin film systems. Some simple examples of such applications are given.
crack; edge stress field analysis; fracture mechanics; internal stresses; multilayers; strain relations; stress; thin films
Small and large deformation of thick and thin-film multi-layers : Effects of layer geometry, plasticity and compositional gradients
Journal of the Mechanics and Physics of Solids
44
5
683-721
1996
10.1016/0022-5096(96)84548-0
The thermomechanical response of multi-layered materials subjected to small and large deformation during temperature excursions is examined in this paper. General bilayer and trilayer plates with comparable layer thicknesses, as well as the limiting cases of thin films on thicker substrates with and without compositionally graded interfaces are examined, all within the context of the classical Kirchoff theory for thin plates. Closed-form analytical formulations for small elastic deformation are presented whereby explicit expressions for stress/curvature relations are obtained for any general bilayer or graded trilayer with isotropic elastic properties, but anisotropic strains. The effects of the variation of Poisson ratio through the thickness of layered and compositionally graded materials on the evolution of multiple curvatures are analyzed. New theoretical results are presented on the effects of layer geometry, plastic flow and compositional gradation on large deformation (small strains and small rotations) in bilayer and trilayer systems comprising thick or thin-film layers. It is shown that the small deformation theory predictions for the generalized plane strain state provide an upper bound for curvature evolution among all the cases considered. By recourse to analytical methods and three-dimensional finite element modeling involving shell elements, particular attention is devoted to the occurrence of bifurcation in the solution for curvature evolution and the associated geometry changes in the thermoelastoplastic response of layered materials during thermal excursions. The model systems chosen for analyses include Ni-Al2O3 layers with a sharp or compositionally graded interfaces, Al/Si thin-film bilayers and a compositionally graded interlayer sandwiched between layers in In0.12Ga0.88As and GaAs for applications in microelectronics and optoelectronics, and a carbon/ epoxy laminated composite.
Cell and biomolecular mechanics in silico
Nature materials
7
15-23
2008
10.1038/nmat2040
Recent developments in computational cell and biomolecular mechanics have provided valuable insights into the mechanical properties of cells, subcellular components and biomolecules, while simultaneously complementing new experimental techniques used for deciphering the structure–function paradigm in living cells. These computational approaches have direct implications in understanding the state of human health and the progress of disease and can therefore aid immensely in the diagnosis and treatment of diseases. We provide an overview of the computational approaches that are currently used in understanding various aspects of cell and bimolecular mechanics. Our emphasis is on state-of-the-art techniques and the progress made in addressing key challenges in biomechanics.
Mixed-mode interfacial adhesive strength of a thin film on an anisotropic substrate
Journal of the Mechanics and Physics of Solids
57
1
51-66
2009
10.1016/j.jmps.2008.10.002
The mixed-mode interfacial adhesion strength between a gold (Au) thin film and an anisotropic passivated silicon (Si) substrate is measured using laser-induced stress wave loading. Test specimens are prepared by bonding a fused silica (FS) prism to the back side of a ???1 0 0??? Si substrate with a thin silicon nitride (SixNy) passivation layer deposited on the top surface. A high-amplitude stress wave is developed by pulsed laser ablation of a sacrificial absorbing layer on one of the lateral surfaces of the FS prism. Due to the negative non-linear elastic properties of the FS, the compressive stress wave evolves into a decompression shock with fast fall time. Careful selection of the incident angle between the pulse and the FS/Si interface generates a mode-converted shear wave in refraction, subjecting the SixNy/Au thin film interface to dynamic mixed-mode loading, sufficient to cause interfacial fracture. A detailed analysis of the anisotropic wave propagation combined with interferometric measurements of surface displacements enables calculation of the interfacial stresses developed under mixed-mode loading. The mixed-mode interfacial strength is compared to the interfacial strength measured under purely tensile loading. ?? 2008 Elsevier Ltd. All rights reserved.
Decompression shock; Dynamic wave propagation; Laser spallation; Mixed-mode loading; Thin film
Molecular insight into the energy levels at the organic donor/acceptor interface: A quantum mechanics/molecular mechanics study
Journal of Physical Chemistry C
115
29
14431-14436
2011
10.1021/jp203387m
We present an investigation of the band levels and charge\ntransfer (CT) states at the interface between two organic semiconductors,\nmetal-free phthalocyanine (H2Pc) and 3,4,9,10-perylenetetracarboxylic\nbisbenzimidazole (PTCBI), using a combined quantum mechanics/molec-\nular mechanics (QM/MM) technique. Near the organic
Classical and Quantum Mechanics via Lie algebras
Book
502
2008
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
Advances in Discrete Element Method Applied to Soil , Rock and Concrete Mechanics
Electronic Journal of Geotechnical Engineering
Bouquet 08
1-43
2008
10.1242/dev.055533
The use of Discrete Element Methods (DEM) to investigate mechanical properties of geomaterials is growing fast and their applications in geotechnics have become almost systematic. Behind the generic name of DEM, different formulations exist and this paper focuses on recent developments in the Molecular Dynamics and Contact Dynamics-based approaches. After reviewing their formulation, a summary of their recent uses as numerical tools to investigate the mechanical behavior of soil, rock and concrete materials is given. Specific issues such as spherical discrete element packings, flow rules, capillarity effects, high-pressure loading response and high strain rate deformation are described in more details. The quantitative capabilities of DEM are also provided by comparing real experimental data to numerical models.
Concrete mechanics; Contact dynamics; Discrete Element Method; Molecular dynamics; Rock mechanics; Soil mechanics
Structural style and evolution of the triangle zone and external Foothills, southwestern Alberta: implications for thin skinned thrust-and-fold belt mechanics
Bulletin of Canadian Petroleum Geology
49
4
472-496
2001
10.2113/49.4.472
A thin-skinned, NNW-striking, structural triangle zone (tectonic wedge) and steep, imbricate, dominantly foreland-vergent thrusts characterize the eastern margin of the Rocky Mountain Foothills belt in southwestern Alberta. Recent 1:50,000 scale mapping indicates that the structure of the triangle zone and outer Foothills varies significantly and systematically along strike. These map-scale variations correlate strongly with lateral changes in the structurally involved Cretaceous-Tertiary foreland stratigraphy and the composition of units structurally inserted into the triangle zone, and correlate less strongly with lateral changes in topography. These variations probably reflect the influence of mechanical stratigraphy, and perhaps the associated role of surface processes (landscape evolution) active during structural evolution. On the basis of structural style, the triangle zone and outer Foothills structures are divisible into three regions between the Oldman River (49°45 N) and Turner Valley (50°40 N), a distance of approximately 80 km. In the southern region, the upper detachment of the triangle zone is localized within the mechanically weak Bearpaw Formation, and the structure is characterized by a series of map-scale, dominantly hinterland-vergent structures in its hanging wall. In the central region, the Bearpaw Formation remains the locus of the upper detachment, but the structure is characterized by an absence of hanging-wall structures, resulting in a simpler "passive roof duplex" geometry. The transition between the central and southern regions is marked by an abrupt but continuous eastward shift in the trace of the upper detachment, coincident with exposure of a south-plunging antiformal stack in its footwall that reflects the subsurface presence of Mississippian carbonates carried on the blind Outwest Thrust. In the northern region, strain associated with the upper detachment becomes distributed over a stratigraphically broad zone (the Longview Deformation Zone), locally over 2 km in width across strike, centred approximately on the northward-thinning Bearpaw shale. The observed structural variations correspond to changes in the lithology of involved units, indicating the importance of "mechanical stratigraphy". However, there is also a correspondence between the change in structural style from the southern to the central region and the topographic expression of Paleocene units (Porcupine Hills Formation) above the upper detachment. This suggests that patterns of syn-deformational erosion, deposition, and lithification may have influenced structural style. "Out-of-sequence" motion is recorded on some faults, as well as reactivation, with deformation apparently accommodated on a number of faults simultaneously.
Patient-specific modeling of cardiovascular mechanics.
Annual review of biomedical engineering
11
April
109-134
2009
10.1146/annurev.bioeng.10.061807.160521
Advances in numerical methods and three-dimensional imaging techniques have enabled the quantification of cardiovascular mechanics in subject-specific anatomic and physiologic models. Patient-specific models are being used to guide cell culture and animal experiments and test hypotheses related to the role of biomechanical factors in vascular diseases. Furthermore, biomechanical models based on noninvasive medical imaging could provide invaluable data on the in vivo service environment where cardiovascular devices are employed and on the effect of the devices on physiologic function. Finally, patient-specific modeling has enabled an entirely new application of cardiovascular mechanics, namely predicting outcomes of alternate therapeutic interventions for individual patients. We review methods to create anatomic and physiologic models, obtain properties, assign boundary conditions, and solve the equations governing blood flow and vessel wall dynamics. Applications of patient-specific models of cardiovascular mechanics are presented, followed by a discussion of the challenges and opportunities that lie ahead.
aneurysms; atherosclerosis; congenital heart; hemodynamics; imaging
Computational continuum mechanics
Book
353
2008
10.1017/CBO9781139059992
This updated text presents the theory of continuum mechanics using compurational methods. The rest covers abroad range of topics including general problems of large rotation and large deformations and the development and limitations of finite clement formulations in solving such problems. Dr. Ahmed A. Shabana introduces theories on motion kinematics, strain, forces, and stresses, and goes on to discuss linear and nonlinear constitutive equations, including viscoclastic and plastic constitutive models. General nonlinear continuum machanics theory is used to develop small and large finite element formulations that correctly describe rigid body motion for use in engineering applications. This second edition features a new chapter that focuses on computational geometry and finite clement analysis. This book is ideal for graduate and undergraduate students, professionals, and researchers who are interested in continuum mechanics.
Impact dynamics in milling of thin-walled structures
Nonlinear Dynamics
22
4
375-392
2000
10.1023/A:1008364405411
The development of reliable high-speed spindles and motioncontrol systems has led to an increase in the industrial use ofhigh-speed milling. One of the primary applications of this newtechnology is the manufacture of thin-walled aluminum components foraircraft. The flexibility of the tools and workpieces, the high spindlefrequencies, and the inherent impact nonlinearities in the millingprocess can lead to complicated dynamic tool-workpieceinteractions . An experiment was constructed to study the vibrations ofa thin-walled part during milling. Time series, power spectra,autocorrelations, auto-bispectra, and phase portraits were examined.From this data, it is inferred that stiffness and damping nonlinearitiesdue to the intermittent cutting action have a pronounced effect on thedynamics of the workpiece. Delay space reconstructions and pointwisedimension calculations show that the associated motions arecharacterized by a fractal geometry. The auto-bispectra suggestquadratic phase coupling among the spectral peaks associated with thecutter frequency. A mechanics-based model with impact-nonlinearities wasdeveloped to explain the observed results. The predicted results agreewell with the experimental observations. The model predictions indicatethat aperiodic motions are possible over a large range ofcontrol-parameter values. These analytical and experimental results haveimplications for the prediction and control of vibrations in milling.
dimension calculation; impact; milling chatter; tool-workpiece interactions
Fracture Mechanics Ch04
Fracture Mechanics
77-103
2012
10.1016/B978-0-12-385001-0.00004-3
Fracture occurs when the stress intensity factor reaches its critical value, that is, the fracture toughness. In the energy approach, the fracture behavior of a material is described by the energy variation of the cracked system during crack extension, which is characterized by the so-called energy release rate. The energy release is considered a global exercise of the cracked system. This chapter also discusses three-dimensional field near crack front; most linear elastic fracture mechanics (LEFM) problems are simplified and modeled as two-dimensional (2-D), though three-dimensional (3-D) effects are often acknowledged. 2-D plane strain and plane stress states are often assumed to approximate thin and thick bodies, respectively. In addition, a stress intensity factor calculation using the finite element method is examined. The finite element method is commonly used in the stress analyses of complex engineering structures. Various techniques have been introduced to calculate stress intensity factors and energy release rates. Two commonly used methods are briefly described.
Energy release rate; J-integral; modified crack closure technique; path-independence; three-dimensional effect
Supramolecular detection of solvent vapours with calixarenes: Mass-sensitive sensors, molecular mechanics and BET studies
Mikrochimica Acta
119
1-2
55-62
1995
10.1007/BF01244854
Abstract. Chemical sensors, based on highly mass sensitive QMB or SAW devices, coated with thin layers of calixarenes, enable the detection of organic solvent vapours , especially halogenated or aromatic hydrocarbons, down to a few ppm. Force field calculations allow the tailoring ...
BET; calixarenes; MM3 force field; QMB-SAW-sensors
Bohmian mechanics contradicts quantum mechanics
arXiv
2
Doadrio
13
2000
It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can be explained by the fact that Bohmian mechanics has no natural way to accomodate the Heisenberg picture, since the local expectation values that define the beables of the theory depend on the Heisenberg time being used to define the operators. Relations to measurement are discussed, too, and shown to leave no loophole for claiming that Bohmian mechanics reproduces all predictions of quantum mechanics exactly.
Fatigue crack propagation law measured from integrated digital image correlation: The example of Ti35 thin sheets
Procedia Engineering
10
1091-1096
2011
10.1016/j.proeng.2011.04.180
In this study, a crack in commercially-pure Titanium (CP-Ti) is observed with optical means during its propagation in fatigue. Digital image correlation is then used to extract directly, with no post-processing step, the crack tip location and the corresponding stress intensity factor amplitude to evaluate the parameters of Paris' law, the T-stress component and an estimate of the plastic zone shape. © 2011 Published by Elsevier Ltd.
Digital image correlation; Fracture mechanics; Paris' law; Titanium
Effects of actin-myosin kinetics on the calcium sensitivity of regulated thin filaments
J Biol Chem
285
50
39150-39159
2010
10.1074/jbc.M110.142232
Activation of thin filaments in striated muscle occurs when tropomyosin exposes myosin binding sites on actin either through calcium-troponin (Ca-Tn) binding or by actin-myosin (A-M) strong binding. However, the extent to which these binding events contributes to thin filament activation remains unclear. Here we propose a simple analytical model in which strong A-M binding and Ca-Tn binding independently activates the rate of A-M weak-to-strong binding. The model predicts how the level of activation varies with pCa as well as A-M attachment, N·k(att), and detachment, k(det), kinetics. To test the model, we use an in vitro motility assay to measure the myosin-based sliding velocities of thin filaments at different pCa, N·k(att), and k(det) values. We observe that the combined effects of varying pCa, N·k(att), and k(det) are accurately fit by the analytical model. The model and supporting data imply that changes in attachment and detachment kinetics predictably affect the calcium sensitivity of striated muscle mechanics, providing a novel A-M kinetic-based interpretation for perturbations (e.g. disease-related mutations) that alter calcium sensitivity.
Testing foundations of quantum mechanics with photons
Nature Physics
10
4
278-286
2014
10.1038/nphys2931
Quantum mechanics continues to predict effects at odds with a classical understanding of nature. Experiments with light at the single-photon level have historically been at the forefront of fundamental tests of quantum theory and the current developments in photonic technologies enable the exploration of new directions. Here we review recent photonic experiments to test two important themes in quantum mechanics: wave-particle duality, which is central to complementarity and delayed-choice experiments; and Bell nonlocality, where the latest theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different experiments.
The Theory of Groups and Quantum Mechanics
Science
75
1953
586-588
1932
10.1126/science.75.1953.586
This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.
A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media
Journal of the Mechanics and Physics of Solids
54
4
708-734
2006
10.1016/j.jmps.2005.10.009
An arbitrarily curved three-dimensional anisotropic thin interphase between two anisotropic solids is considered. The purpose of this study is to model this interphase as a surface between its two neighbouring media by means of appropriately devised interface conditions on it. The analysis is carried out in the setting of unsteady heat conduction and dynamic elasticity, and makes use of the simple idea of a Taylor expansion of the relevant fields in thin regions. It consists of a generalization of a previous study by B??vik [1994. On the modelling of thin interface layers in elastic and acoustic scattering problems. Q. J. Mech. Appl. Math. 47, 17-42] which was confined to the isotropic setting. The remarkable feature of the presently derived anisotropic interface model is that formally it has a more compact form than that of B??vik's isotropic version. This is achieved by a judicious choice of surface differential operators which have been used in the derivation, and makes possible to show that several previously known classical interface models are recovered as special cases of the one obtained in this study, once suitable assumptions are made on the magnitude of the conductivity and elasticity tensors of the interphase. ?? 2005 Elsevier Ltd. All rights reserved.
Composite materials; Imperfect interface; Thin interphases
Muscle mechanics 9.0
Motor Control
224-249
2000
10.1002/9780470549148.ch9
; the of and on . Share/Save/Bookmark. Meijer, Kenneth (1998)
Models and Finite Elements for Thin-Walled Structures
Encyclopedia of Computational Mechanics
59-137
2004
10.1002/0470091355.ecm026
The present study provides an overview of modeling and discretization aspects in finite element analysis of thin-walled structures. Shell formulations based upon derivation from three-dimensional continuum mechanics, the direct approach, and the degenerated solid concept are compared, highlighting conditions for their equivalence. Rather than individually describing the innumerable contributions to theories and finite element formulations for plates and shells, the essential decisions in modeling and discretization, along with their consequences, are discussed. It is hoped that this approach comprises a good amount of the existing literature by including most concepts in a generic format. The contribution focuses on nonlinear finite element formulations for large displacements and rotations in the context of elastostatics. Although application to dynamics and problems involving material nonlinearities is straightforward, these subjects are not taken into account explicitly.
Mechanics of the ion layer gas reaction-A preparation method of nanocrystalline thin layers
Journal of Applied Physics
91
10 I
6691-6694
2002
10.1063/1.1464649
Nanocrystalline CdS thin layers can be prepared using the ion layer gas reaction (ILGAR), a low-cost deposition technique for compound semiconductor thin films. We investigated the layers by optical spectroscopy and transmission electron microscopy, and found that lower <equation><font face='roman'>CdCl</font><sub>2</sub></equation> precursor concentrations and thicker films favor larger nanoparticles and a lower band gap energy, whereby the concentration effect is more pronounced. The nucleation mechanism of the <equation><font face='roman'>CdCl</font><sub>2</sub></equation> precursor seems to determine the particle size and the probability of its growth. A minimum CdS particle diameter of 4.7 nm has been extrapolated, which corresponds to an optical band gap energy of 2.83 eV, as a result of quantum confinement. ILGAR enables deposition of nanoparticles of controlled size. © 2002 American Institute of Physics.
Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory
Composite Structures
72
177-192
2006
10.1016/j.compstruct.2004.11.016
A two-dimensional global higher-order deformation theory is presented for thermal buckling of angle-ply laminated composite and sandwich plates. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through the principle of virtual work. Several sets of truncated Mth order approximate theories are applied to solve the eigenvalue problems of simply supported laminated composite and sandwich plates. In order to assure the accuracy of the present theory, convergence properties of the critical temperatures are examined in detail. Numerical results are compared with those of the published three-dimensional layerwise theory in which both in-plane and normal displacements are assumed to be C0 continuous in the continuity conditions at the interface between layers. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. Effects of the difference of displacement continuity conditions between the three-dimensional layerwise theory and the global higher-order theory are clarified in thermal buckling problems of angle-ply laminated and sandwich plates. ?? 2004 Elsevier Ltd. All rights reserved.
Mechanics of adhesion
Tribology International
31
8
413-418
1998
10.1016/S0301-679X(98)00060-7
The small scale contacts and very smooth surfaces associated with information storage devices result in adhesive forces playing a more significant role than in more conventional tribological applications. Taking the contact of spherical surfaces to be representative of asperity interactions, the mechanics of adhesion will be reviewed. From the point of view of mechanics adhesion is expressed in terms of the `work of adhesion', i.e. the work to separate unit area of the interface, whatever its physical origin; intermolecular forces, electrostatic forces or capillary action. For elastic solids the behaviour is a function of two non-dimensional parameters. One is a measure of the ratio of the adhesive force to the applied load and the other the ratio of elastic deformation to the range of surface forces. A map will be presented having these two parameters as co-ordinates. The effect of inelastic deformation (plastic and viscoelastic) will be considered and a criterion presented for the `brittle' or `ductile' separation of adhering surfaces.
adhesion; contact; surface energy
Mode-I interlaminar fracture of carbon-epoxy cross-ply composites
Composites Science and Technology
62
679-686
2002
10.1016/S0266-3538(01)00223-8
Mode-I double-cantilever beam (DCB) tests were performed on carbon/epoxy[0°/90°]12 specimens. The starter crack was created at mid-thickness, between the 0 and 90° mid-layers. During the tests, however, the crack also propagated along the neighbouring 0°/90° interface and within the 90° mid-layer. Nevertheless, the test results were apparently consistent with the assumptions of the corrected beam theory (CBT) that was used to obtain the interlaminar critical strain energy release rate, GIc. The measured values were higher than those of unidirectional [0°]24 specimens, especially the final propagation values. A finite-element analysis confirmed the applicability of the CBT for interlaminar propagation along the two 0°/90° interfaces. The results also indicated that the intralaminar GIc is significantly smaller than the interlaminar GIc. This will prevent pure interlaminar propagation in multi-directional specimens with high interlaminar fracture toughness. © 2002 Elsevier Science Ltd. All rights reserved.
A. Polymer-matrix composites; B. Fracture toughness; C. Delamination; C. Finite-element analysis; C. Transverse cracking
Design and evaluation of PZT thin-film micro-actuator for hard disk drives
Sensors and Actuators A: Physical
116
2
329-335
2004
10.1016/j.sna.2004.05.006
A new thin-film PZT micro-actuator bonded to a stainless steel (SUS304) suspension for positioning a magnetic head for high-density hard disk devices has been designed, fabricated and investigated. This PZT micro-actuator in dual-stage serve system was made using a sol–gel technique deposited thin-film PZT and applying reactive ion etching processes to fabricate the micro-actuator. The SUS304 cantilever beam integrated with the PZT micro-actuator was also simulated in order to test the driving mechanics. The novel piezoelectric multi-layer micro-actuators possess a useful compromise performance in displacement, resonance frequency and generative force. The results reveal that the new design concept provides a valuable alternative for multi-layer piezoelectric actuators. When a double-layer thin-film PZT micro-actuator was used, an applied voltage of ±15V was sufficient to obtain 0.9866m tip displacement of the cantilever beam and high-resonance frequency over 16.67 kHz, yielding the required servo bandwidth (13 kHz) of several kHz.
dual-stage serve system; hard disk drives; micro-actuator; piezoelectric thin film; pzt
Fluid Mechanics of the Eye
Annual Review of Fluid Mechanics
44
347-372
2012
10.1146/annurev-fluid-120710-101058
Fluid mechanical processes are an intrinsic part of several aspects of the physiology and pathology of the human eye. In this article we describe selected phenomena that are amenable to particularly interesting mathematical, experimental, or numerical analyses. We initially focus on glaucoma, a condition often associated with raised intraocular pressure. The mechanics in this disease is by no means fully understood, but we present some of the modeling work that provides a partial explanation. We next focus on other features of the dynamics of the two specialized ocular fluids: the aqueous and vitreous humors. With regard to the aqueous humor, we discuss problems concerning the transport of heat and proteins and the hydration of the cornea. With regard to the vitreous humor, we discuss the possibility of flow, which occurs primarily as a result of saccades or motions of the eyeball. Finally, we describe a model of the degradation of Bruch's membrane in the retina.
buoyancy-driven flow; deformed sphere; drug; glaucoma; porous medium
Modeling instruction in mechanics
American Journal of Physics
55
August 1984
455
1987
10.1119/1.15130
Modeling theory was used in the design of a method to teach problem solving in introductory mechanics. A pedagogical experiment to evaluate the effectiveness of the method found positive results.
An energy model of segmentation cracking of thin films
Mechanics of Materials
39
845-864
2007
10.1016/j.mechmat.2007.02.004
On the basis of analytical modelling of delamination of a thin film on a stretched substrate an energy model of film segmentation cracking has been formulated. The model focuses on a topological transformation between an intact and a damaged structure, rather than on a constitutive modelling of fracture itself. An energy transition condition should be satisfied in order for cracks to occur. The model provides a unique solution in the number of cracks for given material parameters. It has been validated by measuring the fracture energy of a silicon oxide thin film deposited on a poly(ethylene terephthalate) (PET) substrate, where a constant value of plastic shear stress at the film/substrate interface can be assumed. © 2007 Elsevier Ltd. All rights reserved.
Delamination; Fracture energy; Oxide coating; Segmentation cracking
Optimizing the structure and contractility of engineered skeletal muscle thin films
Acta Biomaterialia
9
7885-7894
2013
10.1016/j.actbio.2013.04.036
An experimental system was developed to tissue engineer skeletal muscle thin films with well-defined tissue architecture and to quantify the effect on contractility. Using the C2C12 cell line, the authors tested whether tailoring the width and spacing of micropatterned fibronectin lines can be used to increase myoblast differentiation into functional myotubes and maximize uniaxial alignment within a 2-D sheet. Using a combination of image analysis and the muscular thin film contractility assay, it was demonstrated that a fibronectin line width of 100 lm and line spacing of 20 lm is able to maximize the formation of anisotropic, engineered skeletal muscle with consistent contractile properties at the millimeter length scale. The engineered skeletal muscle exhibited a positive force-frequency relationship, could achieve tetanus and produced a normalized peak twitch stress of 9.4 ?? 4.6 kPa at 1 Hz stimulation. These results establish that micropatterning technologies can be used to control skeletal muscle differentiation and tissue architecture and, in combination with the muscular thin film contractility, assay can be used to probe structure- function relationships. More broadly, an experimental platform is provided with the potential to examine how a range of microenvironmental cues such as extracellular matrix protein composition, micropattern geometries and substrate mechanics affect skeletal muscle myogenesis and contractility. ?? 2013 Acta Materialia Inc. Published by Elsevier Ltd.
Fibronectin; Microcontact printing; Polydimethylsiloxane; Skeletal muscle; Tissue engineering
The mechanics of breathing
American Journal of Respiratory and Critical Care Medicine
157
4 II SUPPL.
10-5
1998
10.1164/rccm.200401-098OE
In this essay, we provide a brief review of the state of knowl-\nedge of the mechanics of breathing at the time the Division of\nLung Disease (DLD) of the National Heart, Lung, and Blood\nInstitute (NHLBI) was created and how this provided a solid\nfoundation for the explosion of new knowledge that has since\ndeveloped. This new knowledge has had a profound impact on\nthe practice of medicine and surgery. Two elements were re-\nquired to establish the infrastructure: technologic innovations\nin the measurement of volumes, displacements, flows and\npressures; and modeling so that the measurements could be\ninterpreted.
19th Century; 20th Century; History; Humans; Pulmonary Medicine; Pulmonary Medicine: history; Respiratory Mechanics; Respiratory Mechanics: physiology
Global linear stability analysis of thin aerofoil wakes
Journal of Fluid Mechanics
339
239-260
1997
10.1017/S0022112097005314
new form of the perturbation streamfunction follows directly from the expansion of (2.7) about X = X t , and in particular the factor in the exponential arises from the expansion of the WKBJ phase function. The frequency ω G is the (unknown) - frequency, which
Large-scale models reveal the two-component mechanics of striated muscle.
International journal of molecular sciences
9
12
2658-723
2008
10.3390/ijms9122658
This paper provides a comprehensive explanation of striated muscle mechanics and contraction on the basis of filament rotations. Helical proteins, particularly the coiled-coils of tropomyosin, myosin and alpha-actinin, shorten their H-bonds cooperatively and produce torque and filament rotations when the Coulombic net-charge repulsion of their highly charged side-chains is diminished by interaction with ions. The classical "two-component model" of active muscle differentiated a "contractile component" which stretches the "series elastic component" during force production. The contractile components are the helically shaped thin filaments of muscle that shorten the sarcomeres by clockwise drilling into the myosin cross-bridges with torque decrease (= force-deficit). Muscle stretch means drawing out the thin filament helices off the cross-bridges under passive counterclockwise rotation with torque increase (= stretch activation). Since each thin filament is anchored by four elastic alpha-actinin Z-filaments (provided with force-regulating sites for Ca(2+) binding), the thin filament rotations change the torsional twist of the four Z-filaments as the "series elastic components". Large scale models simulate the changes of structure and force in the Z-band by the different Z-filament twisting stages A, B, C, D, E, F and G. Stage D corresponds to the isometric state. The basic phenomena of muscle physiology, i. e. latency relaxation, Fenn-effect, the force-velocity relation, the length-tension relation, unexplained energy, shortening heat, the Huxley-Simmons phases, etc. are explained and interpreted with the help of the model experiments.
Muscle contraction; muscle mechanics; rotating filaments
Another thin-film limit of micromagnetics
Archive for Rational Mechanics and Analysis
178
2
227-245
2005
10.1007/s00205-005-0372-7
We consider the variational problem of micromagnetics for soft, relatively small thin films with no applied magnetic field. In terms of the film thickness t, the diameter l and the magnetic exchange length w, we study the asymptotic behavior in the small-aspect-ratio limit t/l→0, when either (a) w 2/l 2≫(t/l)| log (t/l)| or (b) w 2/l 2∼(t/l)| log (t/l)|. Our analysis builds on prior work by Gioia & James and Carbou. The limiting variational problem is much simpler than 3D micromagnetics; in particular it is two-dimensional and local, with no small parameters. The contribution of shape anisotropy reduces, in this limit, to a constant times the boundary integral of (m·n)2
Press forming a 0/90 cross-ply advanced thermoplastic composite using the double-dome benchmark geometry
Composites Part A: Applied Science and Manufacturing
54
56-69
2013
10.1016/j.compositesa.2013.06.014
A pre-consolidated thermoplastic advanced composite cross-ply sheet comprised of two uniaxial plies orientated at 0/90 has been thermoformed using tooling based on the double-dome bench-mark geometry. Mitigation of wrinkling was achieved using springs to apply tension to the forming sheet rather than using a friction-based blank-holder. The shear angle across the surface of the formed geometry has been measured and compared with data collected previously from experiments on woven engineering fabrics. The shear behaviour of the material has been characterised as a function of rate and temperature using the picture frame shear test technique. Multi-scale modelling predictions of the material's shear behaviour have been incorporated in finite element forming predictions; the latter are compared against the experimental results. ?? 200020-121756.?? 2013 Elsevier Ltd. All rights reserved.
B. Thermomechanical; C. Finite element analysis (FEA); D. Mechanical testing; E. Forming
An analysis of the indentation test to determine the interface toughness in a weakly bonded thin film coating - Substrate system
Acta Materialia
52
10
2989-2999
2004
10.1016/j.actamat.2004.02.046
A study of the mechanics of indentation induced interface delamination is described for systems consisting of a ductile film on an elastic substrate. Special attention is paid to the properties of the interface between coating and substrate. The interface is modeled by the use of a cohesive zone model within the finite element method. Two cases are distinguished, weak interface case and strong interface case. For weak interfaces, buckling of the coating occurs. Existing methods for interface toughness evaluation are evaluated and an alternative method for the determination the interface toughness from indentation delamination experiments is proposed. ?? 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Energy release rate; Finite element analysis; Microindentation; Plastic deformation; Thin films
Nano-mechanics of perfluoropolyether films: Compression versus tension
IEEE Transactions on Magnetics
44
11 PART 2
3698-3701
2008
10.1109/TMAG.2008.2001671
As the head-disk spacing decreases, the contact mechanics between the head and disk becomes one of the critical issues for the head-disk tribology integration. In this paper, molecular dynamics (MD) is employed to simulate the nano-mechanics (i.e., "compression" and "tension") of confined molecularly thin perfluoropolyether (PFPE) films to examine the contact tribology fundamentals. For the "compression" process, functional PFPE demonstrates slightly higher clearance than nonfunctional PFPE; while during the "tension" process, an apparent fluid bridge was observed for functional PFPE. The normal stress profiles were calculated for both "compression" and "tension" processes, where the hysteresis phenomenon indicates the irreversible nature of functional PFPE nano-mechanics. N-modes Maxwell model was then further introduced to analyze the nano-mechanics relaxation process, suggesting that a second relaxation mode in the two-mode Maxwell model was induced by functional endgroups.
Compression and tension; Head-disk interface; Hysteresis; Lubricant pick-up; Molecular dynamics; Nano-mechanics; Viscoelasticity
Model for domain wall avalanches in ferromagnetic thin films
Physica A: Statistical Mechanics and its Applications
390
23–24
4192-4197
2011
10.1016/j.physa.2011.06.071
The Barkhausen jumps or avalanches in magnetic domain-walls motion between successive pinned configurations, due the competition among magnetic external driving force and substrum quenched disorder, appear in bulk materials and thin films. We introduce a model based in rules for the domain wall evolution of ferromagnetic media with exchange or short-range interactions, that include disorder and driving force effects. We simulate in 2-dimensions with Monte Carlo dynamics, calculate numerically distributions of sizes and durations of the jumps and find power-law critical behavior. The avalanche-size exponent is in excellent agreement with experimental results for thin films and is close to predictions of the other models, such as like random-field and random-bond disorder, or functional renormalization group. The model allows us to review current issues in the study of avalanches motion of the magnetic domain walls in thin films with ferromagnetic interactions and opens a new approach to describe these materials with dipolar or long-range interactions.
An extended isogeometric thin shell analysis based on Kirchhoff–Love theory
Computer Methods in Applied Mechanics and Engineering
284
265-291
2015
http://dx.doi.org/10.1016/j.cma.2014.08.025
Abstract An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures is developed. The discretization is based on Non-Uniform Rational B-Splines (NURBS). The proposed XIGA formulation can reproduce the singular field near the crack tip and the discontinuities across the crack. It is based on the Kirchhoff–Love theory where C 1 -continuity of the displacement field is required. This condition is satisfied by the NURBS basis functions. Hence, the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy. The performance and validity of the formulation is tested by several benchmark examples.
Fracture mechanics; Isogeometric analysis; NURBS; Thin shells; XFEM; XIGA
Thin, flexible sensors and actuators as 'instrumented' surgical sutures for targeted wound monitoring and therapy
Small
8
21
3263-3268
2012
10.1002/smll.201200933
Proper healing of incised skin is critical to the natural processes of tissue repair. Concepts in flexible silicon electronics enable integration of actuators, sensors and a variety of semiconductor devices onto thin strips of plastic or biopolymers, to yield 'instrumented' suture threads for monitoring and accelerating the wound healing in this context. Bifacial systems of this type demonstrate various classes of functionality, in live animal models. Detailed modelling of the mechanics reveals stress and strain distributions in such applications, to support design strategies for robust operation.
flexible electronics; implantable devices; sensors; surgical sutures
Exact bending analysis of fully clamped rectangular thin plates subjected to arbitrary loads by new symplectic approach
Mechanics Research Communications
36
6
707-714
2009
10.1016/j.mechrescom.2009.04.001
The exact solutions of fully clamped rectangular thin plates subjected to arbitrary loads are derived by the symplectic geometry method. Since only the basic elasticity equations of thin plates are used, this method eliminates the need to select the deformation function arbitrarily and is hence more accurate than conventional methods. Numerical results were presented to demonstrate the validity and accuracy of this approach as compared to those reported in other literatures. Crown Copyright ?? 2009.
Arbitrary loads; Exact solutions; Rectangular thin plates with all edges clamped; Symplectic geometry method
Stresses around fiber ends at free and embedded ply edges
Composites Science and Technology
68
15-16
3352-3357
2008
10.1016/j.compscitech.2008.09.001
Using the finite element method, the stress state around fiber ends at a free surface in a unidirectional fiber composite was studied. The material is subjected to a thermal load consistent with a cryogenic application as well as ply level transverse tensile loading associated with thermal stresses in a laminate. At the free end the fiber-matrix interface sees tensile radial stresses as well as shear stresses. This makes the fiber end a likely site for interface debonding (crack initiation). These initial cracks can then link up and grow to become full through-thickness matrix cracks. The effect that an epoxy coating over the fiber ends has on the local stress distribution was also considered. These capped models simulate fiber ends embedded within a laminate. The epoxy cap has the effect of suppressing the interface stresses at the fiber end. The significance of these results in relation to cryogenic cycling tests using coupon specimens with free and embedded edges is discussed. © 2008 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites; B. Thermomechanical properties; C. Finite element analysis; C. Stress concentrations
Shell Finite Cell Method: A high order fictitious domain approach for thin-walled structures
Computer Methods in Applied Mechanics and Engineering
200
45-46
3200-3209
2011
10.1016/j.cma.2011.06.005
This article presents a generalization of the recently proposed Finite Cell Method to thin-walled structures. This approach uses a combination of well known Fictitious Domain Methods with high order hierarchical Ansatz spaces known from the p-version of the Finite Element Method. Whereas the original concept embeds a three-dimensional structure in a simple domain being meshed into a grid of cube shaped cells, the extension presented in this paper applies the fictitious domain approach to a two-dimensional master domain defined in the parameter plane of the geometric model. Implementation details are discussed and numerical benchmark problems show the high accuracy and computational efficiency of the new approach. It is also remarked, that the present approach can easily be carried over to isogeometric analysis, opening an attractive possibility to simulate trimmed NURBS-surfaces. © 2011 Elsevier B.V.
Fictitious Domain Method; Finite Cell Method; High-order methods; Isogeometric analysis; P-FEM; Thin-walled structures
A spectral scheme for the simulation of dynamic mode 3 delamination of thin films
Engineering Fracture Mechanics
72
12 SPEC. ISS.
1866-1891
2005
10.1016/j.engfracmech.2004.10.014
Motivated by recent developments in laser-induced spallation testing of thin film structures, we develop a spectral scheme for the simulation of dynamic failure of thin films. In this first study, we focus on the anti-plane shear (mode 3) loading case. The scheme relies on an exact spectral representation of the elastodynamic solutions in the substrate and in the film, and their combination through interface conditions that involve general cohesive failure and/or frictional contact models. A detailed modal analysis of the response of a single spectral mode is performed to assess the stability and precision of the resulting numerical scheme. A set of dynamic fracture problems involving non-propagating and propagating cracks are simulated to show the ability of the numerical scheme to capture the effect of wave reflection on the near-tip stress and displacement fields, and on the dynamic motion of a crack along the film/substrate interface. ?? 2005 Elsevier Ltd. All rights reserved.
Delamination; Dynamic fracture; Spallation; Spectral scheme; Thin film
Distortional mechanics of restrained steel sections
Journal of Constructional Steel Research
66
7
873-884
2010
10.1016/j.jcsr.2010.01.016
This paper presents an overview of the mechanics of distortion in members which have restrained thin-walled steel sections. First, the basic features that characterize the distortion of thin-walled sections under compression and/or bending are explained and the generally adopted kinematical assumptions are presented and discussed. On the basis of these assumptions, a simple procedure to build the distortional displacement fields is proposed. Then, two illustrative examples of restrained sections are given and their distortional displacement fields are built. The I-section illustrates the case of a symmetric section having a distortional displacement field with a single d.o.f. The Z-section exemplifies the case of a non symmetric section having a distortional field with two d.o.f. Based on an energy formulation, the equilibrium equation for buckling analysis of simply supported thin-walled members is derived. For two illustrative examples, the distortional displacement field is used to obtain distortional analytical formulae. Finally, some results (buckling loads and moments) were determined and validated by means of comparison with fully numerical obtained from finite strip analysis. ?? 2010 Elsevier Ltd. All rights reserved.
Analytical formula; Distortional buckling; Distortional mechanics; I-sections; Kinematical assumptions; Restrained thin-walled steel sections; Z-sections
Overview of Bohmian Mechanics
Applied Bohmian Mechanics: From Nanoscale Systems to Cosmology
15-147
2012
10.1201/b12311
This chapter provides a comprehensive overview of the Bohmian formulation of quantum mechanics. It starts with a historical review of the difficulties found by Louis de Broglie, David Bohm, and John S. Bell to convince the scientific community about the validity and utility of Bohmian mechanics. Then, a formal explanation of Bohmian mechanics for nonrelativistic, single-particle quantum systems is presented. The generalization to many-particle systems, where the exchange interaction and the spin play an important role, is also presented. After that, the measurement process in Bohmian mechanics is discussed. It is emphasized that Bohmian mechanics exactly reproduces the mean value and temporal and spatial correlations obtained from the standard, that is the Copenhagen or orthodox, formulation. The ontological characteristics of Bohmian mechanics provide a description of measurements as another type of interaction without the need for introducing the wave function collapse. Several solved problems are presented at the end of the chapter, giving additional mathematical support to some particular issues. A detailed description of computational algorithms to obtain Bohmian trajectories from the numerical solution of the Schrodinger or the Hamilton-Jacobi equations are presented in an appendix. The motivation of this chapter is twofold: first, as a didactic introduction to Bohmian formalism, which is used in the subsequent chapters, and second, as a self-contained summary for any newcomer interested in using Bohmian mechanics in his or her daily research activity.
Prototypical model for tensional wrinkling in thin sheets.
Proceedings of the National Academy of Sciences of the United States of America
108
45
18227-32
2011
10.1073/pnas.1108553108
The buckling and wrinkling of thin films has recently seen a surge of interest among physicists, biologists, mathematicians, and engineers. This activity has been triggered by the growing interest in developing technologies at ever-decreasing scales and the resulting necessity to control the mechanics of tiny structures, as well as by the realization that morphogenetic processes, such as the tissue-shaping instabilities occurring in animal epithelia or plant leaves, often emerge from mechanical instabilities of cell sheets. Although the most basic buckling instability of uniaxially compressed plates was understood by Euler more than two centuries ago, recent experiments on nanometrically thin (ultrathin) films have shown significant deviations from predictions of standard buckling theory. Motivated by this puzzle, we introduce here a theoretical model that allows for a systematic analysis of wrinkling in sheets far from their instability threshold. We focus on the simplest extension of Euler buckling that exhibits wrinkles of finite length--a sheet under axisymmetric tensile loads. The first study of this geometry, which is attributed to Lamé, allows us to construct a phase diagram that demonstrates the dramatic variation of wrinkling patterns from near-threshold to far-from-threshold conditions. Theoretical arguments and comparison to experiments show that the thinner the sheet is, the smaller is the compressive load above which the far-from-threshold regime emerges. This observation emphasizes the relevance of our analysis for nanomechanics applications.
Evaluating crack tip stress field in a thin glass plate under thermal load
Engineering Fracture Mechanics
75
5
1015-1026
2008
10.1016/j.engfracmech.2007.04.025
The stress field around a propagating crack tip in a quenched thin glass plate is discussed through experimental and theoretical analyses. Instantaneous phase-stepping photoelasticity using a CCD camera equipped with a pixelated micro-retarder array is used for measuring the crack tip stress field. From the successive phase maps of principal direction, the position and the velocity of the crack tip are evaluated. On the other hand, the fracture parameters, that is, the stress intensity factors and the T-stress are determined from the phase maps of the retardation. Experimental results obtained for a straight crack show good agreement with those obtained by theory of elasticity. The results also indicate that the direction of the crack propagation arising in the quenching process is not determined by the direction of the maximum principal stress. Furthermore, the results show that the T-stress criterion is inappropriate to evaluate the crack path instability in a quenched thin glass plate.
Fracture mechanics; Mixed mode fracture; Photoelasticity; Stress intensity factor; Thermal stress
Optimal design of symmetric angle-ply laminates subject to nonuniform buckling loads and in-plane restraints
Thin-Walled Structures
26
1
45-60
1996
10.1016/0263-8231(96)00002-X
Optimal buckling designs of symmetrically laminated rectangular plates under in-plane uniaxial loads which have a nonuniform distribution along the edges are presented. In particular, point loads, partial uniform loads and nonuniform loads are considered in addition to uniformly distributed inplane loads which provide the benchmark solutions. Poisson's effect is taken into account when in-plane restraints are present along the unloaded edges. Restraints give rise to in-plane loads at unloaded edges which lead to biaxial loading, and may cause premature instability. The laminate behaviour with respect to fiber orientation changes significantly, in the presence of Poisson's effect as compared to that of a laminate where this effect is neglected. This change in behaviour has significant implications for design optimisation as the optimal values of design variables with or without restraints differ substantially. In the present study, the design objective is the maximisation of the uniaxial buckling load by optimally, determining the fiber orientations. The finite element method, coupled with an optimisation routine, is employed in analysing and optimising the laminates. Numerical results are given for a number of boundary conditions and for uniformly and non-uniformly distributed buckling loads.
The mechanics of the foot
Journal of anatomy
88
Pt 1
25-30.1
1954
10.1159/000141121
Images: Fig. 1: Fig. 2: Fig. 3: Fig. 4: Fig. 5:
Quantum Mechanics and Reality
Physics Today
23
9
155-165
2004
10.1063/1.3022331
We begin by discussing ``What exists?'', i.e. ontology, in Classical Physics which provided a description of physical phenomena at the macroscopic level. The microworld however necessitates a introduction of Quantum ideas for its understanding. It is almost certain that the world is quantum mechanical at both microscopic as well as at macroscopic level. The problem of ontology of a Quantum world is a difficult one. It also depends on which interpretation is used. We first discuss some interpretations in which Quantum Mechanics does not provide a complete framework but has to be supplemented by extra ingredients e.g. (i) Copenhagen group of interpretations associated with the names of Niels Bohr, Heisenberg, von-Neumann, and (ii) de-Broglie-Bohm interpretations. We then look at some interpretations in which Quantum mechanics is supposed to provide the entire framework such as (i) Everett-deWitt many world, (ii) quantum histories interpretations. We conclude with some remarks on the rigidity of the formalism of quantum mechanics, which is sharp contrast to it's ontological fluidity.
Free vibrations of laminated composite plates using second-order shear deformation theory
Computers & Structures
71
6
617-626
1999
10.1016/S0045-7949(98)00301-0
A complete set of linear equations of the second-order theory of laminated composite plates are obtained. A generalized Levy type solution in conjunction with the state space concept is used to analyze the free vibration behavior of cross-ply and antisymmetric angle-ply laminated plates. Exact fundamental frequencies of cross-ply plate strips are obtained for arbitrary boundary conditions. The exact analytical solutions are obtained for thick and moderately thick plates as well as for thin plates and plate strips. It is shown that the results of the second-order theory are very close to the results of the first-order and third-order theories reported in the literature, and different from those of the classical Kirchhoff’s theory for thick laminates.
Composite plates; Deformation theory; Free vibration
Delamination in cross-ply laminated composite subjected to low-velocity impact
AIAA Journal
31
8
1498-1502
1993
10.2514/3.11800
Delamination due to low-velocity impact of simply supported graphite/epoxy cross-ply laminate beams and plates was investigated. Both quasistatic and low-velocity impact testing were carried out in this study. For each loading condition, finite element analysis and experiments were performed to study damage growth and distributions. The mode II energy release rate for dynamic crack arrest GIIa was 75% less than the onset of crack propagation GIIC. A quasistatic three-dimensional finite element analysis coupled with a GII >= GIIC criterion was used for the onset of delamination propagation, and GII <= GIIa criterion was used to arrest the propagating crack and to estimate the delamination area. Delamination area determined by this method correlated well with the test results.
Analysis of interlaminar stresses in general cross-ply laminates with distributed piezoelectric actuators
Composite Structures
92
3
757-768
2010
10.1016/j.compstruct.2009.09.003
This paper represents an analytical solution to determine the interlaminar stresses of general cross-ply laminates with piezoelectric layers as actuators under transverse mechanical loads. The three-dimensional constitutive equations of piezoelectricity are considered and the governing equations are derived within the framework of second-order shear-deformation plate theory as a set of partial differential equations. These equations are solved for two kinds of boundary conditions and the unknown assumed functions of displacement field are found. Numerical results show that this approach can generally predict the behavior of interlaminar stresses. Also, they clearly indicate the singular behavior of interlaminar normal and shear stresses in the boundary region near the edges of the laminate. © 2009 Elsevier Ltd. All rights reserved.
Analytical solution; Edge effect; Interlaminar stresses; Piezoelectric materials
Mixed quantum mechanics and molecular mechanics methods: Looking inside proteins
Wiley Interdisciplinary Reviews: Computational Molecular Science
1
2
315-322
2011
10.1002/wcms.27
Mixed quantum mechanics and molecular mechanics (QM/MM) techniques, wherein the active site is treated with a robust ab initio quantum mechanics methodology and the remainder of the protein is modeled at the molecular mechanics level, offer a valuable tool for looking inside enzymes. We present here a short summary of recent QM/MM applications. We discuss the capabilities of this technology focusing in the main three steps when modeling enzymes: building a model, conformational sampling, and mapping the chemical process.
Stiffness reduction and energy release rate of cross-ply laminates during fatigue tests
Composite Structures
30
2
123-130
1995
10.1016/0263-8223(94)00061-1
The purpose of the paper is to investigate the experimental results obtained during cyclic tensile tests in the case of two equivalent stacking sequences: (0790)s and (039004)s, of carbon fibre laminates. During the fatigue tests, matrix cracking in 90 ° plies has been characterized by the crack distributions in the width of the test specimen, giving the S-N distributions. Then, the longitudinal stiffness reduction has been evaluated from these crack distributions and by a finite element analysis. The results obtained show a linear relationship, in the domain studied, between the stiffness reduction and the crack area, leading to a constant energy release rate during the fatigue tests.
Fabrication of semi-transparent superoleophobic thin film by nanoparticle-based nano-microstructures on see-through fabrics
Journal of Materials Science
48
19
6613-6618
2013
10.1007/s10853-013-7459-6
Superoleophobic thin films have many potential applications including fluid transfer, fluid power systems, stain-resistant and antifouling materials, and microfluidics. Transparency is also desired with superhydrophobicity for numerous applications; however, transparency and oleophobicity are almost incompatible with each other from the point of view of surface structure. Oleophobicity requires a rougher structure on the nano–microscale than hydrophobicity, and this rough structure brings light scattering. So far, there are few reports of compatible transparency and superoleophobicity. In this report, we propose see-through-type fabrics having nanoparticle-based hierarchical structure thin films to improve both oleophobicity and transparency. The vacant space between the fibers of the fabric has two important roles: to allow light to pass through and to induce an air layer to produce a Cassie state of a liquid droplet on the resulting thin film. To realize a low surface energy and nanoscale rough structured surface on fabric fibers, we used a spray method with perfluoroalkyl methacrylic copolymer, silica nanoparticles, and volatile solvent. Scanning electron microscopy images revealed that hierarchical nanoparticle structures were uniformly formed on the fabrics. The transparency of the obtained thin film was approximately 61 %, and the change of transparency between the non-coated and coated fabrics was 11 %. The contact angles of oil (rapeseed oil and hexadecane) and water droplets on the fabricated film were observed to be over 150° during investigation of its surface wettability.
Mechanics of corrugated surfaces
Journal of the Mechanics and Physics of Solids
58
10
1552-1566
2010
10.1016/j.jmps.2010.07.011
Experimental studies of the surface stress of solids typically work with surfaces that are not perfectly planar. The experiment then probes an effectively averaged surface stress. The evolution of the surface morphology, for instance during film growth or reconstruction, is also affected by the surface stress acting on a corrugated surface. Here, we analyze the mechanics of rough surfaces in a continuum framework. In a generalization of the approach of Weissmuller and Duan [2008. Phys. Rev. Lett. 101, 146102] to solids with anisotropic elasticity, anisotropic surface stress and anisotropic roughness, we focus on the effectively averaged surface stress that determines the mean compensating stress in the bulk. Important concepts are the projection of out-of-plane stresses at inclined segments of a surface into the macroscopic surface plane, and the transverse coupling between the out-of-plane and in-plane components of the surface-induced stress in the bulk. We show that the coupling of the surface stress at a corrugated surface into a planar substrate depends on the geometry of the corrugation exclusively through the surface orientation distribution function. Special geometries are inspected with an eye on illustrating the impact of anisotropic elasticity as well as geometric anisotropy, which both feed into the anisotropy of the effective surface stress. (C) 2010 Elsevier Ltd. All rights reserved.
ADSORPTION; Corrugated surface; Elastic anisotropy; ELASTIC-CONSTANTS; EQUATION; EQUILIBRIUM; INTERFACE STRESSES; KINETICS; Roughness; SELF-ASSEMBLED MONOLAYERS; SOLIDS; STRAIN; Surface stress; THIN-FILMS
Adhesion of heterogeneous thin films - I: Elastic heterogeneity
Journal of the Mechanics and Physics of Solids
61
3
838-851
2013
10.1016/j.jmps.2012.10.014
We study the adhesion of thin films on rigid substrates in the presence of spatial heterogeneities. While adhesion is relatively well-understood in the context of homogeneous systems, much remains open concerning the adhesion of heterogeneous systems. In this paper, we focus on thin adhesive tape with heterogeneities in the elastic stiffness, and show that these heterogeneities have a profound effect on adhesion raising the effective force required to peel the film by an order of magnitude with no modification of the actual adhesive interface. We show through theory and experiment that this apparent increase is caused by fluctuations in the elastic bending energy. We also show that heterogeneities can be used to create asymmetry in that the force required to peel the tape in one direction can be different from that in the other. In short, this work shows that fluctuations in a small component of the overall energy of the system can give rise to a significant macroscopic consequence. We comment on the broader implications of this observation. ?? 2012 Elsevier Ltd.
Adhesion asymmetry; Adhesion enhancement; Fracture; Heterogeneity; Thin films
Essential role of domain 4 of pneumolysin from Streptococcus pneumoniae in cytolytic activity as determined by truncated proteins.
Biochemical and biophysical research communications
281
1
37-44
2001
10.1006/bbrc.2001.4297
Pneumolysin (PLY), an important virulence factor of Streptococcus pneumoniae, is one of the members of thiol-activated cytolysins (TACYs) consisting of four domains. TACYs commonly bind to membrane cholesterol and oligomerize to form transmembrane pore. We have constructed full-length and various truncated PLYs to study the role of domains of PLY in the cytolytic activity. Full-length PLY had binding ability to both cell membrane and immobilized cholesterol. A truncated PLY which comprised only domain 4 molecule, the C-terminal domain of PLY, sustained the binding ability to cell membrane and cholesterol, whereas domain 1-3 molecule had no binding ability to them. Furthermore, the domain 4 molecule inhibited both the membrane binding and the hemolytic activity of full-length PLY. Accordingly, the present results provided the direct evidence that domain 4 was essential for the initial binding to membrane cholesterol and the interaction led to the subsequent membrane damage process.
Animals; Bacterial Proteins; Cell Membrane; Cell Membrane: metabolism; Cholesterol; Cholesterol: metabolism; Chromatography, Thin Layer; Dose-Response Relationship, Drug; Erythrocytes; Erythrocytes: metabolism; Hemolysis; Ligands; Plasmids; Plasmids: metabolism; Protein Binding; Protein Structure, Tertiary; Recombinant Proteins; Recombinant Proteins: metabolism; Sheep; Streptococcus pneumoniae; Streptococcus pneumoniae: chemistry; Streptolysins; Streptolysins: chemistry
Thin-blade penetration resistance and snow strength
Journal of Glaciology
57
202
325-336
2011
10.3189/002214311796405924
A thin-blade snow hardness gauge was developed that measures penetration resistance over a length scale (on the order of 10–100 grain contacts) relevant to the fracture of slab avalanches. A thin blade was chosen to measure the ruptures of bonds and grain structures and minimize the effects of snow compaction during penetration. The apparatus consists of a 10 cm wide, 0.6 mm thick stainless- steel blade attached to a digital push–pull gauge. Blade penetration measurements are easy to conduct in the field and laboratory and required no post-processing or subjective interpretation. Measurements were conducted in snow pits to test the effects of penetration rate, blade orientation and blade width. The blade hardness index, defined as the maximum force of penetration, is a highly repeatable measure across observers compared to the hand hardness test. The blade hardness index was a better variable than the density for correlating with tensile strength measurements in a cold laboratory and with a cohesive strength measure in the field. As strength is one of the most important parameters in the fracture mechanics of slab avalanches, the strong correlation between thin-blade penetration and strength should benefit future slope stability evaluations using this gauge
field methods; penetration resistance; snow hardness; tensile strength
Quantum well structures in thin metal films: simple model physics in reality?
Reports on Progress in Physics
65
2
99
2002
10.1088/0034-4885/65/2/201
The quantum wells formed by ultra-thin metallic films on appropriate metallic substrates provide a real example of the simple undergraduate physics problem in quantum mechanics of the `particle in a box'. Photoemission provides a direct probe of the energy of the resulting quantized bound states. In this review the relationship of this simple model system to the real metallic quantum well (QW) is explored, including the way that the exact nature of the boundaries can be taken into account in a relative simple way through the `phase accumulation model'. More detailed aspects of the photoemission probe of QW states are also discussed, notably of the physical processes governing the photon energy dependence of the cross sections, of the influence of temperature, and the processes governing the observed peak widths. These aspects are illustrated with the results of experiments and theoretical studies, especially for the model systems Ag on Fe(100), Ag on V(100) and Cu on fcc Co(100).
EVALUATION OF THIN KEVLAR-EPDXY FABRIC PANELS SUBJECTED TO SHEAR LOADING
Structures, Structural Dynamics, and Materials Conference
1996
doi:10.2514/6.1996-1367
The results of an analytical and experimental investigation of 4-ply Kevlar49-epoxy panels loaded by in-plane shear are presented. Approximately one- half of the panels are thin-core sandwich panels and the other panels are solid-laminate panels. Selected panels were impacted with an aluminum sphere at a velocity of either 150 or 220 ft/sec. The strength of panels impacted at 150 ft/sec was not reduced when compared to the strength of the undamaged panels, but the strength of panels impacted at 220 ft/sec was reduced by 27 to 40 percent. Results are presented for panels that were cyclically loaded from a load less than the buckling load to a load in the postbuckling load range. The thin-core sandwich panels had a lower fatigue life than the solid panels. The residual strength of the solid and sandwich panels cycled more than one million cycles exceeded the baseline undamaged panel strengths. The effect of hysteresis in the response of the sandwich panels is not significant. Results of a nonlinear finite element analysis conducted for each panel design are presented.
Contact mechanics and the adhesion of soft solids
Materials Science and Engineering: R: Reports
36
1-45
2002
10.1016/S0927-796X(01)00039-0
The contact behavior of solid materials is determined by the system geometry, externally applied loads and internal adhesive forces, and by the materials properties. As the size and stiffness of a material decrease, adhesive forces become increasingly important in determining its contact behavior. The current trends toward the use of smaller features in many areas of technology, and the importance of 'soft' materials including biological tissues, elastomers and polymer gels, demand that the effects of adhesion on contact mechanics be properly understood. The focus of this review is on the mechanics of contact experiments that are commonly used to characterize adhesion, and on the materials science of adhesion of elastic and viscoelastic materials. © 2002 Elsevier Science B.V. All rights reserved.
Adhesion; Contact mechanics; Elastomers; Gels
Probabilistic dynamic buckling of composite shell structures
Composites Part A: Applied Science and Manufacturing
36
10 SPEC. ISS.
1368-1380
2005
10.1016/j.compositesa.2004.11.018
A computationally effective method is described to evaluate the probabilistic dynamic buckling of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics and probabilistic structural analysis. The solution method is an incrementally updated Lagrangian. It is illustrated by applying it to a thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different loading rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio, the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties in that order. Published by Elsevier Ltd.
Buckling; Composite mechanics; Computational modeling; Finite element analysis
Phase-Field Modeling of Domain Structure Energetics and Evolution in Ferroelectric Thin Films
Journal of Applied Mechanics
77
4
041014
2010
10.1115/1.4000925
A computational model developed based on the phase-field approach is used to model domain structures in ferroelectric thin films and to quantify the effects of strain and applied electric field on the microstructural evolution, and on the induced dielectric, electrostrictive, and piezoelectric film properties. Theoretically predicted vortex-like polydomain and experimentally observed bidomain and monodomain film morphologies are modeled using the continuum phase-field approach. A nonlinear finite element method is used to solve the boundary value problems relevant to ferroelectric thin films. The computed results agree with the Kittel law for specific ranges of film strain. Simulations that track the domain structure evolution and compute ferroelectric thin film properties given the film dimensions and the imposed electromechanical boundary conditions are also reported.
ferroelectrics; finite element methods; phase-field modeling; thin films; vortex
Foam mechanics: spontaneous rupture of thinning liquid films with Plateau borders
Journal of Fluid Mechanics
658
2010
63-88
2010
10.1017/S0022112010001527
Spontaneous film rupture from van der Waals instability is investigated in two dimensions. The focus is on pure liquids with clean interfaces. This case is applicable to metallic foams for which surfactants are not available. There are important implications in aqueous foams as well, but the main differences are noted. A thin liquid film between adjacent bubbles in a foam has finite length, curved boundaries (Plateau borders) and a drainage flow from capillary suction that causes it to thin. A full linear stability analysis of this thinning film shows that rupture occurs once the film has thinned to ‘tens’ of nanometres, whereas for a quiescent film with a constant and uniform thickness, rupture occurs when the thickness is ‘hundreds’ of nanometres. Plateau borders and flow are both found to contribute to the stabilization. The drainage flow leads to several distinct qualitative features as well. In particular, unstable disturbances are advected by the flow to the edges of the thin film. As a result, the edges of the film close to the Plateau borders appear more susceptible to rupture than the centre of the film.
On the indentation failure of carbon-epoxy cross-ply laminates, and its suppression by elasto-plastic interleaves
Acta Materialia
45
3431-3444
1997
10.1016/S1359-6454(96)00381-3
Elastic and elasto-plastic modelling of indentation in CFRP cross-ply laminates has been performed. Detailed knowledge of the field solutions in the volume below the indentor forms the basis for the reported micromechanical interpretation of the observed damage in test specimens. The analysis shows that matrix cracks originate at sites of maximum tensile stress perpendicular to fibres. The predicted stress fields due to indentation show that stress concentrations occur in the interface between alternating plies. It is found that microcracking in this zone is a precursor to the observed failure. This analysis is supported by in-situ scanning electron microscopy during loading by a cylindrical indentor onto the laminate supported on a rigid substrate. The microscopy reveals microdamage in the region of interfacial tensile stress concentrations. The onset of indentation failure in these layered composites suggests that plastic interleaves would delay failure. It is shown numerically that plastic deformation of the interleaves redistributes stresses and thereby weakens the tensile stress concentrations which arise during indentation. Experimentally it is shown that aluminium interleaves affect the formation of indentation failure. In a cross-ply laminate, where alternating ply groups are separated by aluminium sheets, matrix cracking and delamination failures are suppressed by the occurrence of plastic deformation. Since the aluminium is likely to be weakly bonded to the plies, it is seen that weak interlaminar fracture toughness does not necessarily cause delaminations, nor lead to a lower indentation strength. High indentation strength and delamination resistance are complex qualities which, among others, seem to be achieved in laminate geometries which have a minimum of stress concentration at interfaces between ply groups of different orientation. © 1997 Acta Metallurgica Inc.
8-ply small intestinal submucosa tension-free sling: spectrum of postoperative inflammation.
The Journal of urology
171
1
268-71
2004
10.1097/01.ju.0000098680.60020.32
PURPOSE: We report a series of postoperative inflammatory reactions of a tension-free pubourethral sling procedure using an 8-ply small intestinal submucosa (SIS) and review the literature regarding inflammatory reactions with this material in genitourinary reconstruction.\n\nMATERIALS AND METHODS: Between August 2002 and June 2003, 6 of 10 patients treated for stress urinary incontinence with 8-ply SIS had postoperative inflammatory reactions. Patients underwent a thorough evaluation, including history, physical examination and urodynamic studies, before surgical intervention.\n\nRESULTS: All patients presented with induration and erythema at the abdominal incision site(s) and pain 10 to 39 days postoperatively. Pelvic examinations were negative. In 3 patients the inflammatory reaction resolved with minimal or no intervention. Incision and drainage of a sterile abscess were required in 1 patient. Despite 7 days of prophylactic postoperative antibiotics and anti-inflammatory drugs, 2 patients had delayed inflammatory reactions. One patient had resolution with conservative treatment, while the other had an abscess that spontaneously drained. With short-term followup (mean 7 months, range 4 to 10), 8 patients are dry, 1 is improved and 1 is incontinent.\n\nCONCLUSIONS: While the results with the 8-ply SIS tension-free sling in the short term are encouraging, the additional morbidity is alarming and caution is warranted. It is essential that patients be made aware of potential risks and possible delayed presentation of morbidity with the use of this material. The human to 8-ply SIS interaction needs further investigation to ensure that long-term safety and efficacy will not be jeopardized. Until then we will continue to use other sling materials.
Adult; Female; Humans; Inflammation; Inflammation: epidemiology; Inflammation: etiology; Intestinal Mucosa; Middle Aged; Urinary Incontinence, Stress; Urinary Incontinence, Stress: surgery; Urologic Surgical Procedures; Urologic Surgical Procedures: adverse effects; Urologic Surgical Procedures: methods
Quantum mechanics writ large.
Proceedings of the National Academy of Sciences of the United States of America
107
41
17455-17456
2010
10.1073/pnas.1012399107
Some two centuries before the quantum revolution, Newton (1) suggested that corpuscles of light generate waves in an aethereal medium like skipping stones generate waves in water, with their motion then being affected by these aether waves. Times have changed. Light corpuscles are now known as photons, and the majority of physicists have dispensed with the notion of aether. Nevertheless, certain features of Newton's metaphor live on in one particular version of quantum mechanics. According to pilot wave theory, first proposed by de Broglie (2) and later developed by Bohm (3) with Einstein's encouragement, microscopic elements such as photons and electrons consist of both particle and wave, the former being guided by the latter. Although this physical picture has not been widely accepted, it has had some notable proponents, including Bell (4). Its principal appeal is that it restores realism and determinism to quantum mechanics, its weakness that the physical nature of the guiding wave field remains unclear. At the time that pilot wave theory was developed and then overtaken by the Copenhagen interpretation as the standard view of quantum mechanics, there was no macroscopic pilot wave analog to draw upon. Now there is.
Nuclear lamin A/C deficiency induces defects in cell mechanics, polarization, and migration.
Biophysical journal
93
7
2542-2552
2007
10.1529/biophysj.106.102426
Lamin A/C is a major constituent of the nuclear lamina, a thin filamentous protein layer that lies beneath the nuclear envelope. Here we show that lamin A/C deficiency in mouse embryonic fibroblasts (Lmna(-/-) MEFs) diminishes the ability of these cells to polarize at the edge of a wound and significantly reduces cell migration speed into the wound. Moreover, lamin A/C deficiency induces significant separation of the microtubule organizing center (MTOC) from the nuclear envelope. Investigations using ballistic intracellular nanorheology reveal that lamin A/C deficiency also dramatically affects the micromechanical properties of the cytoplasm. Both the elasticity (stretchiness) and the viscosity (propensity of a material to flow) of the cytoplasm in Lmna(-/-) MEFs are significantly reduced. Disassembly of either the actin filament or microtubule networks in Lmna(+/+) MEFs results in decrease of cytoplasmic elasticity and viscosity down to levels found in Lmna(-/-) MEFs. Together these results show that both the mechanical properties of the cytoskeleton and cytoskeleton-based processes, including cell motility, coupled MTOC and nucleus dynamics, and cell polarization, depend critically on the integrity of the nuclear lamina, which suggest the existence of a functional mechanical connection between the nucleus and the cytoskeleton. These results also suggest that cell polarization during cell migration requires tight mechanical coupling between MTOC and nucleus, which is mediated by lamin A/C.
Antibody response to Streptococcus pneumoniae proteins PhtD, LytB, PcpA, PhtE and Ply after nasopharyngeal colonization and acute otitis media in children
Human Vaccines & Immunotherapeutics
8
6
799-805
2012
10.4161/hv.19820
We prospectively compared serum antibody levels of five Streptococcus pneumoniae (Spn) proteins: PcpA PhtD, PhtE Ply © 2012 Landes Bioscience. and LytB associated with nasopharyngeal (NP) colonization and acute otitis media (AOM) infection in a cohort of 6–30 mo old children. Antigen-specific antibody titers were determined by ELISA. A total of 731 visits among 168 children were studied. There were 301 Spn NP colonization episodes documented in 109 (65%) children and 42 Spn AOM episodes in 34 (20%) children. IgG antibody titers to the 5 proteins were significantly different among children over time (p < 0.001), with a rank order as follows: PcpA > PhtE = PhtD > Ply > LytB Characterization of IgG and IgM acute and convalescent serum antibody levels after Spn AOM infection showed the kinetics of the response differed among children, with the same rank order of antibody levels over time. Individual data showed that some children responded to AOM with an antibody increase to one or more of these Spn proteins but some children failed to respond. We conclude that antibody levels to Spn proteins PcpA PhtD, PhtE, Ply and LytB, all rise over time in children age 6 to 30 mo following natural exposure to Spn after NP colonization and AOM; however, there were significant differences in quantity of antibody elicited among these potential vaccine antigens.
acute otitis media; aom; lytb; nasopharyngeal; np; op; oropharyngeal; pcpa; phtd; phte; ply; streptococcus pneumoniae
Effect of Thin Films on Dynamic Performance of Resonating MEMS
Experimental Mechanics
54
1
25-33
2014
10.1007/s11340-013-9809-3
Continued advances in microelectromechanical systems (MEMS) technology have led to development of a multitude of new sensors and their corresponding advanced applications. Great many of these sensors (e.g., microgyroscopes, accelerometers, biological, chemical, security, medical, etc.) rely on either sensing elements or elastic suspensions that resonate. Regardless of their applications, sensors are always designed to provide the most exact responses to the signals they are developed to detect and/or monitor. One way to quantify this exactness is to use the Quality factor ( Q-factor). MEMS sensors are typically fabricated out of materials that are mechanically sound at the microscale, but can be relatively poor electrical conductors. For this reason, areas of MEMS are coated with various thin metal films to provide electrical pathways. These films, however, adversely alter resonant properties of a device. To facilitate our study, microcantilever configurations were selected to test influence that thin metal films have on resonators. This paper reviews a theoretical analysis of the effect that thermoelastic internal friction has on the Q-factor of microscale resonators and shows that the internal friction relating to TED is a fundamental damping mechanism in determination of quality of high-Q resonators over a range of operating conditions. Using silicon microcantilevers coated with aluminum films from 5 nm to 30 nm thick, on one as well as both sides, Q-factors were experimentally determined using the ring-down method. From the ring-down curve, the Q-factor of each microcantilever was determined. Experimental results show that as thickness of the aluminum film increases, Q-factor of the device decreases. Comparison of analytical and experimental results indicates good correlation, well within the limits based on uncertainty analysis. In addition, preliminary results also show a significant temperature dependence of the Q-factor of aluminum coated microcantilevers. [ABSTRACT FROM AUTHOR]
High-frequency; MEMS; Microcantilever; Quality factor; Resonance; Ring-down; TED; Thin films; Uncertainty analysis
The mechanics of manipulation
Proceedings 1985 IEEE International Conference on Robotics and Automation
2
March
544-548
1985
10.1109/ROBOT.1985.1087242
Many manipulator operations eliminate uncertainty in the locations and shapes of objects by purely mechanical means. Rather than relying on sensors, or on auxiliary parts-feeding machinery, these operations use the intrinsic mechanics of the task environment to eliminate uncertainty. Effective use of these operations requires that a planner be able to analyze the mechanics of a given task.
Stress intensity factors for cracked rectangular cross-section thin-walled tubes
Engineering Fracture Mechanics
71
11
1501-1513
2004
10.1016/S0013-7944(03)00217-0
For cracked structural rectangular thin-walled tubes, an exact and very simple method to determine the stress intensity factors has been proposed based on a new concept of crack surface widening energy release rate. Unlike the classical crack extension energy release rate, the crack surface widening energy release rate can be expressed by the G*-integral and elementary strength theory of materials for slender cracked structures. From present discussions, a series of new and exact solutions of stress intensity factors are derived for cracked rectangular and square tubes. The present method can also be applied to cracked polygon thin-walled tubes. © 2003 Elsevier Ltd. All rights reserved.
Fracture; Mechanics; Stress intensity factor; Tubes
RETRACTED: Fracture of thin-walled structure with SPH shell formulation
Thin-Walled Structures
48
2
118-126
2010
10.1016/j.tws.2009.09.002
A meshless shell method for dynamic fracture problems based on normalized smoothed particle hydrodynamics (SPH) is presented. The SPH method is corrected by a normalization in order to fulfill completeness requirement. Instabilities are controlled by stress-point integration. The method is modified for Mindlin-Reissner shell analysis. Stress based fracture criterion is incorporated based on the visibility method. The method is applied to two dynamic fracture problems. Results are very promising. ?? 2009 Elsevier Ltd. All rights reserved.
Fracture; Mechanics; Shell; SPH; Thin-walled structure
Damage mechanics
Mechanics of Materials
8
2-3
117-197
1989
10.1016/0167-6636(89)90011-2
The objective of the present study is to summarize and recapitulate some of the methods of analyses of brittle response of solids. In general, the discussion is limited to the analyses of influence that the crack-like microdefects have on the compliance and failure of some engineering materials. The attention was focused on the perfectly brittle and semi-brittle response of materials such as concrete, rocks, ceramics and certain brittle solids. Both phenomenological and micromechanical models were discussed at some length emphasizing their relative advantages and drawbacks. A section dealing with simple, one-dimensional damage models is added to help the reader not familiar with this new branch of continuum mechanics.
Mechanics meets medicine.
Science translational medicine
5
212
212fs41
2013
10.1126/scitranslmed.3007731
A new high-throughput measurement technique moves mechanical phenotyping of cells in malignant pleural effusions closer to the clinic (Tse et al., this issue).
articles-editorials; Biological; Biological: analysis; biophysics; cancer; cell-mechanics; Humans; Malignant; Malignant: diagnosis; methods-microfluidics; Pleural Effusion; Tumor Markers
Stick-slip statistical mechanics at the bed of a glacier
Geophysical Research Letters
23
16
2073-2076
1996
10.1029/96GL02069
The multiple processes which control motion at the bed of glaciers are too heterogeneous to be modeled directly, but a simple stick-slip slider-block model of a glacier bed allows a statistical mechanical treatment of the physics beneath thin and shallow sloped glaciers. The technique may reconcile apparently contradictory field observations of the relationship between glacier sliding and basal water pressure. Simulations also predict hysteresis in the relationship between water pressure and basal velocities.
7209 Seismology: Earthquake dynamics and mechanics; 7299 Seismology: General or miscellaneous
Energy Absorption of Thin-Walled Square Tubes With a Prefolded Origami Pattern—Part I: Geometry and Numerical Simulation
Journal of Applied Mechanics
81
1
011003
2013
10.1115/1.4024405
Thin-walled tubes subjected to axial crushing have been extensively employed as energy absorption devices in transport vehicles. Conventionally, they have a square or rectangular section, either straight or tapered. Dents are sometimes added to the surface in order to reduce the initial buckling force. This paper presents a novel thin-walled energy absorption device known as the origami crash box that is made from a thin-walled tube of square cross section whose surface is prefolded according to a developable origami pattern. The prefolded surface serves both as a type of geometric imperfection to lower the initial buckling force and as a mode inducer to trigger a collapse mode that is more efficient in terms of energy absorption. It has been found out from quasi-static numerical simulation that a new collapse mode referred to as the completed diamond mode, which features doubled traveling plastic hinge lines compared with those in conventional square tubes, can be triggered, leading to higher energy absorption and lower peak force than those of conventional ones of identical weight. A parametric study indicates that for a wide range of geometric parameters the origami crash box exhibits predictable and stable collapse behavior, with an energy absorption increase of 92.1% being achieved in the optimum case. The origami crash box can be stamped out of a thin sheet of material like conventional energy absorption devices without incurring in-plane stretching due to the developable surface of the origami pattern. The manufacturing cost is comparable to that of existing thin-walled crash boxes, but it absorbs a great deal more energy during a collision.
axial crushing; devel-; energy absorption; origami pattern; thin-walled tube
Effective Elastic Constants of Bidirectional Laminates Containing Transverse Ply Cracks
Journal of composite materials
34
11
954-978
2000
10.1177/002199830003401103
All nine independent effective elastic constants of [0° m /90° n ] S laminates containing transverse cracks through the middle 90° n layers are determined analytically. The cracks are assumed to be evenly spaced and to extend across the entire laminate width. Each of the 0° m and 90° n ply clusters are modeled as homogeneous, orthotropic materials with the layers connected through continuity of displacements and tractions at the ply interfaces. A stress based homogeneous plate theory which includes the effect of transverse shear and normal stresses is utilized to model the ply clusters. Elastic moduli and stress distributions are compared to shear lag and other analytical models existing in the literature. Moduli of a [±45°] S laminate containing a crack parallel to the fibers in the middle plies are obtained by a rotation of elastic properties obtained from a cracked [0°/90°] S laminate.
Bending and stretching of thin viscous sheets
Journal of Fluid Mechanics
433
135–160
2001
10.1017/S0022112000003360
Thin viscous sheets occur frequently in situations ranging from polymer processing to global plate tectonics. Asympotic expansions in the sheet's dimensionless ‘slenderness’ ε [double less-than sign] 1 are used to derive two coupled equations that describe the deformation of a two-dimensional inertialess sheet with constant viscosity μ and variable thickness and curvature in response to arbitrary loading. Three model problems illustrate the partitioning of thin-sheet deformation between stretching and bending modes: (i) A sheet with fixed (hinged or clamped) ends, initially flat and of length L0 and thickness H0 [identical with] εL0, inflated by a constant excess pressure ΔP applied to one side (‘film blowing’). The sheet deforms initially by bending on a time scale με4/ΔP [identical with] τb, and thereafter by stretching except in bending boundary layers of width δ [similar] L0(t/τb−1/3 at the clamped ends. (ii) An initially horizontal ‘viscous beam’ with length L0 and thickness H0 [identical with] εL0, clamped at one end, deforms by bending on a time scale τb = μH20/gδρL30 until it hangs nearly vertically. Thereafter it deforms by bending in a thin boundary layer at the clamped end, and elsewhere by stretching on a slow time scale ε−2τb. (iii) A sheet extruded horizontally at speed U0 from a slit of width H0 in a gravitational field deforms primarily by bending on a time scale (μH20/U30gδρ)1/4. The sheet's ‘hinge point’ moves in the direction opposite to the extrusion velocity, which may explain the observed retrograde motion of subducting oceanic lithosphere (‘trench rollback’).
Mechanics of composites: A historical review
Mechanics Research Communications
41
1-20
2012
10.1016/j.mechrescom.2012.01.006
This review is concerned with mechanics of continuous fiber composites. The earliest and most important advancements in the field are emphasized. No doubt the coverage is limited to some extent by the interests and experiences of the writer as well as time and space considerations. The advancements in mechanics of composites have been influenced to a great extent by the development of advanced composites through materials science. No attempt is made to discuss these developments. This review emphasizes the use of theoretical and applied mechanics in the development of theories, confirmed by experimentation, to predict the response of composite materials and structures. Citations have been given for many published works, but certainly not all. Apologies to those not listed; numerous additional references can be found in the works cited. ?? 2012 Elsevier Ltd.
Fracture formation in vitrified thin films of cryoprotectants.
Cryobiology
53
1
75-95
2006
10.1016/j.cryobiol.2006.03.013
As a part of an ongoing effort to study the continuum mechanics effects associated with cryopreservation, the current report focuses on fracture formation in vitrified thin films of cryoprotective agents. The current study combines experimental observations with continuum mechanics analysis. Experimental results have been developed using a new imaging device, termed a "cryomacroscope", which has been recently presented by the current research team. A newly developed liquid nitrogen-based cooling stage is presented in this paper. The samples under investigation are 0.5 ml droplets of cryoprotective agents, having a characteristic diameter of 20 mm and a characteristic thickness of 1.5 mm. Tested samples included dimethyl sulfoxide (DMSO) in a concentration range from 6 to 8.4M, and the cryoprotectant cocktails VS55 and DP6. Some samples contained small bovine muscle segments, having a characteristic dimension of 1mm, in order to study stress concentration effects. Experimental results show that the onset of fracturing in vitrified films of cryoprotectants is very consistent, occurring over a small temperature range. Fracture pattern, however, was affected by the cooling rate. The presence of tissue segments did not affect the onset temperature of fracture, but affected the fracture pattern. The continuum mechanics analysis solidified the hypothesis that fracture is driven by thermal stress, not by temperature per se, and allowed fracture strain to be inferred from observed fracture temperature. In conjunction with the current report, additional photos of fracture formation in thin films are available at .
Artificial; Cryoprotective Agents; Cryoprotective Agents: chemistry; Dimethyl Sulfoxide; Formamides; HEPES; Mechanical; Membranes; Propylene Glycols; Stress; Viscosity
On cross-ply cracking in glass and carbon fibre-reinforced epoxy laminates
Composites
18
1
40-46
1987
The transverse tensile strength (or fracture strain) of unidirectional fibre-reinforced materials is an important mechanical property. The transverse fracture strain of a single ply in an angle-ply laminate, however, is not an independent mechanical property as it is influenced by its thickness and neighbouring plies. The present investigation describes the phenomenon of multiple fracture of glass and carbon fibre-reinforced epoxy 90° plies. Based on the model that a 90° ply consists of elements all of which can break, the applicability of Weibull statistics in describing the fracture strain is investigated.
angle-ply laminates; carbon fibres; composite materials; epoxy resin; glass fibres; ply thickness; tensile testing; transverse fracture strain
Computational stochastic mechanics - Recent advances
Computers and Structures
79
22-25
2225-2234
2001
10.1016/S0045-7949(01)00078-5
In this paper some of the most recent developments of computational stochastic structural mechanics and analysis are reviewed. These concepts allow a rational treatment of statistical uncertainties involved in structural analysis and design. Particular emphasis is put on the improvement of the computational efficiency of various methods, such as Monte Carlo simulation, etc. © 2001 Elsevier Science Ltd. All rights reserved.
Computational efficiency; Computational stochastic mechanics; Monte Carlo simulation; Stochastic finite elements; Structural reliability
Overstress accommodation in notched woven-ply thermoplastic laminates at high-temperature: Numerical modeling and validation by Digital Image Correlation
Composites Part B: Engineering
45
1
290-302
2013
10.1016/j.compositesb.2012.06.015
An experimental and numerical study has been conducted on woven-ply PPS-based laminates subjected to static loadings at temperatures higher than the material’s Tg. The fiber – or matrix-dominated mechanical responses of laminates with respectively quasi-isotropic or angle-ply stacking sequences have been investigated in order to emphasize the significant contribution of TP-matrix to the accommodation of overstresses near the hole as temperature increases. Even though the matrix behavior becomes highly ductile, the degree of retention of mechanical properties is quite high, and the hole factor is virtually unchanged as temperature increases in Q-I laminates. In order to understand how matrix ductility is instrumental in reducing the notch-sensitivity (−34%) of A-P laminates, a temperature-dependent and rate-independent plasticity model has been implemented into a finite element code, and validated by a Digital Image Correlation technique. The proposed model shows that the enhanced ductility of C/PPS at T>Tg significantly contributes to the accommodation of overstresses in notched laminates through an extensive plastic deformation along the ±45° fibers, resulting in a clipping of the overstrain peak. When it comes to design TP-based laminates at temperatures around or higher than Tg, the elastic–plastic numerical tool presented in this work can be useful for stress engineers willing to predict the effect of ductility on overstresses accommodation, and to calculate the decrease in notched laminates strength.
A. Thermoplastic resin; B. High-temperature properties; C. Finite element analysis (FEA); D. Mechanical testing
Influence of matrix ductility on the high-temperature fatigue behavior of off-axis woven-ply thermoplastic and thermoset laminates
International Journal of Fatigue
63
85-96
2014
10.1016/j.ijfatigue.2014.01.010
This work was aimed at comparing the influence of ductility on the off-axis tension–tension fatigue behavior of woven-ply TP- and TS-based laminates at a test temperature T such as: TgC/PPS<T<TgEpoxy. Depending on the matrix nature and test frequency, the results confirm that the polymer matrix ductility is instrumental in ruling the fatigue response of woven-ply PMCs thanks to the presence of matrix-rich regions which proved to play a significant role. The fatigue behavior of TP-based laminates at T>Tg is primarily due to fiber reorientation coming along with matrix plasticization during loading phase, as well as the disorientation of fibers and the matrix viscoelastic response during unloading phase, rather than to fatigue damage accumulation. On the contrary, the fatigue behavior of Epoxy-based laminates at T<Tg is primarily due to fatigue damage which is more extensive at high frequency. The reduction of stress intensities in the matrix due to more or less plasticization may delay the initiation–propagation of matrix cracks, the debonding at the fiber/matrix interface, ultimately resulting in an extension of the fatigue life. Thus, a frequency increase virtually does not influence the fatigue life of C/PPS laminates, whereas it dramatically decreases the fatigue life of Epoxy-based laminates (−100%), because of a more extensive damage and a faster damage growth.
Fatigue; High temperature; Thermoplastic resin; Thermosetting resin; Woven fabric
Thin interphase/imperfect interface in elasticity with application to coated fiber composites
Journal of the Mechanics and Physics of Solids
50
2509-2537
2002
10.1016/S0022-5096(02)00050-9
The imperfect interface conditions which are equivalent to the effect of a thin elastic interphase are derived by a Taylor expansion method in terms of interface displacement and traction jumps. Plane and cylindrical interfaces are analyzed as special cases. The effective elastic moduli of a unidirectional coated fiber composite are obtained on the basis of the derived imperfect interface conditions. High accuracy of the method is demonstrated by comparison of solutions of several problems in terms of the imperfect interface conditions or explicit presence of interphase as a third phase. The problems considered are transverse shear of a coated infinite fiber in infinite matrix and effective transverse bulk and shear moduli and effective axial shear modulus of a coated fiber composite. Unlike previous elastic imperfect interface conditions in the literature, the present ones are valid for the entire range of interphase stiffness, from very small to very large. ?? 2002 Elsevier Science Ltd. All rights reserved.
Coated fiber; Displacement jump; Imperfect interface; Thin interphase; Traction jump
Measurement of the mechanical properties of thin films mechanically confined within contacts
Tribology Letters
21
3
245-252
2006
10.1007/s11249-006-9030-y
This study addresses the problem of the measurement of the mechanical properties of thin films using contact mechanics methods. In a first stage, an analytical contact model recently developed by Perriot and Barthel [A. Perriot and Barthel, E. J. Mat. Res, 2004. 19(2): 600-608] is used to derive a first order approximation within the limits of confined geometries. Together with indentation experiments using polymer films on elastic substrates, this approach demonstrates the essentially oedometric nature of the coating's response, provided it is not to close to incompressibility. In a second stage, an extension of this approximate description to lateral contact loading allowed to relate the contact stiffness to the shear modulus of the film. This approach was successfully applied to the determination of the viscoelastic modulus of an acrylate polymer film in the glass transition zone of the film, with an emphasis on its sensitivity to hydrostatic pressure. This study suggests that lateral contact experiments are more appropriate than indentation ones for the measurement of film properties close to incompressibility.
Indentation; Lateral contact stiffness; Mechanical confinement; Thin films; Viscoelastic properties
The cracking and decohesion of thin films
Journal of Materials Research
3
05
1043-1049
1988
10.1557/JMR.1988.1043
The critical stress for the steady-state cracking of adherent thin films on a ductile substrate has been investigated for thin Cr films on Al and stainless steel. The critical stress has been shown to depend on the film thickness, the residual stress, the substrate yield strength, the ratio of elastic moduli and the model I fracture toughness of the film, in accordance with simple non-dimensional parameters determined from energy release rate calculations. Decohesion along the interface has also been found and discussed for stainless steel substrates. Excellent agreement between theory and experiment has been demonstrated. Nous avons étudié la contrainte critique de rupture stationnaire pour des films minces adhérant sur un support ductile, dans le cas de films minces de chrome sur de l'aluminium et de l'acier inoxydable. La contrainte critique dépend de l'épaisseur du film, de la contrainte résiduelle, de la limite élastique du support, du rapport des modules élastiques et de la résistance à la rupture en mode I du film, seien des paramètres simples sans dimension déterminés à partir de calculs de vitesse de dégagement de l'énergie. Nous avons en outre observé une décohésion le long de l'interface dans le cas des supports d'acier inoxydable. L'accord est excellent entre la théorie et l'expérience. Die kritische Spannung für stationäre Riβbildung in dünnen Fimen auf einem duktilen Substrat wurde für den Fall dünner Cr-Filme auf Al und rostfreiem Stahl untersucht. Die kritische Spannung hängt von der Filmdicke, der Restspannung, der Flieβspannung des Substrates, dem Verhältnis der elastischen Moduln und der Bruchzähigkeit für Mode I des Filmes ab. Dieser Befund stimmt mit einfachen Parametern ohne Dimension, die aus Berechnungen der Rate der Energiefreisetzung abgeleitet worden sind, überein. Auβerdem wurde Dekohäsion entlang der Grenzfläche beobachtet; diese wird für die Substrate aus rostfreiem Stahl diskutiert. Es besteht ausgezeichnete übereinstimmung zwischen Theorie und Experiment.
Thermal buckling response of all-edge clamped rectangular plates with symmetric angle-ply lamination
Composite Structures
79
1
148-155
2007
10.1016/j.compstruct.2005.11.059
An analytical solution to thermal buckling response of moderately thick symmetric angle-ply laminated, all-edge clamped rectangular plates subjected to a uniformly distributed temperature load is presented. A boundary continuous solution methodology based on double Fourier series functions that satisfy the rigidly clamped boundary conditions is assumed. The through-thickness formulation of the plate considers transverse shear deformation effects by employing the first order shear deformation theory (FSDT) based on Reissner and Mindlin hypothesis that result in three highly coupled partial differential equations. The numerical results are presented for various parametric effects such as length-to-thickness ratio, plate aspect ratio and major-to-minor modulus of elasticity ratio. The results of the analytical method are compared with the results obtained using finite element method. The numerical results that are presented should serve as a benchmark for future comparisons of such popular approximate methods as finite element, finite difference, Rayleigh–Ritz, Galerkin approach, collocation, or experimental methods.
All-edges clamped; Analytical; Shear flexible; Symmetric angle-ply laminated plate; Thermal buckling response
Free vibration analysis of moderately thick antisymmetric cross-ply laminated rectangular plates with elastic edge constraints
International Journal of Mechanical Sciences
53
9
688-695
2011
10.1016/j.ijmecsci.2011.05.012
This study presents a simple formulation for studying the free vibration of shear-deformable antisymmetric cross-ply laminated rectangular plates having translational as well as rotational edge constraints. The aim is to fill the void in the available literature with respect to the free vibration results of antisymmetric cross-ply laminated rectangular plates. The spatial discretization of the resulting mathematical model in five field variables is carried out using the two-dimensional Differential Quadrature Method (DQM). Several combinations of translational and rotational elastic edge constraints are considered. Convergence study with respect to the number of nodes has been carried out and the results are compared with those from past investigations available only for simpler problems. Effects of stiffness parameters, geometrical features, moduli ratio and lamination schemes on the natural frequencies are studied. © 2011 Elsevier Ltd. All rights reserved.
Antisymmetric; DQM; Elastic edges; Free vibration; Mindlin
Statistical mechanics
Biopolymers
512
1969
Unlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition.
On the mechanics of continua with boundary energies and growing surfaces
Journal of the Mechanics and Physics of Solids
61
1446-1463
2013
10.1016/j.jmps.2013.01.007
Many biological systems are coated by thin films for protection, selective absorption, or transmembrane transport. A typical example is the mucous membrane covering the airways, the esophagus, and the intestine. Biological surfaces typically display a distinct mechanical behavior from the bulk; in particular, they may grow at different rates. Growth, morphological instabilities, and buckling of biological surfaces have been studied intensely by approximating the surface as a layer of finite thickness; however, growth has never been attributed to the surface itself. Here, we establish a theory of continua with boundary energies and growing surfaces of zero thickness in which the surface is equipped with its own potential energy and is allowed to grow independently of the bulk. In complete analogy to the kinematic equations, the balance equations, and the constitutive equations of a growing solid body, we derive the governing equations for a growing surface. We illustrate their spatial discretization using the finite element method, and discuss their consistent algorithmic linearization. To demonstrate the conceptual differences between volume and surface growth, we simulate the constrained growth of the inner layer of a cylindrical tube. Our novel approach toward continua with growing surfaces is capable of predicting extreme growth of the inner cylindrical surface, which more than doubles its initial area. The underlying algorithmic framework is robust and stable; it allows to predict morphological changes due to surface growth during the onset of buckling and beyond. The modeling of surface growth has immediate biomedical applications in the diagnosis and treatment of asthma, gastritis, obstructive sleep apnoea, and tumor invasion. Beyond biomedical applications, the scientific understanding of growth-induced morphological instabilities and surface wrinkling has important implications in material sciences, manufacturing, and microfabrication, with applications in soft lithography, metrology, and flexible electronics. ?? 2013 Elsevier Ltd.
Airway wall remodeling; Boundary energy; Finite elements; Growth; Thin films
Thermal buckling load optimization of angle-ply laminated cylindrical shells
Materials and Design
30
3
532-536
2009
10.1016/j.matdes.2008.05.052
In this study, thermal buckling load optimization of symmetrically laminated cylindrical shells subjected to uniformly distributed temperature load is investigated. The objective function is to maximize the critical temperature capacity of laminated shells and the fibre orientation is considered as design variable. The first-order shear deformation theory is used to study thermal buckling response of the laminates. The modified feasible direction method is used as optimization routine. For this purpose, a program based on FORTRAN is used for the optimization of shells. Finally, the effects of number of layers, length-to-radius ratio and boundary conditions on the optimum results are investigated. © 2008 Elsevier Ltd. All rights reserved.
B. Laminates; E. Mechanical; I. Buckling
Quantum Mechanics as Classical Physics
arXiv preprint arXiv:1403.0014
1-26
2014
10.1086/680190
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.
Disappearance of stress singularity at interface edge due to nanostructured thin film
Engineering Fracture Mechanics
75
10
3073-3083
2008
10.1016/j.engfracmech.2007.12.010
The purpose of this study is to examine the stress distribution near the interface between a nanostructured thin film and a solid body. We focus on a nanostructured thin film that consists of Ta2O5 helical nanosprings fabricated oil a Si substrate by dynamic oblique deposition. The mechanical properties of the thin film are obtained by vertical and lateral loading tests using a diamond tip built into an atomic force microscope. The apparent shear and Young's moduli, C and E, of the thin film are 2-3 orders of magnitude lower than those of a conventional solid Ta2O5 film. Moreover, the thin film shows strong anisotropy. A finite element analysis for two types of components with different interface edges between the thin film and,in elastic solid body is conducted under uniform displacement. One has a free edge where the surface-interface angle is 90 degrees-90 degrees, and the other has a short interface crack. These analyses indicate the absence of not only stress singularity but also high stress concentration near the free edge and the interface crack tip. The characteristic stress distributions near the interface are due to the nanoscopically discrete structure of the thin film. (c) 2008 Elsevier Ltd. All rights reserved.
crack tip; dynamic oblique; free edge; interface; nanosprings; singularity; stress concentration; stress reduction; thin film
A general damage model for woven fabric composite laminates up to first failure
Mechanics of Materials
41
7
820-827
2009
10.1016/j.mechmat.2009.02.009
A ply scale continuum damage model for predicting the mechanical behaviour of an unbalanced woven fabric composite up to first failure is presented. The behaviour of the unbalanced woven plies and the evolution of the damage were investigated experimentally. The damage, consisting of small cracks running parallel to the fibres, led to a loss of stiffness in the warp, weft and shear directions in the ply coordinate system. The model presented here describes the evolution of the damage and the inelastic strain up to the failure of the ply. By replacing the woven ply by two stacked unidirectional plies corresponding to the warp and weft thicknesses, this general model can be applied to a broad range of plies, from quasi-unidirectional to balanced woven plies. Tests in which simulations and experimental results were compared confirmed the validity of the model. ?? 2009 Elsevier Ltd. All rights reserved.
Simulation of ductile crack growth in thin panels using the crack tip opening angle
Engineering Fracture Mechanics
76
1
88-100
2009
10.1016/j.engfracmech.2008.05.008
The aim of this work is the assessment of the efficiency of the crack tip opening angle (CTOA) with respect to the transferability from one geometry to another, in particular the transferability obtained from Kahn tear tests to M(T) panels. The load–displacement behaviour recorded during a Kahn tear test was reproduced by means of finite element analysis using a variable {CTOA} as a function of crack length. The {CTOA} extracted from Kahn tests has then been used to simulate the R-curve of M(T) panels with different widths. Experiments and simulations were run first on a 6013-T6 aluminium alloy and then also on butt, friction stir welded butt joints of the same material.
{CTOA}; Ductile fracture; Friction stir welding; Thin sheets
Measuring the fracture toughness of ultra-thin films with application to AlTa coatings
International Journal of Fracture
144
3
173-179
2007
10.1007/s10704-007-9095-0
An experimental technique is presented for measuring the fracture\ntoughness of brittle thin films. In this technique, long rectangular\nmembranes are fabricated from the film of interest using standard\nsilicon micromachining techniques. A focused ion beam is then used\nto introduce pre-cracks of different lengths along the centerline\nof the membranes and the membranes are pressurized until rupture.\nThe fracture stress of the membrane is measured as a function of\npre-crack length and the fracture toughness of the film is determined\nfrom a simple fracture mechanics analysis. The technique is applicable\nto a wide range of materials and is especially suited for ultra-thin\nfilms. We have demonstrated the experimental procedure for a 150 nm\nAlTa intermetallic film and obtained a room-temperature fracture\ntoughness of K 1c = 4.44 ± 0.21 MPam1/2.
Bulge test; Fracture toughness; Thin films
Fingering phenomena associated with insoluble surfactant spreading on thin liquid films
Journal of Fluid Mechanics
510
169-200
2004
10.1017/S0022112004009437
We study the linear and nonlinear stability of a thick\nsurfactant deposition spreading on a thin liquid film using\ntransient growth analysis (TGA) and direct numerical simulations\n(DNS) of the two-dimensional lubrication equations, respectively.\nResults of the TGA of the one-dimensional spatially and temporally\nevolving base state reveal disturbance growth and the selection of\na perturbation of intermediate wavenumber. This perturbation\ntargets the 'contact region' between the deposition and the\nunderlying thin liquid film and grows despite the absence of\nintermolecular forces. Increasing the initial thickness ratio of\nthe deposition to the thin film and decreasing the relative\nmagnitude of capillarity and surface diffusion further amplify\nperturbation growth. The DNS results clearly show the formation of\nfingers in the contact region behind the surfactant leading edge\nand provide further confirmation of the TGA findings.\n
Metal forming: Mechanics and metallurgy
Journal of Mechanical Working Technology
11
1
122-123
1985
10.1016/0378-3804(85)90124-X
The biggest changes from the second edition are an enlargement and reorganization of the last third of the book, which deals with sheet metal forming. Changes have been made to the chapters on bending, plastic anisotropy, and cup drawing. An entire chapter has been devoted to forming limit diagrams. There is one chapter on various aspects of stampings, including the use of tailor-welded blanks, and another on other sheet- forming operations, including hydroforming of tubes. Sheet testing is covered in a separate chapter. The chapter on sheet metal properties has been expanded to include newer materials and more depth on aluminum alloys. In addition, some changes have been made to the chapter on strain-rate sensitivity. Atreatment of friction and lubrication has been added. A short treatment of swaging has been added. End-of-chapter notes have been added for interest and additional end-of-chapter references have been added.
Quartz crystal resonators with atomically smooth surfaces for use in contact mechanics
Review of Scientific Instruments
74
8
3845
2003
10.1063/1.1588751
A quartz crystal shear resonator was modified by gluing a thin piece of mica on one surface to obtain an acoustic sensor with a macroscopic atomically smooth area. Contact mechanics experiments with this resonator touching a half-spherical mica surface were performed at high shear rate by integrating it into a surface forces apparatus, which provides simultaneous load control and interferometric measurement of the real contact area and surface separation. The procedures for gluing mica on a quartz resonator without significant loss of its sensitivity and gluing a half-spherical mica surface are described in detail. Sensitivity issues and overtone order dependence are discussed. Although our work focuses on contact mechanics experiments, the technique is also relevant for quartz crystal microbalance applications. (C) 2003 American Institute of Physics
Interfacial adhesion of thin-film patterned interconnect structures
Interconnect Technology Conference, 2003. Proceedings of the IEEE 2003 International
168-170
2003
10.1109/IITC.2003.1219744
The interfacial adhesion of lithographically patterned thin film\nstructures has been measured. Fracture mechanics techniques, modified\nfor thin-film geometries, were employed to quantify the interfacial\nadhesion of patterned arrays containing low-k and Cu metal lines\nwith varying channel length scales, aspect ratios and orientations.\nThe results indicate that interfacial adhesion may be affected by\nthe line structures and their orientation. In addition, the fracture\nresistance of debonded interface was dependent on the specific low-k\nmaterial employed in the structure.
adhesion; aspect ratios; channel length; copper; Cu metal lines; dielectric materials; dielectric thin films; fracture mechanics; fracture resistance; integrated circuit interconnections; interface structure; interfacial adhesion; lithographically patterned thin film structures; lithography; low dielectric materials; orientations; patterned arrays; permittivity; surface morphology; surface resistance Cu; thin-film geometries; thin-film patterned interconnect structures
High-cycle fatigue of micron-scale polycrystalline silicon films: fracture mechanics analyses of the role of the silica/silicon interface
International Journal of Fracture
120
1
449-474
2003
10.1023/A:1024988031390
It is known that micron-scale polycrystalline silicon thin films can\nfail in room air under high frequency (40kHz) cyclic loading at fully-reversed\nstress amplitudes as low as half the fracture strength, with fatigue\nlives in excess of 10 11 cycles. This behavior has been attributed\nto the sequential oxidation of the silicon and environmentally-assisted\ncrack growth solely within the SiO 2 surface layer. This ‘reaction-layer\nfatigue’ mechanism is only significant in thin films where the\ncritical crack size for catastrophic failure can be reached by a\ncrack growing within the oxide layer. In this study, the importance\nof the bimaterial (e.g., Si/SiO 2 ) interface to reaction-layer fatigue\nis investigated, and the critical geometry and stress ranges where\nthe mechanism is a viable failure mode are established.
fatigue; mems; silicon; thin films
Phase-field modeling of fracture in linear thin shells
Theoretical and Applied Fracture Mechanics
69
102-109
2014
10.1016/j.tafmec.2013.12.002
We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes. © 2013 Elsevier Ltd.
Local maximum entropy; Manifold learning; Meshfree method; Phase-field model; Point-set surfaces; Thin shells
Nanomechanical and nanotribological properties of carbon-based thin films: A review
International Journal of Refractory Metals and Hard Materials
28
1
51-70
2010
10.1016/j.ijrmhm.2009.08.003
Carbon-based thin films possess unique and adjustable combination of properties such as high hardness and wear resistance, chemical resistance and good tribological performances. Among critical variables to tailor a-C film's properties for specific application is the distribution of the carbon hybridization states (sp1, sp2 and sp3 bonds), the atomic H content, the content in dopants such as Si, F, N, B and O. Here we focus on: (i) a-C and hydrogenated amorphous carbon (a-C:H) films with a mixture of sp2 and sp3 bonding, highly sp3-boned material (ta-C) and sp2-bonded carbon, (ii) carbon nitride (CNx) coatings and (iii) metal/amorphous carbon (a-C:M) composite films. The study is focused on the review of the nanomechanical properties and analysis of the nanoscratching processes at low loads to obtain quantitative analysis, the comparison of their elastic/plastic deformation response, and nanotribological behavior of the a-C, ta-C, a-C:H, CNx, and a-C:M films. For ta-C and a-C:M films new data are presented and discussed. ?? 2009 Elsevier Ltd. All rights reserved.
Amorphous carbon films; Friction; Nanocomposites; Nanoindentation; Nanotribology
Concomitant wrinkling and buckle-delamination of elastic thin films on compliant substrates
Mechanics of Materials
43
11
627-642
2011
10.1016/j.mechmat.2011.08.003
Compressing a thin elastic film attached to a thick compliant substrate can lead to buckling instability. Two commonly observed buckling modes, buckle-delamination and wrinkling, have each been analyzed separately in previous studies. Recent experiments have observed that the two modes can co-exist and co-evolve. In this paper, by analytical and finite element methods, we present a study on concomitant wrinkling and buckle-delamination for an elastic film on a highly compliant substrate. First, without delamination, we present an analytical solution for wrinkling that takes into account the effect of Poisson's ratio of the substrate. In comparison with a nonlinear finite element analysis, an approximate formula is derived to estimate the normal traction at the interface and to predict initiation of wrinkle-induced delamination. Next, with a pre-existing delamination crack, the critical strain for the onset of buckling instability is predicted by finite element eigenvalue analysis. For an intermediate delamination size, a mixed buckling mode is predicted with the critical compressive strain lower than previous solutions for both wrinkling and buckle-delamination. Post-buckling analyses show a significant shear-lag effect with an effective load transfer length three orders of magnitude greater than the film thickness. Finally, concomitant wrinkling and buckle-delamination is simulated to illustrate the interaction between the two buckling modes, and the results are discussed in view of failure mechanisms and applications in thin film metrology. ?? 2011 Elsevier Ltd. All rights reserved.
Buckling; Compliant substrate; Delamination; Thin film; Wrinkling
Scaling Behavior in Non-Hookean Compression of Thin-Walled Structures
Physical Review Letters
105
6
066102
2010
10.1103/PhysRevLett.105.066102
The mechanics and stability of thin-walled structures is a challenging and important branch in structural mechanics. Under vertical compression the deformation of a thin-walled box differs from that of, e.g., a cylindrical shell. It is demonstrated here that compression of a box can be described by a set of generic scaling laws representing three successive regimes: a linear, wrinkled, and collapsed regime. The linear Hookean regime represents the normal behavior before any instability sets in, while the following wrinkled regime is shown to be analogous to compression of thin-film blisters. The compression force reaches its maximum at the onset of the final collapsed regime that has all the characteristics of membrane crumpling. The theoretical scaling laws were confirmed by numerical simulations.
Celestial Mechanics (Poem)
Mathematical Intelligencer
26
7
2004
Presents the poem "Celestial Mechanics," by Philip Holmes. Presents the poem "Celestial Mechanics," by Philip Holmes.
CELESTIAL mechanics; CELESTIAL Mechanics (Poem); HOLMES, Philip; POETRY
Spreading of thin volatile liquid droplets on uniformly heated surfaces
Journal of Fluid Mechanics
528
2
279-296
2005
10.1017/S0022112005003320
We develop a mathematical model for the spreading of a thin volatile liquid droplet on a uniformly heated surface. The model accounts for the effects of surface tension, evaporation, thermocapillarity, gravity and disjoining pressure for both perfectly wetting and partially wetting liquids. Previous studies of non-isothermal spreading did not include the effects of disjoining pressure and therefore had to address the difficult issue of imposing proper boundary conditions at the contact line where the droplet surface touches the heated substrate. We avoid this difficulty by taking advantage of the fact that dry areas on the heated solid surface are typically covered by a microscopic adsorbed film where the disjoining pressure suppresses evaporation. We use a lubrication-type approach to derive a single partial differential equation capable of describing both the time-dependent macroscopic shape of the droplet and the microscopic adsorbed film; the contact line is then defined as the transition region between the two. In the framework of this model we find that both evaporation and thermocapillary stresses act to prevent surface-tension-driven spreading. Apparent contact angle, defined by the maximum interfacial slope in the contact-line region, decays in time as a droplet evaporates, but the rate of decay is different from that predicted in earlier studies of evaporating droplets. We attribute the difference to nonlinear coupling between different physical effects contributing to the value of the contact angle; previous studies used a linear superposition of these effects. We also discuss comparison of our results with experimental data available in the literature.
Quantification of uncertainty modelling in stochastic analysis of FRP composites
Composites Part A: Applied Science and Manufacturing
40
11
1673-1684
2009
10.1016/j.compositesa.2009.08.020
The extensive use of FRP composite materials in a wide range of industries, and their inherent variability, has prompted many researchers to assess their performance from a probabilistic perspective. This paper attempts to quantify the uncertainty in FRP composites and to summarise the different stochastic modelling approaches suggested in the literature. Researchers have considered uncertainties starting at a constituent (fibre/matrix) level, at the ply level or at a coupon or component level. The constituent based approach could be further classified as a random variable based stochastic computational mechanics approach (whose usage is comparatively limited due to complex test data requirements and possible uncertainty propagation errors) and the more widely used morphology based random composite modelling which has been recommended for exploring local damage and failure characteristics. The ply level analysis using either stiffness/strength or fracture mechanics based models is suggested when the ply characteristics influence the composite properties significantly, or as a way to check the propagation of uncertainties across length scales. On the other hand, a coupon or component level based uncertainty modelling is suggested when global response characteristics govern the design objectives. Though relatively unexplored, appropriate cross-fertilisation between these approaches in a multi-scale modelling framework seems to be a promising avenue for stochastic analysis of composite structures. It is hoped that this review paper could facilitate and strengthen this process. ?? 2009 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Mechanical properties; C. Micro-mechanics; C. Statistical properties/methods
Electron doping of ALD-grown ZnO thin films through Al and P substitutions
Journal of Materials Science
48
7
2806-2811
2013
10.1007/s10853-012-6942-9
Several series of Al- and P-doped ZnO thin films have been deposited with atomic layer deposition at different temperatures using diethyl zinc, trimethyl aluminum, trimethyl phosphate, and H2O as the precursors. The optimal deposition temperature range is found at 160-220 A degrees C where the film growth is stable and well-crystallized films with low resistivity are obtained. The effect of the dopant content on the charge carrier density of the films is evaluated based on optical reflectivity, Seebeck coefficient, and electrical resistivity data for the films. Both dopants are found to be effective in controlling the carrier density of ZnO; systematic increase in carrier density is demonstrated for Al-doping up to 2 at.% and for P-doping up to 5 at.%. The conductivity of the as-deposited films remains n-type.
Thermodynamics and statistical mechanics 3774.
Mathematical Reviews
633-636
1993
10.1038/282887a0
A complete set of lecture notes for an upper-division thermodynamics and statistical mechanics course. Topics covered include elementary probability theory, classical thermodynamics, the thermodynamics of the atmosphere, heat engines, specific heat capacities of gases and solids, the Maxwell velocity distribution, paramagnetism, black-body radiation and the Stephan-Bolzmann law, conduction electrons in metals, and degeneracy pressure in white-dwarfs and neutron stars.
Continuum Mechanics and Plasticity
New York
685
2005
Tremendous advances in computer technologies and methods have precipitated a great demand for refinements in the constitutive models of plasticity. Such refinements include the development of a model that would account for material anisotropy and produces results that compare well with experimental data. Key to developing such models-and to meeting many other challenges in the field- is a firm grasp of the principles of continuum mechanics and how they apply to the formulation of plasticity theory. Also critical is understanding the experimental aspects of plasticity and material anisotropy.Integrating the traditionally separate subjects of continuum mechanics and plasticity, this book builds understanding in all of those areas. Part I provides systematic, comprehensive coverage of continuum mechanics, from a review of Carteisian tensors to the relevant conservation laws and constitutive equation. Part II offers an exhaustive presentation of the continuum theory of plasticity. This includes a unique treatment of the experimental aspects of plasticity, covers anisotropic plasticity, and incorporates recent research results related to the endochronic theory of plasticity obtained by the author and his colleagues.By bringing all of these together in one book, Continuum Mechanics and Plasticity facilitates the learning of solid mechanics. Its readers will be well prepared for pursuing either research related to the mechanical behavior of engineering materials or developmental work in engineering analysis and design.
Mechanics of a thin, tensioned shell, wrapped helically around a turn-bar
Journal of Fluids and Structures
23
5
767-785
2007
10.1016/j.jfluidstructs.2006.11.007
The fluid–structure interactions between a flexible web and an externally pressurized air cushion are modeled allowing for the possibility of contact. The web is wrapped around a porous, cylindrical turn-bar at an oblique angle (helically). The turn-bar supplies pressurized air into the web/turn-bar clearance to float the web. The shell model, developed to represent the mechanics of the web, allows it to be wrapped around the cylinder in a helical fashion. The fluid mechanics of the air in the web/turn-bar clearance is a two-dimensional form of the incompressible Navier–Stokes equations averaged in the clearance direction and augmented by nonlinear source terms. Contact between the web and the reverser, which is undesirable in a turn-bar application, is included in the model in order to enable the analysis of the limiting cases. The coupled equilibrium between fluid mechanics, shell deflections and contact is found numerically. This paper describes the theory. Case studies are conducted in order to understand the mechanics of the coupled system, and to make design recommendations. It is shown that the helix angle has a strong influence on the equilibrium configurations: increasing helix-angle results in increased web-reverser separation, while the air pressure settles to a lower value. This behavior is due to the reduced shell stiffness and belt-wrap pressure for the helically wrapped webs. Conditions that render a nearly uniform web/turn-bar clearance in the circumferential direction are identified. The supply pressure and airflow rates necessary to prevent web-scratches are calculated.
Air reverser; Helically wrapped shell; Turn-bar; Web mechanics
A new model for maximizing the bending stiffness of a symmetric three-ply paper or board
Tappi Journal
7
10
28-32
2008
Based on the theoretical bending stiffness model for a symmetrical three-ply structure, researchers developed a model that could predict the maximum bending stiffness of a three-ply symmetric structure as a function of density and elastic modulus. The model was tested with experimental data either generated in the authors' laboratory or reported in the literature. The model accurately predicted the maximum bending stiffness based on the middle-layer share of basis weight. Model results indicate that it is possible to increase the middle-layer share without loss of bending stiffness, leading to reduced costs and lower virgin fiber requirements. Results show that the model is a useful and rapid tool for papermakers to predict the maximum bending stiffness of either coated papers or three-ply boards for a given furnish. Furthermore, the model has potential to be developed further to predict maximum bending stiffness for boards with more than three plies. Application: A model has been developed to predict maximum bending stiffness of three-ply board as a function of a single parameter, the middle-layer share of basis weight. Model results indicate that it is possible to increase the middle-layer share without loss of bending stiffness, leading to reduced costs and lower virgin fiber requirements.
Bending (deformation); Probability density function; Stiffness
Mechanics of axial plastic collapse in multi-cell, multi-corner crush tubes
Thin-Walled Structures
49
1
1-12
2011
10.1016/j.tws.2010.07.002
Quasi-static nonlinear finite element simulations are performed to study the energy absorption characteristics of axially crushed thin-walled aluminum tubes with different multi-cell, multi-corner configurations. By considering the kinematically consistent representation of plastic collapse as observed in the crush simulations, an analytical formula for the mean crush force is derived using the super folding element theory. In this model, the isotropic material is treated as rigid-perfectly plastic and the total internal energy is calculated by considering both bending and membrane deformation during the folding process. The simulation results show a strong correlation between the cross-sectional geometry and the crush response of the tubes. The analytical predictions for the mean crush force are compared with the FE results as well as other analytical models reported in the literature. ?? 2010 Elsevier Ltd.
Crush tube; Energy absorption; Mechanics of crush; Multi-corner tube; Quasi-static crush
Is there life beyond Quantum Mechanics?
Arxiv Preprint
23
2013
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory respectively. We show that even if the second group of axioms is dropped, there are no deformations of Quantum Mechanics which preserve the kinematic axioms. Thus any theory going beyond Quantum Mechanics must represent a radical departure from the usual a priori assumptions about the laws of Nature.
Introduction to quantum mechanics: a time-dependent perspective
Journal of Chemical Education
85
7
662 ST - Introduction To Quantum Mechanics: A Tim
2007
10.1021/ed085p919
Introduction to Quantum Mechanics covers quantum mechanics from a time-dependent perspective in a unified way from beginning to end. Intended for upper-level undergraduate and graduate courses this text will change the way people think about and teach quantum mechanics in chemistry and physics departments.
Plaque mechanics
Journal of Biomechanics
47
763-764
2014
10.1016/j.jbiomech.2014.01.031
The deformation and stress distribution in plaques play an important role in various aspects of atherosclerotic disease. This special issue is composed of reviews and original research articles of the state-of-the-art, focusing on different topics that relate to plaque mechanics. These articles, which represent a snapshot of the cutting edge research currently conducted in this area, were contributed by leading groups in the field. Various vascular components, including the endothelium and vascular smooth muscle cells, respond to the strains that they are exposed to. Their response potentially plays an important role in plaque progression. Understanding the impact of biomechanical stimuli on plaque development is essential for developing and optimizing imaging procedures and (pharmaceutical) interven-tions. When studying plaque mechanobiology, animal studies play a crucial role. This is the reason why the first contribution (Riou et al., 2014) is related to the biomechanical characteriza-tion of murine models and how they relate to human plaques. With appropriate animal models available, the hitherto largely unknown but important territory of strain related mechanobiolo-gical aspects of plaque development can be explored. Mechanical stresses in plaques can potentially be used to assess plaque vulnerability. Accurate assessment of plaque stresses critic-ally depends on the material properties of the plaque components. Akyildiz et al. (2014) show in a perspective review how plaque composition changes during plaque development and how composi-tion might affect plaque properties and explain the wide variation of reported data in literature. The contribution by Chai et al. (2014) focuses on local mechanical properties of carotid plaques derived from compression experiments, using unconfined compression, micro-indentation or nano-indentation and a new method to analyze the local anisotropic mechanical properties of atherosclerotic plaques. The uniaxial mechanical testing approaches to characterize the mechanical properties of carotid, coronary or iliac plaques in vitro are outlined in the paper by Walsh et al. (2014). A more physiological way to assess plaque properties of carotid plaque samples excised from endarterectomy is described by Boekhoven et al. (2014). These contributions on macroscopic plaque properties clearly illustrate that well-controlled and documented experiments under physiologically relevant loading conditions are further needed to establish local non-linear and anisotropic plaque properties. Although in vitro experiments are essential for deepening our understanding of the mechanical plaque properties, in vivo strain measurements are important as a validation for the in vitro find-ings. Furthermore, blood pressure induced strain in atherosclerotic plaques can be associated with plaque composition, with the ultimate aim to classify stable and vulnerable atherosclerotic plaques. In vivo strain data can be obtained by several methodologies. Ultrasound based strain measurements are already used in various clinical applications including strain measurements in carotid plaques. A review and new developments in ultrasound strain imaging are discussed in the paper by Hansen et al. (2014). An alternative but less developed approach to assess carotid plaque strain involves MR-based strain imaging and is discussed by Nederveen et al. (2014). These papers show that these non-invasive imaging techniques show great potential but also require further development with respect to contrast enhancement and improvement of spatial and temporal resolution. Most of the experimental and numerical studies on plaque biomechanics assume that the plaque components can be described with macroscopic continuum models. This continuum approach is the one followed most frequently, and especially when coupled to functional imaging might provide useful information and in essence is the only approach available when looking for clinical applications, when comparing plaque stresses to plaque strength. Whether stresses and strength can be determined using the macroscopic modeling approach is debatable, especially since plaque mechanics probably involve many (spatial) scales. The review article by Holzapfel et al. (2014) summarizes computational studies for different vessel types, and the modeling approaches that were followed in these studies, including studies on rupture mechanics. The contribution by Cardoso et al. (2014) applied multiscale computational analyses to evaluate the stress concentration generated by microcalcifications in plaques in order to shed further light on the issue of plaque rupture. Much is still unknown about the behavior of the individual plaque components and more theoretical, experimental and numerical studies are required to investigate whether we need to include multiscale plaque features for stress and strength analyses. A subset of atherosclerotic plaques develops into a vulnerable phenotype. These vulnerable plaques are characterized by the pre-sence of a large necrotic core, covered by a thin fibrous cap, often infiltrated by macrophages. Rupture of the cap is responsible for the majority of adverse cardiovascular events. Many studies focus on image-based determination of peak stress in the cap of atherosclerotic plaques. Teng et al. (2014) discuss the pathogenesis of plaque hemorrhage in carotid arteries, and its role in dictating plaque vulnerability. They also review imaging techniques, material properties of atherosclerotic tissues, and in particular, those obtained based on in vivo measurements and effect of plaque hemorrhage in modulating local biomechanics. Along the same line, Tang et al. (2014) illustrate findings in image-based models for human carotid and coronary plaques. The results of these manuscripts clearly illustrate that in a clinical setting, we need to deal with sparse and noisy data sets as input for our biomechanical models, and that this uncertainty needs to be accounted for when performing clinical studies.
The buckling of thin viscous jets
Journal of Fluid Mechanics
61
03
449-463
1973
10.1017/S0022112073000807
Thin viscous jets are considered as they slowly fall, in a state of near-neutral buoyancy, through a liquid. An equation is derived which describes the path of the jet. A small perturbation analysis of nearly vertical jets is carried out, and shows that they are necessarily unstable and will eventually deviate significantly from the vertical. Numerical integration of the nonlinear equation describes the nature of this deviation. These results model some experimental observations made by Taylor (1969).
Quantum mechanics: No moon there
Nature Physics
6
6
401-402
2010
10.1038/nphys1698
An experiment reveals that micrometre-sized superconducting circuits follow the laws of quantum mechanics, and thus defy common experience of how macroscopic objects should behave. ” I like to think that the moon is there even if I don't look at it”, Albert Einstein once remarked. He objected to the notion that truly macroscopic objects might behave according to the laws of quantum mechanics, and thus be subject to the same uncertainties as photons or spins.
Damage and permeability evolution in CFRP cross-ply laminates
Composite Structures
76
1-2
73-81
2006
10.1016/j.compstruct.2006.06.011
In this study, damage and permeability in CFRP cross-ply laminates were evaluated experimentally with using cruciform specimens at room temperature. Development of matrix cracks in the CFRP laminate under biaxial loadings and permeability of helium gas through the laminate were acquired. In this acquirement, the permeability was measured in relation to crack density and applied biaxial loads. The results of the experiments indicate that stacking sequences of CFRP laminate influence not only matrix crack development but also leakage prevention. Gas permeability through damaged CFRP composite laminates is influenced mainly by crack densities and crack opening displacements, because matrix cracks play a role as leakage path. Permeability through the damaged laminates increases in accordance with damage development, and increasing rate of permeability in connection with the strains is approximately dominated by the external biaxial loads. © 2006 Elsevier Ltd. All rights reserved.
Biaxial load; CFRP laminate; Cruciform specimen; Matrix crack; Propellant leak
Characterization of 3D morphology and microcracks in composites reinforced by multi-axial multi-ply stitched preforms
Composites Part A: Applied Science and Manufacturing
41
5
653-662
2010
10.1016/j.compositesa.2010.01.015
The micro-structure of polymer matrix composites reinforced by multi-axial multi-ply stitched carbon preforms and manufactured by liquid resin infusion is analyzed. The stitching induces deviations in fibre placement and creates openings which become resin-rich regions after the resin infusion. Characterization of the size and shape of the resin-rich regions of composites with different stitching yarn size and tightness and various stacking sequences has been performed by 2D metallographic micrography and X-ray microtomography. The resin-rich region volume was estimated at roughly 3.0 ± 0.5% of the material volume. The resin-rich regions constitute about 9% of the resin in the entire composite, whose fibre volume fraction is close to 65%. X-ray microtomography was successfully used to characterize the 3D microcracks created by hygrothermal fatigue. © 2010 Elsevier Ltd. All rights reserved.
A. Fabrics/textiles; B. Micro-structures; D. Non-destructive testing; Morphological characterization
A laminate parametrization technique for discrete ply-angle problems with manufacturing constraints
Structural and Multidisciplinary Optimization
48
April 2012
379-393
2013
10.1007/s00158-013-0906-9
In this paper we present a novel laminate parametrization technique for layered composite structures that accounts for problems in which the ply angles are limited to a discrete set. In the proposed technique, the classical laminate stiffnesses are expressed as a linear combination of the discrete options and design-variable weights. An exact l1 penalty function is employed to drive the designs towards discrete, 0-1 designs. The proposed tech- nique can be used as either an alternative or as an enhancement to SIMP-type methods, such as discrete material optimization (DMO). Unlike mixed-integer approaches, our laminate parametrization technique is well suited for gradient-based design optimization. The pro- posed laminate parametrization is demonstrated on compliance design of laminated plates and buckling design of a laminated stiffened panel. The results demonstrate that the approach is an effective alternative to DMO methods.
Discrete angle problems; Laminate parametrization; Manufacturing constraints
Damage growth in constrained angle-ply laminates under cyclic loading
Composites Science and Technology
62
1239-1247
2002
10.1016/S0266-3538(02)00075-1
Damage initiation and growth under quasi-static and cyclic loading of constrained angle-ply laminates [0/±θ4/0] are investigated. Three angle-plies were studied with θ=25°, 45°, and 75°. The life to initiate matrix cracking, the onset of delamination and the saturation of matrix cracking in the three laminate geometries have been determined. It is found that the onset of stiffness reduction coincided with the damage observed visually. The lowest stiffness drop occured in the [0/±254/0]T laminates with the lowest edge crack density. In contrast, the [0/±754/0]T laminates which developed through-width cracking, had the highest stiffness drop. It was observed that when both the in-plane shear and tensile normal stresses in the direction of fibre were high, the crack density became the largest, e.g. the [0/±454/0]T laminates. © 2002 Elsevier Science Ltd. All rights reserved.
A. Polymer-matrix composites; B. Matrix cracking; C. Delamination; D. Life prediction; Glass fibres
Transverse vibration of a two-segment cross-ply composite shafts with a lumped mass
COMPOSITE STRUCTURES
92
5
1126-1131
2010
10.1016/j.compstruct.2009.10.007
The advantages of having higher stiffness to weight ratio and strength\nto weigh ratio that composite materials have resulted in an increasing\ninterest in them. In automotive engineering, weight savings has positive\nimpacts on other attributes like fuel economy, performance and possibly\nnoise, vibration and harshness (NVH). The driveline of an automotive\nsystem can be a target for possible weight reduction. This can be done\nthrough the use of composite materials. The design of the driveshaft of\nan automotive system is primarily driven by its natural frequency. This\npaper presents an exact solution for the vibration of a cross-ply\nlaminated composite driveshaft with an intermediate joint. The joint is\nmodeled as a frictionless internal hinge. The Euler-Bernoulli beam\ntheory is used. Lumped masses are placed on each side of the joint to\nrepresent the joint mass. Equations of motion are developed using the\nappropriate boundary conditions and then solved exactly. (C) 2009\nElsevier Ltd. All rights reserved.
Finite element mesh generation for composites with ply waviness based on X-ray computed tomography
Advances in Engineering Software
58
35-44
2013
10.1016/j.advengsoft.2013.01.002
A method for automated generation of finite element meshes for unidirectional composites with waviness defects is proposed. Images used as input for mesh generation are recorded with X-ray computed micro-tomography. Quality and contrast of the scanned images is such that fiber directions cannot be detected everywhere. To generate finite elements mesh that follow fiber directions it is suggested to interpolate available fiber slope data using radial basis functions and to create mesh nodes by integrating ordinary differential equations for fiber slopes. Examples demonstrate practical steps of detecting waviness from volume slice images and generation of meshes that model waviness defects with acceptable accuracy. ?? 2013 Elsevier Ltd. All rights reserved.
Composite materials; Finite element mesh; Image analysis; Mesh generation; Ply waviness; X-ray computed tomography
Sources of Quantum Mechanics
American Journal of Physics
36
374
1968
10.1119/1.1974534
edited with a historical introduction by B.L. van der Waerden; ;23 cm; [Repr. of 1968 ed.]; Referències bibliogràfiques. Índex
Engineering damage mechanics: Ductile, creep, fatigue and brittle failures
Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures
1-380
2005
10.1007/b138882
Reflecting his major contributions to the field, Jean Lemaitre's "Engineering Damage Mechanics" presents simplified and advanced methods organized within a unified framework for designers of any mechanical component.Explains how to apply continuous damage mechanics to failures of mechanical and civil engineering components in ductile, creep, fatigue and brittle conditions.Incorporates many basic examples, while emphasizing key practical considerations such as material parameter identification, and provides perspective on the advantage and disadvantages of various approaches.
Demonstration of pseudo-ductility in unidirectional discontinuous carbon fibre/epoxy prepreg composites
Composites Science and Technology
106
110-119
2015
10.1016/j.compscitech.2014.10.022
The inherent brittleness of continuous unidirectional fibre reinforced composites is a major drawback to their otherwise outstanding mechanical performance. This paper exploits composites with overlapped discontinuities at the ply level to create a significantly non-linear response, due to progressive interlaminar damage under tensile loading. Two distinct configurations were manufactured with the same carbon/epoxy system and tested under quasi-static tension, showing that varying the thickness and length of the overlapping ply blocks resulted in significantly different mechanical responses and failure modes. A previously developed generalised shear-lag model was successfully used to optimise the overlap configuration, and accurately predicted the response in both strength- and toughness-dominated cases. This work demonstrates that unidirectional composites with well-designed discontinuities at the ply level can provide a significantly non-linear response with clear warning before failure, while retaining similar stiffness and up to 50% of the strength of their continuous counterparts.
B. Delamination; B. Non-linear behaviour; C. Damage mechanics; C. Stress transfer; Discontinuous-ply composites
Some aspects of rubber composite finite element analysis
Computers & Structures
21
1-2
327-339
1985
10.1016/0045-7949(85)90253-6
Structures made of rubber composites normally consist of several plies. Each ply consists of a thin layer of rubber matrix, reinforced with unidirectional cords. Any two adjacent plies, symmetrically located with respect to any global axis, are often treated as a single bias ply. The unidirectional ply and the bias ply may therefore be considered as main elements of these structures. In this paper the mechanical properties of single ply and bias plies are discussed and their kinematics are highlighted. The discussion includes both extensible and inextensible cords. Furthermore, the three-dimensional constitutive equations for rubber composites, suitable for finite element analysis, are also presented. Finally, the status and some of the needs for further research are discussed.
Influence of intercellular tissue connections on airway muscle mechanics.
Journal of applied physiology (Bethesda, Md. : 1985)
86
1
5-15
1999
Contraction of smooth muscle in visceral organs is modified by structures external to the muscle. Within muscle tissue itself, connective tissue plays an important role in force transference among the contractile cells. Connections arranged radially can affect contractile mechanics by limiting tissue expansion at short lengths. Previous work suggests that increased stiffness at extreme shortening is due to such radial constraints. Two approaches to further study of these effects are reported. To increase radial constraints, very thin Silastic bands were placed loosely about strips of canine trachealis muscle at rest length. The strips were allowed to shorten under light afterloads, expanding until restrained by the bands. Subsequent removal of the bands allowed increased shortening, with less increase in stiffness at short lengths. Related isometric effects were observed. To reduce constraints, muscle strips were partially digested with collagenase. Compared with control conditions, this treatment permitted further shortening, with less increase in stiffness at short lengths. These results emphasize the role of extracellular structures in determining mechanical function of smooth muscle.
Animals; Collagenases; Dogs; Intercellular Junctions; Intercellular Junctions: physiology; In Vitro Techniques; Isometric Contraction; Isometric Contraction: physiology; Isotonic Contraction; Isotonic Contraction: physiology; Muscle Contraction; Muscle Contraction: physiology; Respiratory Mechanics; Respiratory Mechanics: physiology; Respiratory Muscles; Respiratory Muscles: physiology
Foundations of quantum mechanics?
Nature Physics insight
84
4
018501
2011
10.1088/0031-8949/84/01/018501
Does quantum mechanics have unsolved foundational problems? Is there a dividing line between the quantum and classical descriptions of the world? In this paper, I give an elementary introduction to the mathematical aspects of quantum and classical models which have prompted such questions.
Classical and Computational Solid Mechanics
Applied Mechanics Reviews
56
1
B1
2003
10.1115/1.1523351
This invaluable book has been written for engineers and engineering scientists in a style that is readable, precise, concise, and practical. It gives first priority to the formulation of problems, presenting the classical results as the gold standard, and the numerical approach as a tool for obtaining solutions. The classical part is a revision of the well-known text Foundations of Solid Mechanics, with a much-expanded discussion on the theories of plasticity and large elastic deformation with finite strains. The computational part is all new and is aimed at solving many major linear and nonlinear boundary-value problems.
Fluid Mechanics
New York
6
3
458-487
1959
10.1146/annurev.fluid.36.050802.122132
Dental thermal pain is a significant health problem in daily life and dentistry. There is a long-standing question regarding the phenomenon that cold stimulation evokes sharper and more shooting pain sensations than hot stimulation. This phenomenon, however, outlives the well-known hydrodynamic theory used to explain dental thermal pain mechanism. Here, we present a mathematical model based on the hypothesis that hot or cold stimulation-induced different directions of dentinal fluid flow and the corresponding odontoblast movements in dentinal microtubules contribute to different dental pain responses. We coupled a computational fluid dynamics model, describing the fluid mechanics in dentinal microtubules, with a modified Hodgkin-Huxley model, describing the discharge behavior of intradental neuron. The simulated results agreed well with existing experimental measurements. We thence demonstrated theoretically that intradental mechano-sensitive nociceptors are not "equally sensitive" to inward (into the pulp) and outward (away from the pulp) fluid flows, providing mechanistic insights into the difference between hot and cold dental pain. The model developed here could enable better diagnosis in endodontics which requires an understanding of pulpal histology, neurology and physiology, as well as their dynamic response to the thermal stimulation used in dental practices.
Active mechanics and dynamics of cell spreading on elastic substrates
Soft Matter
10
7234-7246
2014
10.1039/C4SM00780H
The spreading area of cells has been shown to play a central role in the determination of cell fate and tissue morphogenesis; however, a clear understanding of how spread cell area is determined is still lacking. The observation that cell area and force generally increase with substrate rigidity suggests that cell area is dictated mechanically, by means of a force-balance between the cell and the substrate. A simple mechanical model, corroborated by experimental measurements of cell area and force is presented to analyze the temporal force balance between the cell and the substrate during spreading. The cell is modeled as a thin elastic disc that is actively pulled by lamellipodia protrusions at the cell front. The essential molecular mechanisms of the motor activity at the cell front, including, actin polymerization, adhesion kinetics, and the actin retrograde flow, are accounted for and used to predict the dynamics of cell spreading on elastic substrates; simple, closed-form expressions for the evolution of cell size and force are derived. Time-resolved, traction force microscopy, combined with measurements of cell area are performed to investigate the simultaneous variations of cell size and force. We find that cell area and force increase simultaneously during spreading but the force develops with an apparent delay relative to the increase in cell area. We demonstrate that this may reflect the strain-stiffening property of the cytoskeleton. We further demonstrate that the radial cell force is a concave function of spreading speed and that this may reflect the strengthening of cell–substrate adhesions during spreading.
Cellular Fluid Mechanics
Annual Review Fluid Mechanics
34
211-32
2002
10.1146/annurev.fluid.34.082401.165302
The coupling of fluid dynamics and biology at the level of the cell is an intensive area of investigation because of its critical role in normal physiology and disease. Microcirculatory flow has been a focus for years, owing to the complexity of cell-cell or cell-glycocalyx interactions. Noncirculating cells, particularly those that comprise the walls of the circulatory system, experience and respond biologically to fluid dynamic stresses. In this article, we review the more recent studies of circulating cells, with an emphasis on the role of the glycocalyx on red-cell motion in small capillaries and on the deformation of leukocytes passing through the microcirculation. We also discuss flows in the vicinity of noncirculating cells, the influence of fluid dynamic shear stress on cell biology, and diffusion in the lipid bi-layer, all in the context of the important fluid-dynamic phenomena.
a focus years; biology level; blood flow; cell; critical role normal; disease; fluid dynamics; glycocalyx; intensive area; investigation because its; leukocytes; mechanotransduction; membrane; microcirculatory flow has been; owing complexity; physiology; s abstract coupling
Vascular mechanics for the cardiologist.
Journal of the American College of Cardiology
23
6
1289-1295
1994
10.1016/0735-1097(94)90369-7
Many common problems in clinical cardiology are due to disturbances in vascular mechanics. The terminology and basic principles of vascular mechanics, including fundamentals of the relation of stress and strain, are described in this review. Approaches to measuring vessel wall stiffness and the mechanical basis for vascular catastrophes are introduced.
Channel-cracking of thin films with the extended finite element method
Engineering Fracture Mechanics
70
18
2513-2526
2003
10.1016/S0013-7944(03)00083-3
The recently developed extended finite element method (XFEM) is applied to compute the steady-state energy release rate of channeling cracks in thin films. The method is demonstrated to be able to model arbitrary singularities by using appropriate enriching functions at selected nodes with a relatively coarse mesh. The dimensionless driving force for channeling cracks is obtained as a function of elastic mismatch, crack spacing, and the thickness ratio between the substrate and the film. The results are compared with those from several previous studies when available. Emphasis is placed on the cases with compliant substrates, for which much less information is available from previous studies. It is found that, while it is quite challenging to model the cases with very compliant substrates using regular finite element method because of the strong singularities, the present approach using XFEM is relatively simple and straightforward. © 2003 Elsevier Ltd. All rights reserved.
Channeling crack; Compliant substrate; Thin film; XFEM
Towards a methodology for rock mechanics modelling
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts
25
3
99-106
1988
10.1016/0148-9062(88)92292-9
Rock mechanics models fall into the class of “data-limited problems”; one seldom knows enough about a rock mass to model it unambiguously. Modellers are beginning to realize that data-limited problems require a very different modelling approach from that developed in, for example, electrical or aerospace engineering. It follows that one cannot use models in rock mechanics in a conventional way, and that there is a need to adopt a distinctive and appropriate methodology for rock mechanics modelling. Some guidelines and heuristics, which may be considered as the first steps towards developing such a methodology, are presented. Three case studies are then used to illustrate the application, in practice, of these ideas.
The effect of transverse moduli on dilatation and through-thickness Poisson's ratio in angle-ply laminates
Journal of Reinforced Plastics and Composites
21
18
1653-1670
2002
10.1106/073168402021479
In this article, an investigation of the effect from the transverse elastic moduli of the lamina on the dilatation and the through-thickness Poisson's ratio in the angle-ply laminates is presented. Based on the classical lamination theory and the generalized Hook's law, a dimensionless analysis has been used to study the influence of the various transverse elastic moduli E-2 and E-3 of the lamina on the dilatation and the through-thickness Poisson's ratio in angle-ply laminates. The results from this dimensionless analysis provide a set of general guidelines for designing and evaluating the values of the through-thickness Poisson's ratio and the dilatation of the angle-ply laminates to meet various requirements in engineering applications.
High-Performance Abaqus Simulations in Soil Mechanics
2008 ABAQUS Users' Conference
1-15
2008
Abaqus is often applied to solve geomechanical boundary value problems. Several Abaqus built-in features enable a wide range of simulating such problems. For complex problems Abaqus can be extended via user subroutines. Several extensions for soil mechanics purposes are discussed and corresponding case studies are presented.
abaqus; compaction analysis; hypoplasticity; pile penetration analysis; quay wall deformation analysis; quay wall optimization analysis; soil; soil mechanics; soil plasticity
Fluid mechanics of heart valves.
Annual review of biomedical engineering
6
331-362
2004
10.1146/annurev.bioeng.6.040803.140111
Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review.
000 valve repairs and; 250; and leads to approximately; bioprosthetic valves; computational fluid; disease is a life-threatening; disease that afflicts mil-; dynamics; i abstract valvular heart; laser doppler velocimetry; lions of people worldwide; mechanical heart valves; native heart valves; or
Mechanics of indentation for piezoelectric thin films on elastic substrate
International Journal of Solids and Structures
49
1
95-110
2012
10.1016/j.ijsolstr.2011.09.014
Frictionless normal indentation problem of rigid flat-ended cylindrical, conical and spherical indenters on piezoelectric film, which is either in frictionless contact with or perfectly bonded to an elastic half-space (substrate), is investigated. Both conducting and insulating indenters are considered. With Hankel transform, the general solutions of the homogeneous governing equations for the piezoelectric layer and the elastic half-space are presented. Using the boundary conditions for a vertical point force or a point electric charge, and the boundary conditions on the film/substrate interface, the Green's functions can be obtained by solving sets of simultaneous linear algebraic equations. The solution of the indentation problem is obtained by integrating these Green's functions over the contact area with unknown surface tractions or electric charge distribution, which will be determined from the boundary conditions on the contact surface between the indenter and the film. The solution is expressed in terms of dual integral equations that are converted to a Fredholm integral equation of the second kind and solved numerically. Numerical examples are also presented. The comparison between two film/substrate bonding conditions is made. It shows that the indentation rigidity of the film/substrate system is lower when the film is in frictionless contact with the substrate. The effects of the Young's modulus and Poisson's ratio of the elastic substrate, indenter electrical condition and indenter prescribed electric potential on the indentation responses are presented. ?? 2011 Elsevier Ltd. All rights reserved.
Green's function; Indentation; Integral equations; Piezoelectric film
Branching out in locomotion: the mechanics of perch use in birds and primates.
The Journal of experimental biology
202
1459-1463
1999
Many animals use thin perches, such as the branches of trees, as locomotory substrates. In this paper, I have reviewed the literature concerned with measurements of locomotory forces made by birds and primates on thin and flexible substrates. Through a knowledge of the locomotory forces exerted by animals when using different substrates, the mechanical cost of their use can be established. We are just beginning to learn about the magnitude and patterns of force production in various branch-using vertebrates, primarily as a result of the development of instrumented perches. Instrumented perches have been designed to measure the forces produced by birds and primates when leaping from rigid and flexible horizontal and flexible vertical perches, and also from instrumented handgrips during brachiation. The development of these techniques for birds and primates allows us to compare the way in which they use perches as locomotory substrates. In both birds and primates, the magnitudes of landing forces are smaller than those during take-off. Two explanations have been proposed; the difference is either a consequence of perch compliance or it is a strategic decision to be cautious of 'new' perches. Leaps from flexible perches may be somewhat inefficient because considerable energy is dissipated in bending the perch, and this energy may remain unrecovered when the animal leaves contact with the perch.
biomechanics; bird; landing; perch; primate; take-off
Adhesion: molecules and mechanics.
Science (New York, N.Y.)
263
5154
1720-1725
1994
10.1126/science.263.5154.1720
There is a difference between adhesion at the molecular level and adhesion in engineering. There is no doubt that molecules of solid materials stick together and can be separated mechanically. The problem is explaining the connection between molecular attractions and mechanical measurements. False ideas such as keying and gluing require critical assessment because they confuse molecules and mechanics. Mechanisms such as adhesive hysteresis, stringing, and clustering deserve evaluation. A rational theory of these phenomena should be based on the theoretical concept of reversible work of adhesion and on the measured quantity of adhesive energy, which includes the extra energy required to restructure the interface as surfaces move.
Cracks in thin sheets: When geometry rules the fracture path
Physical Review Letters
95
2
25502
2005
10.1103/PhysRevLett.95.025502
We study the propagation of brittle fractures coupled to large out-of-plane bending, as when a brittle elastic thin sheet is cut by a moving object. Taking into account the separation of the film's bending and stretching energies and using fracture theory we show that such cracks propagate according to a simple set of geometrical rules in the limit of small thickness. In particular, this provides some insight into the geometrical origin of the oscillatory fracture patterns reported in two recent experiments. Numerical integration of our geometrical rules accurately reproduces both the shape of the fracture pattern and the detailed time evolution of the propagation of the crack tip, for various geometries of the cutting object.
Mechanics of capillary forming of aligned carbon nanotube assemblies
Langmuir
29
17
5190-5198
2013
10.1021/la4002219
Elastocapillary self-assembly is emerging as a versatile technique to manufacture three-dimensional (3D) microstructures and complex surface textures from arrangements of micro- and nanoscale filaments. Understanding the mechanics of capillary self-assembly is essential to engineering of properties such as shape-directed actuation, anisotropic wetting and adhesion, and mechanical energy transfer and dissipation. We study elastocapillary self-assembly (herein called "capillary forming") of carbon nanotube (CNT) microstructures, combining in situ optical imaging, micromechanical testing, and finite element modeling. By imaging, we identify sequential stages of liquid infiltration, evaporation, and solid shrinkage, whose kinetics relate to the size and shape of the CNT microstructure. We couple these observations with measurements of the orthotropic elastic moduli of CNT forests to understand how the dynamic of shrinkage of the vapor-liquid interface is coupled to the compression of the forest. We compare the kinetics of shrinkage to the rate of evporation from liquid droplets having the same size and geometry. Moreover, we show that the amount of shrinkage during evaporation is governed by the ability of the CNTs to slip against one another, which can be manipulated by the deposition of thin conformal coatings on the CNTs by atomic layer deposition (ALD). This insight is confirmed by finite element modeling of pairs of CNTs as corrugated beams in contact and highlights the coupled role of elasticity and friction in shrinkage and stability of nanoporous solids. Overall, this study shows that nanoscale porosity can be tailored via the filament density and adhesion at contact points, which is important to the development of lightweight multifunctional materials.
An Introduction to Lagrangian Mechanics, by A.J. Brizard
Contemporary Physics
51
5
448-448
2010
10.1080/00107510903318806
An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat s Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d Alembert that preceded Hamilton s formulation of the Principle of Least Action, from which the Euler Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh s procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory. This textbook is suitable for undergraduate students who have acquired the mathematical skills needed to complete a course in Modern Physics. Contents: The Calculus of Variations; Lagrangian Mechanics; Hamiltonian Mechanics; Motion in a Central-Force Field; Collisions and Scattering Theory; Motion in a Non-Inertial Frame; Rigid Body Motion; Normal-Mode Analysis; Continuous Lagrangian Systems; Appendices:; Basic Mathematical Methods; Elliptic Functions and Integrals; Noncanonical Hamiltonian Mechanics.
Wind load cycle development for evaluating mechanically attached single-ply roofs
Journal of Wind Engineering and Industrial Aerodynamics
77-78
83-96
1998
10.1016/S0167-6105(98)00134-2
Failure modes resulting from the existing North-American roof certification procedures are often not consistent with failures in the field. To develop test procedures for certifying roofing systems under dynamic wind loads, the National Research Council of Canada (NRC) formed an industry-based consortium. The consortium is known as Special Interest Group for Dynamic Evaluation of Roofing Systems (SIGDERS). Using wind tunnel pressure records as source data, SIGDERS developed a dynamic load cycle. With input from industries, building owners and roofing associations, the developed load cycle has been generalized. Based on this extensive investigation, a simplified laboratory test procedure is proposed for the evaluation of mechanically fastened single-ply roofing system.
Certification; Design pressure; Dynamic procedure; Roofing system; Static test; Wind tunnel; Wind uplift
Piezoelectric effect of cellulose nanocrystals thin films
ACS Macro Letters
1
7
867-870
2012
10.1021/mz300234a
Ultrathin films of aligned cellulose nanocrystals (CNCs) were assembled on mica supports by using electric field-assisted shear. The relationship between polarization gradients and strain mechanics of the obtained films was examined by monitoring their deflection with an atomic force microscope operated in contact mode. The piezoelectric response of the films was ascribed to the collective contribution of the asymmetric crystalline structure of the cellulose crystals. The magnitude of the effective shear piezoelectric constant (d25) of highly ordered CNC films was determined to be 2.1 Å/V, which is comparable to that of a reference film of a piezoelectric metal oxide. Ultrathin films of aligned cellulose nanocrystals (CNCs) were assembled on mica supports by using electric field-assisted shear. The relationship between polarization gradients and strain mechanics of the obtained films was examined by monitoring their deflection with an atomic force microscope operated in contact mode. The piezoelectric response of the films was ascribed to the collective contribution of the asymmetric crystalline structure of the cellulose crystals. The magnitude of the effective shear piezoelectric constant (d25) of highly ordered CNC films was determined to be 2.1 Å/V, which is comparable to that of a reference film of a piezoelectric metal oxide.
Exact solutions for the transient response of symmetric cross-ply laminates using a higher-order plate theory
Composites Science and Technology
34
3
205-224
1989
10.1016/0266-3538(89)90029-8
The methods of the orthogonality of principal modes and the state variables technique are used to investigate the dynamic response of symmetric cross-ply laminated composite plates by solving the equation of a higher-order shear deformation plate theory. Exact solutions of simply supported rectangular plates are presented for various loadings. The results obtained using the higher-order theory (HSDT) are compared with those obtained by the Reissner-Mindlin shear deformation plate theory (FSDT) as well as the classical laminate theory (CPT).
United States Patent 6265333: Delamination resistant composites prepared by small diameter fiber reinforcement at ply interfaces
Composites Technology
1-22
2001
A fiber reinforced composite material comprising a resin matrix and primary reinforcement fibers and further comprising secondary, smaller diameter, reinforcement fibers at one or more ply interfaces, or portion thereof, provides improved interlaminar toughness, strength, and delamination resistance without substantial reduction of in-plane properties and without substantial increase in weight. In one embodiment, the small fibers are attached to one side of a conventional prepreg prior to lamination. The small fibers are flexible and are expected to conform to the shape and distribution of the primary reinforcing fibers at the interface.
A detailed experimental and analytical study of the thermal expansion of dielectric thin films on Si by x-ray reflectivity
Journal of Applied Physics
100
1-7
2006
10.1063/1.2353283
We present a method of using x-ray reflectivity to measure the thermal expansion coefficient for submicron dielectric thin films. Technique criteria are discussed including importance of thickness accuracy, thickness boundaries, and detecting thickness changes due to irreversible phenomena. The thin film mechanics required to extract the thermal expansion parameter for a freestanding film as opposed to an attached film are discussed. Thermal expansion measurements on silicon carbide and silicon nitride thin films using this method agree with literature values obtained for bulk samples. The thermal expansion of several carbon-doped silicon oxide thin films was also measured. (c) 2006 American Institute of Physics.
Design and Mechanics of Continuum Robots for Surgery
Russell The Journal Of The Bertrand Russell Archives
29
13
1661-1683
2007
10.1177/0278364910368147
This dissertation describes design and modeling of two new flexible, continuous backbone robotic dexterity enhancement devices, and algorithms to robotically ma- nipulate them in surgery. These steerable needles and active cannulas provide dex- terity in thin (needle-sized) form factors, permitting surgical tools to turn corners inside the human body. The robotic tool manipulation algorithms are useful for rapidly and accurately aligning many kinds of surgical tools with planned poses and entry vectors. Drawing on techniques from artificial intelligence, they do not require cumbersome calibration, complete knowledge of robot kinematics, or even encoding, making them well-suited to uncertain real-world clinical environments. Simulations and experimental results demonstrate the accuracy and speed of the algorithms. When an intervention is needle-based, steerable needles provide a means to achieve dexterity within soft tissue after insertion begins. Asymmetric forces generated by a bevel tip are harnessed robotically to generate controllable deflection, and curvature is enhanced by design of needle properties and geometry. The needle is modeled as a nonholonomic system with model parameters fit to experimental data. A new control law inspired by mouse ballistics enables human users to teleoperatively target more accurately than traditional rate or position control. Active cannulas are capable of similar curved dexterity without relying on tissue reaction force, making steering possible in both soft tissue and free space. Com- posed of multiple concentric precurved tubes, active cannula shape is described using Bernoulli-Euler beam mechanics and minimum energy principles, and predictions are corroborated with a set of experiments. Parameter values fit to experimental data are near ranges calculated from physical tube characteristics. Design tools for surgical application-specific cannula optimization are described, and differential kinematics are derived, enabling future work in image-guided control and teleoperation. The research in this dissertation has been motivated by reducing invasiveness, im- proving clinical outcomes, and enabling surgical treatment for inoperable patients. However, the models and methods developed are broadly applicable within the fields of continuum and nonholonomic robotics.
Game Mechanics: Describing Computer-Augmented Games in Terms of Interaction
Proceedings of Technologies for Interactive Digital Storytelling and Entertainment (TIDSE 2003)
45-56
2003
10.1057/jors.1984.31
We report how new types of games can be created using the possibilities of embedded computing, sensors, new output devices and ad-hoc wireless networks while keeping characteristics from traditional nancomputerized games. Applying both a technological and use-oriented research approach, we identified a number of new interaction acts made possible by the new technology. These are described using game mechanics, a concept developed by the game design community. The identified mechanics, together with examples of games using them, are described as well as the benefits and limitations of using the game mechanic concept.
Statistical Fluid Mechanics: The Mechanics of Turbulence
American Journal of Physics
45
10
1010
1977
10.1119/1.10870
"If ever a field needed a definitive book, it is the study of turbulence; if ever a book on turbulence could be called definitive, it is this book." — ScienceWritten by two of Russia's most eminent and productive scientists working in the fields of turbulence, oceanography, and atmospheric physics, this two-volume survey is renowned for its clarity as well as its comprehensive treatment. Volume One begins with an outline of laminar and turbulent flow. The remainder of the book treats a variety of aspects of turbulence: its statistical and Lagrangian descriptions, shear flows near surfaces and free turbulence, the behavior of thermally stratified media, and diffusion. Volume Two continues and concludes the presentation. Topics include spectral functions, homogeneous fields, isotropic random fields, isotropic turbulence, self-preservation hypotheses, spectral energy transfer, the Millionshchikov hypothesis, acceleration fields, equations for higher moments and the closure problem, and turbulence in a compressible fluid. Additional subjects include general concepts of the local structure of turbulence at high Reynolds numbers, the theory of fully developed turbulence, the propagation of electromagnetic and acoustic waves through a turbulent medium, and the twinkling of stars. The book closes with a discussion of the functional formulation of the problem of turbulence, presenting the equations for the characteristic functional and methods for their solution.
Buckling characteristics of cross-ply elliptical cylinders under axial compression
Composite Structures
62
1
7-17
2003
10.1016/S0263-8223(03)00079-5
Here, the elastic buckling characteristics of laminated cross-ply elliptical cylindrical shells under axial compression is studied through finite element approach. The formulation is based on higher-order theory that accounts for the transverse shear and transverse normal deformations, and incorporates realistic through the thickness approximations of the in-plane displacements. The strain-displacement relations are accurately accounted for in the formulation. The contributions of work done by applied load due to the higher-order function arising from the assumed displacement models are also incorporated. The governing equations obtained using the principle of minimum potential energy are solved through eigenvalue approach. The combined influence of higher-order shear deformation, shell geometry and elliptical cross-sectional parameter, and lay-up on the buckling loads of elliptical cylindrical shells is examined. ?? 2003 Elsevier Ltd. All rights reserved.
Buckling load; Cross-ply; Elliptic cross-section; Finite element; Higher-order; Laminated shell; Non-circular
Controlled buckling of thin film on elastomeric substrate in large deformation
Theoretical and Applied Mechanics Letters
1
2
021001
2011
10.1063/2.1102101
... surface patterning and precision metrology. c⃝ 2011 The Chinese Society of Theoretical and Applied Mechanics. [doi: 10.1063 / 2.1102101 ] Keywords thin film, buckling, large deformation Stretchable electronics enables many ...
1; 1 electronic eye camera; 4; 5 smart surgical gloves; 6 and; buckling; conformable skin sensors; displays; large deformation; new applica-; stretchable electronics enables many; thin film; tions such as flexible
Introduction to Cell Mechanics and Mechanobiology
Garland Science
2012
10.1080/10255842.2013.780048
This book is designed for a course in the mechanics of the cell offered to students in biomedical engineering, bioengineering, and mechanical engineering. It teaches a quantitative understanding of the way cells detect, modify, and respond to the physical properties within the cell environment. Coverage includes the mechanics of single molecule polymers, polymer networks, two-dimensional membranes, whole-cell mechanics, and mechanobiology, as well as primer chapters on solid, fluid, and statistical mechanics.
A Primer on Geometric Mechanics
arXiv preprint arXiv:1206.3302
1-12
2012
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance of the subject for an understanding of "mechanics".
Interlaminar fatigue crack growth of cross-ply composites under thermal cycles
Composite Structures
85
2
175-187
2008
10.1016/j.compstruct.2007.10.018
The fatigue growth of a fiber reinforced composite laminate was characterized under thermal cycling using a combined experimental and computational investigation. Twenty-four ply composite laminates ([0 degrees(12)/90 degrees(12)]) are fabricated with a pre-existing delamination, and subjected to thermal cycling in an environmental chamber. The large mismatch in the coefficients of thermal expansion is used to grow ail interlaininar crack at the interface of the 0 degrees and 90 degrees laminae. This thermal fatigue crack growth behavior is investigated for different amplitudes of temperature change (Delta T= 30-140 degrees C). The inspection of fracture surfaces, after completion of the fatigue tests, reveals ail angled or kinked crack front growth with greater propagation distances near the free-surfaces/edges. Due to the non-uniform crack growth across the specimen thickness, three-dimensional finite element analyses are performed to investigate the fatigue growth mechanisms under thermal load. From the analysis, the energy release rate as well as the mixed-mode stress intensity factors is calculated and the variations of these fracture parameters are found to be consistent with the observed crack front configuration. Using the computed results, the experimentally measured crack growth rates are also correlated with the amplitude of energy release rate, and a power law form of the fatigue law is established. The relevant coefficients as well as the threshold energy release rate are also determined. The present analysis is useful for not only understanding the fatigue delamination mechanisms under thermal cycling but also for estimating the threshold temperature variation that is needed to drive crack growth. (c) 2007 Elsevier Ltd. All rights reserved.
3d finite element; energy release rate; fracture toughness; mixed-mode fracture
Statistical geometry of caging effects in random thin-rod structures
Physica A: Statistical Mechanics and its Applications
235
1-2
186-193
1997
10.1016/S0378-4371(96)00339-1
A derivation is given for the caging density of a static, random thin-rod structure at which uncorrelated contacts on a rod on average form a cage which arrests sidewise translations. Some implications of this result for colloidal sediments, random packings and rod glasses are discussed.
caging effects; colloidal rods; random packing; rigid fibers; rod glasses; sedimentation of colloids
Flexural Resonant Frequencies of Thin Rectangular Cantilever Plates
Journal of Applied Mechanics
75
1
011007
2008
10.1115/1.2745377
Knowledge of the flexural vibration frequencies of thin rectangular cantilever plates forms the basis for numerous applications in sensing and instrumentation. Despite the seemingly simple nature of the problem, an accurate formula for the fundamental reso- nant frequency that is valid for all aspect ratios and Poisson’s ratios is notably lacking in the literature. In this article, we present such a result using a variational and singular perturbation formulation. This yields a simple analytical formula that exhibits a maxi- mum error of 2%.
The mechanics of microneedles
Proceedings of the Second Joint 24th Annual Conference and the Annual Fall Meeting of the Biomedical Engineering Society] [Engineering in Medicine and Biology
1
498-499
2002
10.1109/IEMBS.2002.1136914
We have developed arrays of microscopic needles capable of providing pathways for drug delivery across skin without the pain associated with conventional injections. We measured the force to insert microneedles into human subjects and compared it to the force to cause microneedles to break. Insertion force measured with a force, deflection and electrical resistance meter showed that microneedle insertion force was directly proportional to interfacial area of the needle tip over a broad range of needle geometries. Force of insertion for a representative needle with 42 micron tip radius and 10 micron wall thickness was 1.3 N, which permits easy insertion of needles by hand. Breaking of microneedles under load was measured as a function of needle geometry and found to agree with predictions by ANSYS finite element simulation and thin-shell analytic theory. For example, the applied force at failure for a needle with the same geometry as above was 3.4 N, providing a 2.6-fold margin of safety between insertion and failure. In comparison, the simulation and analytical predictions were 3.5 N and 2.2 N, respectively. Both predictions and experimental results reveal that microneedles over a range of geometries are capable of withstanding the force of insertion.
Bendable ultra-thin chips on flexible foils
IEEE Sensors Journal
13
10
4030-4037
2013
10.1109/JSEN.2013.2269028
This paper presents ultra-thin silicon chips (flex-chips) on flexible foils, realized through post-processing steps such as wafer thinning, dicing, and transferring the thinned chips to flexible polyimide foils. The cost effective chemical etching is adopted for wafer thinning and the transfer printing approach, to transfer quasi 1-D structures such as micro/nanoscale wires and ribbons, that is adapted for transferring large ultra-thin flex-chips (widths 4.5-15 mm, lengths 8-36 mm, and thickness ≈ 15 μm). The post-processing capability is demonstrated with passive structures such as metal interconnects realized on the flex-chips before carrying out the chip thinning step. The resistance values of metal interconnects do not show any appreciable change because of bending of chips for the tested range viz., radius of curvature 9 mm and above. Further, the bending mechanics of silicon membranes on foil is investigated to evaluate the bending limits before a mechanical fracture/failure occurs. The distinct advantages of this paper are: attaining bendability through post-processing of chips, cost effective fabrication process, and easy transfer of chips to the flexible substrates without using conventional and sophisticated equipment such as pick and place set up.
bendable system; bending mechanics; Flex-Chip; flexible electronics; transfer printing
Mechanics of Solids and Materials
Strength of Materials
880
2006
10.1017/CBO9780511755514
Mechanics of Solids and Materials intends to provide a modern and integrated treatment of the foundations of solid mechanics as applied to the mathematical description of material behavior. The 2006 book blends both innovative (large strain, strain rate, temperature, time dependent deformation and localized plastic deformation in crystalline solids, deformation of biological networks) and traditional (elastic theory of torsion, elastic beam and plate theories, contact mechanics) topics in a coherent theoretical framework. The extensive use of transform methods to generate solutions makes the book also of interest to structural, mechanical, and aerospace engineers. Plasticity theories, micromechanics, crystal plasticity, energetics of elastic systems, as well as an overall review of math and thermodynamics are also covered in the book.
Matrix cracking in cross-ply laminates: Effect of randomness
Composites Part A: Applied Science and Manufacturing
36
2 SPEC. ISS.
129-135
2005
10.1016/j.compositesa.2004.06.008
This paper presents a study of the effect of randomness in distribution of matrix cracks in [0m/90n/0m] carbon fibre-epoxy laminates. In contrast to standard approaches based on the unit cell (representative volume element), various crack distributions are introduced directly into finite element models. Magnitudes of crack spacings in 90?? layers are taken from tensile fatigue experiments on T300/914C composites. The purpose of numerical simulations is to estimate the effect of the transverse crack arrangements on the character of the stress distributions in both the stiff 0?? layers and the less stiff 90?? layers. The influence of the crack spacing arrangement on the effective properties of laminates is discussed. ?? 2004 Elsevier Ltd. All rights reserved.
A. Laminates; B. Transverse cracking; C. Finite element analysis
Atomistic and continuum studies of crack-like diffusion wedges and associated dislocation mechanisms in thin films on substrates
Journal of the Mechanics and Physics of Solids
51
2105-2125
2003
10.1016/j.jmps.2003.09.024
Large-scale atomistic simulations are performed to study plastic deformation in sub-micron polycrystalline thin films on substrates. The simulations reveal that stresses in the film are relaxed by mass diffusion from the surface into the grain boundary. This leads to formation of a novel material defect referred to as the diffusion wedge. A crack-like stress field is found to develop around the diffusion wedge as the traction along the grain boundary is relaxed and the adhesion between the film and the substrate prohibits strain relaxation close to the interface. The diffusion wedge causes nucleation of dislocations on slip planes parallel to the plane of the film. We find that nucleation of such parallel glide dislocations from a diffusion wedge can be described by a critical stress intensity factor similar to the case of a crack. Atomistic simulations of parallel glide dislocations associated with the crack-like grain boundary diffusion wedge represent a significant progress in the theory of diffusional creep in thin films on substrates. ?? 2003 Elsevier Ltd. All rights reserved.
Atomistic; Bimaterial interface; Continuum; Diffusion; Discrete dislocations; Dislocation nucleation; Stress intensity factor
Buckling and postbuckling of a compressed thin film bonded on a soft elastic layer: A three-dimensional analysis
Archive of Applied Mechanics
80
2
175-188
2010
10.1007/s00419-009-0313-2
The wrinkling of a stiff thin film bonded on a soft elastic layer and subjected to an applied or residual compressive stress is investigated in the present paper. A three-dimensional theoretical model is presented to predict the buckling and postbuckling behavior of the film. We obtained the analytical solutions for the critical buckling condition and the postbuckling morphology of the film. The effects of the thicknesses and elastic properties of the film and the soft layer on the characteristic wrinkling wavelength are examined. It is found that the critical wrinkling condition of the thin film is sensitive to the compressibility and thickness of the soft layer, and its wrinkling amplitude depends on the magnitude of the applied or residual in-plane stress. The bonding condition between the soft layer and the rigid substrate has a considerable influence on the buckling of the thin film, and the relative sliding at the interface tends to destabilize the system.
Analytical method; Buckling; Postbuckling; Surface pattern; Thin film
Scleral mechanics: comparing whole globe inflation and uniaxial testing.
Experimental eye research
94
1
128-35
2012
10.1016/j.exer.2011.11.017
The purpose of this study was to assess fundamental differences between the mechanics of the posterior sclera in paired eyes using uniaxial and whole globe inflation testing, with an emphasis on the relationship between testing conditions and observed tissue behavior. Twenty porcine eyes, consisting of matched pairs from 10 pigs, were used in this study. Within pairs, one eye was tested with 10 cycles of globe pressurization to 150 mmHg (∼10× normal IOP) while biaxial strains were tracked via an optical system at the posterior sclera. An excised posterior strip from the second eye was subjected to traditional uniaxial testing in which mechanical hysteresis was recorded from 10 cycles to a peak stress of 0.13 MPa (roughly equivalent to the circumferential wall stress produced by an IOP of 150 mmHg under the thin-walled pressure vessel assumption). For approximately equivalent loads, peak strains were more than twice as high in uniaxial tests than in inflation tests. Different trends in the load-deformation plots were seen between the tests, including an extended "toe" region in the uniaxial test, a generally steeper curve in the inflation tests, and reduced variability in the inflation tests. The unique opportunity of being able to mechanically load a whole globe under near physiologic conditions alongside a standard uniaxially tested specimen reveals the effects of testing artifacts relevant to most uniaxially tested soft tissues. Whole globe inflation offers testing conditions that significantly alter load-deformation behavior relative to uniaxial testing; consequently, laboratory studies of interventions or conditions that alter scleral mechanics may greatly benefit from these findings.
Animal; Animals; Biomechanical Phenomena; Cellular; Cellular: physiology; Elasticity; Elasticity: physiology; Intraocular Pressure; Intraocular Pressure: physiology; Mechanical; Mechanotransduction; Models; Ocular Physiological Phenomena; Sclera; Sclera: physiology; Stress; Swine
Fatigue behaviour of cross-ply CFRP laminates made of T300 or T400 fibres
International Journal of Fatigue
12
245-251
1990
10.1016/0142-1123(90)90451-J
The determination of the transverse cracking which occurs during the fatigue of cross-ply materials with two different fibres (T300 or T400) has been undertaken. The study includes an experimental part and a theoretical part containing both an analytical and a numerical approach for modelling the observed stiffness reduction.
SCVNGR’s Secret Game Mechanics Playdeck
TechCrunch
2010
SCVNGR, which makes a mobile game with real-world challenges, has a playdeck. It is a deck of cards listing nearly 50 different game mechanics that can be mixed and matched to create the foundation for different types of games. I’ve republished the accompanying document below, which should be interesting to anybody trying to inject a gaming dimension into their products.
Computational modeling of muscular thin films for cardiac repair
Computational Mechanics
43
4
535-544
2009
10.1007/s00466-008-0328-5
Motivated by recent success in growing biohybrid material from engineered tissues on synthetic polymer films,we derive a computational simulation tool for muscular thin films in cardiac repair. In this model, the polydimethylsiloxane base layer is simulated in terms of microscopically motivated tetrahedral elements. Their behavior is characterized through a volumetric contribution and a chain contribution that explicitly accounts for the polymeric microstructure of networks of long chain molecules. Neonatal rat ventricular cardiomyocytes cultured on these polymeric films are modeled with actively contracting truss elements located on top of the sheet. The force stretch response of these trusses is motivated by the cardiomyocyte force generated during active contraction as suggested by the filament sliding theory. In contrast to existing phenomenological models, all material parameters of this novel model have a clear biophyisical interpretation. The predictive features of the model will be demonstrated through the simulation of muscular thin films. First, the set of parameters will be fitted for one particular experiment documented in the literature. This parameter set is then used to validate the model for various different experiments. Last,we give an outlook of howthe proposed simulation tool could be used to virtually predict the response of multi-layered muscular thin films. These three-dimensional constructs show a tremendous regenerative potential in repair of damaged cardiac tissue.The ability to understand, tune and optimize their structural response is thus of great interest in cardiovascular tissue engineering.
Cardiovascular tissue repair; Finite element modeling; Micromechanics; Muscle contraction; Tissue engineering
Thomas Young on fluid mechanics
Journal of Engineering Mathematics
67
1-2
95-113
2010
DOI 10.1007/s10665-009-9298-7
Thomas Young was a prolific scholar who made many contributions to science, medicine and the humanities. Here, his writings on fluid mechanics are reviewed. The best known of these are on tides and on surface tension; but he did much else besides. These include his wide-ranging lectures to the Royal Institution, his rather eccentric reworking of Book 1 of Laplace's M,canique c,leste, and papers on pneumatics and hydraulics. Among the latter are perhaps the first observation of transition to turbulence in jets of air; an empirical formula for the resistance of hydraulic flow in pipes, suggested by his own experiments with thin tubes; and probably the first, but incomplete, attempt at a theory of the hydraulic jump or bore. All of this work is characterised by sound physical insight but mathematical limitations.
cohesion and surface tension; history of fluid mechanics; hydraulics; ivory,james; tides; water waves; water-wave theory
The stress singularity in surfactant-driven thin-film flows. Part 2. Inertial effects
Journal of Fluid Mechanics
372
301-322
1998
10.1017/S0022112098002377
ABSTRACT A localized, insoluble, surfactant monolayer, spreading under the action of surface-tension gradients over a thin liquid film, has at its leading edge an integrable stress singularity which renders conventional thin-film approximations locally non-uniform. Here high-Reynolds-number asymptotics are used to explore the quasi-steady two-dimensional developing flow near the monolayer tip, assuming that gravity keeps the free surface almost flat, that weak ‘contaminant’ surfactant regularizes the singularity and that the monolayer spreads fast enough for inertial effects to be important in a region which is long compared to the film depth but which is short compared to the length of the monolayer. It is shown how downward displacement of the inviscid core flow by the subsurface viscous boundary layer yields a non-uniform pressure distribution which, when the monolayer is spreading fast enough for cross-stream pressure gradients to be significant at its tip, creates a short free-surface hump which is the thin-film version of a Reynolds ridge. The ridge and other singular flow structures are smoothed as the monolayer slows and levels of contaminant are increased. The conditions under which lubrication theory provides a uniformly accurate approximation for this class of surfactant-spreading flows are established.
The Mechanics of the Circulation
Journal of the Royal Society of Medicine
71
8
629
2012
10.1115/1.3138216
Continuing demand for this book confirms that it remains relevant over 30 years after its first publication. The fundamental explanations are largely unchanged, but in the new introduction to this second edition the authors are on hand to guide the reader through major advances of the last three decades. With an emphasis on physical explanation rather than equations, Part I clearly presents the background mechanics. The second part applies mechanical reasoning to the component parts of the circulation: blood, the heart, the systemic arteries, microcirculation, veins and the pulmonary circulation. Each section demonstrates how an understanding of basic mechanics enhances our understanding of the function of the circulation as a whole. This classic book is of value to students, researchers and practitioners in bioengineering, physiology and human and veterinary medicine, particularly those working in the cardiovascular field, and to engineers and physical scientists with multidisciplinary interests.
Buckling, wrinkling and debonding in thin film systems
IEEE International Reliability Physics Symposium Proceedings
430-439
2010
10.1109/IRPS.2010.5488790
Thin films bonded to substrates commonly occur in semiconductor dielectric stacks. In these systems, many times, the mismatch in the coefficient of thermal expansion between the films and the substrate result in significant compressive stresses during processing. These compressive stresses may lead to instabilities such as buckling or wrinkling, possibly resulting in debonding of the films. In general, at the present time, the mechanics of buckling and wrinkling leading to debonding in thin film systems are not well understood. A further significant challenge to modeling these systems is that the conditions under which the instabilities occur depend on possible plastic deformation in metal films (in turn dictated by processing temperatures) as well as the presence of geometric features such as vias in the film stack. In this paper, we review analytical derivations of conditions under which buckling and wrinkling induced debond occur in thin film systems. We describe the film interface and (where appropriate) the compliant substrate using a bi-linear Cohesive-Zone fracture model. We utilize the developed theory to estimate interfacial fracture toughness of weakly bonded thin film systems through a newly proposed non-contact, thermally driven, patterned buckling delamination test. The proposed test does not need a weakened region of the interface to initiate crack, nor does it require mechanical loading; it relies on inducing a compressive stress due to heating of the film on a thick silicon substrate. The test is demonstrated on a model system consisting of Al/Su-8/Si stack. Finally, we review wrinkling of thin film systems, and analyze the impact of pattern features on the propensity of thin films to wrinkle sooner than predicted for blanket films.
Buckling; Debond; Energy minimization; Thin film; Wrinkling
Fracture mechanics of a V-peel adhesion test - Transition from a bending plate to a stretching membrane
Journal of Adhesion
70
3-4
197-207
1999
10.1080/00218469908009555
A linear elastic solution is proposed for a "V-peel" adhesion test for a thin film adhered to a rigid substrate. The mechanical responses of a stiff plate-like coating under pure bending, a semi-flexible film under mixed bending and stretching, and a flexible membrane-like film under pure stretching are discussed. For delamination to occur, the mechanical energy release rate is shown to be G = chi(Fw(0)/2bl) with chi a numerical constant varying from 3/2 for a plate-like disc to 3/4 for a thin flexible membrane.
adhesion; delamination; pull-off experiment; thin film; v-peel test
Statistical mechanics of complex networks
Reviews of Modern Physics
74
78
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Effects of Delamination and Ply Fiber Waviness on Effective Axial and Bending Stiffnesses in Composite Laminates
Composite Structures
30
3
105-111
1992
Doi 10.1016/0263-8223(94)00044-1
An analytical method based upon a sublaminate modeling approach was developed to quantify the loss of the effective axial and bending stiffnesses due to defects in laminates. Defects considered were single and multiple delaminations as well as ply fiber waviness. Laminates with (45 degrees, -45 degrees, 0 degrees, 90 degrees, 0 degrees, 90 degrees)(s) layup of AS4/35016 graphite/epoxy were used to investigate the stiffness loss due to defects at various interfaces and with various percentages of overlap in the multiple delaminations. It was found that the reductions of the stiffness in a given direction is more pronounced if the thinner sublaminate of the delaminated laminate contains a ply which contributes more stiffness in that direction. For multiple delaminations, reduction of stiffness increases as the overlap percentage of two delaminations decreases. The loss of axial and bending stiffness is significant if a ply contributing more stiffness in the laminate contains a fiber waviness.
Free vibration of antisymmetric angle-ply-laminated plates including transverse shear deformation: Spline method
International Journal of Mechanical Sciences
50
10-11
1476-1485
2008
10.1016/j.ijmecsci.2008.08.009
A free vibration study of antisymmetric angle-ply composite plates including shear deformation and rotatory inertia using the point collocation method and applying spline function approximations is presented. The equations of motion for the plate are derived using the theory of Yang, Norris and Stavsky. The solution is assumed in a separable form to obtain a system of coupled differential equations in displacement and rotational functions and these functions were approximated by Bickley-type splines of order three. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibrations of two- and four-layered plates, made up of several types of layer materials and subjected to two types of boundary conditions are considered. Parametric studies were made of the variation of frequency parameters with respect to the aspect ratio, side-to-thickness ratio and ply angle. The numerical results are presented through diagrams and, in some cases, are compared with results obtained by FEM.
Antisymmetric angle ply; Free vibration; Laminated plates; Shear deformation; Spline method
Three-dimensional piezoelasticity solution for dynamics of cross-ply cylindrical shells integrated with piezoelectric fiber reinforced composite actuators and sensors
Composite Structures
92
10
2431-2444
2010
10.1016/j.compstruct.2010.02.016
A benchmark three-dimensional (3D) exact piezoelasticity solution is presented for free vibration and steady state forced response of simply supported smart cross-ply circular cylindrical shells of revolutions and panels integrated with surface-bonded or embedded monolithic piezoelectric or piezoelectric fiber reinforced composite (PFRC) layers. The effective properties of PFRC laminas for the 3D case are obtained based on a fully coupled iso-field model. The governing partial differential equations are reduced to ordinary differential equations in the thickness coordinate by expanding all entities for each layer in double Fourier series in span coordinates, which identically satisfy the boundary conditions at the simply-supported ends. These equations with variable coefficients are solved using the modified Frobenius method, wherein the solution is constructed as a product of an exponential function and a power series. The unknown constants of the general solution are finally obtained by employing the transfer matrix method across the layers. Results for natural frequencies and the forced response are presented for single layer piezoelectric and multilayered hybrid composite and sandwich shells of revolution and shell panels integrated with monolithic piezoelectric and PFRC actuator/sensor layers. The present benchmark solution would help assess 2D shell theories for dynamic response of hybrid cylindrical shells. © 2010 Elsevier Ltd.
Cross-ply; Cylindrical shell; Dynamic response; Exact solution; Micromechanics; Piezoelasticity
Mechanics and Physics of Porous Solids
Mechanics and Physics of Porous Solids
297
2010
10.1002/9780470710388
Mechanics and Physics of Porous Solids addresses the mechanics and physics of deformable porous materials whose porous space is filled by one or several fluid mixtures interacting with the solid matrix. Coussy uses the language of thermodynamics to frame the discussion of this topic and bridge the gap between physicists and engineers, and organises the material in such a way that individual phases are explored, followed by coupled problems of increasing complexity. This structure allows the reader to build a solid understanding of the physical processes occurring in the fluids and then porous solids. Mechanics and Physics of Porous Solids offers a critical reference on the physics of multiphase porous materials - key reading for engineers and researchers in structural and material engineering, concrete, wood and materials science, rock and soil mechanics, mining and oil prospecting, biomechanics. © 2010 John Wiley & Sons, Ltd.
Short-term plyometric training improves running economy in highly trained middle and long distance runners.
Journal of strength and conditioning research
20
4
947-54
2006
10.1519/R-18235.1
Fifteen highly trained distance runners VO(2)max 71.1 +/- 6.0 ml.min(-1).kg(-1), mean +/- SD) were randomly assigned to a plyometric training (PLY; n = 7) or control (CON; n = 8) group. In addition to their normal training, the PLY group undertook 3 x 30 minutes PLY sessions per week for 9 weeks. Running economy (RE) was assessed during 3 x 4 minute treadmill runs (14, 16, and 18 km.h(-1)), followed by an incremental test to measure VO(2)max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km.h(-1) (4.1%, p = 0.02), but not at 14 or 16 km.h(-1). This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p = 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p = 0.09), and a lower VO(2)-speed slope (14%, p = 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or VO(2)max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics.
Adult; Analysis of Variance; Humans; Lactates; Lactates: blood; Male; Muscle Strength; Muscle Strength: physiology; Oxygen Consumption; Oxygen Consumption: physiology; Physical Education and Training; Physical Education and Training: methods; Physical Endurance; Physical Endurance: physiology; Running; Running: physiology
In-situ and elementally resolved determination of the thickness uniformity of multi-ply films by confocal micro XRF.
Applied radiation and isotopes : including data, instrumentation and methods for use in agriculture, industry and medicine
90
84-8
2014
10.1016/j.apradiso.2014.03.019
Confocal micro X-ray fluorescence (CM-XRF) with quasi-monochromatic excitation based on polycapillary X-ray optics was used to measure the thickness of multi-ply films. The relative errors of measuring an Fe film with a thickness of 16.3 μm and a Cu film with a thickness of 24.5 μm were 7.3% and 0.4%, respectively. The non-destructive and in-situ measurement of the thickness and uniformity of multi-ply films of Cu, Fe and Ni on a silicon surface was performed. CM-XRF was convenient in in-situ and elementally resolved analysis of the thickness of multi-ply films without a cumbersome theoretical correction model.
confocal micro x-ray fl; Confocal micro X-ray fluorescence; in-situ and elementally resolved; In-situ and elementally resolved measurement of th; polycapillary x-ray optics; Polycapillary X-ray optics; uorescence
Mechanics of crural fascia: From anatomy to constitutive modelling
Surgical and Radiologic Anatomy
31
7
523-529
2009
10.1007/s00276-009-0474-2
Ten dissections of inferior limbs and histological studies were performed to describe the structural conformation of the muscular fascia of the leg (crural fascia) and to propose a constitutive model to be adopted for the analysis of its biomechanical behaviour. The crural fascia had a mean thickness of 924 microm and was composed of three layers (mean thickness 277.6 microm) of parallel, collagen fibre bundles separated by a thin layer of loose connective tissue (mean thickness 43 microm). Only a few elastic fibres were highlighted. The disposition of the collagen fibres gives the crural fascia anisotropic characteristics. In addition, their crimped conformation is the cause of the non-linear elastic behaviour of the tissue. Both these aspects are included in the constitutive model. The constitutive modelling of the crural fascia represents a useful tool to rationally interpret the correlation between functional behaviour and structural conformation.
Biomechanics; Collagen; Connective tissue; Fascia; Structural models
Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime
Gravitation and Quantizations: Proceedings of the 1992 Les Houches Summer School
152
1995
These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does not require either a preferred notion of time or a definition of measurement. The "post-Everett" quantum mechanics of closed systems is reviewed. Generalized quantum theories are defined by three elements (1) the set of fine-grained histories of the closed system which are its most refined possible description, (2) the allowed coarse grainings which are partitions of the fine-grained histories into classes, and (3) a decoherence functional which measures interference between coarse grained histories. Probabilities are assigned to sets of alternative coarse-grained histories that decohere as a consequence of the closed system's dynamics and initial condition. Generalized sum-over histories quantum theories are constructed for non-relativistic quantum mechanics, abelian gauge theories, a single relativistic world line, and for general relativity. For relativity the fine-grained histories are four-metrics and matter fields. Coarse grainings are four-dimensional diffeomorphism invariant partitions of these. The decoherence function is expressed in sum-over-histories form. The quantum mechanics of spacetime is thus expressed in fully spacetime form. The coarse-grainings are most general notion of alternative for quantum theory expressible in spacetime terms. Hamiltonian quantum mechanics of matter fields with its notion of unitarily evolving state on a spacelike surface is recovered as an approximation to this generalized quantum mechanics appropriate for those initial conditions and coarse-grainings such that spacetime geometry
Mechanics of fish skin: A computational approach for bio-inspired flexible composites
International Journal of Solids and Structures
51
1
274-283
2014
10.1016/j.ijsolstr.2013.10.001
Natural materials and structures are increasingly becoming a source of inspiration for the design novel of engineering systems. In this context, the structure of fish skin, made of an intricate arrangement of flexible plates growing out of the dermis of a majority of fish, can be of particular interest for materials such as protective layers or flexible electronics. To better understand the mechanics of these composite shells, we introduce here a general computational framework that aims at establishing a relationship between their structure and their overall mechanical response. Taking advantage of the periodicity of the scale arrangement, it is shown that a representative periodic cell can be introduced as the basic element to carry out a homogenization procedure based on the Hill-Mendel condition. The proposed procedure is applied to the specific case of the fish skin structure of the Morone saxatilis, using a computational finite element approach. Our numerical study shows that fish skin possesses a highly anisotropic response, with a softer bending stiffness in the longitudinal direction of the fish. This softer response arises from significant scale rotations during bending, which induce a stiffening of the response under large bending curvature. Interestingly, this mechanism can be suppressed or magnified by tuning the rotational stiffness of the scale-dermis attachment but is not activated in the lateral direction. These results are not only valuable to the engineering design of flexible and protective shells, but also have implications on the mechanics of fish swimming. ?? 2013 Elsevier Ltd. All rights reserved.
Bio-inspired membranes; Biomaterials; Computational homogenization; Thin shells
Interaction between optical fibre sensors and matrix cracks in cross-ply GFRP laminates. Part 2: Crack detection
Composites Science and Technology
66
2367-2378
2006
10.1016/j.compscitech.2005.10.021
Polarimetric optical fibre sensors have been embedded within the 0?? ply and close to the 0??/90?? interface of transparent cross-ply GFRP coupons. The coupons have been subjected to an increasing quasi-static load so that transverse ply cracks initiate and propagate across the coupon. Crack accumulation has been monitored using the optical output signal from the polarimetric sensor, strain measurements from a long gauge-length extensometer, load recordings during the test and by video recording of crack development. These combined observations have enabled a direct correlation to be made between matrix crack growth past the sensor and a step-change in the sensor response. The use of band-pass FFT filtering has demonstrated that such cracks could be detected in real time. ?? 2005 Elsevier Ltd. All rights reserved.
A. Smart materials; B. Matrix cracking
Negative through-the-thickness Poisson’s ratio of elastic-viscoplastic angle-ply carbon fiber-reinforced plastic laminates: homogenization analysis
International Journal of Plasticity
63
152-169
2014
10.1016/j.ijplas.2014.05.007
Negative through-the-thickness Poisson’s ratios are investigated macroscopically and microscopically in the elastic-viscoplastic behavior of angle-ply carbon fiber-reinforced plastic (CFRP) laminates. For this purpose, an analysis method is proposed based on a homogenization theory for nonlinear time-dependent composites with point-symmetric internal structures. This method is able to efficiently analyze both the macroscopic and microscopic elastic-viscoplastic properties of angle-ply CFRP laminates fully modeled with microstructures consisting of fibers and a matrix. Using the proposed method, the elastic-viscoplastic analysis of angle-ply carbon fiber/epoxy laminates with various laminate configurations is performed to investigate their Poisson’s ratios in the viscoplastic region. It is revealed that, for a range of laminate configurations, the through-the-thickness Poisson’s ratios exhibit negative values which become increasingly negative as the viscoplastic deformation progresses in the laminates. The effect of strain rate on this increasing negativity is also demonstrated, and microscopic mechanisms are investigated to explain this trend. It is further shown that the increasing negativity significantly affects microscopic interlaminar stress distributions.
CFRP; Composite; Homogenization; Negative Poisson’s ratio; Viscoplasticity
A fibre direction compressive failure criterion for long fibre laminates at ply scale, including stacking sequence and laminate thickness effects
Composite Structures
94
12
3799-3806
2012
10.1016/j.compstruct.2012.06.013
Long fibre laminate compressive failure is due to a microbuckling instability which leads to a kink band and a brittle failure of the fibres. This failure mechanism is well known, but more or less pertinently explained in the literature. Some references also showed that local microbuckling instability depends on parameters that belong to the scale of the elementary ply, like thickness and corresponding lay-up. The compressive strength of the unidirectional ply is therefore no more an intrinsic material property, but results from a structural effect of the design. In this paper, the so-called " structure effect" is included in a simple way as an analytical formula in the phenomenological compressive failure criterion which was initially presented by Budiansky and Fleck works. The criterion presented is expressed analytically for unidirectional composite and stands for the local compressive failure strength at ply scale in fibres direction. ?? 2012 Elsevier Ltd.
Compressive strength; Laminates; Microbuckling; Structural effect
Statistical mechanics: Principles and selected applications
Journal of Chemical Education
364
1956
10.1016/0016-0032(57)90954-7
Standard text opens with clear, concise chapters on classical statistical mechanics, quantum statistical mechanics, and the relation of statistical mechanics to thermodynamics. Further topics cover fluctuations, the theory of imperfect gases and condensation, distribution functions and the liquid state, nearest neighbor (Ising) lattice statistics, and more.
Chemo-mechanical interactions between adsorbed molecules and thin elastic films
Journal of the Mechanics and Physics of Solids
53
9
2119-2140
2005
10.1016/j.jmps.2005.03.006
A general mechanics framework is presented to describe the interaction of molecular groups adsorbed on deformable thin films. Equations describing film deformation are expressed in terms of the pair potential that governs the interaction between adsorbed groups and large-deflection deformation descriptions. We illustrate that the pair potential can be used to define two-dimensional constitutive parameters for the adsorbed groups that describe their energetic contribution during arbitrary deformations. The framework is applicable to a wide range of interactions, including electrochemical interactions between a solution and film surface, interactions between neighboring adsorbed biopolymers and interactions between living cells. Key dimensionless parameters involving molecular interaction, surface coverage, film dimensions, and elastic properties are highlighted, and simplified governing equations for small deflections are identified. Solutions are presented that describe the influence of adsorbed groups on bending of cantilevers, pinned films and built-in (clamped) films. For clamped films, the critical molecular interaction parameters required to induce buckling are identified, and post-buckling behavior discussed in terms of the implications for making biological sensors. ?? 2005 Elsevier Ltd. All rights reserved.
Adsorption; Buckling; Films; Surface energy
Essential work of fracture compared to fracture mechanics-towards a thickness independent plane stress toughness
Engineering Fracture Mechanics
69
617-631
2002
10.1016/S0013-7944(01)00099-6
The essential work of fracture (EWF) and the J-integral methods were applied in a study of the effect of the thickness on the cracking resistance of thin plates. The paper discusses two themes: (1) the relationships between the two methods or concepts is elucidated, and (2) a new, thickness independent plane stress toughness parameter is proposed. For that purpose, cracked aluminium 6082O thin plates of 1-6 mm thickness were tested in tension until final separation. The EWF, we, and the J-integral at cracking initiation, Ji, increase identically with thickness except at larger thickness for which the increase of Ji levels off. Ji reaches a maximum for 5-6 mm thickness whereas we keeps increasing linearly with thickness. This difference is related to the more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation. A linear regression on the fracture toughness/thickness curve allows partitioning the two contributions of the work of fracture: the plastic work per unit area for crack tip necking and a plane stress work per unit area for material separation. The pertinence of this new measure of the pure plane stress cracking resistance is critically discussed based on a micromechanical model for ductile fracture. The micromechanical void growth model incorporates void shape effects, which is essential in the low stress triaxiality regime. ?? 2002 Elsevier Science Ltd. All rights reserved.
Bohm's Alternative to Quantum Mechanics
Scientific American
270
5
58-67
1994
10.1038/scientificamerican0594-58
This theory, ignored for most of the past four decades, challenges the probabilistic, subjectivist picture of reality implicit in the standard formulation of quantum mechanics
Non-local solutions to direct and inverse problems in mechanics: A fractional calculus approach
Conference Proceedings of the Society for Experimental Mechanics Series
3
267-274
2011
In this paper we present a new non-local model of continuum mechanics based on fractional calculus. The model encompasses in a single unified framework both classical continuum mechanics and non-local theories for continua with discontinuities and long range forces. Our theoretical framework can be used to solve both direct and inverse problems of importance in practical applications. We present results to two direct mechanical problems: (1) the deformation of an infinite bar subjected to a self-equilibrated load distribution, and (2) the propagation of longitudinal waves in a thin finite bar. We also show results to the inverse problem of magnetic resonance elastography using our proposed model.
Combining colloidal probe atomic force and reflection interference contrast microscopy to study the compressive mechanics of hyaluronan brushes
Langmuir
28
3206-3216
2012
10.1021/la204602n
We describe a method that combines colloidal probe atomic force microscopy (AFM) and reflection interference contrast microscopy (RICM) to characterize the mechanical properties of thin and solvated polymer films. When analyzing polymer films, a fundamental problem in colloidal probe AFM experiments is to determine the distance at closest approach between the probe and the substrate on which the film is deposited. By combining AFM and RICM in situ, forces and absolute distances can be measured simultaneously. Using the combined setup, we quantify the compressive mechanics of films of the polysaccharide hyaluronan that is end-grafted to a supported lipid bilayer. The experimental data, and comparison with polymer theory, show that hyaluronan films are well-described as elastic, very soft and highly solvated polymer brushes. The data on these well-defined films should be a useful reference for the investigation of the more complex hyaluronan-rich coats that surround many living cells.
Buckling of a stiff thin film on a pre-strained bi-layer substrate
International Journal of Solids and Structures
51
18
3113-3118
2014
10.1016/j.ijsolstr.2014.05.012
Controlled buckling can impart stretchable mechanics to brittle materials when integrated as thin films on soft, elastomeric substrates. Typical elastomers are permeable to fluids, however, and therefor unable to provide robust barriers to entry of water, for instance, into devices built with the supported thin films. In addition, the mechanical strength of a system dominated by a soft substrate is often unsatisfactory for realistic applications. We show that introduction of a bi-layer substrate yields a robust, high strength system that maintains stretchable characteristics, with a soft layer on top of a relatively stiff layer in the substrate. As a mechanical protection, a soft encapsulation layer can be used on top of the device and the stretchability of the encapsulated system is smaller than that of the system without encapsulation. A simple, analytic model, validated by numerical analysis and FEA, is established for stiff thin films on a bi-layer substrate, and is useful to the design of stretchable systems. © 2014 Elsevier Ltd. All rights reserved.
Bi-layer substrate; Buckling analysis; Pre-strain; Stretchable electronics
An experimental investigation of the biaxial strength of IM6/3501-6 carbon/epoxy cross-ply laminates using cruciform specimens
Composites - Part A: Applied Science and Manufacturing
33
829-839
2002
10.1016/S1359-835X(01)00142-7
Several variations of a thickness-tapered cruciform specimen have previously been used to experimentally determine the biaxial strength of an AS4/3501-6 carbon/epoxy cross-ply laminate. The present work represents a follow-up study of the original specimen design, and incorporates numerous specimen improvements made in an attempt to generate more accurate biaxial results. A total of 52 tests were performed at numerous biaxial stress ratios, utilizing six different specimen configurations. The experimental data generated in the present study for all specimen geometries, as well as a complete biaxial failure envelope in ??1-??2 stress space for this laminate configuration, are presented. A desirable failure mode in the gage section of the specimen was achieved for all specimens tested in the present study, indicating that accurate biaxial stress states were being generated at ultimate specimen failure. The ability of the thickness-tapered cruciform specimen to determine the biaxial strength of composite materials at any stress ratio has been demonstrated. ?? 2002 Published by Elsevier Science Ltd.
A. Laminates; B. Strength; Cruciform specimens; D. Mechanical testing
Investigation of the effect of the Coriolis force on a thin fluid film on a rotating disk
International Journal of Non-Linear Mechanics
33
6
1069-1088
1998
http://dx.doi.org/10.1016/S0020-7462(97)00071-1
The effect of the Coriolis force on the evolution of a thin film of Newtonian fluid on a rotating disk is investigated. The thin-film approximation is made in which inertia terms in the Navier–Stokes equation are neglected. This requires that the thickness of the thin film be less than the thickness of the Ekman boundary layer in a rotating fluid of the same kinematic viscosity. A new first-order quasi-linear partial differential equation for the thickness of the thin film, which describes viscous, centrifugal and Coriolis-force effects, is derived. It extends an equation due to Emslie et al. [J. Appl. Phys. 29, 858 (1958)] which was obtained neglecting the Coriolis force. The problem is formulated as a Cauchy initial-value problem. As time increases the surface profile flattens and, if the initial profile is sufficiently negative, it develops a breaking wave. Numerical solutions of the new equation, obtained by integrating along its characteristic curves, are compared with analytical solutions of the equation of Emslie et al. to determine the effect of the Coriolis force on the surface flattening, the wave breaking and the streamlines when inertia terms are neglected.
breaking surface profile; characteristic curves; Coriolis force; rotating disk; streamlines; thin viscous fluid film
Constrained sintering of alumina thin films: Comparison between experiment and modeling
Journal of the American Ceramic Society
90
6
1733-1737
2007
10.1111/j.1551-2916.2007.01650.x
Alumina thin films deposited by dip coating on alumina substrates were sintered between 1150 degrees and 1350 degrees C. A new measuring system using a rocking arm as a mechanical amplifier allows in situ measurement of the shrinkage of the film. Comparison of experimental densification behavior with the predictions of the isotropic continuum mechanics model (using values of constitutive parameters determined by sinter forging) highlights the inadequacy of the isotropic models. These results, together with other published evidence, provide justification to consider anisotropic models.
Bulge testing of single and dual layer thin films
Proceedings of SPIE - The International Society for Optical Engineering
4344
673-681
2001
10.1117/12.436794
The bulge testing technique determines the mechanical properties of solid thin films by measuring the deformation that forms in response to the application of a controlled differential pressure to a thin film window. By comparing the pressure-displacement relation with a mechanical model, the elastic modulus and residual stress in the film can be measured. While the bulge testing technique can be quite effective, the technique is not routinely used because of difficulties that often arise with using this technique. The difficulties include specimen preparation and mounting, automated bulge height measurement and the correlation of bulge deformation with the mechanical properties of the thin film. This paper describes developments in the bulge testing technique that alleviate many of these difficulties, as well as presenting results from the testing of single and dual layer thin films. Single film tests were conducted on samples of B-doped-Si, SiC, and diamond-like carbon. A total of 135 windows with three different window aspect ratios and two different thicknesses were investigated. In a preliminary study to determine the feasibility of extending the technique to the testing of multilayer films, the mechanics of a dual layer system were measured. The dual layer system was an Al layer on top of B-doped-Si. The results from the single film test were that the elastic moduli of the B-doped-Si were close to nominal bulk values and the diamond-like carbon was about half that of diamond. The SiC elastic moduli measurements were inconclusive because of the large prestress. Elastic moduli measurements from nanoindentation were about 50% higher. It should be noted that neither the variation of the aspect ratio nor the variation of the film thickness led to different results. The measured prestresses agreed quite well with wafer curvature measurement. The dual-layer measurements yielded values for the elastic modulus of thin film Al that were within 5% of the nominal bulk values.
Aspect ratio; Automated; Bulge tester; Bulge testing; Deformation; Diamond like carbon films; Dual layer; Elastic moduli; Residual stresses; Silicon carbide; Thin film; Thin films
Numerical Modeling of Friction Effects on the Ballistic Impact Response of Single-Ply Tri-Axial Braided Fabric
Civil Engineering
1
29-38
2003
It has been shown by experiments that frictional effects play an important role in the energy absorption of fabrics subjected to ballistic impact. However, the specific role of friction is not well understood and established. In this paper, a detailed finite element model was developed, using LS-DYNA®, to parametrically study the frictional effects during the ballistic impact of a square patch of single-ply 2D tri-axially braided fabric. The individual yarns (bias and axial direction) in the fabric were modeled discretely and considered as a continuum by considering the measured properties of the braided fabric (weave architecture, crimp, yarn cross-section etc.). The friction between yarns at their crossovers and the friction between projectile and fabric were taken into account. The damage of a single yarn model were compared with the experimental data and included in the material model of the fabric. It was shown that the friction contributes to decreasing of the residual velocity of the projectile more quickly than the one without friction. Thus the fabric energy absorption capacity can be increased by 18%. The results from the simulation also indicated that the frictional sliding energy starts to play more important role when the fabric begins to get damage and more movements between axial yarns and braider yarns are involved.
DQM free vibration analysis of moderately thick symmetric laminated plates with elastically restrained edges
Composite Structures
74
1
115-125
2006
10.1016/j.compstruct.2006.02.014
The application of differential quadrature method will be shown for free vibration analysis of moderately thick composite plates with edges elastically restrained against translation and rotation. The governing equations employed are based on the first order shear deformation theory including the effects of rotary inertia. Different combinations of constraints at edges are tested, which includes plates with at least a corner without a rigid support. Angle-ply and cross-ply laminates with different aspect ratios, thickness-to-length ratios are examined. Comparisons are made with results for thin as well as moderately thick angle-ply and cross-ply laminated plates. Highly accurate solutions can be achieved with only a few grid points.
DQM; Elastic supports; Laminates; Vibration
A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part I: Material constitutive model
Composites Science and Technology
71
5
742-749
2011
10.1016/j.compscitech.2011.01.023
A life prediction algorithm and its implementation for a thick-shell finite element formulation for GFRP composites under constant or variable amplitude loading is introduced in this work. It is a distributed damage model in the sense that constitutive material response is defined in terms of meso-mechanics for the unidirectional ply. The algorithm modules for non-linear material behaviour, pseudo-static loading-unloading-reloading response, Constant Life Diagrams and strength and stiffness degradation due to cyclic loading were implemented on a robust and comprehensive experimental database for a unidirectional glass/epoxy ply. The model, based on property definition in the principal coordinate system of the constitutive ply, can be used, besides life prediction, to assess strength and stiffness of any multidirectional laminate after arbitrary, constant or variable amplitude multi-axial cyclic loading. Numerical predictions were corroborated satisfactorily by test data from constant amplitude fatigue of glass/epoxy laminates of various stacking sequences. © 2011 Elsevier Ltd.
A. Polymer-matrix composites (PMCs); B. Fatigue; C. Damage mechanics; C. Finite element analysis (FEA); D. Life prediction
Graduate Quantum Mechanics Reform
American Journal of Physics
77
308-319
2009
10.1119/1.3079689
We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.
Vascular Mechanics and Pathology
Springer
520
2007
10.1007/978-0-387-68234-1
Opening new doors for interdisciplinary research, Vascular Mechanics and Pathology establishes a correlation between vascular mechanics and pathology that could lead to the reduction of vascular diseases, as well as the development of new treatments. Vascular Mechanics and Pathology focuses on the artery and arterial diseases. As the fundamental functions of the artery are to serve as a conduit of blood flow and as a container of blood pressure, Vascular Mechanics and Pathology describes both the general principles and the occurrence of stress concentration at the pressure vessel junctions and examines the role of beta-blockers in the reduction of atherosclerosis and related complications. This cutting-edge work presents the use of veins as arterial grafts and discusses the role of vein valves in graft stenosis. Vascular Mechanics and Pathology illustrates aneurysm formation, growth, and rupture, using pressure vessel principles. This new work details the investigation of, amongst other topics, aortic dissection, showing for the first time that the aortic root mechanics plays a vital role in the development of this pathology.
Mechanics of Distributed Cracking
Applied Mechanics Reviews
39
5
675
1986
10.1115/1.3143724
This paper reviews some interesting recent results on mesh sensitivity and strain localization instability, nonlocal and micromechanics models, and the size effect in failure due to distributed cracking.
Mechanics in the embryo
Nature
504
223-225
2013
10.1038/504223a
Mechanical stresses that are intrinsic to the early shape-forming movementsof embryonic tissues have now been shown to play essential and evolutionarily conserved parts in cell-fate specification.
Thin layer flow and film decay modeling for grease lubricated rolling bearings
Tribology International
47
175-187
2012
10.1016/j.triboint.2011.10.019
A model is presented to predict lubricant supply layer changes on tracks in rolling bearings due to centrifugal forces and elastohydrodynamic contact pressure. Experimental validation is shown for centrifugal force driven free surface flow, and layer thickness (film thickness) decay in single elastohydrodynamically lubricated contacts. The model allows prediction of lubricant migratory trends in bearings. The pressure ejection driven layer/film thickness decay can be predicted without the need to solve rolling element-raceway starved elastohydrodynamic contact problems for millions of overrollings. The model provides worst case estimates of a required (local) resupply interval, and contributes to improved lubricant related bearing life predictions. ?? 2011 Elsevier Ltd. All rights reserved.
Elastohydrodynamic lubrication; Fluid mechanics; Rolling bearing; Thin film
Multi-scale modeling of the progressive damage in cross-ply laminates under thermal and mechanical loading
IOP Conference Series: Materials Science and Engineering
40
1
012029
2012
10.1088/1757-899X/40/1/012029
The progressive damage in cross-ply laminates was modeled by discrete element method (DEM). A particle radius expansion method was used to account for thermal loading applied to cross-ply laminates in which nominal fibers were introduced in the 0° plies so as to achieve the anisotropic thermal expansion behaviors. A series of convergence and validation tests of both mechanical and thermal properties of the 0° plies with nominal fibers have been carried out in order to validate the method. The DEM results of interfacial stress distribution of cross-ply laminates under pure thermal loading and under coupled thermal/mechanical loading were compared with other theoretical predictions. Microstructure of 90° plies was also studied by the DEM model. Transverse cracking which was formed by the coalescence of micro cracks in matrix and at fiber/matrix interface has been observed in the modeling results together with the ply-ply delaminations. It was found that the DEM model can predict not only the stress distribution but also the progressive damage initialized from the constituent failure due to its multi scale nature.
Effects of thermal cycling on damage progress in interlaminar-toughened CFRP cross-ply laminates
Journal of Reinforced Plastics and Composites
18
1208
1999
10.1177/073168449901801304
Effects of thermal cycling on transverse cracking behavior in interlaminar-toughened CFRP cross-ply laminates are investigated. Material systems used are T800H/3631 carbon/epoxy composite with FM300 epoxy resin film between 0/90 interface (T800H/3631-FM300) and T800H/3900-2 with polyamide particle-dispersed layers at every ply interface. The laminate configurations are cross-ply (0/90n/0) where n = 4, 8 and 12. The laminates are thermally cycled between -70C and 150 up to 100 cycles. No damage is observed by the thermal cycles. After thermal cycling, the laminates are subjected to static tensile loading at room temperature. The transverse crack density in 90 ply is measured as a function of the laminate strain by using the replica technique. It is found that transverse crack behavior depends on the number of thermal cycles. Transverse crack density increases as the number of thermal cycles increases. Change in thermal residual strain in 90 ply is measured as a function of the number of thermal cycles by measuring the deformation of an unsymmetric laminate. The effects of thermal cycles on the transverse cracking are characterized by a micromechanical model considering the thermal residual stresses.
New aspects of magnetic properties in a transverse Ising thin film
Physica a-Statistical Mechanics and Its Applications
328
1-2
174-184
2003
10.1016/S0378-4371(03)00543-0
The magnetic properties of a transverse Ising thin film are investigated by the use of the two theoretical frameworks, namely the standard mean-field theory and the effective field theory better than the mean-field theory. Some new aspects of the magnetic properties have been clarified firstly by including the modification of both surface exchange interaction and surface transverse field. The phase diagram, magnetization and initial susceptibility of a thin film can exhibit many characteristic behaviors, depending on the ratio between the surface transverse field and the bulk one. (C) 2003 Elsevier B.V. All rights reserved.
ferroelectric-films; ferroelectric thin film; ferromagnetic film; field; model; phase diagram; phase-diagrams; transitions; transverse ising model
Hamiltonian Mechanics with Geometric Calculus
Spinors, Twistors, Clifford Algebras and Quantum Deformations
1-11
1993
10.1007/978-94-011-1719-7
Hamiltonian mechanics is given an invariant formulation in terms of Geometric Calculus, a general differential and integral calculus with the structure of Clifford algebra. Advantages over formulations in terms of differential forms are explained.
Perspectives in mechanics of heterogeneous solids
Acta Mechanica Solida Sinica
24
1
1-26
2011
10.1016/S0894-9166(11)60007-4
The Micro- and Nano-mechanics Working Group of the Chinese Society of Theoretical and Applied Mechanics organized a forum to discuss the perspectives, trends, and directions in mechanics of heterogeneous materials in January 2010. The international journal, Acta Mechanica Solida Sinica, is devoted to all fields of solid mechanics and relevant disciplines in science, technology, and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. On the occasion of the 30th anniversary of Acta Mechanica Solida Sinica, its editor-in-chief, Professor Q.S. Zheng invited some of the forum participants to review the state-of-the-art of mechanics of heterogeneous solids, with a particular emphasis on the recent research development results of Chinese scientists. Their reviews are organized into five research areas as reported in different sections of this paper. §I firstly brings in focus on micro- and nano-mechanics, with regards to several selective topics, including multiscale coupled models and computational methods, nanocrystal superlattices, surface effects, micromechanical damage mechanics, and microstructural evolution of metals and shape memory alloys. §II shows discussions on multifield coupled mechanical phenomena, e.g., multi-fields actuations of liquid crystal polymer networks, mechanical behavior of materials under radiations, and micromechanics of heterogeneous materials. In §III, we mainly address the multiscale mechanics of biological nanocomposites, biological adhesive surface mechanics, wetting and dewetting phenomena on microstructured solid surfaces. The phononic crystals and manipulation of elastic waves were elaborated in §IV. Finally, we conclude with a series of perspectives on solid mechanics. This review will set a primary goal of future science research and engineering application on solid mechanics with the effort of social and economic development. © 2011 The Chinese Society of Theoretical and Applied Mechanics.
biological materials; constitutive relation; damage and fracture; elastic wave; heterogeneous materials; micro- and nano-mechanics; multiscale mechanics; smart materials; surface effects
Cytoskeletal bundle mechanics.
Biophysical journal
94
8
2955-2964
2008
10.1529/biophysj.107.119743
The mechanical properties of cytoskeletal actin bundles play an essential role in numerous physiological processes, including hearing, fertilization, cell migration, and growth. Cells employ a multitude of actin-binding proteins to actively regulate bundle dimensions and cross-linking properties to suit biological function. The mechanical properties of actin bundles vary by orders of magnitude depending on diameter and length, cross-linking protein type and concentration, and constituent filament properties. Despite their importance to cell function, the molecular design principles responsible for this mechanical behavior remain unknown. Here, we examine the mechanics of cytoskeletal bundles using a molecular-based model that accounts for the discrete nature of constituent actin filaments and their distinct cross-linking proteins. A generic competition between filament stretching and cross-link shearing determines three markedly different regimes of mechanical response that are delineated by the relative values of two simple design parameters, revealing the universal nature of bundle-bending mechanics. In each regime, bundle-bending stiffness displays distinct scaling behavior with respect to bundle dimensions and molecular composition, as observed in reconstituted actin bundles in vitro. This mechanical behavior has direct implications on the physiological bending, buckling, and entropic stretching behavior of cytoskeletal processes, as well as reconstituted actin systems. Results are used to predict the bending regimes of various in vivo cytoskeletal bundles that are not easily accessible to experiment and to generate hypotheses regarding implications of the isolated behavior on in vivo bundle function.
Laminated Stiffened Plate-A First Ply Failure Analysis
Journal of Reinforced Plastics and Composites
18
12
1061-1076
1999
10.1177/073168449901801201
A first ply failure analysis of composite stiffened plates has been presented using the finite element method. A new scheme has been formulated to model stiffened composite plates. The plate element has been formulated using an eight noded isoparametric quadratic plate bending element. A three noded isoparametric beam element has been used to formulate the stiffener element. The stiffness matrix of the stiffener element has been developed independently and then the stiffness matrix is transferred to that of the plate element. This technique eliminates the restriction on the orientation of the stiffener within the plate element. The formulation has been validated by analysing a number of problems. The results obtained are compared with those available in published literature.
composite; Failure; finite element; first ply; stiffened plate
Prediction of Transverse Cracking and Stiffness Reduction in Cross-Ply Laminated Composites
Journal of Composite Materials
23
7
695-713
1989
10.1177/002199838902300704
A modified shear lag analysis, taking into account the concept of in terlaminar shear layer, is employed to predict the onset of a transverse crack and multiple transverse cracking. In this analysis, the boundary conditions are satisfied for any trans verse crack spacing. The crack multiplication is simulated by adjusting the crack spacing. Based on this analysis the laminate stiffness reduction due to the multiple transverse crack ing is also evaluated in cross-ply laminated composites. The energy concept is utilized to assess the effect of 90{degrees} layer thickness and the constraining effect of 0{degrees} layer on the trans verse cracking behavior of cross-ply laminated composites. Predictions of the onset of a transverse crack and stiffness reduction due to transverse cracks are compared with those of previous analyses and existing experimental data. The present analysis is simple, yet its results show reasonable agreement with experimental results.
Fracture Mechanics of Thin, Cracked Plates Under Tension, Bending and Out-of-Plane Shear Loading
Growth Lakeland
1999
Cracks in the skin of aircraft fuselages or other shell structures can be subjected to very complex stress states, resulting in mixed-mode fracture conditions. For example, a crack running along a stringer in a pressurized fuselage will be subject to the usual in-plane tension stresses (Mode-I) along with out-of-plane tearing stresses (Mode-III like). Crack growth and initiation in this case is correlated not only with the tensile or Mode-I stress intensity factor, K(sub I), but depends on a combination of parameters and on the history of crack growth. The stresses at the tip of a crack in a plate or shell are typically described in terms of either the small deflection Kirchhoff plate theory. However, real applications involve large deflections. We show, using the von-Karman theory, that the crack tip stress field derived on the basis of the small deflection theory is still valid for large deflections. We then give examples demonstrating the exact calculation of energy release rates and stress intensity factors for cracked plates loaded to large deflections. The crack tip fields calculated using the plate theories are an approximation to the actual three dimensional fields. Using three dimensional finite element analyses we have explored the relationship between the three dimensional elasticity theory and two dimensional plate theory results. The results show that for out-of-plane shear loading the three dimensional and Kirchhoff theory results coincide at distance greater than h/2 from the crack tip, where h/2 is the plate thickness. Inside this region, the distribution of stresses through the thickness can be very different from the plate theory predictions. We have also explored how the energy release rate varies as a function of crack length to plate thickness using the different theories. This is important in the implementation of fracture prediction methods using finite element analysis. Our experiments show that under certain conditions, during fatigue crack growth, the presence of out-of-plane shear loads induces a great deal of contact and friction on the crack surfaces, dramatically reducing crack growth rate. A series of experiments and a proposed computational approach for accounting for the friction is discussed.
Static and dynamic behavior of simply-supported cross-ply laminated piezoelectric cylindrical panels with imperfect bonding
Composite Structures
74
3
265-276
2006
10.1016/j.compstruct.2005.04.011
Three-dimensional state-space analysis is developed for a simply-supported, cross-ply piezoelectric laminated cylindrical panel with interlaminar bonding imperfections. To solve the state equation with variable coefficients, a layerwise method is adopted to transform it to an equation with constant coefficients within each sub-layer of sufficiently small thickness. A linear constitutive relationship, which accounts for the electric field, is adopted to model the adhesive bonding whose effect is considered by introducing interfacial transfer matrices. The problems of bending and free vibration are considered with numerical results presented and discussed.
Bonding imperfection; Cross-ply laminate; Layerwise method; Piezoelectric cylindrical panel; State-space analysis
Hygrothermal effects on the linear and nonlinear analysis of symmetric angle-ply laminated plates
Composite Structures
21
1
41-48
1992
http://dx.doi.org/10.1016/0263-8223(92)90078-Q
The influence of hygrothermal effects on the cylindrical bending of pinned-pinned, clamped-pinned and clamped-clamped support symmetric angle-ply laminated plates subjected to an uniform transverse load is evaluated via classical laminated plate theory and Von Karman's large deflection theory. It is shown that the classical laminated plate theory may not be adequate for the analysis of several composite laminates, even in the small deflection range. The influence of temperature variation, thickness, boundary conditions and the angle of the angle-ply laminates on the accuracy of the analysis is evaluated.
Size effect law and fracture mechanics of the triggering of dry snow slab avalanches
Journal of Geophysical Research
108
1-11
2003
10.1029/2002JB001884
[1] A size effect law for fracture triggering in dry snow slabs of high enough length-to-thickness ratio is formulated, based on simplified one-dimensional analysis by equivalent linear elastic fracture mechanics. Viscoelastic effects during fracture are neglected. The derived law, which is analogous to Baz. ant's energetic size effect law developed for concrete and later for sea ice, fiber composites, rocks, and ceramics, is shown to agree with two-dimensional finite element analysis of mode II cohesive crack model with a finite residual shear stress. Fitting the proposed size effect law to fracture data for various slab thicknesses permits identifying the material fracture parameters. The value of preexisting shear stress in a thin weak zone of finite length is shown to have significant effect. There exists a certain critical snow depth, depending on the preexisting stress value, below which the size effect disappears. Practical applications require considering that the material properties (particularly the mode II fracture toughness or fracture energy) at the snow slab base are not constant but depend strongly on the slab thickness. This means that one must distinguish the material size effect from the structural size effect, and the combined size effect law must be obtained by introducing into the structural size effect law dependence of its parameters on snow thickness. The thickness dependence of these parameters can be obtained by matching the combined law to avalanche observations. Matching Perla's field data on 116 avalanches suggests that the mode II fracture toughness is approximately proportional to 1.8 power of snow thickness.
Fluid Mechanics
Book
17
179-191
2008
10.1111/j.1549-8719.2009.00016.x.Mechanobiology
Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situationswhether in the liquid or gaseous state or bothis introduced and comprehensively covered in this widely adopted text. Fully revised and updated with the addition of a new chapter on biofluid mechanics, Fluid Mechanics, Fourth Edition is suitable for both a first or second course in fluid mechanics at the graduate or advanced undergraduate level. The leading advanced general text on fluid mechanics, Fluid Mechanics, 4e guides students from the fundamentals to the analysis and application of fluid mechanics, including compressible flow and such diverse applications as hydraulics and aerodynamics. Updates to several chapters and sections, including Boundary Layers, Turbulence, Geophysical Fluid Dynamics, Thermodynamics and Compressibility. Fully revised and updated chapter on Computational Fluid Dynamics. New chapter on Biofluid Mechanics by Professor Portonovo Ayyaswamy, the Asa Whitney Professor of Dynamical Engineering at the University of Pennsylvania. New Visual Resources appendix provides a list of fluid mechanics films available for viewing online. Additional worked-out examples and end-of-chapter problems. Updated online Solutions Manual for adopting instructors.
Interfacial fracture toughness measurement for thin film interfaces
Engineering Fracture Mechanics
71
9-10
1219-1234
2004
10.1016/S0013-7944(03)00210-8
Delamination of intrinsically or residually stressed thin films is commonly encountered in microelectronics and MEMS systems. Knowledge of the interfacial fracture toughness (Γ) is necessary to predict if delamination will occur. A new approach based on the decohesion test, called the modified decohesion test (MDT), eliminates shortcomings of current testing methods. In this approach, a highly stressed superlayer is used to drive delamination and produce any mode mix at the crack tip. Since the deformations remain elastic, a mechanics-based solution can be used to correlate test parameters to the energy release rate. Common IC fabrication techniques are used to prepare the sample and execute the test, thereby making the test compatible with current microelectronic or MEMS facilities. MDT uses the change in crack surface area to vary the available energy per unit area for crack growth and thus to bound the interfacial fracture toughness. Therefore, this technique uses a single sample to measure the interfacial fracture toughness, as opposed to the decohesion test that uses several samples to be able to bound the interfacial fracture toughness. Other modifications allow application of the method to highly chemically reactive metals and decrease the sample preparation time. Design, preparation, and execution of the MDT are discussed. Finite element model results of MDT sites are used to validate the approach. Preliminary results of the test show that for a Ti/alumina interface, at a mode mixity of −14.5°, the interfacial fracture toughness is greater than 34 J/m2 and for a Ti/Si interface, at a mode mixity of 23°, the interfacial fracture toughness is 8.9 J/m2 ⩽ Γ(23°) ⩽ 9.89 J/m2.
decohesion test; interfacial fracture toughness; mems; microelectronics; thin films
Geometrical Formulation of Quantum Mechanics
Time
456
week 4
1-41
1801
10.1007/978-1-4612-1422-9_3
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics which, although equivalent to the standard algebraic formulation, has a very different appearance. In particular, states are now represented by points of a symplectic manifold (which happens to have, in addition, a compatible Riemannian metric), observables are represented by certain real-valued functions on this space and the Schr"odinger evolution is captured by the symplectic flow generated by a Hamiltonian function. There is thus a remarkable similarity with the standard symplectic formulation of classical mechanics. Features--such as uncertainties and state vector reductions--which are specific to quantum mechanics can also be formulated geometrically but now refer to the Riemannian metric--a structure which is absent in classical mechanics. The geometrical formulation sheds considerable light on a number of issues such as the second quantization procedure, the role of coherent states in semi-classical considerations and the WKB approximation. More importantly, it suggests generalizations of quantum mechanics. The simplest among these are equivalent to the dynamical generalizations that have appeared in the literature. The geometrical reformulation provides a unified framework to discuss these and to correct a misconception. Finally, it also suggests directions in which more radical generalizations may be found.
Absolute quantum mechanics
British Journal for the Philosophy of Science
52
1
67-73
2001
10.1093/bjps/52.1.67
Whereas one can conceive of a relational classical mechanics in which absolute space and time do not play a fundamental role, quantum mechanics does not readily admit any such relational formulation.
A shear-lag analysis of transverse cracking and delamination in cross-ply carbon-fibre/epoxy composites under dry, saturated and immersed fatigue conditions
Composites Science and Technology
59
2115-2123
1999
10.1016/S0266-3538(99)00069-X
Motivated by experimental observations, the shear-lag method has been employed to model the competition between the transverse cracking and delamination modes of failure that occur in cross-ply AS4/3501-6 carbon-fibre/epoxy coupons subjected to fatigue. The results explain the extensive delaminations and reduced crack densities that arise under immersed fatigue conditions, as compared with fatigue in air.
Mechanics rules cell biology.
Sports medicine, arthroscopy, rehabilitation, therapy & technology : SMARTT
2
16
2010
10.1186/1758-2555-2-16
Cells in the musculoskeletal system are subjected to various mechanical forces in vivo. Years of research have shown that these mechanical forces, including tension and compression, greatly influence various cellular functions such as gene expression, cell proliferation and differentiation, and secretion of matrix proteins. Cells also use mechanotransduction mechanisms to convert mechanical signals into a cascade of cellular and molecular events. This mini-review provides an overview of cell mechanobiology to highlight the notion that mechanics, mainly in the form of mechanical forces, dictates cell behaviors in terms of both cellular mechanobiological responses and mechanotransduction.
Engineering Rock Mechanics: An Introduction to the Principles
Applied Mechanics Reviews
55
2
B30
2002
10.1115/1.1451165
Engineering rock mechanics is the discipline used to design structures built in rock. These structures encompass building foundations, dams, slopes, shafts, tunnels, caverns, hydroelectric schemes, mines, radioactive waste repositories and geothermal energy projects: in short, any structure built on or in a rock mass. Despite the variety of projects that use rock engineering, the principles remain the same. Engineering Rock Mechanics clearly and systematically explains the key principles behind rock engineering. The book covers the basic rock mechanics principles; how to study the interactions between these principles and a discussion on the fundamentals of excavation and support and the application of these in the design of surface and underground structures. Engineering Rock Mechanics is recommended as an across-the-board source of information for the benefit of anyone involved in rock mechanics and rock engineering.
Human actin mutations associated with hypertrophic and dilated cardiomyopathies demonstrate distinct thin filament regulatory properties in vitro
Journal of Molecular and Cellular Cardiology
48
2
286-292
2010
10.1016/j.yjmcc.2009.09.014
Two cardiomyopathic mutations were expressed in human cardiac actin, using a Baculovirus/insect cell system; E99K is associated with hypertrophic cardiomyopathy whereas R312H is associated with dilated cardiomyopathy. The hypothesis that the divergent phenotypes of these two cardiomyopathies are associated with fundamental differences in the molecular mechanics and thin filament regulation of the underlying actin mutation was tested using the in vitro motility and laser trap assays. In the presence of troponin (Tn) and tropomyosin (Tm), ??-cardiac myosin moved both E99K and R312H thin filaments at significantly (p < 0.05) slower velocities than wild type (WT) at maximal Ca++. At submaximal Ca++, R312H thin filaments demonstrated significantly increased Ca++ sensitivity (pCa50) when compared to WT. Velocity as a function of ATP concentration revealed similar ATP binding rates but slowed ADP release rates for the two actin mutants compared to WT. Single molecule laser trap experiments performed using both unregulated (i.e. actin) and regulated thin filaments in the absence of Ca++ revealed that neither actin mutation significantly affected the myosin's unitary step size (d) or duration of strong actin binding (ton) at 20????M ATP. However, the frequency of individual strong-binding events in the presence of Tn and Tm, was significantly lower for E99K than WT at comparable myosin surface concentrations. The cooperativity of a second myosin head binding to the thin filament was also impaired by E99K. In conclusion, E99K inhibits the activation of the thin filament by myosin strong-binding whereas R312H demonstrates enhanced calcium activation. ?? 2009 Elsevier Ltd. All rights reserved.
Heart failure; Laser trap; Motility assay; Single molecule biophysics
Mechanics of a Fatigue Crack Nucleation Mechanism
Journal of the Mechanics and Physics of Solids
17
511-523
1969
doi: DOI: 10.1016/0022-5096(69)90006-4
The mechanics of the build-up of large local plastic strains at the free surface of a polycrystal under fatigue loading is shown. Two closely located thin slices in a most-favourably-oriented crystal located at a free surface of the polycrystal are assumed to have an initial resolved shear stress of a few psi of opposite sign. Under cyclic loading, the two thin slices slide in opposite directions, one during the forward loading and the other during the reversed loading. Based on the dependency of slip on the resolved shear stress, the increase of local plastic strain in the slices with cycles of loading is calculated by applying the analogy between plastic strain and external force. The calculated local plastic shear strain in both slices (one positive and the other negative) reaches 100 per cent at the free surface in a few hundred cycles. These large plastic shear strains clearly cause the start of an extrusion or intrusion and the nucleation of a fatigue crack.
AP-PLY: A New Fibre Placement Architecture for Fabric Replacement
SAMPE Journal
47
2
36-45
2011
Composite laminates made with woven fabric are known to have better damage resistance characteristics than unidirectional laminates. Due to the recent development in fibre placement and tape laying machines, laminates with unidirectional plies are favoured because of the automated production process. AP-PLY combines the advantages of fabrics and unidirectional layers in an automated production process. AP-PLY is a laminate configuration obtained by placing the fibre tows in special patterns that mimic the construction of a woven layer. Any material system can be used for the construction, including glass fibre, carbon fibre, thermoset and thermoplastic resins and even dry fibre placement. No adaptations to current fibre placement machines are necessary. Tests show smaller delaminations and higher residual strength for every tested AP-PLY configuration and lay-up compared to baseline laminates with unidirectional plies. An energy dissipation redistribution is observed between fibre breakage and delaminations. Both thermoset and thermoplastic materials were tested. Possible applications include any number of the plies of wing and fuselage laminates or sandwich panel facesheets. It is also possible that entire laminate structures where the design is driven by damage tolerance can be constructed by AP-PLY. In addition, the prospect of eliminating or minimizing the use of fabric plies, which is a labour intensive process and replacing them with equivalent AP-PLY configurations, makes the present concept attractive for other applications where impact damage may not be the driver.
IMPACT
Cell mechanics: Hydraulic cracking
Nature Materials
14
3
268-269
2015
10.1038/nmat4229
Cracks in stretched epithelial tissue are caused by a build-up of hydraulic pressure beneath the cells when the tissue is unloaded.
Towards a regional approach to cell mechanics
Trends in Cell Biology
14
4
160-166
2004
10.1016/j.tcb.2004.02.003
Here we review studies of the physical, material properties of animal cells and their cytoskeleton, such as elastic stiffness and fluid viscosity, that determine how they respond to, and are shaped by, forces inside and out. Currently and historically, most such studies have reported a single value for a cell property and/or propose a single broad structural model based on nonliving materials. We believe that such physical studies would be of more interest to most cell biologists if greater emphasis were placed on the well-established regional differences within a cell and the ability of the cell to quickly change its mechanical behaviors.
A simplified approach to the damage tolerance design of asymmetric tapered laminates. Part I: Methodology development
Composites Part A: Applied Science and Manufacturing
41
10
1388-1394
2010
10.1016/j.compositesa.2010.05.009
Tapered composite laminates are susceptible to interlaminar damage in the form of delaminations growing from ply drop-off locations. This study presents an analytical method for the calculation of the energy release rates associated with interlaminar cracks emanating from the ply termination in both the laminate thick and thin sections, also accounting for the effects of the tapering angle. The proposed approach is based on modeling asymmetrically tapered composite laminates as assemblies of layered Euler-Bernoulli beam segments; these are split and reconnected through-the-thickness at the ply-drop-off location. The presence of a local resin pocket is explicitly considered in the model. Orthotropic rescaling is employed in order to take into account the material behavior through-the-thickness. This paper presents the analytical formulation of the proposed approach, whose validation follows in part II. © 2010 Elsevier Ltd. All rights reserved.
A. Laminates; B. Damage tolerance; B. Delamination; C. Analytical modelling
Thermocapillary control of rupture in thin viscous fluid sheets
Journal of Fluid Mechanics
541
399-408
2005
10.1017/S0022112005006269
We consider the evolution of a thin viscous fluid sheet subject to\nthermocapillary effects. Using a lubrication approximation we find,\nfor symmetric interfacial deflections, coupled evolution equations\nfor the interfacial profile, the streamwise component of the fluid\nvelocity and the temperature variation along the surface. Initial\ntemperature profiles change the initial flow field through Marangoni-induced\nshear stresses. These changes then lead to preferred conditions for\nrupture prescribed by the initial temperature distribution. We show\nthat the time to rupture may be minimized by varying the phase difference\nbetween the initial velocity profile and the initial temperature\nprofile. For sufficiently large temperature differences, the phase\ndifference between the initial velocity and temperature profiles\ndetermines the rupture location.
bowen; control; thermocapillarity
Fracture mechanics testing on specimens with low constraint - Standardisation activities within ISO and ASTM
Engineering Fracture Mechanics
72
4
557-576
2005
10.1016/j.engfracmech.2004.04.006
Fracture mechanics tests are traditionally designed to measure material resistance to stable or unstable crack extension using specimens that are highly constrained to plastic deformation. For a variety of reasons, structural members may be made of thin gage-materials with inherently low constraint to plastic deformation. There is currently little guidance for measuring crack extension resistance under such conditions. The international standards organisations ISO and ASTM are responding to that need, and this paper describes one aspect of their current activity. Two procedures are being developed; one based on the ??5 crack opening displacement parameter, the other on the constant value of the crack tip opening angle, ??c. The measurement of ??5 is well established and relatively simple, whereas ??c is more difficult to determine experimentally. Evaluations of ??c from finite-element analyses are currently the most accurate approach, since measurements can only be made on the exterior surfaces similar to ??5. Questions naturally arise regarding the correspondence of surface indication with full-thickness response in the laboratory experience. Both measures of crack extension resistance are suitable for structural assessment. The ??5 concept is applied by means of crack driving force formulae from existing assessment procedures and hence relatively easy to use. On the other hand, the CTOA concept is potentially more accurate and can be applied to cases of multiple cracks and complex structures. But its structural application requires numerical methods, which have been successful in predicting the failure of large-scale cracked structural components. ?? 2004 Elsevier Ltd. All rights reserved.
Crack extension resistance; Crack opening displacement; Crack tip opening angle; R curve; Thin-walled structures
Review of solid mechanics in tribology
International Journal of Solids and Structures
37
391-400
2000
10.1016/S0020-7683(99)00101-8
The study of solid mechanics is essential to the field of tribology, (friction, lubrication and wear). Tribology is of immense economic importance. The potential savings, were tribological principles better understood and applied to friction and wear reduction) may be several percent of the gross national product. Solutions to tribology problems often enable current technologies in a broad spectrum of applications from friction contact in the turbine shrouds of aircraft engines, to bearing contact in motor vehicle gear assemblies, to the sliding contact of magnetic storage disk drives. Conversely, tribology issues, e.g., the coefficient of friction, may impact solid mechanics problems and tangential tractions are essentially free parameters in many cases. Active issues of research in tribology where solid mechanics is applied include: friction and wear in dynamic loading of bearings to extend bearing life; models for contact and thermal stresses of sliding surface asperities; design criteria for magnetic recording heads, and behavior of human artificial joints to extend service life. Countless other applications exist, requiring the development of essential theories of conforming and non-conforming surface behavior. Information such as the frictional response of surfaces in relative motion, and modes of stress and deformation emerges from the fusion of solid mechanics and tribology.
Contact mechanics; Friction; Lubrication; Tribology; Wear
Elastic instabilities for strain-stiffening rubber-like spherical and cylindrical thin shells under inflation
International Journal of Non-Linear Mechanics
42
2
204-215
2007
10.1016/j.ijnonlinmec.2006.10.010
This paper is concerned with investigation of the effects of strain-stiffening on the classical limit point instability that is well-known to occur in the inflation of internally pressurized rubber-like spherical thin shells (balloons) and circular cylindrical thin tubes composed of incompressible isotropic non-linearly elastic materials. For a variety of specific strain-energy densities that give rise to strain-stiffening in the stress-stretch response, the inflation pressure versus stretch relations are given explicitly and the non-monotonic character of the inflation curves is examined. While such results are known for constitutive models that exhibit a gradual stiffening (e.g. exponential and power-law models), our primary focus is on materials that undergo severe strain-stiffening in the stress-stretch response. In particular, we consider two phenomenological constitutive models that reflect limiting chain extensibility at the molecular level. It is shown that for materials with sufficiently low extensibility no limit point instability occurs and so stable inflation is then predicted for such materials. Potential applications of the results to the biomechanics of soft tissues are indicated. ?? 2007 Elsevier Ltd. All rights reserved.
Incompressible rubber-like materials and soft biol; Inflation of spherical and cylindrical thin shells; Instabilities; Strain-stiffening constitutive models
Geometrization of quantum mechanics
Communications in Mathematical Physics
65
2
189-201
1979
10.1007/BF01225149
Quantum mechanics is cast into a classical Hamiltonian form in terms of a symplectic structure, not on the Hilbert space of state-vectors but on the more physically relevant infinite-dimensional manifold of instantaneous pure states. This geometrical structure can accommodate generalizations of quantum mechanics, including the nonlinear relativistic models recently proposed. It is shown that any such generalization satisfying a few physically reasonable conditions would reduce to ordinary quantum mechanics for states that are “near” the vacuum. In particular the origin of complex structure is described.
Physics and Astronomy
Relation between crack surface displacements and strain energy release rate in thin rubber sheets
Mechanics of Materials
34
8
459-474
2002
10.1016/S0167-6636(02)00174-6
The classical problem of a small crack in the center of a large, thin rubber sheet deformed in simple tension, pure shear or equi-biaxial extension is revisited. Following Key (1969) and Lake (1970), the strain energy release rate for crack growth is derived by examining the crack surface displacements (crack opening) and considering the work that would be done by forces applied to close the crack again. It is shown that the strain energy release rate may be expressed in the same form for all three modes of deformation. The results have been verified using non-linear finite element analysis. Differences arising from the use of different hyper-elastic material models are discussed.
crack surface displacements; fracture mechanics; griffith crack; hyper-elasticity; linear finite element analysis; non-; rubber; strain energy release rate; tearing energy
Perfectly matched layers in the thin layer method
Computer Methods in Applied Mechanics and Engineering
217-220
262-274
2012
10.1016/j.cma.2011.12.006
This paper explores the coupling of the perfectly matched layer technique (PML) with the thin layer method (TLM), the combination of which allows making highly efficient and accurate simulations of layered half-spaces of infinite depth subjected to arbitrary dynamic sources anywhere. It is shown that with an appropriate complex stretching of the thickness of the thin-layers, one can assemble a system of layers which fully absorbs and attenuates waves for any angle of propagation. An extensive set of numerical experiments show that the TLM. +. PML performance is clearly superior to that of a standard TLM model with paraxial boundaries augmented with buffer layers (TLM + PB). This finding strongly suggests that the proposed combination may in due time constitute the preferred choice for this class of problems. © 2012 Elsevier B.V.
Elastodynamics; Green functions; Perfectly matched layer method; Soil-structure interaction; Thin-layer method
A direct method of determining complex depth profiles of residual stresses in thin films on a nanoscale? Mechanics of residually stressed systems
Microelectromechanical Systems - Materials and Devices
1052
87-92
2008
The basic ideas behind the calculation procedure of the developed ion beam layer removal method (ILR method) to determine complex depth profiles of residual stresses in thin films are explained. The mechanics of thin films on substrates in general and the effect of the substrate thickness on the stresses in particular are presented by means of a simple model system in order to improve the understanding and facilitate the application of the ILR method. © 2008 Materials Research Society.
calculation procedure; Coatings; Composite micromechanics; Computer networks; depth profiling; Direct method (DM); Electrochemical sensors; Electromechanical devices; General (CO); In order; Ion bombardment; layer removal; Materials Research Society (MRS); Mechanics; Mechatronics; MEMS; Microelectromechanical devices; Micro-electro- mechanical system (MEMS); Micromechanics; Molecular beam epitaxy; Nano scaling; Pigments; Residual stresses; Simple modeling; Solids; Strength of materials; Stresses; Substrates; Substrate thicknesses; Thick films; Thin films
Stress intensity factor of an arbitrarily located circumferential crack in a thin-walled cylinder with axisymmetrically loaded ends
Engineering Fracture Mechanics
62
4-5
371-382
1999
10.1016/S0013-7944(98)00104-0
A simplified method has been developed to approximately calculate the stress intensity factor of a circumferential crack in a thin-walled cylinder with ends subjected to axisymmetric radial and bending loads, based on the theory of cylindrical shell and method similar to Rice and Levy’s line spring method. The effects of cylinder length and crack location on the value can be evaluated by this method. The numerical results for the problem with the ends subjected to a pair of axisymmetric bending loads showed the necessity of considering the effects of cylinder length and crack location on the stress intensity factor for the problem.
Axisymmetric loads; Circumferential crack; Compliance; Crack location; Finite length; Fracture mechanics; Stress intensity factor; Thin-walled cylinder
Quantum mechanics from a universal action reservoir
arXiv preprint physics/0605068
4
2006
A heuristic derivation of quantum mechanics using information theory requires a foundational physical principle: the existence of a universal action reservoir, analogous to the energy reservoir of a canonical ensemble.
Dynamical foundations of nonextensive statistical mechanics
Physical Review Letters
87
18
180601
2001
10.1103/PhysRevLett.87.180601
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which ordinary Langevin equations underly ordinary statistical mechanics to the more general nonextensive case. As a main example, we construct a dynamical model of velocity fluctuations in a turbulent flow, which generates probability densities that very well fit experimentally measured probability densities in Eulerian and Lagrangian turbulence. Our approach provides a dynamical reason why many physical systems with fluctuations in temperature or energy dissipation rate are correctly described by Tsallis statistics.
Progress in Solid Mechanics
Progress in Solid Mechanics
I
399
1960
harmonic solution to thermoelastic 3D problem using Hankel transform\n\nSnedon and Hill editors
DNA mechanics.
Annual review of biomedical engineering
7
21-53
2005
10.1146/annurev.bioeng.6.062403.132016
We review the history of DNA mechanics and its analysis. We evaluate several methods to analyze the structures of superhelical DNA molecules, each predicated on the assumption that DNA can be modeled with reasonable accuracy as an extended, linearly elastic polymer. Three main approaches are considered: mechanical equilibrium methods, which seek to compute minimum energy conformations of topologically constrained molecules; statistical mechanical methods, which seek to compute the Boltzmann distribution of equilibrium conformations that arise in a finite temperature environment; and dynamic methods, which seek to compute deterministic trajectories of the helix axis by solving equations of motion. When these methods include forces of self-contact, which prevent strand passage and preserve the topological constraint, each predicts plectonemically interwound structures. On the other hand, the extent to which these mechanical methods reliably predict energetic and thermodynamic properties of superhelical molecules is limited, in part because of their inability to account explicitly for interactions involving solvent. Monte Carlo methods predict the entropy associated with supercoiling to be negative, in conflict with a body of experimental evidence that finds it is large and positive, as would be the case if superhelical deformations significantly disrupt the ordering of ambient solvent molecules. This suggests that the large-scale conformational properties predicted by elastomechanical models are not the only ones determining the energetics and thermodynamics of supercoiling. Moreover, because all such models that preserve the topological constraint correctly predict plectonemic interwinding, despite these and other limitations, this constraint evidently dominates energetic and thermodynamic factors in determining supercoil geometry. Therefore, agreement between predicted structures and structures obtained experimentally, for example, by electron microscopy, does not in itself provide evidence for the correctness or completeness of any given model of DNA mechanics.
Biophysical Phenomena; Biophysics; DNA; DNA: chemistry; DNA, Superhelical; Models, Theoretical; Nucleic Acid Conformation; Thermodynamics
On new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported
International Journal of Solids and Structures
44
5396-5411
2007
10.1016/j.ijsolstr.2007.01.007
This paper presents a bridging research between a modeling methodology in quantum mechanics/relativity and elasticity. Using the symplectic method commonly applied in quantum mechanics and relativity, a new symplectic elasticity approach is developed for deriving exact analytical solutions to some basic problems in solid mechanics and elasticity which have long been bottlenecks in the history of elasticity. In specific, it is applied to bending of rectangular thin plates where exact solutions are hitherto unavailable. It employs the Hamiltonian principle with Legendre's transformation. Analytical bending solutions could be obtained by eigenvalue analysis and expansion of eigenfunctions. Here, bending analysis requires the solving of an eigenvalue equation unlike in classical mechanics where eigenvalue analysis is only required in vibration and buckling problems. Furthermore, unlike the semi-inverse approaches in classical plate analysis employed by Timoshenko and others such as Navier's solution, Levy's solution, Rayleigh-Ritz method, etc. where a trial deflection function is pre-determined, this new symplectic plate analysis is completely rational without any guess functions and yet it renders exact solutions beyond the scope of applicability of the semi-inverse approaches. In short, the symplectic plate analysis developed in this paper presents a breakthrough in analytical mechanics in which an area previously unaccountable by Timoshenko's plate theory and the likes has been trespassed. Here, examples for plates with selected boundary conditions are solved and the exact solutions discussed. Comparison with the classical solutions shows excellent agreement. As the derivation of this new approach is fundamental, further research can be conducted not only on other types of boundary conditions, but also for thick plates as well as vibration, buckling, wave propagation, etc. © 2007 Elsevier Ltd. All rights reserved.
Eigenvalue; Eigenvector; Hamiltonian; Legendre; Plate bending; Symplectic elasticity; Timoshenko
Breakage mechanics—Part I: Theory
Journal of the Mechanics and Physics of Solids
55
6
1274-1297
2007
10.1016/j.jmps.2006.11.003
Different measures have been suggested for quantifying the amount of fragmentation in randomly compacted crushable aggregates. A most effective and popular measure is to adopt variants of Hardin's [1985. Crushing of soil particles. J. Geotech. Eng. ASCE 111(10), 1177–1192] definition of relative breakage ‘Br’. In this paper we further develop the concept of breakage to formulate a new continuum mechanics theory for crushable granular materials based on statistical and thermomechanical principles. Analogous to the damage internal variable ‘D’ which is used in continuum damage mechanics (CDM), here the breakage internal variable ‘B’ is adopted. This internal variable represents a particular form of the relative breakage ‘Br’ and measures the relative distance of the current grain size distribution from the initial and ultimate distributions. Similar to ‘D’, ‘B’ varies from zero to one and describes processes of micro-fractures and the growth of surface area. However, unlike damage that is most suitable to tensioned solid-like materials, the breakage is aimed towards compressed granular matter. While damage effectively represents the opening of micro-cavities and cracks, breakage represents comminution of particles. We term the new theory continuum breakage mechanics (CBM), reflecting the analogy with CDM. A focus is given to developing fundamental concepts and postulates, and identifying the physical meaning of the various variables. In this part of the paper we limit the study to describe an ideal dissipative process that includes breakage without plasticity. Plastic strains are essential, however, in representing aspects that relate to frictional dissipation, and this is covered in Part II of this paper together with model examples.
Breakage; Comminution; Continuum mechanics; Grain size distribution; Granular materials
Plastic deformation of multicrystalline thin films: Grain size distribution vs. grain orientation
Computational Materials Science
52
1
20-24
2012
10.1016/j.commatsci.2011.03.001
A continuum model of plasticity, Mesoscopic Field Dislocation Mechanics (MFDM), is used to study the interplay between grain size and grain orientation on the mechanical response of multicrystalline thin films undergoing plane strain tension. It is shown that the grain size dependence in the case of multicrystals is controlled by those grains which are relatively more susceptible to plastic deformation. This effect is captured to some extent by conventional crystal plasticity theory; however, the explicit incorporation of polar dislocations in the MFDM model significantly enhances the overall mechanical response as demonstrated in the paper.
Dislocation mechanics; Finite element analysis; Plasticity; Thin films
Quantifying the stress relaxation modulus of polymer thin films via thermal wrinkling
ACS Applied Materials and Interfaces
3
331-338
2011
10.1021/am100956q
The viscoelastic properties of polymer thin films can have a significant impact on the performance in many small-scale devices. In this work, we use a phenomenon based on a thermally induced instability, termed thermal wrinkling, to measure viscoelastic properties of polystyrene films as a function of geometric confinement via changes in film thickness. With application of the appropriate buckling mechanics model for incompressible and geometrically confined films, we estimate the stress-relaxation modulus of polystyrene films by measuring the time-evolved wrinkle wavelength at fixed annealing temperatures. Specifically, we use time-temperature superposition to shift the stress relaxation curves and generate a modulus master curve for polystyrene films investigated here. On the basis of this master curve, we are able to identify the rubbery plateau, terminal relaxation time, and viscous flow region as a function of annealing time and temperatures that are well-above its glass transition. Our measurement technique and analysis provide an alternative means to measure viscoelastic properties and relaxation behavior of geometrically confined polymer films.
Polystyrene; Stress relaxation modulus; Thin films; Viscoelastic properties; Wrinkling
A reappraisal of nonlocal mechanics
European Journal of Mechanics - A/Solids
18
1
17-46
1999
10.1016/S0997-7538(99)80002-3
A new approach to nonlocal damage coupled to nonlocal plasticity within a small strain formalism will be discussed. Elasticity remains local and the nonlocal framework is set up by the definition of the free energy function, which depends on nonlocal measures of damage and plasticity. The potential functions for damage and plasticity follow in a straightforward manner, as well as the evolution laws for the internal variables using the thermodynamics of irreversible processes. Numerical algorithms for the integration of the nonlocal damage/plasticity evolution equations have been derived. In the second part of the paper, the modelling of interfacial damage is considered and a material surface model for a thin adhesive undergoing nonlocal damage coupled to nonlocal plasticity is derived. The numerical scheme for the integration of the constitutive equations is further elaborated and illustrated for an adhesive joints problem.
coupled phenomena; model 2; nonlocal damage; nonlocal plasticity; numerical scheme
Onset of matrix cracking in angle-ply ceramic matrix composites
International Journal of Mechanical Sciences
44
10
2173-2187
2002
10.1016/S0020-7403(02)00163-7
The problem of initial damage in angle-ply [- ??m/0n/??m] and [- ??/??] ceramic matrix composites subjected to axial tension is considered in this paper. The damage is in the form of matrix cracks that may appear in either inclined (- ?? and ?? lamination angle) or longitudinal layers. As follows from the analysis, if the lamination angle of the inclined layers is small, the initial failure occurs in the 0-layers of [- ??m/0n/??m] composites or in [- ??/??] composites in the form of bridging cracks. However, if the inclined layers form a larger angle with the load direction, they fail due to tunneling cracks. It is shown that the boundary between two different modes of failure in a representative SiC/CAS composite corresponds to a lamination angle equal to 35?? in the case of [- ??m/0n/??m] composites. In the case of [- ??/??] laminates, the boundary value of the lamination angle is equal to 45??, i.e. bridging cracks form if ??<45?? and tunneling cracks appear if ?? > 45??. ?? 2002 Elsevier Science Ltd. All rights reserved.
Ceramic matrix composites; Fracture; Matrix cracks; Residual stresses
Deflection of cross-ply composite laminates induced by piezoelectric actuators
Sensors
10
1
719-733
2010
10.3390/s100100719
The coupling effects between the mechanical and electric properties of piezoelectric materials have drawn significant attention for their potential applications as sensors and actuators. In this investigation, two piezoelectric actuators are symmetrically surface bonded on a cross-ply composite laminate. Electric voltages with the same amplitude and opposite sign are applied to the two symmetric piezoelectric actuators, resulting in the bending effect on the laminated plate. The bending moment is derived by using the classical laminate theory and piezoelectricity. The analytical solution of the flexural displacement of the simply supported composite plate subjected to the bending moment is solved by using the plate theory. The analytical solution is compared with the finite element solution to show the validation of present approach. The effects of the size and location of the piezoelectric actuators on the response of the composite laminate are presented through a parametric study. A simple model incorporating the classical laminate theory and plate theory is presented to predict the deformed shape of the simply supported laminate plate.
Bending moment; Flexural displacement; Piezoelectric actuator; Plate theory
Nonclassical States of Light and Mechanics
Cavity Optomechanics
31
2012
This book chapter reports on theoretical protocols for generating nonclassical states of light and mechanics. Nonclassical states are understood as squeezed states, entangled states or states with negative Wigner function, and the nonclassicality can refer either to light, to mechanics, or to both, light and mechanics. In all protocols nonclassicallity arises from a strong optomechanical coupling. Some protocols rely in addition on homodyne detection or photon counting of light.
Interfacial toughening of solution processed Ag nanoparticle thin films by organic residuals.
Nanotechnology
23
48
485704
2012
10.1088/0957-4484/23/48/485704
Reliable integration of solution processed nanoparticle thin films for next generation low-cost flexible electronics is limited by mechanical damage in the form of delamination and cracking of the films, which has not been investigated quantitatively or systematically. Here, we directly measured the interfacial fracture energy of silver nanoparticle thin films by using double cantilever beam fracture mechanics testing. It was demonstrated that the thermal annealing temperature and period affect the interfacial fracture energy. Also it was found that the interfacial fracture resistance can be maximized with optimized annealing conditions by the formation of organic residual bridges during the annealing process.
Embryo Mechanics. Balancing Force Production with Elastic Resistance During Morphogenesis
Current Topics in Developmental Biology
95
215-241
2011
10.1016/B978-0-12-385065-2.00007-4
Morphogenesis requires the spatial and temporal control of embryo mechanics, including force production and mechanical resistance to those forces, to coordinate tissue deformation and large-scale movements. Thus, biomechanical processes play a key role in directly shaping the embryo. Additional roles for embryo mechanics during development may include the patterning of positional information and to provide feedback to ensure the success of morphogenetic movements in shaping the larval body and organs. To understand the multiple roles of mechanics during development requires familiarity with engineering principles of the mechanics of structures, the viscoelastic properties of biomaterials, and the integration of force and stress within embryonic structures as morphogenesis progresses. In this chapter, we review the basic engineering principles of biomechanics as they relate to morphogenesis, introduce methods for quantifying embryo mechanics and the limitations of these methods, and outline a formalism for investigating the role of embryo mechanics in birth defects. We encourage the nascent field of embryo mechanics to adopt standard engineering terms and test methods so that studies of diverse organisms can be compared and universal biomechanical principles can be revealed. ?? 2011 Elsevier Inc.
Cell mechanics; Coefficient of viscosity; Compressibility; Elastic modulus; Embryonic; Epithelia; Gastrulation; Mesenchymal; Modulus; Neurulation; Nonlinear geometry; Nonlinear materials; Poisson's ratio; Rigidity; Strain; Stress; Tissue mechanics; Viscoelasticity; Young's modulus
Nuclear mechanics: lamin webs and pathological blebs.
Nucleus (Austin, Tex.)
4
3
156-9
2013
10.4161/nucl.25019
Anomalies in the three-dimensional shape of the nucleus are associated with a number of genetic diseases. These shape distortions include lobulated structures, with localized bulges referred to as nuclear blebs. Blebbing can result from mutations in genes encoding lamin intermediate filaments that form the lamin cortex, a thin meshwork lining the nuclear envelope. However, the biophysical origins of nuclear blebs remain a mystery. A recent study by Funkhouser et al. provides a theoretical model in which the lamin cortex is modeled as a thin, inhomogeneous elastic shell. This model shows that partial segregation of different lamin sub-networks-each with distinct mechanical properties-can lead to shell morphologies similar to blebbed nuclei in living cells.
ar membrane; elasticity; filaments; lamiopathies; nucle-; progeria; shape
Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities
Journal of Fluid Mechanics
543
183-202
2005
Doi 10.1017/S0022112005006348
The stability of an evaporating thin liquid film on a solid substrate is investigated within lubrication theory. The heat flux due to evaporation induces thermal gradients; the generated Marangoni stresses are accounted for. Assuming the gas phase at rest, the dynamics of the vapour reduces to diffusion. The boundary condition at the interface couples transfer from the liquid to its vapour and diffusion flux. The evolution of the film is governed by a lubrication equation coupled with the Laplace problem associated with quasi-static diffusion. The linear stability of a flat film is studied in this general framework. The subsequent analysis is restricted to diffusion-limited evaporation for which the gas phase is saturated in vapour in the vicinity of the interface. The stability depends then only on two control parameters, the capillary and Marangoni numbers. The Marangoni effect is destabilizing whereas capillarity and evaporation are stabilizing processes. The results of the linear stability analysis are compared with the experiments of Poulard et al. (2003) performed in a different geometry. In order to study the resulting patterns, an amplitude equation is obtained through a systematic multiple-scale expansion. The evaporation rate is needed and is computed perturbatively by solving the Laplace problem for the diffusion of vapour. The bifurcation from the flat state is found to be a supercritical transition. Moreover, it appears that the non-local nature of the diffusion problem affects the amplitude equation unusually.
droplets; evolution; liquid-films; natural-convection; stability; surface; tears; thermocapillary instabilities; wine
Influence of Layer Thickness on the Strength of Angle-Ply Laminates
Journal of Composite Materials
16
3
216
1982
10.1177/002199838201600305
Experimental results are presented showing that the strength and toughness of finite-width angle-ply laminates can be increased significantly by using an alternating layer stacking sequence as opposed to a clustered con figuration. The ultimate tensile stress of an alternating plus/minus {theta} laminate of the form [({+/-}{theta})2]s can be as much as 1.5 times that a clustered configura tion of the form [{theta}2/--{theta}2] s. Further, the toughness of the alternating layer configuration can be as much as 2.7 times that of the clustered configuration. These differences are explained analytically through consideration of the in fluence of layer thickness on the magnitude of the interlaminare shear stress and by examination of failed specimens. It is shown that the two laminate configurations exhibit distinctly different failure modes for some fiber angles. Both laminate configurations exhibit catastrophic failure with the damage limited essentially to a small region defined by the length of a single crack across the face of the specimen, parallel to the fiber direction. Results are presented for T300/5208 graphite-epoxy for fiber orientations of 10{degrees}, 30 {degrees}, and 45 {degrees}.
The Parenthetical Method of Spin-Ply Notation: A Case Study
Northeastern Andean Archaeology and Ethnohistory Conference
2006
This poster illustrates a new method for recording spin and ply structures in archaeological and ethnographic textile analysis. Reviewing the disadvantages of traditional notational methods, the authors suggest that Parenthetical Notation provides a standardized, formulaic means of recording spin and ply data that greatly improves upon graphical or descriptive techniques. To illustrate the advantages of the Parenthetical Notation, a case study of textile materials from the Lower Ica Valley site of Casa Vieja is presented.
Surfactant spreading on a thin weakly viscoelastic film
Journal of Non-Newtonian Fluid Mechanics
105
1
53-78
2002
10.1016/S0377-0257(02)00061-7
A mathematical model is presented for surfactant-driven thin weakly viscoelastic film flows on a flat, impermeable plane. The Oldroyd-B constitutive relation is used to model the viscoelastic fluid. Lubrication theory and a perturbation expansion in powers of the Weissenberg number (We) are employed, which give rise to non-linear coupled evolution equations governing the transport of insoluble surfactant and thin liquid film thickness. Spreading on a Newtonian film is recovered to leading order and corrections to viscoelasticity are obtained at order We. These equations are solved numerically over a wide range of viscosity ratio (ratio of solvent viscosity to the sum of solvent and polymeric viscosities), pre-existing surfactant level and Peclet number (Pe). The effect of viscoelasticity on surfactant transport and fluid flow is investigated and the mechanisms underlying this effect are explored. Shear stress, streamwise normal stress and the temporal rate of change of extra shear stress generated from gradients in surfactant concentration dominate thin viscoelastic film flows whereas only shear stresses play a role in Newtonian thin film flows. Our results also reveal that, for weak viscoelasticity, the influence of viscosity ratio on the evolution of surfactant concentration and film thickness can be significant and varies considerably, depending on the concentration of pre-existing surfactant and surfactant surface diffusivity.
Interfaces; Lubrication; Marangoni; Oldroyd-B fluid; Surfactant transport; Viscoelastic thin film
Micro-Cantilevers for Thin Films: Young’s Modulus
IUTAM Symposium on Mechanical Behavior and Micro-Mechanics of Nanostructured Materials
71-83
2007
A simple and effective characterisation technique based on micro-cantilever beams for thin film materials using commonly available\nequipment — scanning surface profiler — is described. The advantages of this class of techniques are simplicity, speed, cost\nand a wide applicability. A technique for extracting the Young’s modulus from static deflection data is developed and validated\nin experiments on thin film specimens of silicon nitride deposited on a silicon substrate under different conditions. Finite\nelement analysis is used to assess the influence of factors affecting the bending of thin films, and thus guide the analysis\nof micro-cantilever deflection data for reliable characterisation of the material.
Mechanics of Locomotion
The International Journal of Robotics Research
3
2
4-28
1984
10.1177/027836498400300202
Energetic and mechanical principles of walking and running are reviewed, using information available from force-plate studies. A mathematical model of walking is described that conserves the sum of the kinetic and gravitational potential energies of the body. In running, energy is stored transiently in the elastic deformations of stretched muscles and tendons. Theory and experiments are described using these principles and others to find the range of stiffness values for a running track that both lowers the potential for injuries and increases running speed.
Statics and mechanics of materials
Connect, learn, succeed
xv, 714 p.
2011
1. General Principles -- 2. Force Vectors -- 3. Force System Resultants -- 4. Equilibrium of a Rigid Body -- 5. Structural Analysis -- 6. Center of Gravity, Centroid, and Moment of Inertia -- 7. Stress and Strain -- 8. Mechanical Properties of Materials -- 9. Axial Load -- 10. Torsion -- 11. Bending -- 12. Transverse Shear -- 13. Combined Loadings -- 14. Stress and Strain Transformation -- 15. Design of Beams and Shafts -- 16. Deflection of Beams and Shafts -- 17. Buckling of Columns -- App. A. Mathematical Review and Expressions -- App. B. Geometric Properties of an Area and Volume -- App. C. Geometric Properties of Wide-Flange Sections -- App. D. Slopes and Deflections of Beams.
Materials.; Mechanics, Applied.; Statics.
Free vibration and buckling of symmetric cross-ply laminated plates by an exact method
Journal of Sound and Vibration
126
3
447-461
1988
10.1016/0022-460X(88)90223-4
An exact mathematical tool to analyze the free vibration and buckling of symmetric cross-ply laminated plates is developed. The procedure, based on a generalized Lévy type solution considered in conjunction with the state space concept, enables one to solve exactly the equations governing the laminated anisotropic plate theory as considered by Reddy [3,4]. Combinations of simply supported, clamped and free boundary conditions are considered. Comparisons with other higher order, first order and classical plate theories are made.
Influence of edge conditions on the modal characteristics of cross-ply laminated shells
Computers & Structures
34
6
817-826
1990
10.1016/0045-7949(90)90352-3
The dynamic and static behavior of cross-ply laminated shells are\ninvestigated using the third-order shear deformation shell theory\nof Reddy. The theory is a modification of the Sanders shell theory\nand accounts for parabolic distribution of the transverse shear strains\nthrough the thickness of the shell and does not require shear correction\ncoefficients. The Lévy-type exact solutions for bending, buckling\nand natural vibration are presented for doubly curved, cylindrical\nand spherical shells under various boundary conditions. © 1990.
The dynamics of a localized surfactant on a thin film
Journal of Fluid Mechanics
213
127
1990
10.1017/S0022112090002257
We investigate the flow induced by a localized insoluble surfactant on a thin film. This problem is intended to model the behaviour of the lung's thin-film lining after an aerosol droplet lands on its surface. The surfactant-induced surface-tension gradients drive convection (Marangoni convection) within the film, disrupting the film surface and causing the surfactant to spread. The surfactant may also spread on the film's surface by surface diffusion without inducing convection. Gravity provides a restoring force that decreases film disturbances. Lubrication theory is employed to derive equations that describe the evolution of the film thickness and surfactant concentration. A nonlinear surface-tension equation of state describes the relationship between the surfactant concentration and the surface tension. Solutions of the evolution equations are found numerically using the method of lines and analytically under limiting cases of small and large surface diffusivity. The results elucidate the behaviour of the thin-film/surfactant system. We find that surface-tension-induced convection creates film disturbances that increase the film thickness near the surfactant's leading edge, and thins the film in the central region. Surface diffusion causes more rapid spreading of the surfactant, and decreases the film disturbances. Gravity decreases the film disturbances by creating bi-directional flow in the form of a ring vortex. This behaviour may have implications for the delivery of medications or toxins by aerosol inhalation.
Bohmian mechanics without pilot waves
Chemical Physics
370
1-3
4-14
2010
10.1016/j.chemphys.2009.12.024
In David Bohm’s causal/trajectory interpretation of quantum mechanics, a physical system is regarded as consisting of both a particle and a wavefunction, where the latter “pilots” the trajectory evolution of the former. In this paper, we show that it is possible to discard the pilot wave concept altogether, thus developing a complete mathematical formulation of time-dependent quantum mechanics directly in terms of real-valued trajectories alone. Moreover, by introducing a kinematic definition of the quantum potential, a generalized action extremization principle can be derived. The latter places very severe a priori restrictions on the set of allowable theoretical structures for a dynamical theory, though this set is shown to include both classical mechanics and quantum mechanics as members. Beneficial numerical ramifications of the above, “trajectories only” approach are also discussed, in the context of simple benchmark applications.
Bohmian mechanics; Interpretation of quantum mechanics; Pilot wave; Quantum trajectory methods; Time-dependent quantum mechanics; Trajectory formulation of quantum mechanics
Fracture patterns induced by desiccation in a thin layer.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
60
6 Pt A
6449-6464
1999
10.1103/PhysRevE.60.6449
We study a theoretical model of mud cracks, that is, the fracture patterns resulting from the contraction with drying in a thin layer of a mixture of granules and water. In this model, we consider the slip on the bottom of this layer and the relaxation of the elastic field that represents deformation of the layer. Analysis of the one-dimensional model gives results for the crack size that are consistent with experiments. We propose an analytical method of estimation for the growth velocity of a simple straight crack to explain the very slow propagation observed in actual experiments. Numerical simulations reveal the dependence of qualitative nature of the formation of crack patterns on material properties.
Adhesion-delamination mechanics of a prestressed rectangular film adhered onto a rigid substrate
Journal of Applied Physics
101
2
024903
2007
10.1063/1.2422775
A prestressed rectangular film clamped at both ends delaminates from a rigid punch. Based on a thermodynamic energy balance, the delamination mechanics is derived to relate the simultaneous external tensile force applied to the punch, punch displacement, and contact area. Effects of the coupled tensile residual membrane stress and adhesion energy at the punch-film interface are investigated. A “pinch off” (stable shrinking of the contact area to a line) is predicted, contrasting the nonzero “pull-off” radius in a clamped circular film. The model is useful in understanding the behavior of various adhesion-delamination phenomena, especially in one dimensional capacitive microelectromechanical systems radio frequency switches, microstructure network, and nanostructures.
Time-dependent free-surface thin film flows over topography
Physics of Fluids
15
9
2512-2524
2003
10.1063/1.1590978
We consider the slow motion of a thin viscous film flowing over a topographical feature (trench or mound) under the action of an external body force. Using the lubrication approximation, the equations of motion simplify to a single nonlinear partial differential equation for the evolution of the free surface in time and space. It is shown that the problem is governed by three dimensionless parameters corresponding to the feature depth, feature width and feature steepness. Quasi-steady solutions for the free surface are reported for a wide range of these parameters. Our computations reveal that the free surface develops a ridge right before the entrance to the trench or exit from the mound and that this ridge can become large for steep substrate features of significant depth. Such capillary ridges have also been observed in the contact line motion over a planar substrate where the buildup of pressure near the contact line is responsible for the ridge. For flow over topography, the ridge formation is a manifestation of the effect of the capillary pressure gradient induced by the substrate curvature. In addition, the minimum film thickness is always found near the concave corner of the feature. Both the height of the ridge and the minimum film thickness are found to be strongly dependent on both the profile depth and steepness. Finally, it is found that either finite feature width or a significant vertical component of gravity can suppress these effects in a way that is made quantitative and which allows the operative physical mechanism to be explained. © 2000 American Institute of Physics.
Dynamic response of antisymmetric angle-ply laminated plates subjected to arbitrary loading
Journal of Sound and Vibration
126
3
437-445
1988
10.1016/0022-460X(88)90222-2
The transient response of simply supported antisymmetric angle-ply\nrectangular plates subjected to arbitrary loading is investigated.\nThe state variable technique is used to solve exactly the equations\nof motion of the first-order transverse shear deformation theory\n(FSDT) as well as the classical laminate theory (CPT). The solutions\nof these two theories are considered to bring out the influence of\nthe transverse shear deformation, the degree of anisotropy, and the\nnumber of layers. © 1988.
Mechanics of particle adhesion
Journal of Adhesion Science and Technology
8
1333-1355
1994
10.1163/156856194X00645
The adhesion of particles to surfaces is accompanied by deformations of the materials arising from adhesion force-induced stresses. These deformations, which can be the result of an elastic, a nonlinear elastic, a viscoelastic, or a plastic response of the materials to the stresses, can significantly affect the forces needed to remove the particles from the substrate. The mechanics of adhesion-induced deformations between micrometer-size particles and various substrates are discussed in this paper. Examples of elastic and plastic deformations resulting from the adhesion forces are presented. The experimental results are analyzed in terms of various adhesion theories, which, under certain circumstances, permit the calculation of the thermodynamic work of adhesion for contacting solids. The ranges of validity of these theories and their predictions are discussed. Finally, adhesion-induced deformations which are not currently explicable in terms of these theories are presented.
Adhesion; deformation; particle; work of adhesion
Novel multifunctional materials based on oxide thin films and artificial heteroepitaxial multilayers
Physica Status Solidi (A)
208
2
232-251
2011
10.1002/pssa.201026403
Transition metal oxides show fascinating physical properties such as high temperature superconductivity, ferro- and antiferromagnetism, ferroelectricity or even multiferroicity. The enormous progress in oxide thin film technology allows us to integrate these materials with semiconducting, normal conducting, dielectric or non-linear optical oxides in complex oxide heterostructures, providing the basis for novel multi-functional materials and various device applications. Here, we report on the combination of ferromagnetic, semiconducting, metallic, and dielectric materials properties in thin films and artificial heterostructures using laser molecular beam epitaxy. We discuss the fabrication and characterization of oxide-based ferromagnetic tunnel junctions, transition metal-doped semiconductors, intrinsic multiferroics, and artificial ferroelectric/ferromagetic heterostructures - the latter allow for the detailed study of strain effects, forming the basis of spin-mechanics. For characterization we use X-ray diffraction, SQUID magnetometry, magnetotransport measurements, and advanced methods of transmission electron microscopy with the goal to correlate macroscopic physical properties with the microstructure of the thin films and heterostructures.
magnetic semiconductors; magnetic tunnel junctions; multiferroics; oxide electronics; pulsed laser deposition; transmission electron microscopy
Foundations of quantum mechanics
Physica Scripta
84
1
018501
2011
10.1088/0031-8949/84/01/018501
Does quantum mechanics have unsolved foundational problems? Is there a dividing line between the quantum and classical descriptions of the world? In this paper, I give an elementary introduction to the mathematical aspects of quantum and classical models which have prompted such questions.
Giant electrocaloric effect of PbTiO3 thin film tuned in a wide temperature range by the anisotropic misfit strain
Mechanics Research Communications
55
40-44
2014
10.1016/j.mechrescom.2013.10.016
The influence of anisotropic in-plane strains on the electrocaloric effect (ECE) in PbTiO3 (PT) epitaxial ferroelectric thin films is investigated by using a Landau-Devonshire thermodynamic theory. The calculation results show that the anisotropic strain can tune the ECE of PT ferroelectric thin films to obtain a large adiabatic temperature change in a wide temperature range which is attributed to the shift of c-phase boundary of PT thin films under the anisotropic strains with an external electric field. These results indicate that the anisotropic strain can provide an efficient way to adjust the ECE of ferroelectric thin films to refrigerate in a wide temperature range. (C) 2013 Elsevier Ltd. All rights reserved.
Damage characterization of a cross-ply carbon fiber/epoxy laminate by an optical measurement of the displacement field
Composites Science and Technology
70
1
94-101
2010
10.1016/j.compscitech.2009.09.010
Using Electronic Speckle Pattern Interferometry (ESPI), full-field displacement measurement was performed on the edge of a cracked cross-ply graphite/epoxy laminate subjected to a tensile loading. The displacement jumps corresponding to cracks are clearly visible and can be used to determine the crack opening displacement (COD) values along the cracks. The main objective of this study is to determine if the application of successive loads of increasing magnitude may have modified the existing cracks and thereby changed the COD dependence on the applied stress. Moreover, we have tested the applicability of the assumed linear elastic COD behavior in the presence of very high stress concentration at the crack tips. The profile of the opening along the crack was also studied. ?? 2009 Elsevier Ltd. All rights reserved.
Identification of delamination position in cross-ply laminated composite beams using S0 Lamb mode
Composites Science and Technology
68
6
1548-1554
2008
10.1016/j.compscitech.2007.10.015
In this work, a Lamb wave based technique has been developed for delamination detection in cross-ply laminated beams. By measuring the propagation speed of S0 Lamb mode and the traveling time of a signal reflected from a delamination site, the location of the delamination can be identified. It has been also confirmed by the experiment that the location of a delamination can be accurately determined by only using the data collected from the sensors in a defect-containing beam, without referring to the baseline signals. Finally, to gain a better understanding of the complex interaction between a Lamb wave and a long delamination, numerical simulations have been carried out using finite element method (FEM). The signal modes generated at the boundaries of the delamination have been analyzed. © 2007 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites; A. Smart materials; C. Delamination; C. Finite element analysis; D. Non-destructive testing
Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories
Composite Structures
44
4
279-287
1999
10.1016/S0263-8223(98)00135-4
Various theories of homogeneous laminated plates are extended to study the buckling and free vibration behavior of non-homogeneous rectangular composite laminates. The equations governing the dynamic response of non-homogeneous composite laminates are deduced. Numerical results for the natural frequencies and critical buckling loads of symmetric cross-ply laminates are presented. The influences of the degree of non-homogeneity, aspect ratio, thickness ratio and in-plane orthotropy ratio on the natural frequencies and critical buckling loads are investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature. The study concludes that the classical plate theory is inadequate for predicting the structural response of non-homogeneous laminates, and that the free vibration and the state of the stability are affected strongly by the degree of nonhomogeneity.
Buckling and free vibration; Non-homogeneous laminated plates
A numerical fracture analysis of indentation into thin hard films on soft substrates
Engineering Fracture Mechanics
70
10
1323-1338
2003
10.1016/S0013-7944(02)00112-1
In this paper, finite element simulations of spherical indentation of a thin hard film deposited on a soft substrate are carried out. The primary objective of this work is to understand the mechanics of fracture of the film due to formation of cylindrical or circumferential cracks extending inwards from the film surface. Also, the role of plastic yielding in the substrate on the above mechanics is studied. To this end, the plastic zone development in the substrate and its influence on the load versus indentation depth characteristics and the stress distribution in the film are first examined. Next, the energy release rate J associated with cylindrical cracks is computed. The variation of J with indentation depth and crack length is investigated. The results show that for cracks located near the indenter axis and at small indentation depth, J decreases over a range of crack lengths, which implies stability of crack growth. This regime vanishes as the location of the crack from the axis increases, particularly for a substrate with low yield strength. Finally, a method for combining experimental load versus indentation depth data with simulation results in order to obtain the fracture energy of the film is proposed. (C) 2002 Elsevier Science Ltd. All rights reserved.
Mechanics of hexagonal atomic lattices
International Journal of Solids and Structures
45
3-4
732-745
2008
10.1016/j.ijsolstr.2007.08.026
A theoretical framework for describing the kinematics and energetics of hexagonal atomic lattices, including planar carbon graphene sheets and cylindrical nanotubes, is proposed. By analogy with the membrane theory of thin shells, the deformation of the particulate lattice in the neighborhood of each atom is described in terms of a uniquely defined deformation gradient and companion local inner displacement. Expressions for the pointwise tensions developing in the plane of the lattice are developed, and a rational procedure for deriving discrete equilibrium equations is discussed. An alternative formulation involving the second-order deformation gradient that parallels the strain gradient theory of bulk media is proposed, and a tentative analogy with a the theory of micropolar elastic media is outlined. ?? 2007 Elsevier Ltd. All rights reserved.
Graphene; Hexagonal lattice; Inner displacement; Micropolar media; Nanotube; Particulate sheet; Strain gradient theory
In Situ Qualitative Inspection of Hole Exit Delamination at Bottom-Ply during Drilling of Woven CFRP Epoxy Composite Laminates
Advanced Engineering Materials
15
6
449-463
2013
DOI 10.1002/adem.201200342
Exploiting very high speed digital videography, an in situ examination of the hole exit delamination at the bottom-most ply during drilling holes in the selected woven CFRP epoxy laminates is presented. At the beginning, a rotating elastic bulge of the carbon fibers at the bottom-ply, which is just the impression of the protruding drill chisel edge, was always observed. Following the elastic bulging, a few, initial cracks along the weak fiber/matrix interfaces appeared. Thereafter, tensile failures in the carbon fibers were seen. The exact location of the initiation of these fiber failures specifically depends on the actual drill-hole position with respect to the woven configuration of the bottom-ply. A visual model for the weak interstitial or undulated regions at the bottom-ply is also proposed in this paper, showing the undulating fibers, which are susceptible to mostly tensile failures under the drilling loads. During a sub-completion drilling-phase at the bottom-ply, various cracks were seen to be propagating mostly via linear paths. Also, the exit delamination at the bottom-ply during a sub-completion drilling-phase was always observed as to be divided into various small, independent localized contourseach of which propagated almost independently through within several individual warps/wefts during drill-feed. Also, the shape of each such tiny contour within a single warp/weft was identified as elliptic, which is observed around an entire drill-hole in unidirectional (UD) composites as reported in literature. It was also observed that the overhanging cantilever-like fibers at the bottom-ply are really difficult to cut, once their base-location or their exit delamination contour reaches outside the hole nominal diameter. Moreover, by referring to some very basic cutting angle configurations for the orthogonal trimming of UD-composites as found rarely in archival literature, an illustrative model diagram is also proposed for the drilling of the selected laminate material. This idea is also approximately validated via a few visual observations. The proposed visual model is generally an attempt in correlating the observed peripheral hole quality (delamination) with various instantaneous tool/fiber engagement configurations occurring across the entire drill-hole periphery at the bottom-ply, during the very last drilling-phase.
fiber-reinforced plastics
Damage mechanics: accomplishments, trends and needs
International Journal of Solids and Structures
37
1-2
267-277
2000
10.1016/S0020-7683(99)00081-5
The objective of this study is to highlight the accomplishments, weaknesses and trends of damage mechanics and research needed for further development. The growing interest in damage mechanics is a proof that the accomplishments are significant. However, one of the messages is that the damage mechanics, in its focus on the dilute density of micro-defects and homogeneous solids, did not address the problems that are of primary interest in applications. The list of references in this paper is restricted to the current papers that list the older works.
Brittle deformation; Continuum models; Damage mechanics; Failure; Micromechanics
A novel technique for characterizing elastic properties of thin biological membrane
Mechanics of Materials
34
11
749-754
2002
10.1016/S0167-6636(02)00182-5
We present a new technique to characterize the elastic properties of a thin biological membrane. An effective instrument that embodies video enhanced microscope was developed primarily to provide the capability of simultaneously measuring both the applied force and the resultant displacement of the biological membrane under a central point force. A theoretical linear elastic solution was applied to quantitatively interpret the measured central deflection of the membrane under a central point load. The Young's modulus of raw and boiled Leghorn egg inner tissue can be easily determined once the applied point load and the central deflection, together with the essential dimensions are known. The viscoelasticity property of natural tissue was manifest in the experiment. The experimental results have verified that the novel technique is applicable to determine the Young's modulus and other viscoelatic properties of thin biological tissue. (C) 2002 Elsevier Science Ltd. All rights reserved.
apparatus; biological membrane; central point loading; cycle curve; elastic properties; instrument; loading; mechanical characterization; stress relaxation; unloading
"TiGr" Laminates: Development of New Thin Adhesive Systems and Associated Test Methods
SAMPE Journal
45
3
30-36
2009
Titanium-Graphite laminates belong to a class of materials called Fiber-Metal Laminates (FML) and consist of layers of titanium interleafed through the thickness of a Carbon Fiber Reinforced Plastic (CFRP) or graphite composite laminate. TiGr offers advantages over metallic structures in terms of weight, fatigue characteristics, damage tolerance, and design flexibility. TiGr also offers advantages over traditional composite materials through higher bearing capabilities, greater toughness, more efficient layups, and an expanded design space. Optimization of surface preparation methods and development of new thin film adhesive systems have resulted in an extremely robust and environmentally durable titanium to CFRP interface architecture which is tailored for prepreg system families, and sized to facilitate titanium ply integration into CFRP structures for minimal impact to production. New hybrid screening test methods have been developed based on metal bond and carbon fiber composite testing techniques which efficiently assess the metal to carbon fiber prepreg interfacial strength and durability. The development and testing of these adhesive systems will be discussed in this talk.
Engineering Fracture Mechanics
Engineering Fracture Mechanics
70
3-4
367-369
2003
10.1016/S0013-7944(02)00124-8
The method of accelerated evaluation of the threshold value of stress intensity factor, in materials under stress corrosion cracking by registration of the crack jumps is proposed. It is based on the model of subcritical jump-like propagation of mode 1 crack as a source of acoustic signals, when material is subjected to the corrosive environment and durable static loading simultaneous effect. The method was experimentally verified during evaluation of K~ of 9HF steel in NaCl water solution and gaseous hydrogen using the up-to-date equipment for recording the acoustic signals.
Grain boundary interface mechanics in strain gradient crystal plasticity
Journal of the Mechanics and Physics of Solids
61
12
2659-2679
2013
10.1016/j.jmps.2013.08.011
Interactions between dislocations and grain boundaries play an important role in the plastic deformation of polycrystalline metals. Capturing accurately the behaviour of these internal interfaces is particularly important for applications where the relative grain boundary fraction is significant, such as ultra fine-grained metals, thin films and micro-devices. Incorporating these micro-scale interactions (which are sensitive to a number of dislocation, interface and crystallographic parameters) within a macro-scale crystal plasticity model poses a challenge. The innovative features in the present paper include (i) the formulation of a thermodynamically consistent grain boundary interface model within a microstructurally motivated strain gradient crystal plasticity framework, (ii) the presence of intra-grain slip system coupling through a microstructurally derived internal stress, (iii) the incorporation of inter-grain slip system coupling via an interface energy accounting for both the magnitude and direction of contributions to the residual defect from all slip systems in the two neighbouring grains, and (iv) the numerical implementation of the grain boundary model to directly investigate the influence of the interface constitutive parameters on plastic deformation. The model problem of a bicrystal deforming in plane strain is analysed. The influence of dissipative and energetic interface hardening, grain misorientation, asymmetry in the grain orientations and the grain size are systematically investigated. In each case, the crystal response is compared with reference calculations with grain boundaries that are either ‘microhard’ (impenetrable to dislocations) or ‘microfree’ (an infinite dislocation sink).
Crystal plasticity; Grain boundary; Interface model; Strain gradients
Geometric quantum mechanics
Journal of Geometry and Physics
38
1
19-53
2001
10.1016/S0393-0440(00)00052-8
The manifold of pure quantum states can be regarded as a complex projective space endowed with the unitary-invariant Fubini-Study metric. According to the principles of geometric quantum mechanics, the physical characteristics of a given quantum system can be represented by geometrical features that are preferentially identified in this complex manifold. Here we construct a number of examples of such features as they arise in the state spaces for spin 12, spin 1, spin 32 and spin 2 systems, and for pairs of spin 12 systems. A study is then undertaken on the geometry of entangled states. A locally invariant measure is assigned to the degree of entanglement of a given state for a general multi-particle system, and the properties of this measure are analysed for the entangled states of a pair of spin 12 particles. With the specification of a quantum Hamiltonian, the resulting Schr??dinger trajectories induce an isometry of the Fubini-Study manifold, and hence also an isometry of each of the energy surfaces generated by level values of the expectation of the Hamiltonian. For a generic quantum evolution, the corresponding Killing trajectory is quasiergodic on a toroidal subspace of the energy surface through the initial state. When a dynamical trajectory is lifted orthogonally to Hilbert space, it induces a geometric phase shift on the wave function. The uncertainty of an observable in a given state is the length of the gradient vector of the level surface of the expectation of the observable in that state, a fact that allows us to calculate higher order corrections to the Heisenberg relations. A general mixed state is determined by a probability density function on the state space, for which the associated first moment is the density matrix. The advantage of a general state is in its applicability in various attempts to go beyond the standard quantum theory, some of which admit a natural phase-space characterisation. ?? 2001 Elsevier Science B.V.
81 P 99; Generalised quantum mechanics; Kibble-Weinberg theory; Quantum information and uncertainty; Quantum measurement and entanglement; Quantum mechanics; Quantum phase space
A three-segment anisomorphic constant life diagram for the fatigue of symmetric angle-ply carbon/epoxy laminates at room temperature
Composites Part A: Applied Science and Manufacturing
41
10
1498-1510
2010
10.1016/j.compositesa.2010.06.012
The anisomorphic constant fatigue life (CFL) diagram approach that was developed in an earlier study is further tested for applicability to the matrix-dominated fatigue failure in symmetric angle-ply carbon/epoxy laminates. An extension of the CFL diagram approach is also attempted to improve the accuracy of fatigue life prediction. The original anisomorphic CFL diagram approach can be used for approximately predicting the CFL diagrams for the [??30]3S and [??45]3S laminates, while it fails to accurately predict the CFL diagram for the [??60]3S laminate due to its significant local distortion. For accommodating the anisomorphic CFL diagram approach to the local distortion in CFL curves due to a significant change in mean stress sensitivity in fatigue, a transitional segment is inserted between the tension-tension and compression-compression dominated segments. It is demonstrated that the three-segment anisomorphic CFL diagram approach allows improved predictions of the CFL diagrams and S-N relationships for the angle-ply laminates. ?? 2010 Elsevier Ltd. All rights reserved.
A. Polymer matrix composites (PMCs); B. Fatigue; C. Analytical modeling; D. Mechanical testing
Heat transfer in thin films
Proceedings of the 3rd International Conference on Quantum, Nano and Micro Technologies, ICQNM 2009
73-76
2009
10.1109/ICQNM.2009.18
Heat transfer in thin films treats phonons as particles in the Boltzmann Transport Equation (BTE). However, phonons only allow slow thermal response. Rapid film heat transfer is possible provided films are allowed to promptly emit non-thermal electromagnetic (EM) radiation. Quantum mechanics (QM) used in the response of nanoparticles (NPs) is extended to thin films through the theory of QED induced EM radiation. Here QED stands for quantum electrodynamics. Atoms in thin films are generally under EM confinement at vacuum ultraviolet (VUV) levels that by QM are restricted to vanishing small levels of thermal kT energy, and therefore heat gain cannot be conserved by an increase in temperature. Heat is low frequency EM energy, and therefore the gain is conserved by VUV emission following QED induced up-conversion to the VUV confinement frequency of the film. The effective conductivity appears reduced only because EM emission is excluded from the heat balance. If included, the film maintains bulk conductivity through the thickness. The generality of QED induced EM radiation in thin films is extended to NPs that enhance heat transfer in nanofluids and as nanocatalysts increase the rate of chemical reactions.
Comparison of different stress-state dependent cohesive zone models applied to thin-walled structures
Engineering Fracture Mechanics
78
534-543
2011
10.1016/j.engfracmech.2010.05.003
Two different approaches that explicitly incorporate the stress triaxiality into cohesive zone models applicable to thin-walled structures are compared to identify the relative merits and limitation of these models. The number of model parameters involved, the ease of parameter determination and the predictive capabilities of the models over a wide range of thin-walled geometries are investigated. The first model, proposed recently by the authors, uses basic elastic-plastic constitutive equations combined with a model parameter depending on the average triaxiality in plane stress conditions. The second model incorporates stress-state through exponential dependence of cohesive strength on triaxiality, similar to plane strain studies earlier. The respective parameters for both models are identified and subsequently applied to several notched and precracked specimens. It is shown that in contrast to stress-state independent models, both constraint dependent models are able to predict well failure of a wide range of structures. While the model incorporating triaxiality dependent cohesive parameters has more parameters to be determined, it is not restricted to any specific stress condition and therefore can be extended to arbitrary three-dimensional stress-states. ?? 2010 Elsevier Ltd.
Cohesive zone model; Ductile fracture; Plane stress; Thin-walled structures; Triaxiality
Quantum Chaos and Statistical Mechanics
Quantum
77
2-3
6
2006
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
Fracture mechanics
International Journal of Solids and Structures
37
1-2
171-183
1986
The application of fracture mechanics to the design of ceramic structures will require the precise measurement of crack growth and fracture resistance of these materials over their entire range of anticipated service temperatures and standardized test methods for making such measurements. The development of a standard test for measuring the plane strain fracture toughness is sought. Stress intensity factor coefficients were determined for three varieties of chevron-notch specimens, and fracture toughness measurements were made on silicon nitrides, silicon carbides, and aluminum oxides to assess the performance of each specimen variety. It was determined that silicon nitride and silicon carbides have flat crack growth resistance curves, but aluminum oxide does not. Additionally, batch-to-batch differences were noticed for the aluminum oxide. Experiments are continuing to explain the rising crack growth resistance and batch-to-batch variations for the aluminum oxide.
Fracture mechanics in railway applications––an overview
Engineering Fracture Mechanics
72
2
163-194
2005
10.1016/j.engfracmech.2003.11.010
This paper gives a general introduction to fracture mechanics application to railway components as well as to the papers within this special issue. It is preluded by a brief discussion of various fracture control concepts such as safe-life, fail-safe and damage tolerance. Following this, an introduction to the most important damage tolerance issues of safety relevant railway components such as axles, wheels and rails is provided.
damage tolerance; fatigue crack extension; fracture mechanics; rails; railway axles; railway wheels
Probability and quantum mechanics
American Journal of Physics
66
11
967
1998
10.1119/1.19007
We discuss the use of probability theory in quantum mechanics, and suggest that there are some interpretations of quantum mechanics in which probabilities may be used inappropriately.
On the wrinkling of a pre-stressed annular thin film in tension
Journal of the Mechanics and Physics of Solids
55
8
1601-1617
2007
10.1016/j.jmps.2007.01.006
Asymptotic properties of the neutral stability curves for a linear boundary eigenvalue problem which models the wrinkling instability of an annular thin film in tension are considered. The film is subjected to imposed radial displacement fields on its inner and outer boundaries and, when these loads are sufficiently large, the film is susceptible to wrinkling. The critical values at which this onset occurs are dictated by the solution of a fourth-order ordinary differential eigensystem whose eigenvalue ?? is a function of ?? (??? 1), a quantity inversely proportional to the non-dimensional bending stiffness of the film, and n, the number of half-waves of the wrinkling pattern that sets in around the annular domain. Previously, Coman and Haughton [2006. Localised wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185, 179-200] employed the compound matrix method together with a WKB technique to characterise the form of ?? (??, n) which essentially is related to a turning point in a reduced eigenproblem. The asymptotic analysis conducted therein pertained to the case when this turning point was not too close to the inner edge of the annulus. However, in the thin film limit ?? ??? ???, the wrinkling load and the preferred instability mode are given by a modified eigenvalue problem that involves a turning point asymptotically close to the inner rim. Here WKB and boundary-layer asymptotic methods are used to examine these issues and comparisons with direct numerical simulations made. ?? 2007 Elsevier Ltd. All rights reserved.
Asymptotics; Boundary layers; Thin films; Turning points; Wrinkling
Determination of transverse compressive strength of long fibre composites by three-point bending of [90m/0n] cross-ply laminated strips
Polymer Testing
30
5
578-584
2011
10.1016/j.polymertesting.2011.04.012
A new test configuration is proposed for measuring transverse compressive strength of unidirectional composite laminates by three-point bending. A cross-ply configuration [90m/0n] has been chosen in order to get failure due to transverse compressive stresses. Thermal and mechanical stresses have been calculated based on hypotheses of classical beam theory. The optimal cross-ply configuration has been obtained by maximizing the ratio between maximum compressive stresses at the 90(grad) layer and maximum tensile stresses at the 0? layer. Cross-ply carbon/epoxy strips with different thicknesses have been tested in three-point bending until failure. The appearance of the transverse compressive damage has been found to agree well with that found in the literature for end-loaded compression tests.
transverse compressive strength
The influence of ply sequence and thermoelastic stress field on asymmetric delamination crack growth behavior of embedded elliptical delaminations in laminated FRP composites
Composites Science and Technology
66
3-4
417-426
2006
10.1016/j.compscitech.2005.07.017
The influence of ply lay up and the interaction of residual thermal stresses and mechanical loading on the interlaminar asymmetric embedded delamination crack growth behavior have been investigated. Two sets of full three-dimensional thermo-elastic finite element analyses have been performed for the interlaminar elliptical delaminations, which may be due to manufacturing defects or other reasons and are located symmetrically with respect to the midplane in a quasi-isotropic FRP composite laminate lay up. Depending upon the through-the-thickness location of the embedded elliptical delaminations, four different laminate configurations have been considered. Strain energy release rate (SERR) procedures have been employed to assess the delamination crack growth characteristics at the interfaces. It is found that the individual fracture modes exhibit asymmetric and non self-similar crack growth behavior along the delamination front depending upon the location of the interfacial delaminations; ply sequence and orientation and thermo-elastic anisotropy of the laminae. ?? 2005 Elsevier Ltd. All rights reserved.
A. Fibers; B. Thermo-mechanical properties; C. Delamination; C. Finite element analysis; C. Residual thermal stresses
Contact analysis of thin films bonded to graded coatings
International Journal of Mechanical Sciences
55
50-64
2012
10.1016/j.ijmecsci.2011.12.003
In this study, the contact mechanics of thin films bonded to graded coatings is investigated both analytically and numerically. In these problems, the stresses may be arisen due to uniform temperature changes and temperature excursions, far field mechanical loading, and residual stresses resulting from film processing or manufacturing process of the graded coatings. The primary interest in this study is the examination of the stress concentrations or singularities near the film ends. The underlying mechanics problem is formulated by assuming the film acts as a "membrane" and the graded coating as a functionally graded material (FGM). In the analytical formulation, the problem is reduced to a singular integral equation for the unknown interfacial shear stresses through an asymptotic expansion and then solved numerically using a suitable collocation technique. Finite Element Method (FEM) is utilized in the computational studies. The calculated results include interfacial shear stress between the film and the graded coating, strength of stress singularity at the film ends and the axial normal stress in the film. This study reveals that both mechanical and geometrical parameters of the system as well as the loading type have a great effect on the stress distribution and the strength of shear stress singularity at the film ends. Adjusting these parameters and selecting the appropriate type of grading will reduce these stresses that may have a bearing on the failure of the coating. © 2011 Elsevier Ltd. All rights reserved.
Coatings; Contact mechanics; Functionally graded materials; Stress singularity; Thin films
Finite element analyses of low-velocity impact damage of foam sandwiched composites with different ply angles face sheets
Materials & Design
47
189-199
2013
10.1016/j.matdes.2012.12.016
In the current studies, low-velocity impact properties and impact damage response of foam sandwiched composite with different ply angle face sheets were investigated experimentally and numerically. Low-velocity impact tests were performed using an instrumented Drop-Weight Machine (Instron 9250HV). The FE (finite element) software, ABAQUS/Explicit was employed to simulate low-velocity impact properties of foam sandwiched composite. A crushable foam model was used in order to explore core behaviors, while the Hashin criteria were used to predict the failure of the face sheets. The contact load histories, peak load, and energy absorption were obtained to compare the numerical and experimental results at several impact energy levels. The failure morphologies, damage size and damage shape were evaluated and compared with different types of sandwich structures. The comparisons illustrated the existence of a good agreement between the experimental and FEM results.
Absorbed energy; Failure morphologies; Finite element method; Foam sandwiched composites; Impact tests
Carbon composites based on multi-axial multi-ply stitched preforms. Part 7: Mechanical properties and damage observations in composites with sheared reinforcement
Composites Part A: Applied Science and Manufacturing
39
1380-1393
2008
10.1016/j.compositesa.2008.05.004
Biaxial multi-ply carbon fabrics (+45??/-45?? and 0??/90??) were sheared up to 30??, 45?? and 50?? using a shearing frame. The carbon/epoxy composite plates were made using resin transfer moulding. Tensile properties were measured in two principal directions and compared with results computed with the classical laminate theory and meso-scale finite element analysis. Damage initiation in laminates due to tensile loading was investigated using acoustic emission and X-ray radiography. Shearing changes the fibre orientation and hence the behaviour of the composites, leading to the shear angle dependence of damage initiation. Thermal cracks in composites with unsheared reinforcements, induced by post-curing, are not present in the composites with sheared reinforcement. The analysis of the experimental observations of the damage initiation and development is supported by finite element analysis. ?? 2008 Elsevier Ltd. All rights reserved.
A. Fabrics/textiles; A. Laminates; B. Mechanical properties; C. FEA; D. Mechanical testing
Effects of morphology on the decohesion of compressed thin films
Materials Science and Engineering: A
245
168-181
1998
10.1016/S0921-5093(97)00848-4
Residually compressed thin films are susceptible to spalling from substrates. A prerequisite for this to occur is that a separation develop at the interface large enough to allow buckling. Thereafter, the mechanisms of spalling are well-established, In this article, the mechanics of formation of the initial separation are addressed. Perturbations on the interface ale deemed responsible for this process. Calculations of energy release rates for various interface morphologies have revealed that aperiodic perturbations can initiate and extend the separations to a length sufficient for buckling. Conversely, periodic perturbations trap separations at dimensions too small to buckle. Illustrations are given for an alumina film (scale) on Ni-based superalloys. Implications for life prediction models are explored. (C) 1998 Elsevier Science S.A. All rights reserved.
decohesion; morphology; thin films
Mechanics and models of the myosin motor
Phil. Trans. R. Soc. Lond. B
355
1396
433-440
2000
10.1098/rstb.2000.0584
In striated muscles, shortening comes about by the sliding movement of thick filaments, composed mostly of myosin, relative to thin filaments, composed mostly of actin. This is brought about by cyclic action of 'cross-bridges' composed of the heads of myosin molecules projecting from a thick filament, which attach to an adjacent thin filament, exert force for a limited time and detach, and then repeat this cycle further along the filament. The requisite energy is provided by the hydrolysis of a molecule of adenosine triphosphate to the diphosphate and inorganic phosphate, the steps of this reaction being coupled to mechanical events within the cross-bridge. The nature of these events is discussed. There is good evidence that one of them is a change in the angle of tilt of a 'lever arm' relative to the 'catalytic domain' of the myosin head which binds to the actin filament. It is suggested here that this event is superposed on a slower, temperature-sensitive change in the orientation of the catalytic domain on the actin filament. Many uncertainties remain.
Actins; Actins: chemistry; Actins: physiology; Animals; Biological; Biomechanics; Models; Molecular Motor Proteins; Molecular Motor Proteins: chemistry; Molecular Motor Proteins: physiology; Muscle; Muscle Contraction; Muscle Contraction: physiology; Myosins; Myosins: chemistry; Myosins: physiology; Skeletal; Skeletal: physiology
The behavior of cracked cross-ply composite laminates under shear loading
International Journal of Solids and Structures
29
24
3251-3267
1992
10.1016/0020-7683(92)90039-V
An interlaminar-shear-stress analysis developed earlier by Tsai et al. (1990, Micro-cracking-Induced Damage in Composites) for a [φm/θn], bi-directional composite laminate is used to solve the case of a cross-ply [0m/90n]x laminate with the 90° layer only or both layers cracked under pure shear loading. Strains, forces and laminate shear modulus reduction due to matrix cracking were obtained. Experimental results for shear modulus as a function of crack densities were obtained by a simple shear test and they agree very well with the theoretical prediction.
Application of the Paris Equation to the Fatigue Growth of Transverse Ply Cracks
Journal of Composite Materials
23
7
735-754
1989
10.1177/002199838902300706
A model based on a stress intensity factor for a growing transverse ply crack is outlined. The model is applied to experimental observations of crack growth in a trans parent 0/90/0 glass fibre/epoxy laminate under fatigue loading. The crack growth rate is found to be independent of crack length but to depend on the spacing between cracks. Under static loading and fatigue loading at high maximum stress, cracks grow by fast frac ture. Slow crack growth is observed at lower maximum fatigue stresses and in the later stages of fatigue tests at higher stresses when the crack spacing is small. Crack growth rates can be described using a Paris relation.
Reinforced concrete: mechanics and design
Canadian Journal of Civil Engineering
27
6
1316
2000
10.1139/l00-087
Reinforced Concrete: Mechanics and Design, 6/e is a perfect text for professionals in the field who need a comprehensive reference on concrete structures and the design of reinforced concrete. Reinforced concrete design encompasses both the art and science of engineering. This book presents the theory of reinforced concrete as a direct application of the laws of statics and mechanics of materials. In addition, it emphasizes that a successful design not only satisfies design rules, but also is capable of being built in a timely fashion and for a reasonable cost. A multi-tiered approach makes Reinforced Concrete: Mechanics and Design an outstanding textbook for a variety of university courses on reinforced concrete design. Topics are normally introduced at a fundamental level, and then move to higher levels where prior educational experience and the development of engineering judgment will be required.
On the Fluid Mechanics of Fires
Annual Review of Fluid Mechanics
33
67-92
2001
10.1146/annurev.fluid.33.1.67
? Abstract? Fluid mechanics research related to fire is reviewed with a focus on canonical flows, multiphysics coupling aspects, and experimental and numerical techniques. Fire is a low-speed, chemically reacting flow in which buoyancy plays an important role. Fire research has focused on two canonical flows, the reacting boundary layer and the reacting free plume. There is rich, multilateral, bidirectional coupling among fluid mechanics and scalar transport, combustion, and radiation. There is only a limited experimental fluid mechanics database for fire owing to measurement difficulties in the harsh environment and to the focus within the fire community on thermal/chemical consequences. Increasingly, computational fluid dynamics techniques are being used to provide engineering guidance on thermal/chemical consequences and to study fire phenomenology.
boundary layers; buoyancy; non-premixed combustion; plumes; turbulence
Bending analysis of thin functionally graded plates using generalized differential quadrature method
Archive of Applied Mechanics
81
11
1523-1539
2011
10.1007/s00419-010-0499-3
In this paper, the differential quadrature (DQ) method is presented for easy and effective analysis of isotropic functionally graded (FG) and functionally graded coated (FGC) thin plates with constant Poisson's ratio and varying Young's modulus in the thickness direction. The bending of FG and FGC plates under transverse loading has been studied using the polynomial differential quadrature (PDQ) and the harmonic differential quadrature (HDQ) methods. A three-dimensional elasticity solution for a moderately thick FG plate with exponential Young's modulus is used as the benchmark. Two examples, including a thin FG rectangular plate and a thin FGC rectangular plate with sigmoidal Young's modulus, are investigated. The numerical results of PDQ and HDQ methods reveal good agreement with other solutions. Also, it is shown that the formulations for thin FG plates and homogeneous plates are similar, except that the plane strain components of the middle surface in FG plates are not zero. © 2011 Springer-Verlag.
Bending analysis; Differe; Differential quadrature; Differentiation (calculus); Elast; Elastic moduli; Numerical methods
Analysis of super-cooled water droplet impact on a thin water layer and ice growth
44th AIAA Aerospace Sciences Meeting and Exhibit
466
2006
10.2514/6.2006-466
The mechanics and heat flow of the impact and freezing of a Super-cooled Large Droplet (SLD) on to a thin mobile water layer is considered in the parameter range of interest to airframe icing. A series of 2-D Navier-Stokes solutions for droplet impact are presented. These simulations show the formation, ejection and break-up of splashed off jets and the freezing process. The simulations are compared critically to experiments performed under similar conditions.
Mechanics of stretchable electronics and soft machines
MRS Bulletin
37
03
218-225
2012
10.1557/mrs.2012.32
In the emerging field of soft machines, large deformation of soft materials is harnessed to provide functions such as regulating flow in microfluidics, shaping light in adaptive optics, harvesting energy from ocean waves, and stretching electronics to interface with living tissues. Soft materials, however, do not provide all of the requisite functions; rather, soft machines are mostly hybrids of soft and hard materials. In addition to requiring stretchable electronics, soft machines often use soft materials that can deform in response to stimuli other than mechanical forces. Dielectric elastomers deform under a voltage. Hydrogels swell in response to changes in humidity, pH, temperature, and salt concentration. How does mechanics meet geometry, chemistry, and electrostatics to generate large deformation? How do molecular processes affect the functions of transducers? How efficiently can materials convert energy from one form to another? These questions are stimulating intriguing and useful advances in mechanics. This review highlights the mechanics that enables the creation of soft machines.
Localized necking in thin sheets
Journal of the Mechanics and Physics of Solids
23
421-441
1975
10.1016/0022-5096(75)90004-6
By using a simplified constitutive model of a pointed vertex on subsequent yield loci, namely, such that the equations of deformation-theory of rigid-plastic solids apply for fully-active stress increments, the onset of localized necking under biaxial stretching has been predicted. The predictions agree reasonably well with reported experimental observations. Since localized necking under biaxial stretching of a uniform and homogeneous sheet is impossible when flow theories of plasticity with smooth yield-loci are used, this result supports the hypothesis of vertex-formation on the yield locus under continued plastic flow. The implications of this conclusion with respect to the study of the inception of ductile fracture in solids, viewed as a material instability, may be far-reaching. Still, explanations based on a smooth yield-locus but small initial inhomogeneities cannot be ruled out, and both initial imperfections and yield-vertex effects may contribute in general to localization instabilities.
Photoluminescence of barium titanate and barium zirconate in multilayer disordered thin films at room temperature
Journal of Physical Chemistry A
112
8938-8942
2008
10.1021/jp801610y
The emission of wide band photoluminescence showed a synergic effect on barium zirconate and barium titanate thin films in alternate multilayer system at room temperature by 488 nm exiting wavelength. The thin films obtained by spin-coating were annealed at 350, 450, and 550 degrees C for 2 h. The X-ray patterns revealed the complete separation among the BaTiO3 and BaZrO3 phases in the adjacent films. Visible and intense photoluminescence was governed by BaZrO3 thin films in the multilayer system. Quantum mechanics calculations were used in order to simulate ordered and disordered thin films structures. The disordered models, which were built by using the displacement of formers and modifier networks, showed a different symmetry in each system, which is in accordance with experimental photoluminescence emission, thus allowing to establish a correlation among the structural and optical properties of these multilayered systems.
Extension during active collision in thin-skinned wedges: Insights from laboratory experiments
Geology
36
475-478
2008
10.1130/G24718A.1
The occurrence of strike-normal extension in mountain belts undergoing active contraction is not predicted by analytical solutions for the mechanics of purely frictional orogens. To test the idea that ductile rocks at depth might allow extensional deformation to occur in otherwise frictional and contractional orogens, we have conducted a series of analog experiments with purely frictional and layered frictional-ductile rheologies. By precisely measuring the horizontal deformation field, we have quantitatively confirmed the qualitative observation that analog frictional wedges do not extend. This is consistent with published numerical models, and is in contrast to purely viscous models that commonly display coeval extension with contraction. Our modeling also demonstrates that layered frictional-ductile models can, during active convergence, result in discrete extensional normal faulting even when only a relatively thin ductile layer is present. The resulting extension, though relatively small in magnitude compared to the active contraction, can greatly modify the final profile of a convergent orogen and can lead to the formation of a broad plateau between the pro-wedge and the retro-wedge.
Analog modeling; Bivergent wedge; Normal faulting; Rheology; Thin-skinned tectonics
Determining the Elastic Modulus of Compliant Thin Films Supported on Substrates from Flat Punch Indentation Measurements
Experimental Mechanics
53
January
931-941
2013
10.1007/s11340-012-9705-2
Instrumented indentation is a technique that can be used to measure the elastic properties of soft thin films supported on stiffer substrates, including polymer films, cellulosic sheets, and thin layers of biological materials. When measuring thin film properties using indentation, the effect of the substrate must be considered. Most existing models for determining the properties of thin films from indentation measurements were developed for metal and dielectric films bonded to semiconductor substrates and have been applied to systems with film-substrate modulus ratios between 0.1 and 10. In the present work, flat punch indentation of a thin film either bonded to or in contact with a substrate is examined using finite element modeling. A broad range of film-substrate modulus ratios from 0.0001 to 1 are investigated. As the substrate is effectively rigid compared to the film when the film-substrate modulus ratio is less than 0.0001, the results are also useful for understanding systems with lower film-substrate modulus ratios. The effects of the contact radius, film thickness, elastic properties, and friction between the film and the substrate on the measured stiffness were quantified using finite element modeling in order to understand how the elastic properties of the film can be extracted from indentation measurements. A semi-analytical model was developed to describe the finite element modeling results and facilitate the use of the results to analyze experimental measurements. The model was validated through analysis of indentation measurements of thin polyethylene sheets that were supported on substrates of various stiffness.
Finite elements; Indentation; Soft materials; Substrate effects; Thin films
Numerical analysis of a red blood cell flowing through a thin micropore
Physical Review E
89
1
013008
2014
10.1103/PhysRevE.89.013008
Red blood cell (RBC) deformability plays a key role in microcirculation, especially in vessels that have diameters even smaller than the nominal cell size. In this study, we numerically investigate the dynamics of an RBC in a thin micropore. The RBC is modeled as a capsule with a thin hyperelastic membrane. In a numerical simulation, we employ a boundary element method for fluid mechanics and a finite element method for membrane mechanics. The resulting RBC deformation towards the flow direction is suppressed considerably by increased cytoplasm viscosity, whereas the gap between the cell membrane and solid wall becomes smaller with higher cytoplasm viscosity. We also measure the transit time of the RBC and find that nondimensional transit time increases nonlinearly with respect to the viscosity ratio, whereas it is invariant to the capillary number. In conclusion, cytoplasmic viscosity plays a key role in the dynamics of an RBC in a thin pore. The results of this study will be useful for designing a microfluidic device to measure cytoplasmic viscosity.
Thermomechanical Behavior of Thin Metal Films under Different Ambient Conditions
AIP Conference Proceedings
817
98-103
2006
10.1063/1.2173537
We present measurements on the thermomechanical properties of thin copper and gold films on substrates tested under vacuum and in a nitrogen flow ambient. The differences observed can be attributed to a native oxide layer on the copper surface that is removed under vacuum conditions but is present during experiments in inert atmosphere. This result hints to the importance of surface properties for thin film mechanics. © 2006 American Institute of Physics.
Copper; Diffusion; Oxide; Substrate curvature; Surface; Thin film
Warp field mechanics 101
JBIS - Journal of the British Interplanetary Society
66
7-8
242-247
2013
This paper will begin with a short review of the Alcubierre warp drive metric and describes how the phenomenon might work based on the original paper.
Boost; Brane; Bulk; Warp; York Time
Active auditory mechanics in mosquitoes.
Proceedings. Biological sciences / The Royal Society
268
September 2000
333-339
2001
10.1098/rspb.2000.1376
In humans and other vertebrates, hearing is improved by active contractile properties of hair cells. Comparable active auditory mechanics is now demonstrated in insects. In mosquitoes, Johnston's organ transduces sound-induced vibrations of the antennal flagellum. A non-muscular 'motor' activity enhances the sensitivity and tuning of the flagellar mechanical response in physiologically intact animals. This motor is capable of driving the flagellum autonomously, amplifying sound-induced vibrations at specific frequencies and intensities. Motor-related electrical activity of Johnston's organ strongly suggests that mosquito hearing is improved by mechanoreceptor motility.
active sensation; bioacoustics; cell motility; insect ear; mechanotransduction; otoacoustic emissions
Determination of residual stress in thin films: A comparative study of X-ray topography versus laser curvature method
Thin Solid Films
415
21-31
2002
10.1016/S0040-6090(02)00489-3
The residual stress in thin films has been determined by X-ray diffraction and laser scanning methods. The usual procedure is to measure the strain via lattice or physical curvature analysis and then to calculate the stress using continuum mechanics models. X-ray and laser techniques measure different physical quantities. In the former case, the curvature of crystal lattice planes is assessed while in the latter situation the curvature of physical surface of the sample is measured. In principle, these two methods should yield the same results. The current experiments use the latest two-dimensional X-ray double crystal diffraction topography (DCDT) and a laser scanning technique (LST) to determine the quantities of interest for a variety of thin films deposited on Si (1 0 0) wafers. The measurements by the two techniques were performed on the same samples, at the same time, under exactly identical conditions. For specimens where the residual stresses produce large curvatures of both types (lattice curvature and surface curvature), the results for DCDT and LST agree within the experimental error. When small to moderate curvatures are present, the two methods deviate to varying degrees. This deviation is of special significance in determining residual stress in nanometer-thickness films. Nevertheless, DCDT and LST generally yield similar results on differential curvatures, i.e. the stress induced curvature differentials. When proper consideration is taken for the inherent limits of each technique, both DCDT and LST can be used as valid procedures for stress measurement in thin film-substrate systems. © 2002 Elsevier Science B.V. All rights reserved.
Double crystal diffraction topography; Laser scanning; Stress; X-ray diffraction
Effect of surface stress on the stiffness of thin elastic plates and beams
Physical Review B - Condensed Matter and Materials Physics
85
8
1-4
2012
10.1103/PhysRevB.85.085440
Nanomechanical doubly-clamped beams and cantilever plates are often used to sense a host of environmental effects, including biomolecular interations, mass measurements, and responses to chemical stimuli. Understanding the effects of surface stress on the stiffness of such nanoscale devices is essential for rigorous analysis of experimental data. Recently, we explored the effects of surface stress on cantilever plates and presented a theoretical framework valid for thin plate structures. Here, we generalize this framework and apply it to cantilever plates and doubly-clamped beams, exploring in detail the relative physical mechanisms causing a stiffness change in each case. Specifically, Poisson's ratio is found to exert a dramatically different effect in cantilevers than in doubly-clamped beams, and here we explain why. The relative change in effective spring constant is also examined, and its connection to the relative frequency shift is discussed. Interestingly, this differs from what is naively expected from elementary mechanics. Finally, a discussion of the practical implications of our theoretical findings is presented, which includes an assessment of available experimental results and potential future measurements on nanoscale devices.
Are the hydrodynamic forces and torques zero during the electrophoresis of multiparticle systems with thin debye layers?
Mechanics Research Communications
36
1
39-45
2009
10.1016/j.mechrescom.2008.08.007
A commonly used result in electrophoresis is that a swarm of insulating particles of any shape and size, in any configuration, with the same slip condition (i.e. with the same zeta potential and infinitesimally thin Debye layers), moves with the same electrophoretic velocity as a single isolated particle. The objective of this paper is to prove this general result and review its implications.
CdSe; counterion-condensation; Electrophoresis; ellipsoid; Hydrodynamic force; Potential flow; Similarity solution; spom; Thin Debye layer
Creep behavior of unidirectional and angle-ply T800H/3631 laminates at high temperature and simulations using a phenomenological viscoplasticity model
Composites Science and Technology
64
2373-2384
2004
10.1016/j.compscitech.2004.04.004
High-temperature creep behavior of symmetric angle-ply laminates made of unidirectional T800H/3631 carbon/epoxy composite is examined at relatively high stress levels. Constant-stress creep tests in tension are performed at 100 ??C for 5 h on plain coupon specimens of three types of angle-ply laminates [??30]3S [??45]3S and [??60]3S under load control conditions. For each angle-ply laminate, creep tests are carried out at three different stress levels. Creep strain recovery following the 5-h creep is also observed for 5 h at the same temperature, after completely removing the creep stress. Creep responses are clearly observed in all kinds of angle-ply laminates. The creep strain rate in the angle-ply laminates tends to rapidly disappear as the creep strain increases. The transient creep is thus dominant in the angle-ply laminates, regardless of the fiber orientations. The prior creep strain does not completely recover with time after removing the creep stress, which indicates certain inelastic mechanisms have operated with creep. Similar features are also observed for the off-axis creep behavior of the unidirectional laminates of the same composite system. A whole history consisting of the prior instantaneous elastoviscoplastic behavior at a constant strain rate and the subsequent creep response at a constant stress level is simulated using the classical laminated plate theory and a phenomenological viscoplasticity model for individual plies. Material constants involved by the ply viscoplasticity model are identified on the basis of the off-axis creep behavior for unidirectional laminates. It is demonstrated that excellent agreements between the predicted and observed results are obtained by additionally taking into account the fiber rotation induced by deformation. ?? 2004 Elsevier Ltd. All rights reserved.
A. Polymer matrix composites; B. Creep; B. High temperature properties; Carbon/epoxy; C. Laminates; Viscoplasticity
Modeling of initial geometrical imperfections in stability analysis of thin-walled structures
Journal of Theoretical and Applied Mechanics
47
3
667-684
2009
Imperfections are modeled using actual values measured in situ. The method proposed in the paper is based on the concept of developing the imperfections in series of eigenmodes, using a limited number of most critical eigenmodes. Error minimization of this representation is performed. The method is applied to the nonlinear stability analysis of structures made of steel thin-walled cold-formed sigma profiles. FEM with shell elements and the Riks method are used. Numerical examples illustrate the influence of initial imperfections on post buckling behavior of structures.
Cold-formed; Initial geometrical imperfections; Initial geometric imperfection; Initial geometric imperfections; Initial imperfection; Mechanics; Nonlinear stability analysis; Postbuckling behavior; Stability analysis; Stability of cold-formed bars; Thin-walled beam; Thin-walled beams; Thin walled structures
Analysis and design of pultruded FRP shapes under bending
Composites Part B: Engineering
27
95
295-305
1996
10.1016/1359-8368(95)00015-1
A comprehensive approach for the analysis and design of pultruded FRP beams in bending is presented. It is shown that the material architecture of pultruded FRP shapes can be efficiently modeled as a layered system. Based on the information provided by the material producers, a detailed procedure is presented for the computation of fiber volume fraction (Vf) of the constituents, including fiber bundles or rovings, continuous strand mats, and cross-ply and angle-ply fabrics. Using the computed Ffs, the ply stiffnesses are evaluated from selected micromechanics models. The wall or panel laminate engineering constants can be computed from the ply stiffnesses and macromechanics, and it is shown that the predictions correlate well with coupon test results. The bending response of various H and box sections is studied experimentally and analytically. The mechanics of laminated beams (MLB) model used in this study can accurately predict displacements and strains, and it can be used in engineering design and manufacturing optimization of cross-sectional shapes and lay-up configurations. The experimental results agree closely with the MLB predictions and finite element verifications.
Experimental results; Finite elements; FRP shapes; Laminated beams; Micromechanics; Modeling; Pultrusion
Sliding mechanics with microscrew implant anchorage
Angle Orthodontist
74
5
703-710
2004
10.1043/0003-3219(2004)074<0703:SMWMIA>2.0.CO;2
AIM: To show the effectiveness of sliding mechanics used with microscrew implants in managing a dentoalveolar protrusion. There are several advantages, including reduced treatment time, simplified treatment mechanics, early profile changes, and elimination of interarch mechanics. MATERIAL AND METHODS: A step-by-step procedure for microscrew implant anchorage sliding mechanics is shown, with records of treated patients, which demonstrate the aforementioned advantages of this technique. The associated biomechanics and theoretical explanation follow. RESULTS: The authors show how the microscrew implant can provide anchorage for en masse retraction of six anterior teeth and the efficiency and ease of the mechanics in managing a dentoalveolar protrusion. CONCLUSION: The microscrew implant offers orthodontic clinicians a minimally intrusive method of intra-arch anchorage that can retract the anterior teeth without the anchorage loss that is expected in conventional techniques. Sliding mechanics used with microscrew implants is shown to be simple and efficient.
Absolute anchorage; Microscrew implants; Skeletal class II malocclusion; Sliding mechanics with MIA
Determination of the yield properties of thin films using enhanced coherent gradient sensing
Experimental Mechanics
41
4
403-411
2001
10.1007/BF02323934
This paper describes coherent gradient sensing (CGS) as an optical, full-field, real-time, nonintrusive, non-contact technique for measurement of curvature and curvature changes in single-layered and multilayered thin films deposited on substrates. The sensitivity of the basic CGS technique is enhanced using optical fringe multiplication to map curvature in very flat specimens (K ≤ 0.001 m<sup>-1</sup>). Subsequently, this curvature measurement technique is applied to the determination of the yield properties of thin films subjected to cyclic thermomechanical loading.
Coherent gradient sensing; Curvature; Deposits; film; Gradient sensing; Loading; Sensitivity analysis; sensor; Stress; Thin films; yield stress
Morphological stability of epitaxial thin elastic films by van der Waals force
Archive of Applied Mechanics (Ingenieur Archiv)
72
1
77-84
2002
10.1007/s004190100194
The morphological stability of epitaxial thin elastic films on a substrate\nby van der Waals force is discussed. It is found that only van der\nWaals force with negative Hamaker constant (A < 0) tends to stabilize\nthe film, and the lower bound for the Hamaker constant is also obtained\nfor the stability of thin film. The critical value of the undulation\nwavelength is found to be a function of both film thickness and external\nstress. The characteristic time-scale for surface mass diffusion\nscales to the fourth power to the wavelength of the perturbation.
elasticity; epitaxial thin film; morphological; perturbation; van der waals force
Mechanics of F-actin characterized with microfabricated cantilevers.
Biophysical journal
83
5
2705-15
2002
10.1016/S0006-3495(02)75280-6
In this report we characterized the longitudinal elasticity of single actin filaments manipulated by novel silicon-nitride microfabricated levers. Single actin filaments were stretched from zero tension to maximal physiological tension, P(0). The obtained length-tension relation was nonlinear in the low-tension range (0-50 pN) with a resultant strain of approximately 0.4-0.6% and then became linear at moderate to high tensions (approximately 50-230 pN). In this region, the stretching stiffness of a single rhodamine-phalloidin-labeled, 1-microm-long F-actin is 34.5 +/- 3.5 pN/nm. Such a length-tension relation could be characterized by an entropic-enthalpic worm-like chain model, which ascribes most of the energy consumed in the nonlinear portion to overcoming thermal undulations arising from the filament's interaction with surrounding solution and the linear portion to the intrinsic stretching elasticity. By fitting the experimental data with such a worm-like chain model, an estimation of persistence length of approximately 8.75 microm was derived. These results suggest that F-actin is more compliant than previously thought and that thin filament compliance may account for a substantial fraction of the sarcomere's elasticity.
Actins; Actins: chemistry; Animals; Biophysics; Biophysics: instrumentation; Biophysics: methods; Chickens; Entropy; Hot Temperature; Microscopy, Confocal; Microscopy, Confocal: methods; Microscopy, Fluorescence; Microscopy, Fluorescence: methods; Microscopy, Video; Microscopy, Video: methods; Oscillometry; Phalloidine; Phalloidine: pharmacology; Rhodamines; Rhodamines: pharmacology; Sarcomeres; Sarcomeres: chemistry; Silicon Compounds; Silicon Compounds: chemistry; Temperature; Thermodynamics
The Influence of Ply Design and Thermal Fatigue on Mechanical property of Glass Fiber/Epoxy Composite
Advanced Materials, Pts 1-4
239-242
269-272
2011
DOI 10.4028/www.scientific.net/AMR.239-242.269
In this paper, the influence of different ply designs and thermal fatigue on the mechanical property of glass fiber/epoxy composite have been investigated. Four different ply designs ([0](20), [0/90](10), [0/90/45/-45](5), [45/-45](10)) were used to manufacture glass fiber/epoxy composite according to laminated plates design principles. Through different thermal cycles (0,60,120,180 cycles), it was found that the mechanical property of different ply of glass fiber/epoxy matrix composites was decreased due to the debonding effect of glass fiber/epoxy matrix interfacial layer and the increase of pores.
epoxy prepreg; mechanical property; ply design; thermal fatigue
Proper particle mechanics
Journal of Mathematical Physics
15
10
1768
1974
10.1063/1.1666540
Spacetime algebra is employed to formulate classical relativistic mechanics without coordinates. Observers are treated on the same footing as other physical systems. The kinematics of a rigid body are expressed in spinor form and the Thomas precession is derived.
Mechanics of Materials and Structures
Materials and Structures
2
June
1059–1086
2007
10.2140/jomms.2011.6.361
In this paper effective material properties of randomly distributed short fiber composites are calculated with a developed comprehensive tool for numerical homogenization. We focus on the influence of change in volume fraction and length/diameter aspect ratio of fibers. Two types of fiber alignments are considered: fiber orientations with arbitrary angles and parallel oriented fibers. The algorithm is based on a numerical homogenization technique using a unit cell model in connection with the finite element method. To generate the three-dimensional unit cell models with randomly distributed short cylindrical fibers, a modified random sequential adsorption algorithm is used, which we describe in detail. For verification of the algorithm and checking the influence of different parameters, unit cells with various fiber embeddings are created. Numerical results are also compared with those from analytical methods.
Growth of magnetic thin films using CO2 RESS expansions
The Journal of Supercritical Fluids
42
3
410-418
2007
10.1016/j.supflu.2006.11.002
A continuous-flow rapid expansion of supercritical solution (RESS) apparatus is used to grow thin iron oxide thin films under ambient and vacuum conditions. The magnetic thin films are produced by expanding a supercritical solution of ferric acetylacetonate (Fe(acac)3) and CO2 and directing the resulting supersonic jet onto both hot and cold silicon wafers. The concentration of the expanding solution is monitored in-line with a UV-vis high pressure view cell which is also used to perform solubility measurements. The resulting films contain nano- and sub-micronic particles in the 13-700 nm size range and show magnetic order. Structural and magnetic data for these thin particle films have been obtained by SQUID and SEM measurements and compared as a function of substrate surface temperature, growth times, and initial solute concentrations. Experimental and theoretical analysis of the thermodynamics and fluid mechanics appropriate for this RESS process is discussed.
Ferric acetylacetonate; Iron oxide; Magnetic particles; Nanoparticles; Rapid expansion of supercritical solutions; Supercritical fluids
Effect of Longitudinal Stress Gradients on Elastic Buckling of Thin Plates
Journal of Engineering Mechanics
133
4
452-463
2007
10.1061/(ASCE)0733-9399(2007)133:4(452)
This paper analyzes the effect of longitudinal stress gradients on the elastic buckling of thin isotropic plates. Two types of thin plates are considered: (1) a plate simply supported on all four edges and rotationally restrained on two longitudinal edges; and (2) a plate simply supported on three edges with one longitudinal edge free and the opposite longitudinal edge rotationally restrained. These two cases illustrate the influence of longitudinal stress gradient on stiffened and unstiffened elements, respectively. A semianalytical method is derived and presented herein to calculate the elastic-buckling stress of both types of rectangular thin plates subjected to nonuniform applied longitudinal stresses. Finite-element analysis using ABAQUS is employed to validate the semianalytical model for plates with fixed and/or simple supports. Empirical formulas are produced to calculate the buckling coefficients of plates with fixed and/or simple supports under longitudinal stress gradients. The results help establish a better understanding of the effect of longitudinal stress gradients on the elastic buckling of thin plates and are intended to aid in the development of design provisions to include these effects in the strength prediction of thin-walled beams under moment gradients. © 2007 ASCE.
Buckling; Cold-formed steel; Elasticity; Plates; Stability; Thin wall structures
Heart mechanics using mathematical modelling
of Second NZ Postgraduate Conference for
1
1-5
1995
Heart failure is a leading cause of death in New Zealand. In order to determine the causes of rhythm disturbances leading t o failure a knowledge of the structure and mechanical behaviour of cardiac tissue is important. This paper presents reali stic stress and strain distributions for the passive heart that h ave been reproduced using a three-dimensional finite element model of the ventricles based on finite deformation analysis of elastic bodies. The geometry and structure of the ventric les have been accurately described using a mathematical model that combines a prolate spheroidal coordinate system with high order interpolation schemes to minimise the number of d egrees of freedom. A fully orthotropic constitutive relati on, based on in vitro biaxial tests and observations of cardiac microstructure, is used to describe the stress-strain properties of myocardial tissue. The parameters of the constitutive rela tion are estimated using a combination of biaxial stress-strain tests on thin myocardial sections and 3D deformation fields derived from non-invasive MRI tagging techniques.
Improved flexural–torsional stability analysis of thin-walled composite beam and exact stiffness matrix
International Journal of Mechanical Sciences
49
8
950-969
2007
10.1016/j.ijmecsci.2007.01.007
A simple but efficient method to evaluate the exact element stiffness\nmatrix is newly presented in order to perform the spatially coupled\nstability analysis of thin-walled composite beams with symmetric\nand arbitrary laminations subjected to a compressive force. For this,\nthe general bifurcation-type buckling theory of thin-walled composite\nbeam is developed based on the energy functional, which is consistently\nobtained corresponding to semitangential rotations and semitangential\nmoments. A numerical procedure is proposed by deriving a generalized\neigenvalue problem associated with 14 displacement parameters, which\nproduces both complex eigenvalues and multiple zero eigenvalues.\nThen the exact displacement functions are constructed by combining\neigenvectors and polynomial solutions corresponding to non-zero and\nzero eigenvalues, respectively. Consequently exact element stiffness\nmatrices are evaluated by applying member force–displacement relationships\nto these displacement functions. As a special case, the analytical\nsolutions for buckling loads of unidirectional and cross-ply laminated\ncomposite beams with various boundary conditions are derived. Finally,\nthe finite element procedure based on Hermitian interpolation polynomial\nis developed. In order to verify the accuracy and validity of this\nstudy, the numerical, analytical, and the finite element solutions\nusing the Hermitian beam elements are presented and compared with\nthose from ABAQUS's shell elements. The effects of fiber orientation\nand the Wagner effect on the coupled buckling loads are also investigated\nintensively.
arbitrary; coupled buckling loads; exact stiffness matrix; semitangential moment; semitangential rotation; thin-walled composite beam
Peridynamic Theory of Solid Mechanics
Advances in Applied Mechanics
44
73-168
2010
10.1016/S0065-2156(10)44002-8
The classical theory of solid mechanics is based on the assumption of a continuous distribution of mass within a body and all internal forces are contact forces that act across zero distance. The mathematical description of a solid that follows from these assumptions relies on PDEs that additionally assume sufficient smoothness of the deformation for the PDEs to make sense in their either strong or weak forms. The classical theory has been demonstrated to provide a good approximation to the response of real materials down to small length scales, particularly in single crystals, provided these assumptions are met. Nevertheless, technology increasingly involves the design and fabrication of devices at smaller and smaller length scales, even interatomic dimensions.
An energy method to analyze through thickness thin film fracture during indentation
Thin Solid Films
515
6
3298-3304
2007
10.1016/j.tsf.2006.01.043
Nanoindentation was utilized to induce fracture of brittle thin oxide\nfilms on compliant substrates. The energies were calculated from\nintegrating the resulting load-depth curves from indentation. The\ntotal energy applied to the system is a superposition of the energy\nto deform the substrate and the energy to fracture the film. The\napplied energy to deform the compliant substrate was separated from\nthe energy applied to the film/substrate system resulting in the\nenergy to fracture the film. The energy for fracture was then converted\nto a crack extension force and a stress intensity using linear elastic\nfracture mechanics. The toughness of thermally grown aluminum oxides\nis between 0.37 and 0.83 MPa m0.5, and tends to decrease as film\nthickness increases over the range of 25 to 63 nm.
energy; fracture; thin films
Survey of current fracture mechanics studies at AMMRC
Engineering Fracture Mechanics
5
4
881-908
1973
10.1016/0013-7944(73)90055-6
The fracture and fatigue studies at AMMRC encompass both experimental and analytical thrusts. This presentation will cover a few representative activities. The status of a test program on fracture behavior of unidirectionally reinforced composites using double cantilevered type specimens will be reported. Material systems include ‘S’ glass/epoxy and graphite/epoxy. Limited fracture toughness data is available. Additionally, some effort has been initiated on cross ply specimens. Fatigue studies at AMMRC in metals reflect a continuing interest in both initiation and propagation aspects. A technique has been developed for detection of crack initiation using an automated photographic process for recording, periodically, potential initiation sites. The observations are discussed in conjunction with damage criteria. Crack propagation studies have focussed in developing a ‘law’ which accounts for the extremes of propagation rates at threshold levels of stress intensity and at the higher levels associated with unstable growth. Additionally, crack propagation experiments are described which are aimed at exploring the transient effects on crack propagation of sudden changes in stress intensity levels. Supplementing these experimental studies are extensive analytical efforts directed toward defining the stress states in anisotropic material when used in lap and/or mechanical joint configurations. Additionally, extensive effort by one team of investigators has been devoted to analytical techniques for crack analysis. These techniques have been applied to a wide variety of geometric configurations and to a range of material types including anisotropic. This effort will be described briefly.
(i) An introduction to basic mechanics
Current Orthopaedics
20
1-8
2006
10.1016/j.cuor.2005.09.003
The principles of solid mechanics have many important applications in orthopaedics. The aim of this paper is to cover the basic concepts of statics and dynamics, including both kinetics and kinematics. The equations most commonly used in biomechanical analysis are introduced and examples are given of their use in orthopaedic applications. ?? 2005 Elsevier Ltd. All rights reserved.
Biomechanics; Dynamics; Mechanics; Statics
Tensile properties of fibre-reinforced metals: fracture mechanics
Journal of the Mechanics and Physics of Solids
15
4
279-297
1967
10.1016/0022-5096(67)90017-8
Experiments have been designed to study how a material reinforced with aligned fibres fails at the root of a notch. Ductile adn brittle tungsten wires and silica fibres have been introduced into a copper matrix made either by casting or by electrodeposition. A completely notch-insensitive composite can be produced provided splitting is tolerated parallel to the fibres. In these experiments splitting appears to occur in shear. If splitting does not occur then it is shown experimentally for thin sheets that fracture is governed by the established rules of fracture mechancis. The contribution of the matrix to the work fo fracture is assessed. An important result is that the work of fracture varies linearly with the fibre diameter and in a copper matrix at room temperature is less than 10^7 ergs.cm^-2 for a fibre diameter of 20 um.
Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement
International Journal for Numerical Methods in Fluids
65
1‐3
135-149
2010
10.1002/fld.2415
Arterial fluid–structure interaction (FSI) computations involve a number of numerical challenges. Because blood flow is incompressible, iterative solution of the fluid mechanics part of the linear equation system at every nonlinear iteration of each time step is one of those challenges, especially for computations over slender domains and in the presence of boundary layer mesh refinement. In this paper we address that challenge. As test cases, we use equation systems from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm, with thin layers of elements near the arterial wall. We show how the preconditioning techniques, we propose for solving these large sparse nonsymmetric systems, perform at different time steps of the computation over a cardiac cycle. We also present a new hybrid parallel sparse linear system solver ‘DD-Spike’ and demonstrate its scalability. Copyright © 2010 John Wiley & Sons, Ltd.
Modeling and analysis of bias-ply motorcycle tires
Mathematical Modelling
6
1
80
1985
10.1016/0045-7949(83)90078-0
Physical properties of motorcycle tire structures are considered to help select a good and true-to-life mechanistic model for finite element analysis of tires. Rubber and bias-ply layered-cord together make the inflated unhomogeneous tire structure anisotropic and geometrically highly nonlinear. A mathematical model made of 3-D solid and truss elements is discussed, and presented as realistic and adequate to accommodate the anisotropy and nonlinearity inherent in the tire problem. Various loading cases, including a cambered tire with inflation pressure and vertical load on contact patch, are studied and evaluated for force and moment acting on the tire. The results are very encouraging and satisfactory
Mechanics of nanostructures
Physics
1
199-203
2006
10.1007/1-4020-3951-4_19
Quantized fracture mechanics is applied for studying the mechanics of nanostructures. An application for predicting the strength of defective nanotubes, compared with atomistic simulations and experiments, clearly shows that materials are sensitive to flaws (also) at nanoscale.
nanomechanics; nanostructures; nanotubes; quatized fracture mechanics
An Approximate Analysis of Stresses in Multilayered Elastic Thin Films
Journal of Applied Mechanics
55
1
143
1988
10.1115/1.3173620
The analysis contains an engineering method for the approximate evaluation of thermally induced stresses in single and multilayered heteroepitaxial structures fabricated on thick substrates, with consideration of the finite size of the structure. The examined stresses include normal stresses, acting in the film layers themselves and responsible for their ultimte and fatigue strength, as well as interfacial stresses, responsible for film blistering and peeling. The developed formula are simple, easy-to-use, and clearly indicate how material and structural characteristics affect the magnitude and the distribution of stresses and deflections. Som recommendations for smaller stresses in film structures are presented. the obtained results can be utilized as a guidance for physical design of multilayered heteroepitaxial structures in mircoelectronics.
Using your friends: Social mechanics in social games
Foundations of Digital Games
188-195
2011
10.1145/2159365.2159391
This paper analyzes the social mechanics in top social games. It identifies several mechanisms by which social games encourage sociality: the friend bar, gifting, visiting, challenge/competition, and communication. Different implementations of these components result in varying gameplay experiences. However, no mechanics were found to offer very deep or sustained social interactions between players.
facebook; game mechanics; gameplay; social games
Two-dimensional patterns in Rayleigh-Taylor instability of a thin layer
Journal of Fluid Mechanics
236
-1
349
1992
10.1017/S0022112092001447
We study experimentally and theoretically the evolution of two-dimensional patterns in the Rayleigh-Taylor instability of a thin layer of viscous fluid spread on a solid surface. Various kinds of patterns of different symmetries are observed, with possible transition between patterns, the preferred symmetries being the axial and hexagonal ones. Starting from the lubrication hypothesis, we derive the nonlinear evolution equation of the interface, and the amplitude equation of its Fourier components. The evolution laws of the different patterns are calculated at order two or three, the preferred symmetries being related to the non-invariance of the system by amplitude reflection. We also discuss qualitatively the dripping at final stage of the instability.
Thermoelastic relaxation in elastic structures with applications to thin plates
The Quarterly Journal of Mechanics and Applied Mathematics
58
1
22
2004
10.1093/qjmamj/hbi002
A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined with the Kirchhoff assumption to obtain a new equation for the flexural vibration of thin plates incorporating thermoelastic loss as a damping term. The thermal relaxation loss is inhomogeneous and depends upon the local state of vibrating flexure, specifically, the principal curvatures at a given point on the plate. Thermal loss is zero at points where the principal curvatures are equal and opposite, that is, saddle shaped or pure anticlastic deformation. Conversely, loss is maximum at points where the curvatures are equal, that is, synclastic or spherical flexure. The influence of modal urvature on the thermoelastic damping is described through a modal pparticipation factor. The effect of transverse thermal diffusion on plane wave propagation is also examined. It is shown that transverse diffusion effects are always small provided the plate thickness is far greater than the thermal phonon mean free path, a requirement for the validity of the classical theory of heat transport. These results generalize Zener's theory of thermoelastic loss in beams and are useful in predicting mode widths in MEMS and NEMS oscillators.
Delocalizing strain in a thin metal film on a polymer substrate
Mechanics of Materials
37
261-273
2005
10.1016/j.mechmat.2004.02.002
Under tension, a freestanding thin metal film usually ruptures at a smaller strain than its bulk counterpart. Often this apparent brittleness does not result from cleavage, but from strain localization, such as necking. By volume conservation, necking causes local elongation. This elongation is much smaller than the film length, and adds little to the overall strain. The film ruptures when the overall strain just exceeds the necking initiation strain, ??\n N, which for a weakly hardening film is not far beyond its elastic limit. Now consider a weakly hardening metal film on a steeply hardening polymer substrate. If the metal film is fully bonded to the polymer substrate, the substrate suppresses large local elongation in the film, so that the metal film may deform uniformly far beyond ??\n N. If the metal film debonds from the substrate, however, the film becomes freestanding and ruptures at a smaller strain than the fully bonded film; the polymer substrate remains intact. We study strain delocalization in the metal film on the polymer substrate by analyzing incipient and large-amplitude nonuniform deformation, as well as debond-assisted necking. The theoretical considerations call for further experiments to clarify the rupture, behavior of the metal-on-polymer laminates. ?? 2004 Elsevier Ltd. All rights reserved.
Stability of an evaporating thin liquid film
Journal of Fluid Mechanics
584
1999
157
2007
10.1017/S0022112007006350
We use a newly developed set of interface conditions to revisit the problem of an evaporating thin liquid film. In particular, instead of the conventional Hertz-Knudsen-Langmuir equation for the evaporation mass flux, we impose a more general equation expressing the balance of configurational momentum. This balance, which supplements the conventional conditions enforcing the balances of mass, momentum and energy on the film surface, arises from a consideration of configurational forces within a thermodynamical framework. We study the influence of two newly introduced terms on the evolution of the liquid film. One of these terms accounts for the transport of energy within the liquid-vapour interface. The other term, which we refer to as the effective pressure, accounts for vapour recoil. Both new terms are found to be stabilizine. Furthermore, the effective pressure is found to affect a time-dependent base state of the evaporating film and to be an important factor in applications involving liquid films with thicknesses of one or two monolayers. Specifically, we demonstrate that consideration of the effective pressure makes it possible to observe the influence of the van der Waals interactions on film evolution close to the instant of rupture. Dimensional considerations indicate that one of the most significant influences of these effects occurs for molten metals.
Study of the influence of the number of inter-ply interfaces on the bearing rupture of riveted composite assemblies
Composite Structures
84
99-113
2008
10.1016/j.compstruct.2007.06.008
Within the framework of composite structures crashworthiness, bearing rupture specific to composite riveted joints shows an interesting potential insofar this benign failure mode exhibits relevant energy absorption capacities. Therefore, one could anticipate using such properties as a contributing mechanism to address safety in transportation vehicles where composite materials are increasingly introduced. As a contribution to this scientific and economical challenge, the presented paper aims at analysing mechanisms involved in the bearing fracture of composite assemblies. An experimental ASTM procedure is therefore first adapted to the studied material, in terms of specimen dimensions. This new protocol is then applied to conduct a comprehensive static experimental study focused on the analysis of the influence of the number of inter-ply interfaces on bearing properties. The results confirm the strong influence of this parameter on the initiation of bearing failure in composite laminates. ?? 2007 Elsevier Ltd. All rights reserved.
Assemblies; Bearing; Composite; Delamination; Rivets
The 1925 Born and Jordan paper “On quantum mechanics”
American Journal of Physics
77
2
128
2009
10.1119/1.3009634
The 1925 paper “On quantum mechanics” by M. Born and P. Jordan, and the sequel “On quantum mechanics II” by M. Born, W. Heisenberg, and P. Jordan, developed Heisenberg’s pioneering theory into the first complete formulation of quantum mechanics. The Born and Jordan paper is the subject of the present article. This paper introduced matrices to physicists. We discuss the original postulates of quantum mechanics, present the two-part discovery of the law of commutation, and clarify the origin of Heisenberg’s equation. We show how the 1925 proof of energy conservation and Bohr’s frequency condition served as the gold standard with which to measure the validity of the new quantum mechanics.
Multiobjective optimization of angle-ply laminated plates for maximum buckling load
Finite Elements in Analysis and Design
46
3
273-279
2010
10.1016/j.finel.2009.10.003
This paper deals with multiobjective optimization of symmetrically angle-ply square laminated plates subjected to biaxial compressive and uniform thermal loads. The design objective is the maximization of the buckling load for weighted sum of the biaxial compressive and thermal loads. The design variable is the fiber orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain optimal solutions of the design problem. The first-order shear deformation theory (FSDT) is used in the mathematical formulation of buckling analysis of laminated plates. The modified feasible direction (MFD) method is used for optimization routine. For this purpose, a program based on FORTRAN is used. Finally, the effect of different weighting factors, number of layers, aspect ratios, load ratios and boundary conditions on the optimal design is investigated.
Buckling; Laminated plates; Modified feasible direction method; Multiobjective optimization
Free vibration of antisymmetric, angle-ply laminated plates including transverse shear deformation by the finite element method
Journal of Sound and Vibration
66
4
565-576
1979
10.1016/0022-460X(79)90700-4
A finite element formulation of the equations governing the laminated anisotropic plate theory of Yang, Norris and Stavsky, is presented. The theory is a generalization of Mindlin's theory for isotropic plates to laminated anisotropic plates and includes shear deformation and rotary inertia effects. Finite element solutions are presented for rectangular plates of antisymmetric angle-ply laminates whose material properties are typical of a highly anisotropic composite material. Two sets of material properties that are typical of high modulus fiber-reinforced composites are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle. The numerical results are compared with the closed form results of Bert and Chen. As a special case, numerical results are presented for thick isotropic plates, and are compared with those for 3-D linear elasticity theory and Mindlin's thick plate theory.
Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading
Composite Structures
65
3-4
367-379
2004
10.1016/j.compstruct.2003.11.012
The static thermo-elastic response of symmetric and anti-symmetric cross-ply laminated plates has been investigated by the use of a unified shear deformation plate theory. The present plate theory enables the trial and testing of different through-the-thickness transverse shear-deformation distributions and, among them, strain distributions that do not involve the undesirable implications of the transverse shear correction factors. The validity of the present theory is demonstrated by comparison with solutions available in the literature. A wide variety of results is presented for the static response of simply supported rectangular plates under non-uniform sinusoidal mechanical and/or thermal loadings. The influence of material anisotropy, aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the thermally induced response is studied. ?? 2003 Elsevier Ltd. All rights reserved.
Laminated plates; Thermo-mechanical load; Unified theory
A C0 zig-zag model for the analysis of angle-ply composite thick plates
Composite Structures
127
211-223
2015
10.1016/j.compstruct.2014.10.008
From a theoretical and practical viewpoint, the zig-zag theory is well adopted in the analysis of laminated composite structures. Nevertheless, for the available zig-zag models, artificial constraints in which the first derivatives of transverse displacement are replaced by the assumed variables have to be employed to avoid C1 interpolation functions in the finite element implementation. Such artificial constraints violate continuity conditions of interlaminar transverse stresses at interfaces. To avoid using artificial constraints, a C0-type zig-zag model is proposed in this paper. C0 interpolation functions are only required in the finite element formulation as first derivatives of transverse displacement have all been eliminated from the displacement field based on stress compatibility conditions between plies and on the top and bottom surfaces of the plate. Moreover, the number of variables involved in the proposed zig-zag model is less than that of the existing zig-zag models, yet accurate results are produced comparable to analytical solutions and three-dimensional finite element results. Effects of ply orientations, boundary conditions and length-to-thickness ratio on displacements and stresses of laminated composite plates have been studied.
Angle-ply; C0 zig-zag theory; Composite plates; Finite element formulation
A study of bending, vibration and buckling of cross-ply circular cylindrical shells with various shell theories
International Journal of Engineering Science
27
11
1337-1351
1989
10.1016/0020-7225(89)90058-X
Analytical solutions for displacements, natural frequencies and buckling\nloads of cross-ply circular cylindrical shells under various boundary\nconditions are developed using the classical, first-order and third-order\nshell theories and the state-space technique. The third-order theory\nof shells of Reddy accounts for cubic variation of surface displacements\nthrough the thickness of the laminate and there is no need for shear\ncorrection factors. Analytical solutions are developed for simply-supported,\nclamped and free boundary conditions, and the effect of boundary\nconditions, lamination schemes and shear deformation on the deflections.\nstresses, natural frequencies and buckling loads is investigated.\n© 1989.
The magnetic mechanism of Zn0.93Co0.07O thin films
Science in China, Series G: Physics, Mechanics and Astronomy
52
10674059
21-25
2009
10.1007/s11433-009-0010-8
Zn0.93Co0.07O thin films infiltrated with nitrogen and aluminum were prepared by means of magneton sputtering. The structural and magnetic properties of the films were studied systematically. The materials were single phase (wurtzite structure) with surfaces showing signs of homogeneous growth. The films were ferromagnetic at room temperature, and magnetic domains could be clearly observed on the surfaces. In the case of Al infiltration, saturated magnetization increased with Al concentration increasing; whereas in the case of N infiltration, saturated magnetization decreased with the increase in N concentration. The results show that ferromagnetic interactions in Co-doped ZnO diluted magnetic semiconductor may be transferred by electrons.
Ferromagnetism; Thin film; ZnO-based diluted magnetic semiconductor
Complex extension of quantum mechanics.
Physical Review Letters
89
27
270401
2002
10.1103/PhysRevLett.89.270401
Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian. Using C, an inner product whose associated norm is positive definite can be constructed. The procedure is general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.
Analysis of thin shells using anisotropic polyconvex energy densities
Computer Methods in Applied Mechanics and Engineering
197
9-12
1015-1032
2008
10.1016/j.cma.2007.10.005
In this contribution the numerical framework for the simulation of anisotropic thin shells is presented on the basis of polyconvex strain energy functions. The nonlinear shell theory is based on the Reissner-Mindlin kinematic along with inextensible director vectors. For the variational framework we consider a three field variational functional taking into account independent displacements, enhanced strains and stress resultants, where the latter field is eliminated by the evaluation of some orthogonality conditions. The iterative enforcement of the zero normal stress condition at the integration points allows consideration of arbitrary three-dimensional constitutive equations. Due to the fact that we are interested in fiber-reinforced materials we consider an additive structure of the energy decoupled in an isotropic part for the matrix and a superposition of transversely isotropic parts for the fiber families. For the representation of the anisotropy we use the concept of structural tensors and formulate the strain energy function in terms of principal and mixed invariants of the right Cauchy-Green tensor and the structural tensor. In order to guarantee the existence of minimizers we focus on polyconvex strain energy functions. The anisotropy effect is documented in several representative examples. © 2007 Elsevier B.V. All rights reserved.
Anisotropy; Invariant theory; Polyconvexity; Thin shells
A discrete-vortex model for the arbitrary motion of a thin airfoil with fluidic control
Journal of Fluids and Structures
27
5-6
680-693
2011
10.1016/j.jfluidstructs.2011.02.008
A low-order model for the arbitrary motion of a thin airfoil with trailing edge fluidic control is derived from basic fluid mechanics principles. The model consist of solving a single ordinary differential equation with a special treatment of a vortex shedding criteria. The model is compared with experimental and high-order numerical simulations and the results give a reasonable means of predicting the lift and moment on a thin airfoil. Furthermore, the model is extended to account for the actuation and control due to the synthetic jet actuation near the trailing edge. The model response is compared to experimental results. ?? 2011 Elsevier Ltd.
Flow control; Low-order model; Potential flow
New model to predict static strength of tapered laminates
Composites
26
2
141-146
1995
10.1016/0010-4361(95)90414-U
Tapered laminates have wide applications in engineering structures. However, the problem of predicting static strength accurately has still not been satisfactorily resolved. Many models are available but all have limitations. In this paper, a new model called the variable fracture energy model is proposed. This model is established based on a comprehensive experimental and analytical study on constant thickness specimens with the central plies cut across the complete width. Many experimental results on tapered specimens indicate that this model can be used to predict the static strength of tapered laminates satisfactorily.
delamination; finite element analysis; fracture mechanics; ply drop off; strength prediction; tapered laminates
Cohesive zone modeling of mode I tearing in thin soft materials
Journal of the Mechanical Behavior of Biomedical Materials
28
37-46
2013
10.1016/j.jmbbm.2013.07.015
The use of modeling and simulation is growing rapidly in applications such as surgery simulations, injury mechanics and tissue engineering. The aim of this study is to model and simulate tissue tearing and the resulting failure for use in such applications. In particular, our goal is to characterize the mechanics of mode I tearing in thin soft materials. We use the cohesive zone modeling approach to characterize the propagation of tears in a processed meat product (PMP). The bulk response of the PMP is modeled with a hyperelastic material model and the interface with a cohesive zone model. A multistep parameter estimation approach is developed to determine the bulk and the cohesive model parameters from uniaxial extension and tearing experiments. Results show that the proposed approach is able to capture both material and geometrical nonlinearities inherent to such problems, and accurately model the overall force-displacement response of thin soft materials during tearing at slow rates. ?? 2013 Elsevier Ltd.
Cohesive zone modeling; Soft material; Tearing
Mechanics of composite materials 2nd
Optics Express
18
473
2006
We report the first demonstration of a Yb:YAG thin disk laser wherein the gain medium is intracavity face-cooled through bonding to an optical quality SiC prism. Due to the particular design of the composite bonded Yb:YAG/SiC-prism gain element, the laser beam impinges on all refractive index interfaces inside the laser cavity at Brewster's angles. The laser beam undergoes total internal reflection (TIR) at the bottom of the Yb(10%):YAG thin disk layer in a V-bounce cavity configuration. Through the use of TIR and Brewster's angles, no optical coatings, either anti-reflective (AR) or highly reflective (HR), are required inside the laser cavity. In this first demonstration, the 936.5-nm diode pumped laser performed with ~38% slope efficiency at 12 W of quasi-CW (Q-CW) output power at 1030 nm with a beam quality measured at M(2) = 1.5. This demonstration opens up a viable path toward novel thin disk laser designs with efficient double-sided room-temperature heatsinking via materials with the thermal conductivity of copper on both sides of the disk.
Mechanics of fretting fatigue
Tribology International
29
2
107-113
1994
10.1016/S0301-679X(99)80001-2
Several aspects of the mechanics of cracks originating at sites of fretting are considered. It is argued that the problem may be distilled into three separate parts: the contact problem itself in full or partial slip, the initiation of a crack from a surface suffering severe distress, and the propagation of a crack under combined contact and bulk loading. The first of these may be solved by either a classical or numerical means, whilst the last merely requires the careful use of fracture mechanics. However, it is the second element which remains elusive to quantify, and the influence of the intrinsic length scales in the problem, including contact length, surface roughness and amplitude of relative tangential displacement on initiation conditions, is discussed and explored.
Computational Fracture Mechanics
Continuum Scale Simulation of Engineering Materials
621-637
2005
10.1002/3527603786.ch32
This chapter contains sections titled: * Introductory Remarks on Inelastic Material Behaviour * FE Meshes for Structures with Crack-Like Defects General Aspects and ExamplesSingular Elements for Stationary CracksRegular Element Arrangements for Extending Cracks * The J-Integral as Characteristic Parameter in Elasto-Plastic Fracture Mechanics FoundationThe Domain Integral or VCE MethodPath Dependence of the J-Integral in Incremental Plasticity * The Cohesive Model FundamentalsExample: Simulation of Ductile Tearing in a Laser Weld * Summary * References
application to engineering microstructures; cohesive model; computational fracture mechanics; continuum scale simulation; engineering materials; FE meshes for structures with crack-like defects; inelastic material behaviour; J-integral as characteristic parameter in elasto-p
A meso/micro-mechanical model for damage progression in glass-fiber/epoxy cross-ply laminates by finite-element analysis
Composites Science and Technology
60
8
1171-1179
2000
10.1016/S0266-3538(00)00022-1
A three-dimensional multi-cell meso/micro-mechanical finite-element model has been developed for the prediction of the overall mechanical behavior of a [0,903,0](T) glass-fiber/epoxy laminate, and for the study of damage mechanisms in fiber-reinforced polymer laminates. The epoxy matrix is represented by a non-linear viscoelastic constitutive model, which was incorporated into the finite-element analysis code, ADINA, through the user-defined subroutine. In addition, a damage criterion for the epoxy matrix is introduced into the finite-element model. Numerical results from the finite-element analysis are compared with experimental data, and it is found that both the predicted overall stress/strain response and the prediction of the initiation and propagation of the damage are in good agreement with the experimental results. (C) 2000 Elsevier Science Ltd. All rights reserved.
A. Polymer matrix; C. Finite-element analysis; Damage simulation; Fiber-reinforced cross-ply laminate; Meso/micro-mechanical modeling
Multiobjective optimization of laminated plates for maximum prebuckling, buckling and postbuckling strength using continuous and discrete ply angles
Composite Structures
35
117-130
1996
10.1016/0263-8223(96)00030-X
The optimal design of uniaxially loaded laminated plates subject to elastic in-plane restraints along the unloaded edges are given for a maximum combination of prebuckling stiffness, postbuckling stiffness and buckling load. The results are also obtained for biaxially loaded plates without elastic restraints. The method of solution involves defining a design index comprising a weighted average of the objective functions and identifying candidate configurations which have to be optimized and compared to determine the best stacking sequence. This multiobjective approach leads to improved prebuckling, buckling and postbuckling performance. A similar approach is adopted in the case of discrete ply angles with the provision that these angles can only take predefined values. From a manufacturing viewpoint, using only certain fibre orientations such as 0, ±45 and 90° is advantageous and cost-effective. The multiobjective design results are compared to single objective ones, and the effect of various problem parameters on the optimal designs are numerically studied. It is observed that the resulting trade-off among the different objectives are not severe leading to well-balanced laminates with regard to the range of loads they are required to carry. A comparison of continuous and discrete optimization indicates that both designs lead to comparable load carrying capacity, with regard to different objectives. Copyright © 1996 Elsevier Science Ltd.
Contact Mechanics and Adhesion
Surface and Interfacial Forces
22
219-250
2010
10.1002/9783527629411.ch8
This chapter contains sections titled: * Surface Energy of Solids * Contact Mechanics * Influence of Surface Roughness * Adhesion Force Measurements * Summary * Exercises
Substrate Size Primate Forelimb Mechanics: Implications for Understanding the Evolution of Primate Locomotion
International Journal of Primatology
24
5
1023-1036
2003
10.1023/A:1026224211797
Did the anatomical and locomotor specializations of primates evolve in response to requirements of locomotion and foraging on thin branches? Laboratory studies of primates and other mammals provide data suggesting that as substrate size decreases primates will protract their arms to a greater degree, lower the center of gravity by increasing elbow flexion, and decrease forelimb substrate reaction forces. I tested these hypotheses by calculating maximum arm protraction, shoulder height, elbow flexion, and substrate reaction forces during stance phase in 5 species of Old World monkeys walking on a flat runway and raised poles of varying diameters. As substrate size decreased most subjects increased elbow flexion and lowered their shoulder height. Three of the 5 species lowered peak substrate reaction forces as substrate size decreased but, only 2 of the species increased arm protraction as substrate size decreased. These results reject the hypothesis that arm protraction is a function of branch size, but provide stronger support for the notion that branch size influences elbow flexion, shoulder height, and peak substrate reaction forces in some primates. The fact that biomechanical expectations are met in some ( but not all) cases and some ( but not all) species suggests that the topic is quite complex and requires further study. Nonetheless, preliminary data suggest that biomechanical accommodations to substrate size may have played a role in the early differentiation of primates from other mammals.
Biomechanics; Evolution; Primate locomotion; Primate origins; Substrate
Classical Mechanics - Point Particles And Relativity - W
Journal of Bioenergetics and Biomembranes
2004
10.1007/b97649
The frequency of opportunistic fungal infection has increased drastically, mainly in patients who are immunocompromised due to organ transplant, leukemia or HIV infection. In spite of this, only a few classes of drugs with a limited array of targets, are available for antifungal therapy. Therefore, more specific and less toxic drugs with new molecular targets is desirable for the treatment of fungal infections. In this context, searching for differences between mitochondrial mammalian hosts and fungi in the classical and alternative components of the mitochondrial respiratory chain may provide new potential therapeutic targets for this purpose.
Prandtl-Essentials of Fluid Mechanics
Applied Mathematical Sciences
158
723 p.
2010
10.1007/978-1-4419-1564-1
This book is an update and extension of the classic textbook by Ludwig Prandtl, Essentials of Fluid Mechanics.
Mechanics of fluidization
Chemical Engineering Progress, Symposium Series
62
1
100-111
1966
10.1016/S0032-0633(98)00014-2
A correlation of the bed expansion of particulately fluidized spheres based on dynamic equilibrium of individual particles is presented. This correlation may be used to obtain minimum fluidization velocities agreeing with those calculated from a proposed general correlation based on pressure-drop considerations. Criteria for multisized particle systems are discussed.
The Four Variational Principles of Mechanics
Annals of Physics
251
1
1-25
1996
10.1006/aphy.1996.0104
We argue that there arefourbasic forms of the variational principles of mechanics: Hamilton's least action principle (HP), the generalized Maupertuis principle (MP), and their two reciprocal principles, RHP and RMP. This set is invariant under reciprocity and Legendre transformations. One of these forms (HP) is in the literature: only special cases of the other three are known. The generalized MP has a weaker constraint compared to the traditional formulation: only the mean energy Ē is kept fixed between virtual paths. This reformulation of MP alleviates several weaknesses of the old version. The reciprocal Maupertuis principle (RMP) is the classical limit of Schrödinger's variational principle of quantum mechanics, and this connection emphasizes the importance of the reciprocity transformation for variational principles. Two unconstrained formulations (UHP and UMP) of these four principles are also proposed, with completely specified Lagrange multipliers. Percival's variational principle for invariant tori and variational principles for scattering orbits are derived from the RMP. The RMP is very convenient for approximate variational solutions to problems in mechanics using Ritz type methods. Examples are provided.
Multi-scale computational homogenization of structured thin sheets
Modelling and Simulation in Materials Science and Engineering
15
S393-S404
2007
10.1088/0965-0393/15/4/S06
Structured and layered thin sheets are used in a variety of innovative applications, e.g. flexible displays, rollable solar cells or flexible electronics. Stacks of different materials, with often highly complex interconnects between layers, are thereby used, which are typically loaded in bending combined with intrinsic thermo-mechanical mismatches. As a result, different failure mechanisms at the level of the layered substructure occur, which constitutes a serious reliability concern. This paper deals with the two-scale homogenization of structured thin sheets, whereby a higher-order through-thickness representative volume element (RVE) is used. The methodology relies on the computational homogenization of the mechanics of microstructures, for which first-order and second-order solution strategies have been developed in the past decade. The upscaling of the deformation of structured thin sheets towards a shell-type continuum is second-order in nature. The higher-order kinematics is defined on the basis of a microstructural RVE, which represents the full thickness of the macroscopic structure and a periodic in-plane cell (e.g. a single pixel in a flexible display). The elaboration of the boundary conditions and the solution of the micro-scale boundary value problem are discussed. The obtained micro-scale stress state is homogenized towards a 3D macroscopic shell structure, for which detailed aspects will be emphasized. The coupled numerical solution strategy is briefly outlined. Finally, an example is given and the application to a number of practical problems is highlighted, where the solution provides direct information on each scale. The incorporation of failure events at the substructure level is thereby naturally at hand. © 2007 IOP Publishing Ltd.
In vitro fatigue-crack growth and fracture toughness behavior of thin-walled superelastic Nitinol tube for endovascular stents: A basis for defining the effect of crack-like defects
Biomaterials
28
4
700-709
2007
10.1016/j.biomaterials.2006.09.034
Endovascular stents made of the superelastic nickel-titanium alloy Nitinol are subjected in service to tens of millions of loading cycles and even "single-event" overloads, both of which can potentially result in fracture and/or complete failure of the device. A fracture-mechanics-based methodology can provide a means to quantify relevant material parameters critical to the design against such failures. However, there is a dearth of relevant experimental data in the literature on such fracture-mechanics-based approaches to fatigue in Nitinol; furthermore, that which does exist invariably pertains to product forms that are not appropriate for stent manufacture, e.g., bulk Nitinol bar and strip. Consequently, the current work is focused on characterizing in vitro both subcritical and critical crack growth (fatigue-crack growth and R-curve fracture toughness) behavior in thin-walled (???400 ??m thick) Nitinol tubing similar to that used for medical device manufacture (following shape-setting procedures to flatten the material), with a resultant austenite finish temperature of Af???25-30 ??C, identical to self-expanding Nitinol stents. Fatigue-crack growth behavior, measured in Hanks' Balanced Saline Solution over a wide spectrum of growth rates (down to 10-10 m/cycle) and at a range of positive load ratios (R = 0.1 - 0.7), revealed significantly higher fatigue thresholds than had been previously reported for bulk Nitinol material. In addition, we examine the critical effect of test frequency, as most fatigue experiments on Nitinol have been performed at 30 Hz or above, despite the fact that this is far in excess of the frequency of physiological loading. Finally, the fracture toughness properties are characterized in thin-section Nitinol and show marked crack-resistance (R-curve) behavior with a dependence on crack-growth angle (with respect to the tube drawing axis); additionally, measured toughnesses are found to be lower than has been previously reported for bulk Nitinol. ?? 2006 Elsevier Ltd. All rights reserved.
Fatigue; Fracture mechanism; Fracture toughness; Nickel-titanium alloy; Nitinol; Stent
Dynamic domain model for magnetic thin films
IEEE Transactions on Magnetics
27
2
729-741
1991
10.1109/20.133286
A domain model for computing magnetization dynamics in small (≈100 μm) patterned, magnetically soft thin films is described. The magnetization distribution of the film is modeled by a dynamic grid of contiguous polygonal domains with uniform in-plane magnetization. Dynamic variables for this system include both the magnetization directions and the domain wall positions (i.e. domain vertex locations) of each domain. The formulation of the model is motivated in part by the analogy to a nonlinear system of coupled, viscously damped oscillators with geometrically constrained motion. The equations of motion for the magnetic system are obtained via methods of Lagrangian mechanics and solved numerically by computer. The model is demonstrated on the computation of the frequency-dependent permeability in narrow Permalloy stripes. Also included are results on flux propagation in film geometries resembling those typical of inductive thin-film head poles. Predictions obtained are compared with other experimental and theoretical results
contiguous polygonal domains; Couplings; domain model; domain vertex locations; domain wall positions; dynamic grid; ferromagnetic properties of substances; flux propagation; frequency-dependent permeability; geometrically constrained motion; Lagrangian mechanics; magnetically soft thin films; Magnetic domains; magnetic domain walls; Magnetic domain walls; Magnetic films; magnetic flux; Magnetic flux; magnetic heads; magnetic permeability; magnetic thin films; magnetisation; Magnetization; magnetization dynamics; Nonlinear dynamical systems; Nonlinear systems; Permalloy; Soft magnetic materials; Solid modeling; thin-film head poles; viscously damped oscillators
Can mechanics control pattern formation in plants?
Current Opinion in Plant Biology
10
1
58-62
2007
10.1016/j.pbi.2006.11.014
Development of the plant body entails many pattern forming events at scales ranging from the cellular level to the whole plant. Recent evidence suggests that mechanical forces play a role in establishing some of these patterns. The development of cellular configurations in glandular trichomes and the rippling of leaf surfaces are discussed in depth to illustrate how intricate patterns can emerge from simple and well-established molecular and cellular processes. The ability of plants to sense and transduce mechanical signals suggests that complex interactions between mechanics and chemistry are possible during plant development. The inclusion of mechanics alongside traditional molecular controls offers a more comprehensive view of developmental processes. ?? 2006 Elsevier Ltd. All rights reserved.
Progressive Transverse Cracking In Composite Laminates
Journal of Composite Materials
22
10
900-916
1988
10.1177/002199838802201001
L. R. Dharani, J. Wei, F. S. Ji, and J. H. Zhao Saturation of Transverse Cracking with Delamination in Polymer Cross-Ply Composite Laminates International Journal of Damage Mechanics, April 1, 2003; 12(2): 89 - 114.
Numerical study of conjugated heat transfer in evaporating thin-films near the contact line
International Journal of Heat and Mass Transfer
55
1–3
61-68
2012
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.08.039
The study of the mechanics of evaporating thin-films is important for improving the performance of phase-change heat transfer equipment. Various factors, including the changing profile of the thin-film with superheating and the use of small-scale and one-dimensional higher-order nonlinear governing differential equations, create difficulties for the study of the conjugated heat transfer of the thin-film and its surrounding regions. In previous studies, models of the conjugated heat transfer are simplified. The shape of the evaporating thin-film is treated as fixed, or the constant substrate temperature (CST) thin-film model is used. In this paper, a full conjugated heat transfer model, including the evaporating thin-film, the near-solid substrate and the intrinsic liquid, is proposed to study the heat transfer characteristics in the contact line region in a micro channel or a micro groove. The results show that a temperature valley value exists on the surface of the solid substrate corresponding to the peak value of the heat flow rate in the thin-film. The apparent contact angle is smaller than that of the CST model. The CST model overestimates the peak and the total heat flow rate, especially when the thermal conductivity ks of the substrate is low. For convenience in engineering applications, two simplified conjugated models are developed and evaluated by the full model. For low ks substrates, the simplified models can be used directly. Changing the thickness of the substrates affects the relative errors only slightly.
Conjugated heat transfer; Contact line; Evaporating thin-film; Micro heat transfer; Numerical study; Phase-change heat transfer
Transdermal delivery devices: Fabrication, mechanics and drug release from silk
Small
9
21
3704-3713
2013
10.1002/smll.201202075
Microneedles are a relatively simple, minimally invasive and painless approach to deliver drugs across the skin. However, there remain limitations with this approach because of the materials most commonly utilized for such systems. Silk protein, with tunable and biocompatibility properties, is a useful biomaterial to overcome the current limitations with microneedles. Silk devices preserve drug activity, offer superior mechanical properties and biocompatibility, can be tuned for biodegradability, and can be processed under aqueous, benign conditions. In the present work, the fabrication of dense microneedle arrays from silk with different drug release kinetics is reported. The mechanical properties of the microneedle patches are tuned by post-fabrication treatments or by loading the needles with silk microparticles, to increase capacity and mechanical strength. Drug release is further enhanced by the encapsulation of the drugs in the silk matrix and coating with a thin dissolvable drug layer. The microneedles are used on human cadaver skin and drugs are delivered successfully. The various attributes demonstrated suggest that silk-based microneedle devices can provide significant benefit as a platform material for transdermal drug delivery.
micromachining; microneedles; microparticles; silk; transdermal drug delivery
Thin-oil-film interferometric skin-friction measurements in short-duration supersonic flow
Experiments in Fluids
15
315-322
1993
- -film interferometric skin-friction measurements in short-duration supersonic flow JP , BF Department of Aerospace Engineering, Mechanics
Respiratory mechanics derived from signals in the ventilator circuit.
Respiratory care
50
1
55-65; discussion 65-67
2005
The aim of this article is to identify and interpret the data provided by modern ventilators that provide the greatest clinical help in evaluating respiratory mechanics during mechanical ventilation. In intensive care, respiratory mechanics can be assessed in dynamic conditions (no flow-interruption) or static conditions (occlusion techniques) to record compliance and resistance and to monitor pressure, flow, and volume. Real-time visualization of the pressure curve is crucial for monitoring during volume-controlled ventilation, in which pressure is the dependent variable. Analysis of the pressure curve has little clinical utility during pressure-controlled ventilation, in which the dependent variable is the flow waveform, which varies according to changes in the mechanics of the respiratory system. Pressure-volume loops and flow-volume loops provide useful information on the dynamic trends of the respiratory system compliance and resistance, respectively. Modern ventilators provide complete monitoring of respiratory system mechanics, which is our guideline for optimizing ventilatory support and avoiding complications associated with mechanical ventilation.
The thin liquid lining of a weakly curved cylindrical tube
Journal of Fluid Mechanics
331
373-403
1997
10.1017/S0022112096004120
A thin-film approximation is used to study the effects of surface tension on a thin liquid layer lining the interior of a cylindrical tube, where the tube has radius a and a centreline with weak, uniform curvature δ/a. Centreline curvature induces a pressure gradient in the fluid layer, analogous to that due to a weak gravitational field, that drives fluid from the inner to the outer wall of the tube, i.e. away from the centre of centreline curvature. The resulting draining flow is computed numerically under the assumption of axial uniformity, and the large-time asymptotic draining regimes and flow structures are identified. In the absence of destabilizing intermolecular interactions, the inner wall remains wet, covered with a vanishingly thin fluid layer, while a near-equilibrium lobe forms on the outer wall. The stability of this quasi-static lobe to axial variations is then investigated by using numerical and perturbation methods to solve the linearized Young–Laplace equation, prescribing zero contact angle at the lobe's free boundary. Conditions on δ, the fluid volume a3V and the tube length aL are identified separating axially uniform lobes (which are stable for low V/(δL) or small L), wavy lobes (some with a solitary structure) and localized fluid droplets (which exist for sufficiently large V/δ and L). Hysteresis is demonstrated between multiple equilibria, the topology of which can change dramatically as parameters are varied. The application of these results to lung airways is discussed.
A deeper analysis of the epitope/paratope of PLY-5, a mouse monoclonal antibody which recognises the conserved undecapeptide tryptophan-rich loop (ECTGLAWEWWR) of bacterial cholesterol-dependent cytolysins
Biochemical and Biophysical Research Communications
430
1
14-19
2013
10.1016/j.bbrc.2012.11.012
A previous study showed that the minimal epitope recognised by the PLY-5 mAb in the conserved undecapeptide Trp-rich loop of bacterial CDCs should consist of WEWWRT (Jacobs et al., 1999) [5]. Now, through immunoscreening of amino acid substitution analogues, it is concluded that the second Trp and the Arg residues are essential in the PLY-5 epitope. The E residue is an auxiliary epitope contributor. Antibody modelling and docking simulations provided support for these findings. For recognition by the antibody, the Trp-rich loop flipped out, mimicking the mechanism of membrane insertion. The displaced second Trp was seen to establish aromatic stacking interactions with aromatic residues of the antibody paratope and the notably extruded guanidium tip of the arginine residue mediated electrostatic interactions with well-exposed carboxylic groups of glutamic residues on the surface of the paratope. Thus, the epitope/paratope interaction is mainly mediated by aromatic and by ionic interactions. © 2012 Elsevier Inc.
Cholesterol-dependent cytolysin; Epitope; Paratope; PLY-5; Tryptophan-rich loop
Epigenetics: Biology's Quantum Mechanics
Frontiers in Plant Science
2
April
1-4
2011
10.3389/fpls.2011.00010
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
aperiodic crystal; aperiodic crystal, paragenetics, parachromatin, tr; histone code; parachromatin; paragenetics; physics and the molecular; transgenerational inheritance; understanding
Nanomaterials: Mechanics and mechanisms
Nanomaterials: Mechanics and Mechanisms
1-316
2009
10.1007/978-0-387-09783-1
The methods of monitoring cellular processes are either snap-shots or based on in vitro measurements. Nanomaterials have specific advantages to be excellent probes to monitor in vivo processes. In this study we have demonstrated that attachment of neurotransmitter, serotonin to iron oxide nanoparticles brings about enhanced contrast in cells that express the receptor for serotonin specifically.
Cytokinesis mechanics and mechanosensing
Cytoskeleton
69
October
700-709
2012
10.1002/cm.21045
Cytokinesis shape change occurs through the interfacing of three modules, cell mechanics, myosin II-mediated contractile stress generation and sensing, and a control system of regulatory proteins, which together ensure flexibility and robustness. This integrated system then defines the stereotypical shape changes of successful cytokinesis, which occurs under a diversity of mechanical contexts and environmental conditions.
Actin network; Contractility; Control system; Feedback; Mechanosensing; Myosin II
Droplet Spreading On A Thin Viscous Film
Journal Of Fluid Mechanics
235
399-414
1992
10.1017/S0022112092001162
We investigated experimentally the flows induced by a localized surfactant\n(oleic acid) on thin glycerol films. The oleic acid creates surface-tension\ngradients, which drive convention on the surface and within the film.\nQualitative descriptions of the Lagrangian flow field were provided\nby flow-visualization experiments. Quantitative measurements of surface\nflows were conducted using dyed glycerol markers, where the initial\nmotion of these markers is used to define the position of the time-dependent\n'convection front'. The flow characteristics were found to depend\nlargely upon the magnitude of a gravitational parameter, G, representing\nthe ratio Of gravitational to surface-tension gradient (Marangoni)\nforces. Small G (G < 0.5) caused net outflow of the film leading\nto this thinning and, in some cases, to film rupture. When G < 1,\nbi-directional flows were caused by hydrostatic pressure gradients\nwhich served to stabilize the film. Additionally, the position of\na surface convection front was found to differ significantly from\nthat of the surfactant's leading edge for all G > 0. For this reason,\nsurface markers may not be used to measure accurately the position\nof the droplet's leading edge. Finally, simulations of the Lagrangian\nflows conducted using the theory of Gaver & Grotberg (1990) compare\nfavourably with these experimental results in the limit of dilute\nsurfactant concentrations, and thus experimental verification of\nthat theory is provided by this work. The results of this study may\nbe useful for understanding the behaviour of the lung's thin-film\nlining after an aerosol droplet of insoluble exogenous surfactant\nlands upon its surface.
Analysis of the transpiration cooling of a thin porous plate in a hot laminar convective flow
European Journal of Mechanics - B/Fluids
18
2
245-260
1999
10.1016/S0997-7546(99)80025-9
This paper deals with the asymptotic and numerical analysis for the steady-state transpiration cooling of a thin porous flat plate in a laminar hot convective flow, taking into account the streamwise heat conduction through the plate. For high conductivity plates, a regular perturbation analysis has been carried out, yielding a three-term asymptotic solution for the distribution of plate temperature. In the limit of a very poorly conducting plate, a singular perturbation technique, based on matched asymptotic expansions, is employed to solve the governing equations. We also solved the equations numerically using a quasilinearization technique. The numerical results are in good agreement with the asymptotic solution close to the asymptotic limits studied.
Free vibration analyses of thin sector plates by the new version of differential quadrature method
Computer Methods in Applied Mechanics and Engineering
193
36-38
3957-3971
2004
10.1016/j.cma.2004.02.010
The new version of differential quadrature (DQ) method is extended to analyze the free vibration of thin sector plates with various sector angles and six combinations of boundary conditions. Detailed formulations are given. Various numerical examples are studied. Comparisons are made with existing analytical and/or numerical data. Numerical results indicate that convergence can be achieved with increasing in number of grid points and accurate results could be obtained with 9 ?? 9 gird or even higher grid by using the extended DQ method for the cases considered. ?? 2004 Elsevier B.V. All rights reserved.
Differential quadrature method; Free vibration; Sector plates
The transactional interpretation of quantum mechanics
Reviews of Modern Physics
58
3
647-687
1986
10.1103/RevModPhys.58.647
The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of
doi:10.1103/RevModPhys.58.647 url:http://dx.doi.or
Optimization of thin shell structures subjected to thermal loading
Structural Engineering and Mechanics
7
4
401-412
1999
The purpose of this paper is to show how the Evolutionary Structural Optimization (ESO) algorithm developed by Xie and Steven can be extended to optimal design problems of thin shells subjected to thermal loading. This extension simply incorporates an evolutionary iterative process of thermoelastic thin shell finite element analysis. During the evolution process, lowly stressed material is gradually eliminated from the structure. This paper presents a number of examples to demonstrate the capabilities of the ESO algorithm for solving topology optimization and thickness distribution problems of thermoelastic thin shells.
A THIN RIVULET OF PERFECTLY WETTING FLUID SUBJECT TO A LONGITUDINAL SURFACE SHEAR STRESS
Q J Mechanics Appl Math
hbm023
2008
10.1093/qjmam/hbm023
The lubrication approximation is used to obtain a complete description of the steady unidirectional flow of a thin rivulet of perfectly wetting fluid on an inclined substrate subject to a prescribed uniform longitudinal surface shear stress. The quasi-steady stability of such a rivulet is analysed, and the conditions under which it is energetically favourable for such a rivulet to split into one or more subrivulets are determined.
NURBS-based isogeometric analysis for thin plate problems
Structural Engineering and Mechanics
41
5
617-632
2012
An isogeometric approach is presented for static analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection, as for description of the geometry. The governing equation based on Kirchhoff plate theory, is discretized using the standard Galerkin method. The essential boundary conditions are enforced by the Lagrange multiplier method. Several typical examples of thin plate and thin plate on elastic foundation are solved and compared with the theoretical solutions and other numerical methods. The numerical results show the robustness and efficiency of the proposed approach.
Elastic foundation; Isogeometric analysis; Lagrange multiplier method; NURBS; kirchhoff plate
Mode II interlaminar fracture of filament wound angle-ply specimens
Applied Composite Materials
9
2
117-129
2002
Doi 10.1023/A:1013898312796
This paper presents a study of the interlaminar fracture of filament wound composites. Mode II end notched flexure (ENF) tests were performed on flat glass/polyester specimens. The tested specimens had asymmetric [+/-theta](4) angle-ply stacking-sequences, with theta values from 0.8degrees (hoop winding) to 30degrees. Due to the low stiffness and probable high toughness, it was not possible to propagate the crack in [+/-60degrees](4) specimens before they suffered considerable permanent deformations. A short support span had to be employed for [+/-30degrees](4) specimens in order to obtain crack propagation. Nevertheless, the results for those specimens should be viewed with caution, as some nonlinear behaviour and small permanent deformations were detected. No other unusual features, such as crack jumping to other interface, were observed. The scatter in the critical strain energy release rate values (G(IIc)) was higher for [+/-10degrees](4) and [+/-30degrees](4) specimens than for the quasi-unidirectional ones. G(IIc) values from the insert were generally lower than those from mode II pre-cracks, except for quasi-unidirectional specimens. A plot of average G(IIc) values against theta showed a minimum at theta=5degrees.
angle-plies; delamination growth; double-cantilever beam; end notched flexure (enf) tests; energy-release rate; filament wound composites; glass/epoxy composite cylinders; glass/polyester composites; interlaminar fracture; mode ii; orientation; permanent deformations
Cohesive crack modelling of thin sheet material exhibiting anisotropy, plasticity and large-scale damage evolution
Engineering Fracture Mechanics
79
50-60
2012
10.1016/j.engfracmech.2011.10.001
The crack tip region in notched structures generally exhibit damage evolution before ultimate failure occurs. In some materials, the damaged regions may reach considerable sizes prior to structural collapse. In this work, a cohesive crack model suitable for static fracture mechanics analysis of thin sheet materials exhibiting anisotropy, plasticity, and large-scale damage evolution was developed. The material parameters of the model were calibrated solely by tensile testing of unnotched test specimens. The predictive capability of the model was verified by comparisons with experiments on notched test specimens with different crack sizes. The predictions of failure were shown to be in excellent agreement with the experiments. © 2011 Elsevier Ltd.
Anisotropy; Cohesive zone; Damage; Fracture; Plasticity
An approach to analyse the special rolling of thin strip
Journal of Materials Processing Technology
177
130-133
2006
10.1016/j.jmatprotec.2006.04.065
Work roll edge contact may affect the mechanics of cold rolling of thin strip and the crown of the rolled strip. In this paper, the authors developed a modified influence function method to simulate this special rolling. The rolling force, intermediate force, roll edge contact force, the crown of the rolled strip and the edge contact length for different strip widths and traverse friction coefficients are obtained. The calculated rolling forces are compared to experimental values. The developed model is effective and applicable in the cold rolling of thin strip with work roll edge contact. ?? 2006 Elsevier B.V. All rights reserved.
Crown; Modified influence function method; Roll edge contact rolling; Rolling force; Thin strip
Geometrically nonlinear formulation for thin shells without rotation degrees of freedom
Computer Methods in Applied Mechanics and Engineering
197
33-40
2778-2788
2008
10.1016/j.cma.2008.01.001
A finite element formulation is presented for modelling geometrically nonlinear thin shells which exploits standard Lagrange finite element basis functions without introducing rotation degrees of freedom. The classical regularity requirements associated with thin bending problems are circumvented by introducing special integrals over inter-element edges. The use of Lagrange finite element basis functions and the absence of rotation degrees of freedom make the formulation relatively simple, and discontinuities in material properties and non-smooth shell geometry can be incorporated trivially. The variational problem can be exactly linearised, leading to an efficient Newton-Raphson solution process. The performance of the approach is demonstrated via a range of numerical benchmarks for both geometrically linear and nonlinear problems. It is shown that cubic elements perform particularly well. ?? 2008 Elsevier B.V. All rights reserved.
Discontinuous Galerkin methods; Geometrically nonlinear; Rotation-free; Thin shells
Characterisation of thin oxide scale and its surface roughness in hot metal rolling
Materials Science and Engineering A
435-436
434-438
2006
10.1016/j.msea.2006.07.070
The deformation of the thin oxide scale formed in hot metal rolling and its surface roughness characterisation are very important for the quality of the finished product. Finite element (FE) simulation of the thin oxide scale deformation and surface roughness transfer has been carried out. The authors focus on the surface asperity deformation of the thin oxide scale and strip. Surface characterisation and the mechanics of the thin oxide scale deformation are obtained from the FE simulation and experimental measurements. Simulation results are close to the measured values. The forming features of surface roughness transfer during hot metal rolling with lubrication are also discussed. © 2006 Elsevier B.V. All rights reserved.
Finite element simulation; Oxide scale; Surface characterisation; Surface roughness transfer
Characterization of fracture modes in stitched and unstitched cross-ply laminates subjected to low-velocity impact and compression after impact loading
International Journal of Impact Engineering
35
7
591-608
2008
10.1016/j.ijimpeng.2007.02.009
The insertion of transverse reinforcing threads by stitching is a very promising technique to restrict impact damage growth and to improve post-impact residual strength of laminates. In order to develop general models capable of addressing the issues of impact resistance and damage tolerance of stitched laminates, detailed understanding of the nature and extent of damage, identification of the dominant fracture modes and assessment of the effect of stitches on the damage development are essential. In this study, both instrumented drop-weight tests and compression-after-impact tests were carried out to examine and compare the damage responses of stitched and unstitched graphite/epoxy laminates subjected to low-velocity impact. The progression of damage and its effect on post-impact performance was investigated in detail in two classes of cross ply laminates ([03/903]s and [0/90]3s) by means of an extensive series of damage observations, conducted with various complementary techniques (X-radiography, ultrasonics, optical microscopy, deply). The results of the analyses carried out during the study to characterize the key fracture modes and to clarify their relationship with the structural performance of both stitched and unstitched laminates are reported and discussed in the paper. ?? 2007 Elsevier Ltd. All rights reserved.
Composite laminates; Compression after impact; Damage; Low-velocity impact; Stitching
Fundamental natural frequencies of thin-walled elliptical composite cylinders
Journal of Composite Materials
46
10
1169-1190
2012
10.1177/0021998311413691
Hamilton's principle coupled with the Rayleigh-Ritz technique is used to compute the fundamental frequencies of simply supported thin-walled fiber-reinforced composite cylinders with elliptical cross sections. Owing to the decreased geometric stiffness resulting from less curvature, it is expected that the normal displacement component of the vibratory motion will be larger in the flatter regions of the cross section than that in the more curved regions. Accordingly, in the Rayleigh-Ritz formulation, the normal displacement component of the vibratory motion is modulated with circumferential location to represent this characteristic by using a so-called shape factor. A number of simplifications in the analysis lead to a hierarchy of expressions for the fundamental frequency, including the one termed Lo's approximation. The so-called large and small cylinders, as measured by cylinder circumference and with wall laminates [+/-theta/0/90](2S) and[+/-theta/0/90](S), respectively, theta in the range of 0 to 90 degrees, are considered. It is demonstrated that the comparisons with finite element calculations are good, particularly for Lo's approximation. Then, parameter studies using Lo's approximation are conducted to illustrate the dependence of the fundamental frequency on fiber angle theta, cross-sectional geometry, cylinder circumference, and cylinder length. It is shown that for cylinders of the same circumference, an elliptical cylinder has a lower fundamental frequency than a circular one and that difference is quantified. However, the dependence of the fundamental frequency on other geometric parameters and fiber angle is much the same for cylinders with elliptical cross sections as for circular cylinders.
anisotropic coefficients; circular cylindrical-shells; cross-ply; free-vibrations; Hamilton's principle; natural frequencies; noncircular cylinders; Rayleigh-Ritz technique; shape factor
Grid indentation analysis of composite microstructure and mechanics: Principles and validation
Materials Science and Engineering: A
430
1-2
189-202
2006
10.1016/j.msea.2006.05.125
Several composites comprise material phases that cannot be recapitulated ex situ, including calcium silicate hydrates in cementitous materials, hydroxyapatite in bone, and clay agglomerates in geomaterials. This requirement for in situ synthesis and characterization of chemically complex phases obviates conventional mechanical testing of large specimens representative of these material components. Current advances in experimental micro and nanomechanics have afforded new opportunities to explore and understand the effect of thermochemical environments on the microstructural and mechanical characteristics of naturally occurring material composites. Here, we propose a straightforward application of instrumented indentation to extract the in situ elastic properties of individual components and to image the connectivity among these phases in composites. This approach relies on a large array of nano to microscale contact experiments and the statistical analysis of the resulting data. Provided that the maximum indentation depth is chosen carefully, this method has the potential of extracting elastic properties of the indented phase which are minimally affected by the surrounding medium. An estimate of the limiting indentation depth is provided by asssuming a layered, thin film geometry. The proposed methodology is tested on a “model” composite material, a titanium-titanium monoboride (Ti–TiB) of various volumetric proportions. The elastic properties, volume fractions, and morphological arrangement of the two phases are recovered. These results demonstrate the information required for any micromechanical model that would predict composition-based mechanical performance of a given composite material.
Composites; Indentation analysis; Material characterization; Titanium-titanium boride
Variational analysis for angle-ply laminates with matrix cracks
International Journal of Solids and Structures
51
21-22
3669-3678
2014
10.1016/j.ijsolstr.2014.06.028
A stress-based variational model is developed to study stiffness reduction and stress distribution in angle-ply laminates [θ2l/ θ1m/90n]s with matrix cracks. The inter-laminar shear stresses between 90° and θ1°-plies and between θ1° and θ2°-plies, respectively, are assumed to be in the form of general functions. The normal stresses σx in θ1°-plies and θ2°-plies are introduced with partition coefficient λ for solving the problem of statically indeterminate boundary because the normal stresses σx cannot be obtained by using the condition of statics due to the loads at the boundary for each uncracked layer. This leads to expressions derived from equilibrium equations and boundary conditions for stress components in terms of the general functions and the partition coefficient. The governing equations for the general functions and the partition coefficient are derived by using a variational approach with the principle of minimum complementary energy. As an application, reduction of Young's modulus for different laminates is evaluated and compared with available experimental results. Distributions of in-planar and inter-laminar stresses are also presented by means of the finite difference method. The results show that the present approach is suitable to analyze stiffness reduction for multi-angle-ply laminates with transverse cracks in 90° layer. © 2014 Elsevier Ltd. All rights reserved.
Investigation of the stresses and stress intensity factors responsible for fracture of thin protective films during ultra-micro indentation tests with spherical indenters
Thin Solid Films
286
1-2
111-121
1996
10.1016/S0040-6090(95)08525-4
This paper reports on the mechanical characterization of thin hard films deposited on softer substrates using the micro- indentation technique together with spherically tipped indenters. After a short review of the deformation and fracture behavior the indentation process is simulated using a finite element analysis in order to determine the stresses responsible for the first fracture event of the film. A fracture mechanics analysis is presented that uses the weight function method to calculate the stress intensity factors K-I and K-II within the near surface region of the film, A fracture criterion for multiaxial loading conditions is used to calculate the stress intensity factor K-I appl. It will be shown that for films which are thin compared to the radius of the indenter first fracture should occur under a Mode-I loading condition. For the cases where the film was thick compared to the indenter radius mixed mode loading conditions prevail and the resultant fracture path is dependent on the nature of the film microstructure.
physical vapour deposition; pvd; stress; thin flints
Cellulose thin films: Degree of cellulose ordering and its influence on adhesion
Biomacromolecules
8
3
912-919
2007
10.1021/bm061164w
Adhesion measurements have been performed with thin cellulose films using continuum contact mechanics with application of the JKR theory. Three different cellulose surfaces were prepared, one crystalline and two surfaces with a lower degree of crystalline order. Adhesion between two cross-linked poly(dimethylsiloxane) (PDMS) caps, as well as the adhesion between PDMS and the various cellulose surfaces, was measured. The work of adhesion (from loading) was found to be similar for all three surfaces, and from contact angle measurement with methylene iodide it was concluded that dispersive interactions dominate. However, the adhesion hysteresis differed significantly, being larger for a less ordered cellulose surface and decreasing with increasing degree of crystalline order. This is suggested to be due to the surface groups' ability to orient themselves and participate in specific or nonspecific interactions, where a surface with a lower degree of crystalline order has a higher possibility for reorientation of the surface groups. The mobility of cellulose chains increases with water uptake, resulting in stronger adhesive joints. These films will hence allow for determination of the contributions of hydrogen bonding and inter-diffusion on the adhesion, determined from the unloading data, as the thermodynamic work of adhesion was found to be independent of the cellulose surface used.
Boundary-discontinuous Fourier analysis of simply supported cross-ply plates
Applied Mathematical Modelling
37
3
1378-1389
2013
10.1016/j.apm.2012.03.038
A new higher order theory based analytical solution to the static analysis of general cross-ply plates is presented. The boundary-discontinuous generalized double Fourier series approach is used to solve highly coupled linear partial differential equations with the mixed type simply supported boundary conditions prescribed on the edges. The present results will provide data for the unsolved boundary conditions and provide benchmark comparisons for early design stages and verifications of numerical results such as finite element and boundary element. Analytical results are compared with finite element counterparts using commercially available software under uniformly distributed load. Present results are in good agreement with the finite element counterparts. The effects of important parameters such as lamination scheme, material property, thickness effects as well as their interactions are investigated in detail. ?? 2012 Elsevier Inc.
Boundary discontinuous Fourier; Cross-ply plates; Higher order theory; Mixed simply supported
The fascination of fluid mechanics
Journal of Fluid Mechanics
106
59-80
1981
10.1017/S0022112081001523
Two topics are discussed in order to illustrate the author's own enjoyment of fluid mechanics. The first and longer discourse is about splashes. It makes no attempt at completeness but includes a little new research. The second part deals briefly with many variations on the theme of flow in pipes.
A model of damage initiation in singly oriented ply fiber metal laminate under concentrated loads
Journal of Composite Materials
37
3
269-281
2003
10.1177/0021998303037003497
Damage initiation is modeled in singly oriented ply (SOP) Fiber Metal Laminate (FML) under concentrated loading conditions. The finite element method (FEM) is used based on the first order shear deformation theory for modeling damage initiation in SOP FML. The failure indices of the fiber prepreg and the metal laminate were calculated using the Tasi-Hill failure criterion and the Miser yield criterion respectively. To verify the model, failure analysis was conducted under uniaxial loading and cylindrical bending, then under concentrated loading. Results show that the model is good. An indentation test was then conducted to compare the damage initiation load with the calculated failure index. The test was conducted under two side clamped conditions in order to study the fiber orientation effect. The indentation curve was fitted using the Hertz equation, and the damage initiation load was defined as the point of divergence of the fitted curve from the real indentation curve. The damage initiation loads were obtained for various fiber orientations and were compared with the calculated failure index. The experiment results closely matched the calculated failure index. It follows that the present method accurately captures damage initiation of SOP FML.
Concentrated loads; Cylindrical bending; Damage initiation; Failure analysis; Failure index; Fiber metal laminate; Fiber orientation; Fiber orientation effect; Fiber reinforced metals; Finite element method; First order shear deformation theory; Indentation; Laminated composites; Miser yield criterion; Shear deformation; Singly oriented ply fiber metal laminate; Tasi-Hill criterion; Uniaxial loading
Higher-order 2-D/3-D layerwise mechanics and finite elements for composite and sandwich composite plates with piezoelectric layers
Aerospace Science and Technology
40
150-163
2015
http://dx.doi.org/10.1016/j.ast.2014.10.015
Abstract Coupled higher-order layerwise piezoelectric laminate mechanics are presented, applicable to composite and sandwich composite plates subjected to static mechanical loads and/or electric voltages. In the development of these formulations through-thickness compressibility is either considered (3-D) or neglected (2-D). Their advantage compared to linear layerwise theories lies in the efficient prediction of the local through-thickness response by using a gross through-thickness discretization, while retaining simplicity in through-thickness kinematic assumptions. Moreover, they enable prediction of interlaminar shear and transverse normal stress at the interface between discrete layers, which is crucial information for prediction of delamination initiation. Using the developed mechanics, the effects of transverse compressibility and ply angle on the local through-thickness response of composite and sandwich plates are studied.
Composite; Finite element; Higher-order layerwise; Piezoelectric; Plates; Sandwich
The Diffraction of Cathode Rays by Thin Films of Platinum
Nature
120
802
1927
10.1038/119890a0
IN a letter to NATURE of June 18, Mr. Reid and I described the rings formed when a beam of cathode rays was sent at normal incidence through a thin film of celluloid and struck a photograph plate placed some distance behind the film. These were attributed to a diffraction of the cathode rays by the film, the cathode rays behaving as waves of wave-length h/mv according to do Broglie’s theory of wave mechanics, and regularities in the structure of the film, or in the size of the molecules, making it behave as a kind of diffraction grating. In a paper now awaiting publication by the Royal Society, this work has been confirmed and extended to films of gold, aluminium, and of an unknown (probably organic) substance. In particular, the relation that the size of the rings is in all cases inversely as the momentum of the cathode rays is fully confirmed, and the number and size of the rings correspond remarkably with what is to be expected from the known crystalline structure of gold and aluminium, using de Broglie’s expression for the wave- length of the cathode rays.
Long interfacial waves in multilayer thin films and coupled Kuramoto–Sivashinsky equations
Journal of Fluid Mechanics
391
45-65
1999
10.1017/S0022112099005297
The coupled Kuramoto-Sivashinsky (CKS) equations for\nmultilayer downflowing films are derived and explored. The CKS\nequations exhibit a wealth of dynamical behaviour, displaying\ntravelling periodic waves, regular and chaotic-like patterns,\ncoexistence of different attractors, and perfect and imperfect\nsynchronization of the interfaces. New physical effects are found,\nsuch as suppression of the Rayleigh-Taylor instability for\nheavy-top stratified films, and new surface-tension-driven\ninstability.\n
Spreading characteristics of an insoluble surfactant film on a thin liquid layer: comparison between theory and experiment
Journal of Fluid Mechanics
544
23
2005
10.1017/S002211200500621X
We describe measurements of the surface slope and reconstruction of\nthe interface shape during the spreading of an oleic acid film on\nthe surface of a thin aqueous glycerol mixture. This experimental\nsystem closely mimics the behaviour of an insoluble surfactant film\ndriven to spread on a thin viscous layer under the action of a tangential\n(Marangoni) surface stress. Refracted image Moire topography is used\nto monitor the evolution of the surface slope over macroscopic distances,\nfrom which the time variant interface shape and advancing speed of\nthe surfactant film are inferred. The interfacial profile exhibits\na strong surface depression ahead of the surfactant source capped\nby an elevated rim at the surfactant leading edge. The surface slope\nand shape as well as the propagation characteristics of the advancing\nrim can be compared directly with theoretical predictions. The agreement\nis quite strong when the model allows for a small level of pre-existing\nsurface contamination of the initial liquid layer. Comparison between\ntheoretical and experimental profiles reveals the importance of the\ninitial shear stress in determining the evolution in the film thickness\nand surfactant distribution. This initial stress appears to thin\nthe underlying liquid support so drastically that the surfactant\ndroplet behaves as a finite and not an infinite source, even though\nthere is always an excess of surfactant present at the origin.
Effect of ply stacking sequence on stress in a scarf joint
AIAA Journal
27
1
79-86
1989
10.2514/3.10097
Closed-form solutions for the stresses in an adhesive-bonded scarf joint indicate that the load is transferred over the entire overlap region. These solutions, however, do not consider the nonhomogeneity of laminated composites. This study investigates the effect of the stiffness discontinuity between individual plies and the variation of laminate stacking sequence on the joint's stress distribution. Highly detailed plane stress finite-ele- ment models of four- and twelve-layer scarf joints having alternating 0 and 90 deg plies were constructed. When subjected to a unit tensile load, these models produced stresses that were significantly different from the smooth curves predicted by closed-form solution. The different load-carrying capacity of the oriented plies caused irregular stress distributions whose characteristics were related to the location of each ply within the stack. Also, as the number of plies was increased, the stresses tended to oscillate within a limited band whose average was close to the results produced by an equivalent homogeneous laminate. Because the closed-form solution does not consider nonhomogeneous materials, this detailed analysis predicted trends in the stress distribution that otherwise could not be obtained.
Quantum Mechanics
American Journal of Physics
53
9
925
1985
10.1119/1.14383
The identification of BACE-1, a key enzyme in the production of Amyloid-β (Aβ) peptides, generated by the proteolytic processing of amyloid precursor protein, was a major advance in the field of Alzheimer's disease as this pathology is characterized by the presence of extracellular senile plaques, mainly comprised of Aβ peptides. Hydroxyethylamines have demonstrated a remarkable potential, like candidate drugs, for this disease using BACE-1 as target. Density Functional Theory calculations were employed to estimate interaction energies for the complexes formed between the hydroxyethylamine derivated inhibitors and 24 residues in the BACE-1 active site. The collected data offered not only a general but a particular quantitative description that gives a deep insight of the interactions in the active site, showing at the same time how ligand structural variations affect them. Polar interactions are the major energetic contributors for complex stabilization and those ones with charged aspartate residues are highlighted, as they contribute over 90% of the total attractive interaction energy. Ligand-ARG296 residue interaction reports the most repulsive value and decreasing of the magnitude of this repulsion can be a key feature for the design of novel and more potent BACE-1 inhibitors. Also it was explained why sultam derivated BACE-1 inhibitors are better ones than lactam based. Hydrophobic interactions concentrated at S1 zone and other relevant repulsions and attractions were also evaluated. The comparison of two different theory levels (X3LYP and M062X) allowed to confirm the relevance of the detected interactions as each theory level has its own strength to depict the forces involved, as is the case of M062X which is better describing the hydrophobic interactions. Those facts were also evaluated and confirmed by comparing the quantitative trend, of selected ligand-residue interactions, with MP2 theory level as reference standard method for electrostatic plus dispersion energies.
Flow and instability of thin films on a cylinder and sphere
Journal of Fluid Mechanics
647
221
2010
10.1017/S0022112009993818
We investigate the dynamics of thin films driven by gravity on the outer surface of a cylinder and sphere. The surface is rigid, stationary and the axis of the cylinder is horizontal. An instantaneous release of a constant volume of fluid at the top of the cylinder or sphere results initially in a two-dimensional or axisymmetric current respectively. The resultant flow of a thin film of fluid is described using lubrication theory when gravity and viscous forces govern the dynamics. We show that the thickness of the flow remains uniform in space and decreases in time like t−1/2 near the top of both the cylinder and the sphere. Analytic solutions for the extent of the flow agree well with our experiments until the advancing front splits into a series of rivulets. We discuss scalings of the flow at the onset of the instability as a function of the Bond number, which characterizes the relative importance of gravity and surface tension. The experiments, conducted within an intermediate range of Bond numbers, suggest that the advancing front becomes unstable after it has propagated a critical distance, which depends primarily and monotonically on the volume of fluid and not on the viscosity of fluid. Releasing a sufficiently large volume of fluid ensures that rivulets do not develop on either a cylinder or sphere.
P.A.M. Dirac and the Discovery of Quantum Mechanics
American Journal of Physics
79
3
11
2003
10.1119/1.3536639
Dirac's contributions to the discovery of non-relativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described.
A structural mechanics approach for the analysis of carbon nanotubes
International Journal of Solids and Structures
40
10
2487-2499
2003
10.1016/S0020-7683(03)00056-8
This paper presents a structural mechanics approach to modeling the deformation of carbon nanotubes. Fundamental to the proposed concept is the notion that a carbon nanotube is a geometrical frame-like structure and the primary bonds between two nearest-neighboring atoms act like load-bearing beam members, whereas an individual atom acts as the joint of the related load-bearing beam members. By establishing a linkage between structural mechanics and molecular mechanics, the sectional property parameters of these beam members are obtained. The accuracy and stability of the present method is verified by its application to graphite. Computations of the elastic deformation of single-walled carbon nanotubes reveal that the Young’s moduli of carbon nanotubes vary with the tube diameter and are affected by their helicity. With increasing tube diameter, the Young’s moduli of both armchair and zigzag carbon nanotubes increase monotonically and approach the Young’s modulus of graphite. These findings are in good agreement with the existing theoretical and experimental results.
atomistic modeling; carbon nanotube; force fields; molecular mechanics; nanomechanics; structural mechanics
The Philosophy of Quantum Mechanics
Philosophy in Science Tucson
10
2
191-211
1974
Observables in quantum mechanics may be divided into two classes of different ontological and epistemological character: undeterminate (undecided) like position, and predeterminate as e.g., momentum, helicity, isospin and other conserved quantities for free particles. the existence of predetermined quantities prior to their possible measurement secures a realistic character of quantum mechanics. the state in quantum mechanics means an optimal information, but not an immanent property of the physical system.
Torsional models of two-ply yarn
Journal of Dong Hua University (English Edition)
15
1
31-37
1998
The vector equation of a generalized doubly wound helix was derived. Treloar's plied yarn geometry could be obtained as a special case of the generalized doubly wound helix. The shortest fibre length around the surface of a helical tube (formed by fibre helices) was determined by applying variational principles. The fibre length calculated by using Treloar's geometry was compared indirectly with the shortest possible fibre length at different levels of yarn deformation when some of Treloar's rigid geometrical constraints were relaxed. A new idea based on non-concentric circles was introduced to approximate the fibre helix movement in a two-ply yarn. A torsional model of two-ply yarn was developed and the theoretical predictions were compared with some preliminary experimental results.
Cotton yarn; Deformation; Mathematical models; Textile fibers; Torsional stress
Combinatorial approach to the edge delamination test for thin film reliability—adaptability and variability
Thin Solid Films
476
2
379-385
2005
10.1016/j.tsf.2004.10.028
A high-throughput combinatorial approach to edge delamination test is proposed to map the failure of adhesion as a function of both temperature and film thickness in a single step. In this approach, a single specimen of a thin film bonded to a substrate with orthogonal thickness and temperature gradients is subdivided into separate samples. This approach can be adopted to measure the adhesion reliability for films with thicknesses in the nano regime by the addition of an overlayer. In addition, it can increase the pace of material innovations in nanoscale science and technology. The experimental requirements for a valid combinatorial test are analyzed using three-dimensional computational fracture mechanics. A simulation result is presented to demonstrate the feasibility of the combinatorial approach and to design the experimental protocol. (C) 2003 Elsevier Science B.V. All rights reserved.
adhesion; combinatorial methods; contact angle; surface energy; thin film reliability
Phase diagrams of ferroelectric thin films described by the transverse Ising model
Physica a-Statistical Mechanics and Its Applications
319
355-361
2003
10.1016/S0378-4371(02)01516-9
The phase diagram of a ferroelectric thin film described by the transverse Ising model is discussed by the use of the standard mean field approximation and other approximations better than the mean field approximation. Some characteristic features have been observed in the results of mean field approximation. It is investigated whether they are specific to the mean field approximation. (C) 2002 Elsevier Science B.V. All rights reserved.
effective-field theory; ferroelectric thin films and phase diagram; transverse ising model
Some methods of composites non-leakage improvement
Composites Part B: Engineering
30
221-226
1999
10.1016/S1359-8368(98)00060-2
Principles of optimization of plies orientation are considered from the viewpoint of enhancement of their tolerance to loading up to leakage. The method efficiency was borne out by tests of GFRP pipes with various structure. Dependence of the first cracks deformation on the ply thickness was used to increase `weepage' pressure of wound pipes (??55??). Leaking pressure fell to 55% when the rowing Tex was increased to 2520 as that of Tex less than 840. Tests of model samples of different structure composites and a simplified method of fracture mechanics were used to study the mechanics of cracking of surface mat proofing plies when neighboring with different structure plies. The investigation allowed to formulate the requirements to the dividing ply to prevent propagation of cracks appearing in structural plies in the surface mat based barrier layer. The application of thin woven fabrics instead of commonly used chopped strands increased failure deformation of the barrier layer.
a; fabrics; leakage; textiles
On the evolution of the distribution of entrapped air at the tool/first ply interf‘ace during lay-up and debulk
Advanced Manufacturing: Polymer & Composites Science
1
1
36-43
2015
10.1179/2055035914Y.0000000005
Air entrapped during the material deposition stage of prepreg layup can contribute to voidage in the cured laminate, which is a major factor in determining the quality of the resulting laminates and components. Removal of this entrapped air is therefore a priority to achieve maximum part performance. To date, there does not appear to have been any consistent study of the processes by which voids can be entrapped. This paper seeks to address this by presenting direct observations of the contact between a glass tool surface and the first ply of carbon fiber prepreg laid down onto it. The entrapment of air between the tool and ply is investigated, in terms of its distribution and evolution during debulk under vacuum at room temperature. A counterintuitive inverse relationship between initial area of contact and the final level of entrapped air was observed, with higher levels of initial contact leading to higher final levels of entrapped air. An initial examination was also carried out to review the effects ...
1; 2015; 36-43; a; adv; bloom; c; cite this article l; compos; composite; d; debulk; gas transport; m; manuf; napper; polym; potter; sci; vacuum bagging; voids; ward and k
Nonextensive statistical mechanics and economics
Physica A: Statistical Mechanics and its Applications
324
1-2
89-100
2008
10.1016/S0378-4371(03)00042-6
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, natu- rally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous success in describing, among others, the particular stationary state corresponding to thermal equilibrium. There are, however, vast classes of complex systems which accomodate quite badly, or even not at all, within the BG formalism. Such dynamical systems exhibit, in one way or another, nonergodic aspects. In order to be able to theoretically study at least some of these systems, a formalism was proposed 14 years ago, which is sometimes referred to as nonextensive statistical mechanics. We briefly introduce this formalism, its foundations and applications. Furthermore, we provide some bridging to important economical phenomena, such as option pricing, return and volume distributions observed in the financial markets, and the fasci- nating and ubiquitous concept of risk aversion. One may summarize the whole approach by saying that BG statistical mechanics is based on the entropy SBG = −ki pi ln pi, and typically provides exponential laws for describing stationary states and basic time-dependent phenomena, while nonex- tensive statistical mechanics is instead based on the entropic form Sq = k(1−i pq i )/(q −1) (with S1 = SBG), and typically provides, for the same type of description, (asymptotic) power laws.
55-21-2586-7190; 55-21-2586-7400; anteneodo; borland; br; c; cbpf; celia; com; corresponding author; e-mail addresses; fax; l; lisa; nonextensive statistical mechanics; option pricing; osorio; r; risk aversion; roberto; sphinx; tel; tsallis
Recent Developments in Thin Film Adhesion Measurement
IEEE Transactions on Device and Materials Reliability
4
2
163-168
2004
10.1109/TDMR.2004.829071
Interfacial fracture energies of thin films may be calculated using many different techniques. Nanoindentation and stressed overlayers are by far the most common and more reliable of the testing techniques. They depend on mechanics-based models to calculate the interfacial fracture energy of an interface using only the site specific material properties and the dimensions of the delaminated region, either in spontaneous buckle or indentation-induced blister form. This study will focus on four adhesion measurement techniques: spontaneous buckles, stressed overlayer-induced buckles, and nanoindentation-induced blisters with and without stressed overlayers, to demonstrate that the techniques will produce similar results for the measurement of adhesion energy. Films of tungsten (W), platinum (Pt), and titanium (Ti) on SiO<sub>2</sub> (amorphous glass) substrates are examined and values of interfacial fracture energies reported. Results of interfacial fracture energy calculated from spontaneous buckles and indentation-induced blisters compare well to one another and values are reported for the aforementioned films.
adhesion; buckling; delaminated region; delamination; fracture; indentation-induced blister form; interface structure; interfacial fracture energies; nanoindentation; nanoindentation-induced blisters; platinum; Pt; SiC substrates; silicon compounds; site specific material properties; spontaneous buckles; stressed overlayer-induced buckles; stressed overlayers; testing techniques; thin film adhesion measurement; thin films; Ti; titanium; tungsten; W; wide band gap semiconductors
Non-linear analysis of functionally graded fiber reinforced composite laminated plates, Part II: Numerical results
International Journal of Non-Linear Mechanics
47
9
1055-1064
2012
10.1016/j.ijnonlinmec.2012.03.003
In this Part, the extensive parametric studies performed are reported and numerical results are presented for the non-linear vibration, non-linear bending and compressive postbuckling of uniformly distributed and functionally graded fiber reinforced unsymmetric cross-ply and/or antisymmetric angle-ply laminated plates resting on Pasternak elastic foundations under different hygrothermal environmental conditions. The numerical results show that the functionally graded fiber reinforcement has a significant effect on the postbuckling response and load-bending moment curves of plate bending, whereas this effect is less pronounced on the load-deflection curves of plate bending and the linear and non-linear frequencies of the same plate.
Two ply tubular scaffolds comprised of proteins/poliglecaprone/polycaprolactone fibers.
Journal of materials science. Materials in medicine
21
2
541-9
2010
10.1007/s10856-009-3922-y
Electrospun bi-layer tubular hybrid scaffolds composed of poliglecaprone (PGC), polycaprolactone (PCL), elastin (E), and gelatin (G) were prepared and thereafter crosslinked by 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC). Scanning electron microscopic (SEM) images revealed a highly porous micro-structure comprising randomly distributed non-woven fibers with the majority of fibers in submicron diameters. The EDC-crosslinking yielded an average crosslinking degree of 40%. Uni-axial tensile test of hydrated scaffolds in both longitudinal and circumferential directions revealed tensile properties, comparable to those of native arteries. The graft (PGC:PCL = 1:3) did not demonstrate significant difference before and after EDC-crosslinking in tensile strength or % strain in either longitudinal or circumferential directions. However, crosslinking increased the Young's modulus of the graft along the longitudinal direction (from 5.84 to 8.67 MPa). On the contrary, the graft (3:1) demonstrated a significant decrease in maximum strain in both directions. Cyto-assay using human umbilical vein endothelial cells (HUVECs) showed excellent cell viability.
Biocompatible Materials; Biocompatible Materials: chemistry; Cells, Cultured; Cell Survival; Crystallization; Crystallization: methods; Dioxanes; Dioxanes: chemistry; Elastic Modulus; Elastin; Elastin: chemistry; Endothelial Cells; Endothelial Cells: cytology; Endothelial Cells: physiology; Gelatin; Gelatin: chemistry; Humans; Materials Testing; Polyesters; Polyesters: chemistry; Tensile Strength; Tissue Engineering; Tissue Engineering: instrumentation; Tissue Engineering: methods; Tissue Scaffolds
Minimum Weight Design of Symmetrical Angle-Ply Laminates under Multiple Uncertain Loads
Structural Optimization
9
2
89-95
1995
10.1007/BF01758825
An angle-ply laminated plate is optimized with the objective of minimizing the weight of the plate taking into account uncertainties in the multiple transverse loads. The weight is proportional to the laminate thickness which is minimized subject to deflection and buckling constraints under the least favourable loading with the ply angles taken as design variables. The convex modelling approach is employed to analyse the uncertain loading with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirements that these variations are bounded in L(2) norm and represented by a finite number of eigenmodes. The effect of uncertainty on the optimal design is investigated quantitatively. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.
Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility
International Journal of Solids and Structures
33
18
2647-2658
1996
10.1016/0020-7683(95)00174-3
A global numerical technique, the differential quadrature (DQ) method, is examined here for its suitability to solve the boundary-value problem of symmetric cross-ply laminates using the first-order shear deformation plate theory by Whitney and Pagano [J. Appl. Mech. 37, 1031-1036 (1970)]. The bending behaviours of symmetric cross-ply laminates, subject to different boundary constraints, are investigated. In this study, the method is used to transform the sets of governing differential equations and boundary conditions of the laminated plates into sets of linear algebraic equations. Boundary conditions along the edges are implemented through the discrete grid points by constraining the displacements, bending moments and rotations. The theoretical formulations and solution procedures of the method are illustrated through solving several numerical examples. The accuracy and validity of the present formulation, if available, are examined by direct comparison with the known values. Copyright © 1996 Elsevier Science Ltd.
Bending (deformation); Bending moments; Boundary conditions; Boundary value problems; Differential equations; Differential quadrature method; Discrete grid points; First order shear deformation plate theory; First order shear flexibility; Laminated composites; Linear algebra; Numerical methods; Plates (structural components); Shear deformation; Thick symmetric cross ply laminates
Three-dimensional microscopic interlaminar analysis of cross-ply laminates based on a homogenization theory
International Journal of Solids and Structures
44
8274-8284
2007
10.1016/j.ijsolstr.2007.06.010
In this study, a method for three-dimensional microscopic interlaminar analysis of cross-ply laminates is developed based on a homogenization theory to analyze microscopic interactions between unidirectional long fiber-reinforced laminae. For this, a unit cell of a cross-ply laminate, which includes interlaminar areas, is defined under the assumption that each lamina in the laminate has a transversely square fiber array. Then, showing that the laminate has a point-symmetric internal structure, the symmetry is utilized to introduce half of the unit cell as the domain of analysis. Moreover, the domain of analysis is divided into substructures using a substructure method combined with the homogenization theory, significantly reducing the computational costs. The present method is then applied to the analysis of interlaminar stress distributions in a carbon fiber/epoxy cross-ply laminate subjected to in-plane uniaxial tension. It is shown that microscopic shear stress noticeably occurs at the interface between the 0°- and 90°-plies. It is also shown that the microscopic interaction between the two plies is observed only in the vicinity of the interface. © 2007 Elsevier Ltd. All rights reserved.
Domain of analysis; Homogenization; Interlaminar; Long fiber-reinforced laminate; Point-symmetry; Substructure
Rockfill mechanics
Advances in Unsaturated Soils Proceedings of the 1st PanAmerican Conference on Unsaturated Soils PanAmUNSAT 2013
61-86
2013
The paper examines several aspects of rockfill behaviour, which are relevant to interpret and analyze the field response of dams and embankments. Experimental observations on rockfill compressibility, time-dependent deformation and deviatoric stress-strain behaviour are presented. Special attention is given to the role of relative humidity. The physics of rockfill deformation, explained by particle breakage are described. Particle breakage is explained by crack propagation, a phenomenon discussed within the framework of fracture mechanics. A macroscopic elastoplastic constitutive model is outlined. Rockfill mechanics are also approached by a Distinct Element modelling of grain assemblages experiencing grain breakage. Finally, rockfill mechanics are discussed from the wider perspective offered by unsaturated soil mechanics. 2013 Taylor & Francis Group, London.
Quantum mechanics as a classical theory
Physical Review D
31
6
1341-1348
1985
10.1103/PhysRevD.31.1341
The generator aspect of observables in classical mechanics leads naturally to a generalized classical mechanics, of which quantum mechanics is shown to be a particular case. Basic features of quantum mechanics follow, such as the identification of observables with self-adjoint operators, and canonical quantization rules. This point of view also gives a new insight on the geometry of quantum theory: Planck’s constant is related for instance to the curvature of the quantum-mechanical space of states, and the uniqueness of quantum mechanics can be proved. Finally, the origin of the probabilistic interpretation is discussed.
Physiological Fluid Mechanics
Bioengineering
September
1-130
2009
After a brief survey of the whole field, three problems are selected for more detailed consideration: the flow of blood near the mouth of an arterial side branch, in an attempt to predict the wall shear stress in the parent artery; fluid flow in collapsible tubes such as veins; coupled salt and water transport by pumping epithelia. It is concluded that the problems of greatest biological importance are generally of microscopic scale, and fluid mechanics research must proceed in close conjunction with physiological experiment (65 Refs.)
Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory
International Journal of Mechanical Sciences
49
1060-1075
2007
10.1016/j.ijmecsci.2006.11.008
Natural frequencies and buckling stresses of cross-ply laminated composite circular cylindrical shells are analyzed by taking into account the effects of higher-order deformations such as transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for laminated composite circular cylindrical shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate higher-order theories are applied to solve the vibration and buckling problems of laminated composite circular cylindrical shells subjected to axial stresses. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the first natural frequency and corresponding buckling stress for the fundamental mode r = s = 1 are examined in detail. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite circular cylindrical shells within small number of unknowns. ?? 2006 Elsevier Ltd. All rights reserved.
Buckling stress; Circular cylindrical shells; Cross-ply laminated composite shells; Global higher-order deformation theory; Interlaminar stresses; Natural frequency
TOPOLOGICAL IDEAS AND FLUID MECHANICS
Physics Today
December
28-34
1996
10.1063/1.881574
New mathematical techniques and greater computational power have made it possible to apply knot theory and braid theory to fluids flows
fluid mechanics; Topology
Hybrid Quantum Mechanics / Molecular Mechanics Approaches
Modern Methods and Algorithms of Quantum Chemistry, Proceedings, NIC Series, Vol. 3
285-305
2000
An overview is provided of the range of approaches to hybrid QM/MM (quantum mechanics/molecular mechanics) calculations. The factors considered include the choice of QM and MM methods, the construction of the total QM/MM energy ex- pression, the nature of the QM/MM coupling, and the treatment of bonds between QM and MM regions. The practical issues associated with handling the increased conformational complexity of macromolecular systems, and the construction of QM/MM codes are discussed.
A Course on Quantum Techniques for Stochastic Mechanics
Arxiv preprint arXiv:1209.3632
235
2012
Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of "chemical reaction networks", which describes the interactions of molecules in a stochastic rather than quantum way. Computer science and population biology use the same ideas under a different name: "stochastic Petri nets". But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas - but in a context where probabilities replace amplitudes. We explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics. We use this analogy to present new proofs of two major results in the theory of chemical reaction networks: the deficiency zero theorem and the Anderson-Craciun-Kurtz theorem. We also study the overlap of quantum mechanics and stochastic mechanics, which involves Hamiltonians that can generate either unitary or stochastic time evolution. These Hamiltonians are called "Dirichlet forms", and they arise naturally from electrical circuits made only of resistors.
Buckling of cracked thin-plates under tension or compression
Thin-Walled Structures
43
2
209-224
2005
10.1016/j.tws.2004.07.006
Plates are easily susceptible to buckling under compression, in particular when plate's thickness becomes sufficiently small with respect to others plate's sizes; such a mode of failure is often prevalent with respect to strength failure. The buckling phenomena under tension loading can also occur, especially in plates containing defects such as cracks or holes; when the buckling load is reached, complex wrinkling deflection patterns in compressed regions develops around such imperfections. In the present paper, the buckling analysis of variously cracked rectangular elastic thin-plates under tension and compression is considered. A short explanation of the buckling phenomena in plates is recalled and several numerical analyses, carried out by using the Finite Element Method (FEM), are performed in order to determine the critical load multiplier, both in compression and in tension, by varying some plates' parameters. In particular, the critical load multiplier is determined for different relative crack length, crack orientation and Poisson's coefficient of the plate's material which is made to range between 0.1 and 0.49. Moreover a simple approximate theoretical model to explain and predict the buckling phenomena in cracked plates under tension is proposed and some comparisons are made with FE numerical results in order to assess its reliability in predicting buckling load multipliers. Finally, the obtained results are graphically summarised (in dimensionless form) in several graphs and some interesting conclusions are drawn.
Buckling; Cracked tensioned plates; Fracture mechanics; Wrinkling
Ag-Coated Fe3O4@SiO2 Three-Ply Composite Microspheres: Synthesis, Characterization, and Application in Detecting Melamine with Their Surface-Enhanced Raman Scattering
The Journal of Physical Chemistry C
114
17
7738-7742
2010
10.1021/jp100141c
Ag nanoparticles with average sizes of 20 nm were well-dispersed on the surfaces of Fe3O4@SiO2 composite microspheres through a simple wet-chemical method employing the Ag-mirror reaction. The as-synthesized Ag-coated Fe3O4@SiO2 three-ply composite microspheres are monodisperse and bifunctional, with ferromagnetic and surface-enhanced Raman scattering (SERS) properties. The products were characterized by means of X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy dispersive X-ray analysis (EDX). SERS signals of typical analytes such as rhodamine 6G (Rh 6G) were observed on Ag nanoparticles from the Ag-coated Fe3O4@SiO2 microspheres, even though the concentration of the analyte was as low as 1 ? 10?15 M (Rh 6G). The Ag-coated Fe3O4@SiO2 microspheres were applied to detecting melamine, and strong SERS signals were obtained with melamine concentration of 1 ? 10?6 M. This work may provide a potential and unique technique to detect melamine.
Adhesive fracture mechanics
International Journal of Fracture
10
33-43
1974
10.1007/BF00955077
Recently Williams, Malyshev and Salganik and others have applied the\nconcepts of fracture mechanics to predict\n\nadhesive fracture. The specific adhesive fracture energy, 7a, is defined\nas the energy released per unit of new surface\n\ncreated on separation of dissimilar materials. Williams has elucidated\nthe similarity between adhesive and cohesive\n\nfracture from the standpoint of a Griffith energy balance analysis.\nOne finds that for either cohesive or adhesive\n\nfracture, crack instability (where the crack has a characteristic\ndimension, a) is predicted by a general equation of the\n\nform Scr = k~/E-~ where k =f[geometry and loading] and includes all\nloading and geometric factors, E and y are\n\nYoung's modulus and specific fracture energy, respectively, and ac,\nis the applied load at incipient failure.\n\nWithin the fracture mechanics interpretation the adhesive fracture\nenergy 7a is viewed as a fundamental property of\n\nthe adhesive system. It is important to note, however, that it may\ndepend on surface preparation, curing conditions,\n\nabsorbed monolayers, etc. It is, therefore, essential that if To is\nused to predict adhesive fracture for different geometries,\n\nthen the surface preparation must be identical with that for the test\nspecimen.\n\nIf Ya is a system parameter, then it would be possible to predict\nfracture by conducting an energy balance analysis\n\nof the configuration, utilizing values of Ya, Young's modulus, and\nPoisson's ratio as determined from separate simple\n\ntest specimens.\n\nThere is, however, a need to establish that 7a is a system parameter\nwhich is independent of geometry. One can in\n\nprinciple perform a number of tests on several specimen configurations\nor, more effectively, several tests on a single\n\nspecimen which changes configuration between successive tests. In\nthis latter case the surface and dissimilar materials\n\nremain constant. A specimen which is suitable for our purpose was\ndeveloped by Williams and Jones by incorporating\n\naspects of tests first suggested by Dannenburg and Salganik and Malyshev.\n\nThe test method considers a disk or plate which has been bonded to\na substrate material except for a central portion\n\nof radius a. When pressure, p, is injected into the unbonded region,\nthe plate lifts off the substrate and forms a blister\n\nwhose radius stays fixed until a critical pressure, Pcr, is reached.\nAt this critical value the radius of the blister increases\n\nin size, signifying an adhesive failure along the interface.\n\nAn energy balance analysis is available for the circular blister specimen\nin the two limiting cases of a thick plate\n\n(Williams) or a very thick medium (Mossakovskii), each with an infinite\nouter radius. Having established the utility\n\nof this general test method, we have considered it necessary to extend\nthe analysis and test calibration capability to\n\nother thicknesses for more general engineering applications, as for\nexample, very thin membranes which are used in\n\npaint coatings.\n\nAn axisymmetric finite element numerical analysis was, therefore,\nconducted for specimens of different thickness and\n\ndebond radii to establish the energy balance for the various arbitrary\nthicknesses. A continuous curve for arbitrary\n\nspecimen thickness was then produced on a dimensionless plot ofp2a/E~,\nversus h/a where h is the specimen thickness.\n\n[he region of h/a over which the limiting case equations are valid\nwas also established within the accuracy of the\n\nnumerical analysis. Since many, if not most, bond geometries are not\nreadily analyzed in closed form, the numerical\n\nprocedures for energy balance analysis is included and may be used\nfor analyzing geometries other than the blister test\n\nspecimens.\n\nExperiments were conducted over a broad range of h/a and found to\nagree with the analytical elasticity solutions\n\nwhich assumed a constant (for given surface preparation, temperature,\nloading conditions, strain rate independence,\n\netc.) value for ?'a- These experiments confirm that for this system\nat least ya is a constant independent of geometry.
Fracture mechanics of functionally graded materials
MRS Bulletin
20
01
43-44
1995
10.1016/0961-9526(95)00029-M
In today's highly demanding technological environment, one of the main challenges in new material design is combining seemingly irreconcilable thermomechanical properties in the same component (e.g., high heat and corrosion resistance, high strength in elevated-temperature applications and high resistance to wear, and high toughness in load-bearing elements). In many cases, the problem may be solved by using coatings or by layering dissimilar materials. From a structural viewpoint, a major disadvantage of these techniques, particularly in ceramic coating of metals, has been the resulting high thermal and residual stresses and relatively poor bonding strength. Thus, in thin films, coatings, and layered materials, surface cracking and debonding or delamination have been common forms of mechanical failure. One effective way of reducing residual and thermal stresses and enhancing bonding strength has been to eliminate material-property discontinuities by grading the material composition near the interfaces or through the coating. These new materials, with continuously varying compositions or volume fractions, are known as functionally graded materials (FGMs). In developing FGMs, research on the mechanics, and particularly on the fracture mechanics of these inhomogeneous materials, is needed to provide technical support to materials scientists and to manufacturing and design engineers. In the past, fracture mechanics has been useful both as a screening tool during material processing and as a design and maintenance tool for service-life assessment. Broadly speaking, fracture mechanics involves studying the effect of the applied loads, the component/flaw geometry, and the environmental conditions on the fracture of engineering materials.
Quantum Mechanics of Individual Systems
American Journal of Physics
36
8
704
1968
10.1119/1.1975096
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for individual systems. A discussion of the meaning of the “state” of an individual quantum mechanical system is given, and an application is made to the clarification of some of the paradoxical features of the theory.
Large Deflection of Thin Plates in Pressure Sensor Applications
Journal of Applied Mechanics
69
6
785-789
2002
10.1115/1.1507767
The present paper examines the large deflections of a clamped circulate thin plate for pressure sensor applications and establishes a simple solution using the singular pertur- bation technique. The perturbation solution for the slope of the lateral deflection is in a closed form in terms of the load-induced radial stress resultant. The nonlinearity has a strong stiffened effect. The nondimensional load-induced stress resultants are functions of the nondimensional initial stress resultant, lateral load, and Poisson’s ratio.
Meshless thin plate spline methods for the modified Helmholtz equation
Computer Methods in Applied Mechanics and Engineering
197
3733-3741
2008
10.1016/j.cma.2008.02.029
In this paper, we investigate the application of the meshless radial basis function method for solving the Helmholtz equation using thin plate splines. We use a meshless method mixed with a boundary and a fundamental solution methods. The numerical computation is achieved by using the generalized minimal residual (GMRES), the least-square (LSQR) methods associated with Tikhonov regularization. ?? 2008 Elsevier B.V. All rights reserved.
Helmholtz equation; Krylov subspaces; Radial basis functions; Regularization
The Role of Micro-Mechanics in Soil Mechanics
International Workshop on Soil Crushability
September
25
1999
It is suggested that observations of the changing microstructure of\nsoils will permit the selection and refinement of relevant micro-mechanisms\nwhich control soil behaviour. A few micromechanical models are introduced\nto demonstrate how they might shed light on shortcomings in the classical\ncontinuum approach to soil mechanics. The ultimate objective is to\nreduce the number and enhance the physical meaning of parameters\nrequired to describe soil behaviour, so as to raise the confidence\nof geotechnical engineers in the constitutive modelling of soils.
Pressure-driven flow of a thin viscous sheet
Journal of Fluid Mechanics
292
359–376
1995
10.1017/S002211209500156X
Systematic asymptotic expansions are used to find the leading-order equations for the pressure-driven flow of a thin sheet of viscous fluid. Assuming the fluid geometry to be slender with non-negligible curvatures, the Navier–Stokes equations with appropriate free-surface conditions are simplified to give a ‘shell-theory’ model. The fluid geometry is not known in advance and a time-dependent coordinate frame has to be employed. The effects of surface tension, gravity and inertia can also be incorporated in the model.
3-D computer vision in experimental mechanics
Optics and Lasers in Engineering
47
3-4
282-291
2009
10.1016/j.optlaseng.2007.11.009
Optical methods that give displacement or strain fields are now widely used in experimental mechanics. Some of the methods can only measure in-plane displacements/strains on planar specimens and some of them can give both in-plane and out-of-plane displacement/strain fields on any kind of specimen (planar or not). In the present paper, the stereovision technique that uses two cameras to measure 3-D displacement/strain fields on any 3-D object is presented. Additionally, a quite inclusive list of references on applications of stereovision (and 3-D DIC) to experimental mechanics is given at the end of the paper. ?? 2007 Elsevier Ltd. All rights reserved.
3-D digital image correlation (3D-DIC); Displacement/strain measurement; Experimental mechanics; Shape measurement; Stereo-correlation; Stereovision
Mechanics with fractional derivatives
Physical Review E
55
3
3581-3592
1997
10.1103/PhysRevE.55.3581
Lagrangian and Hamiltonian mechanics can be formulated to include derivatives of fractional order [F. Riewe, Phys. Rev. 53, 1890 (1996)]. Lagrangians with fractional derivatives lead directly to equations of motion with nonconservative classical forces such as friction. The present work continues the development of fractional-derivative mechanics by deriving a modified Hamilton's principle, introducing two types of canonical transformations, and deriving the Hamilton-Jacobi equation using generalized mechanics with fractional and higher-order derivatives. The method is illustrated with a frictional force proportional to velocity. In contrast to conventional mechanics with integer-order derivatives, quantization of a fractional-derivative Hamiltonian cannot generally be achieved by the traditional replacement of momenta with coordinate derivatives. Instead, a quantum-mechanical wave equation is proposed that follows from the Hamilton-Jacobi equation by application of the correspondence principle.
Stress intensity factor of mode-III cracks in thin sheets
Physical Review E
83
2
026106
2011
10.1103/PhysRevE.83.026106
The stress field at the tip of a crack of a thin plate of elastic material that is broken due to a mode III shear tearing has a universal form with a nonuniversal amplitude, known as the stress intensity factor, which depends on the crack length and the boundary conditions. We present in this paper exact analytic results for this stress intensity factor, thus enriching the small number of exact results that can be obtained within linear elastic fracture mechanics.
Instability of a nearly inextensible thin layer in a shear flow
European Journal of Mechanics, B/Fluids
22
1
39-50
2003
10.1016/S0997-7546(03)00002-5
The stability of a nearly inextensible thin layer in a shear flow is investigated using an adjoint-based approach of the perturbed Stokes flow, i.e., for small inertia effects. The thin layer may be a very viscous fluid or an elastic sheet. We show that long waves are unstable, and that short waves are also unstable when the effect of inertia dominates that of surface tension. In contrast with the two-layer flow with a clean interface, the instability persists even when the fluids on either side of the thin layer have the same viscosity. © 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
Contacts (fluid mechanics); Elasticity; Elastic sheets; Hydrodynamics; Hydrodynamic stability; Interfacial waves; Perturbation techniques; Shear flow; Surface tension; Viscous flow; Viscous fluids
Discrete variational Hamiltonian mechanics
Journal of Physics A: Mathematical and General
39
19
5509-5519
2006
10.1088/0305-4470/39/19/S11
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms.
Mechanics: From Newton’s Laws to Deterministic Chaos (Florian Scheck)
SIAM Review
34
1
135-137
1992
10.1137/1034022
This book covers all topics in mechanics from elementary Newtonian\nmechanics, the principles of canonical mechanics and rigid body mechanics\nto relativistic mechanics and nonlinear dynamics. It was among the\nfirst textbooks to include dynamical systems and deterministic chaos\nin due detail. As compared to the previous editions the present fifth\nedition is updated and revised with more explanations and additional\nexamples. Symmetries and invariance principles, the basic geometric\naspects of mechanics as well as elements of continuum mechanics also\nplay an important role. The book will enable the reader to develop\ngeneral principles from which equations of motion follow, to understand\nthe importance of canonical mechanics and of symmetries as a basis\nfor quantum mechanics, and to get practice in using general theoretical\nconcepts and tools that are essential for all branches of physics.\nThe book contains more than 120 problems with complete solutions,\nas well as some practical examples which make moderate use of personal\ncomputers. This will be appreciated in particular by students using\nthis textbook to accompany lectures on mechanics. The book ends with\nsome historical notes on scientists who made important contributions\nto the development of mechanics.
Postbuckling of bilaterally constrained rectangular thin plates
Journal of the Mechanics and Physics of Solids
50
11
2379-2401
2002
10.1016/S0022-5096(02)00028-5
The post-buckling response of bilaterally constrained thin plates submitted to a height reduction is investigated by a joint experimental-theoretical-numerical study. A detailed determination of the shape of plates is compared to predictions based on modelling the plate as an Elastica and a phase portrait of the system is worked out. An integral relationship for unloaded plates is derived and checked experimentally. The variation of the length of flat contacts with compression is first identified from measurements and then introduced in a virtual work analysis so as to determine the plate reaction. The existence of asymmetric solutions is clarified and the robustness of the Elastica to friction is demonstrated. These results improve the predictions of the Euler model in the fully non-linear regime and validate its relevance beyond the ideal limits of frictionless rod or of frictionless infinite plate on which it is established. They should therefore be useful for addressing buckling in different, albeit close, configurations. ?? 2002 Elsevier Science Ltd. All rights reserved.
A. Buckling; B. Plates; C. Stability and bifurcation elastic materials
Titin elasticity and mechanism of passive force development in rat cardiac myocytes probed by thin-filament extraction.
Biophysical journal
73
October
2043-2053
1997
10.1016/S0006-3495(97)78234-1
Titin (also known as connectin) is a giant filamentous protein whose elastic properties greatly contribute to the passive force in muscle. In the sarcomere, the elastic I-band segment of titin may interact with the thin filaments, possibly affecting the molecule's elastic behavior. Indeed, several studies have indicated that interactions between titin and actin occur in vitro and may occur in the sarcomere as well. To explore the properties of titin alone, one must first eliminate the modulating effect of the thin filaments by selectively removing them. In the present work, thin filaments were selectively removed from the cardiac myocyte by using a gelsolin fragment. Partial extraction left behind approximately 100-nm-long thin filaments protruding from the Z-line, whereas the rest of the I-band became devoid of thin filaments, exposing titin. By applying a much more extensive gelsolin treatment, we also removed the remaining short thin filaments near the Z-line. After extraction, the extensibility of titin was studied by using immunoelectron microscopy, and the passive force-sarcomere length relation was determined by using mechanical techniques. Titin's regional extensibility was not detectably affected by partial thin-filament extraction. Passive force, on the other hand, was reduced at sarcomere lengths longer than approximately 2.1 microm, with a 33 +/- 9% reduction at 2.6 microm. After a complete extraction, the slack sarcomere length was reduced to approximately 1.7 microm. The segment of titin near the Z-line, which is otherwise inextensible, collapsed toward the Z-line in sarcomeres shorter than approximately 2.0 microm, but it was extended in sarcomeres longer than approximately 2.3 microm. Passive force became elevated at sarcomere lengths between approximately 1.7 and approximately 2.1 microm, but was reduced at sarcomere lengths of >2.3 microm. These changes can be accounted for by modeling titin as two wormlike chains in series, one of which increases its contour length by recruitment of the titin segment near the Z-line into the elastic pool.
Introduction to Lagrangian and Hamiltonian mechanics
Lectures Notes given at the Department of Chemistry …
2004
10.1119/1.18858
The original purpose of the present lecture notes on Classical Mechanics was to sup- plement the standard undergraduate textbooks (such as Marion and Thorton’s Classical Dynamics of Particles and Systems) normally used for an intermediate course in Classi- cal Mechanics by inserting a more general and rigorous introduction to Lagrangian and Hamiltonian methods suitable for undergraduate physics students at sophomore and ju- nior levels. The outcome of this effort is that the lecture notes are now meant to provide a self-consistent introduction to Classical Mechanics without the need of any additional material. It is expected that students taking this course will have had a one-year calculus-based introductory physics course followed by a one-semester course in Modern Physics. Ideally, students should have completed their three-semester calculus sequence by the time they enroll in this course and, perhaps, take a course in ordinary differential equations concur- rently. On the other hand, this course should be taken before a rigorous course in Quantum Mechanics in order to provide students with a sound historical perspective involving the connection between Classical Physics and Modern Physics. Hence, the second semester of the sophomore year provides a perfect niche for this course. The structure of the lecture notes presented here is based on achieving several goals. As a first goal, I originally wanted to model these notes after the wonderful monograph of Landau and Lifschitz on Mechanics, which is often thought to be too concise for most undergraduate students. One of the many positive characteristics of Landau and Lifschitz’s Mechanics is that Lagrangian mechanics is introduced in its first chapter and not in later chapters as is usually done in more standard textbooks used at the sophomore/junior undergraduate level. Consequently, Lagrangian mechanics becomes the centerpiece of the course and it provides a continous thread throughout the text. As a second goal, the lecture notes introduce several numerical investigations of dynam- ical equations appearing throughout the text. These numerical investigations present an interactive pedagogical approach, which should enable students to begin their own numer- ical investigations. As a third goal, an attempt was made to introduce relevant historical facts (whenever appropriate) about the pioneers of Classical Mechanics. Much of the his- torical information included in the Notes is taken from Ren ́ Dugas (History of Mechanics, e 1955), Wolfgang Yourgrau and Stanley Mandelstam (Variational Principles in Dynamics and Quantum Theory, 1968), or Cornelius Lanczos (The Variational Principles of Me- chanics, 1970). In fact, from a pedagogical point of view, this historical perspective helps educating undergraduate students in establishing the deep connections between Classical and Quantum Mechanics, which are often ignored or even inverted (as can be observed when undergraduate students are surprised to hear that Hamiltonians have an indepen- dent classical existence). As a fourth and final goal, I wanted to keep the scope of these notes limited to a one-semester course in contrast to standard textbooks, which often include an extensive review of Newtonian Mechanics as well as additional material such as Hamiltonian chaos. The standard topics covered in these notes are listed in order as follows: Introduction to the Calculus of Variations (Chapter 1), Lagrangian Mechanics (Chapter 2), Hamiltonian Mechanics (Chapter 3), Motion in a Central Field (Chapter 4), Collisions and Scattering Theory (Chapter 5), Motion in a Non-Inertial Frame (Chapter 6), Rigid Body Motion (Chapter 7), Normal-Mode Analysis (Chapter 8), and Continuous Lagrangian Systems (Chapter 9). Each chapter contains a problem set with variable level of difficulty; sections identified with an asterisk may be omitted.
Effects of fiber misalignment and transverse shear modulus on localization and shear crippling instability in thick imperfect cross-ply rings under external pressure
Composite Structures
82
4
587-599
2008
DOI 10.1016/j.compstruct.2007.02.006
The effect of transverse shear modulus on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. The present study is primarily motivated to obtain the hitherto unavailable results pertaining to the effect of reduced transverse shear modulus, G(LT)(*) of a lamina weakened by the presence of randomly distributed fiber misalignments. A simple expression for the reduced transverse shear modulus, G(LT)(*) of a layer material is derived in terms of the average fiber misalignment angle. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element and is based on the assumption of layer-wise linear displacement distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. The interaction of a micro-structural defect in the form of initial fiber misalignments with its macro-structural counterpart represented by a modal imperfection is a key to understanding this meso-structural level phenomenon. Hitherto unavailable numerical results pertaining to the influence of this effect on the localization of buckling patterns and the ensuing shear crippling instability are also presented. (c) 2007 Elsevier Ltd. All rights reserved.
composite; compression; cross-ply ring; fiber misalignment; interlaminar shear/normal deformation; kinkband instability; localization; modal imperfection; shear crippling instability; shells
The role of initial flaw size, elastic compliance and plasticity in channel cracking of thin films
Thin Solid Films
419
144-153
2002
10.1016/S0040-6090(02)00718-6
In this paper, we consider the effects of initial flaw size and plasticity in adjacent layers on the formation of channeling cracks in thin films. Fully three-dimensional finite element analyses are used to determine energy release rates as a function of flaw size for both contained through cracks and edge cracks intersecting free surfaces. The results indicate that substantially larger flaws are required to achieve steady state for edge flaws and when the substrate is more compliant than the film. For edge flaws, the crack length required to achieve steady state is significantly larger than the film thickness, in contrast to conventional wisdom, which assumes steady state is reached when the crack length exceeds only several film thickness. The effect of residual stress in adjacent ductile layers is illustrated for a two-layer system bonded to an elastic substrate. Residual stress in the middle layer promotes plasticity adjacent to the crack and leads to much larger energy release rates than similar scenarios with films on ductile substrates without residual stress. Comparisons are made between several methods for predicting energy release rates, with the goal of identifying the validity of 2-D steady state approximations. The results can be used to predict critical flaws sizes that lead to film failure and to identify potential susceptibility to inelastic cracking mechanisms. ?? 2002 Elsevier Science B.V. All rights reserved.
channel cracking; Channel cracking; multilayers; Multilayers; structural properties; Structural properties; toughness; Toughness
A continuum damage model for composite laminates: Part I - Constitutive model
Mechanics of Materials
39
10
897-908
2007
10.1016/j.mechmat.2007.03.005 ER
A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level. © 2007 Elsevier Ltd. All rights reserved.
Constitutive models; Continuum damage mechanics; Crack closure; Failure (mechanical); Fracture mechanics; Laminated composites; Plastic laminates; Stress analysis
Bones: structure and mechanics
Journal of Biomechanics
36
6
893
2003
10.1016/S0021-9290(03)00033-2
This is a comprehensive and accessible overview of what is known about the structure and mechanics of bone, bones, and teeth. In it, John Currey incorporates critical new concepts and findings from the two decades of research since the publication of his highly regarded The Mechanical Adaptations of Bones. Crucially, Currey shows how bone structure and bone's mechanical properties are intimately bound up with each other and how the mechanical properties of the material interact with the structure of whole bones to produce an adapted structure. For bone tissue, the book discusses stiffness, strength, viscoelasticity, fatigue, and fracture mechanics properties. For whole bones, subjects dealt with include buckling, the optimum hollowness of long bones, impact fracture, and properties of cancellous bone. The effects of mineralization on stiffness and toughness and the role of microcracking in the fracture process receive particular attention. As a zoologist, Currey views bone and bones as solutions to the design problems that vertebrates have faced during their evolution and throughout the book considers what bones have been adapted to do. He covers the full range of bones and bony tissues, as well as dentin and enamel, and uses both human and non-human examples. Copiously illustrated, engagingly written, and assuming little in the way of prior knowledge or mathematical background, Bones is both an ideal introduction to the field and also a reference sure to be frequently consulted by practicing researchers.
Nonlinear elastic mechanics of the ball-loaded blister test
International Journal of Engineering Science
49
9
839-855
2011
10.1016/j.ijengsci.2011.04.007
The nonlinear elastic mechanics of spherically capped shaft or ball-loaded blister tests is presented. In the test model, a thin film is attached to a substrate with a circular hole running through the thickness of the substrate. A central load is applied to the film through the hole by a spherically capped shaft or a ball with a finite radius. The deformed blister is divided into two parts: a circular region in contact with the sphere of the cap or ball and an outer noncontact annulus. The Reissner’s plate theory is employed to describe the deformation of the contact part and the von Kármán plate theory for the noncontact annulus. A constitutive equation of coupled linear springs is obtained to quantify the effect of the substrate deformation on the blister deflection. For small deflection, the analytical solution of load-deflection is derived. For large deflection, an iteration approach is adopted to predict numerically the load-deflection curve. Finite-element analysis is conducted to verify the analytical and numerical solutions. The influence of the substrate deformation, residual stress, radius of the spherical cap or ball and the friction between the film and ball on the load–deflection relation is investigated.
Blister test; Compliant substrate; Contact; Deflection–load relation; Thin film
Measurement and modeling of the mechanical and electrochemical response of amorphous Si thin film electrodes during cyclic lithiation
Journal of the Mechanics and Physics of Solids
62
1
276-294
2014
10.1016/j.jmps.2013.10.005
A combination of experimental measurements and numerical simulations are used to characterize the mechanical and electrochemical response of thin film amorphous Si electrodes during cyclic lithiation. Parameters extracted from the experiment include the variation of elastic modulus and the flow stress as functions of Li concentration; the strain rate sensitivity; the diffusion coefficient for Li transport in the electrode; the free energy of mixing as a function of Li concentration in the electrode; the exchange current density for the Lithium insertion reaction; as well as reaction rates and diffusion coefficients characterizing the rate of formation of solid-electrolyte interphase layer at the electrode surface. Model predictions are compared with experimental measurements; and the implications for practical Si based electrodes are discussed. ?? 2013 Elsevier Ltd. All rights reserved.
Diffusion; Elastic-viscoplastic material; Electrochemical-mechanical process; Lithium-ion battery; Si anode
Is Quantum Mechanics An Island In Theoryspace?
Phys. Rev. A
71
9
2004
10.1103/PhysRevA.71.032325
This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2-norm by some other p-norm, then there are no nontrivial norm-preserving linear maps. Second, if we relax the demand that norm be preserved, we end up with a theory that allows rapid solution of PP-complete problems (as well as superluminal signalling). And third, if we restrict amplitudes to be real, we run into a difficulty much simpler than the usual one based on parameter-counting of mixed states.
Theoretical, experimental and computational mechanics of fracture in constrained interlayers
Experimental Mechanics
40
3
307-311
2000
The constraint of a thin silver interlayer is used to create high triaxial stresses to evaluate the applicability of theoretical models for ductile fracture. Rice and Tracey's model for cavity expansion under high triaxial states of stress and Huang et al.'s model for cavity instability were considered. The experimentally determined σ(m)/σ(y) values suggest that further investigation of the Huang et al. theory is warranted. Microstructural analysis revealed that multiple cavities were initially present in the silver interlayers, and the number and size of the cavities increased as failure was approached. Finite element analysis and experimental results showed excellent agreement in a computational determination of cavity instability. Thus, it appears that ductile fracture in constrained thin interlayers can be explained with unstable cavity growth. The constraint of a thin silver interlayer is used to create high triaxial stresses to evaluate the applicability of theoretical models for ductile fracture. Rice and Tracey's model for cavity expansion under high triaxial states of stress and Huang et al.'s model for cavity instability were considered. The experimentally determined σm/σy values suggest that further investigation of the Huang et al. theory is warranted. Microstructural analysis revealed that multiple cavities were initially present in the silver interlayers, and the number and size of the cavities increased as failure was approached. Finite element analysis and experimental results showed excellent agreement in a computational determination of cavity instability. Thus, it appears that ductile fracture in constrained thin interlayers can be explained with unstable cavity growth.
Cavity growth; Cavity instability; Ductile fracture; Ductility; Failure analysis; Finite element method; Fracture mechanics; Instability; Mathematical models; Metallic films; Metallographic microstructure; Silver; Stress analysis; Thin films; Triaxial stress; Yield stress
Buckling and postbuckling behavior of composite cross-ply laminates with multiple delaminations
Composite Structures
43
4
257-274
1998
10.1016/S0263-8223(98)00101-9
In this study, buckling and postbuckling analysis was conducted for the composite cross-ply laminates with multiple delaminations under compressive loading. The geometries of multiple delaminations are a one-dimensional through-the-width type and a two-dimensional embedded circular type. In a nonlinear finite element formulation, the updated Lagrangian description and the modified arc-length method were adopted. For a finite element modeling of composite laminates, the eight-node degenerated shell element was used. To avoid overlapping between delaminated areas, the contact node pair was defined by virtual beam element. Numerical results showed that multiple delaminations lower buckling loads and load carrying capacities in the postbuckling region. The buckling load varies with the projected area of the delaminations. However, the geometry of multiple delaminations has an influence on the postbuckling behavior. The load carrying capacity differed with the distribution type due to the local reduction of bending stiffness and the contact behavior of the sublaminates.
Composite laminate; Contact analysis; Delamination buckling; Multiple delaminations; Postbuckling behavior
Ply cracking and property degradations of symmetric balanced laminates under general in-plane loading
Composites Science and Technology
35
4
377-397
1989
10.1016/0266-3538(89)90059-6
The authors have previously proposed a method of using a resistance curve to characterize transverse crack multiplication in balanced symmetric laminates. The method was based on the concept of a through-the-thickness inherent flaw and energy balance principle. In the present paper, this model is further extended to shear and general in-plane loading conditions. The corresponding mechanical property degradations due to transverse ply cracking are also investigated. The effective longitudinal modulus and Poisson's ratio depend not only on the crack density but also on the thermal residual and applied stresses. The reason is that the cracks do not close tightly even upon unloading due to the residual stress. Experimental results for the mechanical property degradations correlate well with the analysis except for the shear modulus. The nonlinear behavior of the shear modulus should be considered for better correlation.
Stochastic free vibration analysis of angle-ply composite plates – A RS-HDMR approach
Composite Structures
122
526-536
2015
http://dx.doi.org/10.1016/j.compstruct.2014.09.057
Abstract This paper presents a generic random sampling-high dimensional model representations (RS-HDMR) approach for free vibration analysis of angle-ply composite plates. A metamodel is developed to express stochastic natural frequencies of the system. A global sensitivity analysis is carried out to address the influence of input random parameters on output natural frequencies. Three different types of input variables (fiber-orientation angle, elastic modulus and mass density) are varied to validate the proposed algorithm. The present approach is efficiently employed to reduce the sampling effort and computational cost when large number of input parameters is involved. The stochastic finite element approach is coupled with rotary inertia and transverse shear deformation based on Mindlin’s theory. Statistical analysis is carried out to illustrate the features of the RS-HDMR and to compare its performance with full-scale Monte Carlo simulation results. The stochastic mode shapes are also depicted for a typical laminate configuration. Based on the numerical results, some new physical insights are drawn on the dynamic behavior of the system.
Composite plate; Natural frequency; Random sampling – high dimensional model represent; Sensitivity analysis; Uncertainty
Modelling the transverse cracking in cross-ply laminates: Application to fatigue
Composites Part B: Engineering
30
569-577
1999
10.1016/S1359-8368(99)00023-2
When cross-ply laminates are subjected to tensile loading, the transverse cracking is the early stage of damage which occurs. In the case of static loading, cracks are initiated on the edges of test specimens and cross instantaneously the whole width of the specimens. The analysis of the transverse cracking is then reduced to a two-dimensional problem. A generalized model of the transverse cracking, including progressive shear within the 0?? layers is presented. In the case of fatigue tests, matrix cracks in 90?? layers initiate at the free edges of test specimens and grow slowly across the specimen width as a function of cycle number. So, the analysis of transverse cracking has to be implemented using a three-dimensional model. The finite element analysis shows how it is possible to reduce this problem by dividing the test specimen into bands along its width, using then the previously derived generalized model in each band. Next, the paper presents a simulation of the progression of the damage based on a statistical distribution within the volume of the test specimen for the criterion of the damage progression.
a; b; fatigue; laminates; modelling; transverse cracking
Molecular Mechanics Tutorial
Structure
November
2003
The goal of molecular mechanics is to predict th e detailed structure and physical properties of molecules. Examples of physical prope rties that can be calculated include enthalpies of formation, entropies, dipole moments, and strain energies. Molecular mechanics calculates the energy of a molecule and then adjust s the energy through changes in bond lengths and angles to obtain the minimum energy structure.
The anomalous wake accompanying bubbles rising in a thin gap: a mechanically forced Marangoni flow
Journal of Fluid Mechanics
352
283-303
1997
10.1017/S0022112097007350
A novel wake structure, observed as penny-shaped air bubbles rise at moderate Reynolds number through a thin layer of water bound between parallel glass plates inclined at a shallow angle relative to the horizontal, is reported. The structure of the wake is revealed through tracking particles suspended in the water. The wake completely encircles the rising bubble, and is characterized by a reverse surface flow or ‘edge jet’ which transports fluid in a thin boundary layer along the bubble surface from the tail to the nose at speeds which are typically an order of magnitude larger than the bubble rise speed. A consistent physical explanation for the wake structure is proposed. The wake is revealed to be a manifestation of the three-dimensionality of the flow in the suspending fluid. The bubble surface advances through a rolling motion, thus generating regions of surface divergence and convergence at, respectively, the leading and trailing edges of the bubble. A nose-to-tail gradient in surfactant concentration is thus established, and the associated surface tension gradient drives the edge jet. The dependence of the wake structure on the suspending fluid is examined experimentally. Surfactants play an anomalous role in the reported flow, serving to promote rather than suppress surface motions. The wake structure is an example of a mechanically forced Marangoni flow, and so represents a mechanical analogue of that accompanying thermocapillary drop motion in microgravity. A theoretical model is developed which reproduces the salient features of the flow, and on the basis of which an estimate is made of the mechanically induced surface tension gradient along the bubble surface.
Supersymmetry in quantum mechanics
AIP Conference Proceedings
744
133-165
2005
10.1063/1.1853201
An elementary introduction is given to the subject of Supersymmetry in Quantum Mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct new exactly solvable n Hamiltonians having n-1,n-2,...,0 bound states. The relationship between the eigenvalues, eigenfunctions and scattering matrix of the supersymmetric partner potentials is derived and a class of reflectionless potentials are explicitly constructed. We extend the operator method of solving the one-dimensional harmonic oscillator problem to a class of potentials called shape invariant potentials. Further, we show that given any potential with at least one bound state, one can very easily construct one continuous parameter family of potentials having same eigenvalues and s-matrix. The supersymmetry inspired WKB approximation (SWKB) is also discussed and it is shown that unlike the usual WKB, the lowest order SWKB approximation is exact for the shape invariant potentials. Finally, we also construct new exactly solvable periodic potentials by using the machinery of supersymmetric quantum mechanics.
Mechanics of Materials
Mechanics of Materials
2
June
913
2008
10.1016/j.mechmat.2009.01.011
Now in 4-color format with more illustrations than ever before, the Seventh Edition of Mechanics of Materials continues its tradition as one of the leading texts on the market. With its hallmark clarity and accuracy, this text develops student understanding along with analytical and problem-solving skills. The main topics include analysis and design of structural members subjected to tension, compression, torsion, bending, and more. The book includes more material than can be taught in a single course giving instructors the opportunity to select the topics they wish to cover while leaving any remaining material as a valuable student reference.
The static and dynamic axial crumbling of thin-walled fibreglass composite square tubes
Composites Part B: Engineering
28
96
439-451
1997
10.1016/S1359-8368(96)00066-2
In the present paper we report on the behaviour and crashworthiness characteristics of square composite tubes subjected to static and dynamic axial compression exerted by a hydraulic press and a drop-hammer, respectively. The effect of specimen geometry, i.e. of thickness and axial length, and of the loading rate on the energy absorbing capability are studied in detail. Attention is directed towards the mechanics of the axial crumbling process from macroscopic and microscopic point of view for facilitating engineering design calculations of the amount of energy dissipated and for a somewhat more complete aspect on the actual fracture mechanism during the failure of the composite material tested. A theoretical analysis of the collapse mechanism of the components tested under axial compression is proposed, leading to a good approximation of the energy absorbed during crushing.
A finite volume method for analysing the bending deformation of thick and thin plates
Computer Methods in Applied Mechanics and Engineering
147
96
199-208
1997
10.1016/S0045-7825(96)00003-5
The formulation of a novel finite volume based procedure for determining deformations and moment distributions within transversely loaded plates is described in detail. The formulation employs the Mindlin theory of plate deformation. Transverse displacement and bending moment distributions are determined for a number of test problems. The effect of mesh refinement upon the accuracy of the displacement and moment fields is investigated. The finite volume procedure exhibits a number of interesting features; it is conservative in the sense that equilibrium is satisfied locally within each cell and across cell boundaries, it has the capacity to represent the behaviour of thick and thin plates and it is geometrically versatile because the cell shapes can take the form of multifaceted polygons.
Confined Thin Film Delamination in the Presence of Intersurface Forces With Finite Range and Magnitude
Journal of Applied Mechanics
76
5
051005
2009
10.1115/1.3112745
A circular membrane clamped at the periphery is allowed to adhere to or to delaminate from a planar surface of a cylindrical punch in the presence of intersurface forces with finite range and magnitude. Assuming a uniform disjoining pressure within the cohesive zone at the delamination front, the adhesion-delamination mechanics is obtained by a thermodynamic energy balance. Interrelations between the instantaneous applied load, punch displacement, and contact circle, and the resulting critical thresholds of “pinchoff,” “pull-off,” and “pull-in” are derived from the first principles. Two limiting cases are obtained: (i) intersurface force with long range and small magnitude in reminiscence of the classical Derjaguin–Muller–Toporov (DMT) model and (ii) short range and large magnitude alluding to the Johnson–Kendall–Roberts (JKR) model. The DMT-JKR transitional behavior has significant impacts on adhesion measurements, microelectromechanical systems, and life-sciences.
cohesive; delamination; disjoining pressure; surface force; thin film adhesion
Size effects in single crystal thin films: Nonlocal crystal plasticity simulations
European Journal of Mechanics, A/Solids
24
2
183-193
2005
10.1016/j.euromechsol.2005.01.002
Stress relaxation in single crystalline thin films on substrates subjected to thermal loading is studied using a recently proposed nonlocal continuum crystal plasticity theory. The theory is founded on a statistical-mechanics description of the collective behaviour of dislocations in multiple slip, which is coupled to a small-strain continuum crystal plasticity description. The theory is inherently nonlocal with the length scale being determined by the evolving dislocation density. Symmetric double slip is considered with the film being in plane strain. The predicted stress versus temperature response and the evolution of the dislocation structure are analyzed for different orientations and film thicknesses. The effect of film size is associated with the formation of a boundary layer of dislocations at the film-substrate interface which does not scale with the film thickness. The width of the boundary layer itself is shown to be dependent on the slip system orientation. The results are consistent with those of recent discrete dislocation simulations. ?? 2005 Elsevier SAS. All rights reserved.
Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part I: Data reduction
Composites Science and Technology
70
4
606-613
2010
10.1016/j.compscitech.2009.12.016
The fracture toughness associated with fibre tensile failure was measured for a T300/920 laminated carbon/epoxy material system using the compact tension specimen configuration. Six methods of data reduction were investigated for calculation of the toughness with the aim of finding the best technique, in terms of reproducibility of results and simplicity. The calculated fracture toughnesses were found to correlate well, though varying amounts of scatter were produced by each method. An optimum method was proposed that does not rely on the use of an optically measured crack length. ?? 2010 Elsevier Ltd. All rights reserved.
B. Fracture toughness; C. Notch; Fibre failure
Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe
Journal of Fluid Mechanics
137
-1
363
1983
10.1017/S0022112083002451
A nonlinear analysis, based on lubrication theory, is presented for the adjustment under surface tension of an initially uniform annular film of viscous fluid confined within a circular cylindrical pipe. The film surrounds a thread of another viscous fluid. Small axisymmetric interfacial disturbances of sufficiently long wavelength are found to grow, leading to the break-up of the initially continuous outer film into a number of isolated rings of fixed length on the pipe wall. The implications for the rupture of fluid threads surrounded by moderately thin films in confined geometries are discussed.
Computational and experimental study of the mechanics of embryonic wound healing
Journal of the Mechanical Behavior of Biomedical Materials
28
125-146
2013
10.1016/j.jmbbm.2013.07.018
Wounds in the embryo show a remarkable ability to heal quickly without leaving a scar. Previous studies have found that an actomyosin ring (purse string) forms around the wound perimeter and contracts to close the wound over the course of several dozens of minutes. Here, we report experiments that reveal an even faster mechanism which remarkably closes wounds by more than 50% within the first 30. s. Circular and elliptical wounds (~ 100 ??m in size) were made in the blastoderm of early chick embryos and allowed to heal, with wound area and shape characterized as functions of time. The closure rate displayed a biphasic behavior, with rapid constriction lasting about a minute, followed by a period of more gradual closure to complete healing. Fluorescent staining suggests that both healing phases are driven by actomyosin contraction, with relatively rapid contraction of fibers at cell borders within a relatively thick ring of tissue (several cells wide) around the wound followed by slower contraction of a thin supracellular actomyosin ring along the margin, consistent with a purse string mechanism. Finite-element modeling showed that this idea is biophysically plausible, with relatively isotropic contraction within the thick ring giving way to tangential contraction in the thin ring. In addition, consistent with experimental results, simulated elliptical wounds heal with little change in aspect ratio, and decreased membrane tension can cause these wounds to open briefly before going on to heal. These results provide new insight into the healing mechanism in embryonic epithelia. ?? 2013 Elsevier Ltd.
Biomechanics; Chick embryo; Epithelial morphogenesis; Epithelium; Finite elements; Growth; Mechanobiology
An investigation of nanoindentation tests on the single crystal copper thin film via an atomic force microscope and molecular dynamics simulation
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
221
2
259-266
2007
10.1243/0954406JMES448
Nanoindentation tests performed in an atomic force microscope have been utilized to directly measure the mechanical properties of single crystal metal thin films fabricated by the vacuum vapour deposition technique. Nanoindentation tests were conducted at various indentation depths to study the effect of indentation depths on the mechanical properties of thin films. The results were interpreted by using the Oliver-Pharr method with which direct observation and measurement of the contact area are not required. The elastic modulus of the single crystal copper film at various indentation depths was determined as 67.0 > 6.9 GPa on average, which is in reasonable agreement with the results reported by others. The indentation hardness constantly increases with decreasing indentation depth, indicating a strong size effect. In addition to the experimental work, a three-dimensional nanoindentation model of molecular dynamics (MD) simulations with embedded atom method (EAM) potential is proposed to elucidate the mechanics and mechanisms of nanoindentation of thin films from the atomistic point of view. MD simulations results show that due to the size effect no distinct dislocations were observed in the plastic deformation processes of the single crystal copper thin films, which is significantly different from the plastic deformation mechanism in bulk materials.
Boundary layer analysis of the ridge singularity in a thin plate
Physical Review E
53
4
3750-3759
1996
10.1103/PhysRevE.53.3750
Large deformations of thin elastic plates and shells present a formidable problem in continuum mechanics that is generally intractable except by numerical methods. Conventional approaches break down in the limit of small plate thickness due to the appearance of discontinuities in the solution that require a boundary layer treatment. We examine a simple case of a plate bent by forces exerted along its boundary so as to create a sharp crease in the limit of infinitely small thickness. We find a separable boundary layer solution of the von Kármán plate equations that is valid along the ridge line. We confirm a scaling argument [T. A. Witten and Hao Li, Europhys. Lett. 23, 51 (1993)] that the ridge possesses a characteristic radius of curvature R given by the thickness of the sheet h and the length of the ridge X, viz., R∼h1/3X2/3. The elastic energy of the ridge scales as E∼κ(X/h)1/3, where κ is the bending modulus of the sheet. We determine the dependence of these quantities on the dihedral angle of the ridge π-2α. For all angles R∼α-4/3 and E∼α7/3. The framework developed in this paper is suitable for the determination of other properties of ridges such as their interaction or behavior under various types of loading. We expect these results to have broad importance in describing forced crumpling of thin sheets.
On the origin of probability in quantum mechanics
Science
7
2011
10.1142/S0217732312300145
I give a brief introduction to many worlds or "no wavefunction collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability.
Ply-level failure analysis of thick-section composite structures based on "smeared" finite element results
Journal of Thermoplastic Composite Materials
9
2
108-117
1996
Conventional failure criteria for laminated composite materials require stresses and strains at the ply level. However, finite element analysis of practical thick-section composite structures is often based on equivalent homogeneous ("smeared" or effective) material models, which predict only laminate-averaged stresses and strains. This paper describes a post-processor to the ABAQUS general-purpose finite element code that performs ply-level failure analysis of a thick-section laminated composite structure given the results of a smeared ABAQUS analysis. The program, called ABAFAIL, provides ABAQUS users with an automated tool for composite first-ply failure analysis and produces thorough results that are easily interpreted. The ply-level stresses and strains required for failure analysis are extracted from the effective quantities at each node in the finite element model via a 3-D lamination theory. The failure criteria currently incorporated in ABAFAIL are Maximum Stress, Maximum Strain, Tsai-Hill, Tsai-Wu, and a modified version of Hashin's theory; other criteria can be easily added. Printed output includes failure indices and extrapolated failure loads. In addition, files may be obtained which are suitable for PATRAN visualization of failure index data.
3 d finite element analysis; composite failure analysis; composite structures; computer software; equivalent continuum model; equivalent continuum modeling; failure analysis; finite element method; laminated composites; mathematical models; software package abafail; structural analysis; thick section composites
Statistical mechanics of the neocortex.
Progress in biophysics and molecular biology
99
2-3
53-86
2009
10.1016/j.pbiomolbio.2009.07.003
We analyze neocortical dynamics using field theoretic methods for non-equilibrium statistical processes. Assuming the dynamics is Markovian, we introduce a model that describes both neural fluctuations and responses to stimuli. We show that at low spiking rates, neocortical activity exhibits a dynamical phase transition which is in the universality class of directed percolation (DP). Because of the high density and large spatial extent of neural interactions, there is a "mean field" region in which the effects of fluctuations are negligible. However as the generation and decay of spiking activity becomes balanced, there is a crossover into the critical fluctuation driven DP region, consistent with measurements in neocortical slice preparations. From the perspective of theoretical neuroscience, the principal contribution of this work is the formulation of a theory of neural activity that goes beyond the mean-field approximation and incorporates the effects of fluctuations and correlations in the critical region. This theory shows that the scaling laws found in many measurements of neocortical activity, in anesthetized, normal and epileptic neocortex, are consistent with the existence of DP and related phase transitions at a critical point. It also shows how such properties lead to a model of the origins of both random and rhythmic brain activity.
Animals; Biomechanical Phenomena; Computer Simulation; Humans; Models, Biological; Neocortex; Neocortex: physiology; Nerve Net; Probability
Nonsmooth Lagrangian Mechanics and Variational Collision Integrators
SIAM Journal on Applied Dynamical Systems
2
3
381-416
2003
10.1137/S1111111102406038
Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for colli- sions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics are developed by using the methodology of vari- ational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated.
1; 10; 1137; 37m15; 58e30; 70f35; ams subject classifications; collisions; discrete mechanics; doi; in this paper; introduction; mechanics and its; s1111111102406038; variational integrators; we investigate nonsmooth lagrangian
Analysis of Thin-Walled Structures With Longitudinal and Transversal Stiffeners
Journal of Applied Mechanics
80
1
011006
2013
10.1115/1.4006939
This paper deals with the dynamic analysis of reinforced thin-walled structures by means of refined one-dimensional models. Complex reinforced structures are considered which are built by using different components: skin, ribs, and stringers. Higher-order one- dimensional model based on the Carrera unified formulation (CUF) are used to model panels, stringer, and ribs by referring to a unique model. The finite element method (FEM) is used to provide a solution that deals with any boundary condition configura- tion. The structure is geometrically linear and the materials are isotropic and elastic. The dynamic behavior of a number of reinforced thin-walled cylindrical structures have been analyzed. The effects of the reinforcements (ribs and stringers) are investigated in terms of natural frequencies and modal-shapes. The results show a good agreement with those from commercial codes by reducing the computational costs in terms of degrees of freedom (DOFs). [DOI:
Fluid Mechanics of Papermaking
Annual Review of Fluid Mechanics
43
195-217
2011
10.1146/annurev-fluid-122109-160700
Papermaking is to a large extent a multiphase flow process in which the structure of the material and many of the relevant properties of the final product are determined by the interaction between water and the wood fibers. The dominant feature of a suspension composed of wood fibers and water is its inherent propensity to form bundles of mechanically entangled fibers, known as fiber flocs. However, the phenomena apparent throughout the papermaking process are not unique but in fact have a generic fluid dynamical nature.
fiber orientation; fiber suspension; jet flow; stability
Application of the European flaw assessment procedure SINTAP to thin wall structures subjected to biaxial and mixed mode loadings
Engineering Fracture Mechanics
73
5
626-642
2006
10.1016/j.engfracmech.2005.10.002
A recently proposed slightly modified version of the European flaw assessment procedure SINTAP for thin wall structures has been applied to another 35 thin sheets made of two different aluminium alloys and two ferritic steels. The specimens were subjected to biaxial and mixed mode loadings. It is shown that the method allows predictions of the load versus crack extension characteristics with acceptable conservatism.
Mechanical Modeling of Thin Films and Cover Plates Bonded to Graded Substrates
Journal of Applied Mechanics
75
5
051105
2008
10.1115/1.2936237
In this study the contact problems for thin films and cover plates will be considered. In these problems the loading consists of any one or combination of stresses caused by uniform temperature changes and temperature excursions, far field mechanical loading, and residual stresses resulting from film processing or welding. The primary interest in this study is in examining stress concentrations or singularities near the film ends for the purpose of addressing the question of crack initiation and propagation in the substrate or along the interface. The underlying contact mechanics problem is formulated and solved analytically by reducing it to an integral equation.
contact stress; cover plate; functionally graded material; stress in-; thin film
Combinatorial edge delamination test for thin film adhesion---concept, procedure, results
European Structural Integrity Society
Volume 32
365-371
2003
10.1016/s1566-1369(03)80109-7
A high-throughput combinatorial approach to edge delamination test is proposed to map the failure of adhesion as a function of both temperature and film thickness in a single step. In this approach, a single specimen of a thin film bonded to a substrate with orthogonal thickness and temperature gradients is subdivided into separate samples. This approach can be adopted to measure the adhesion for films with thickness in the sub-micron range by the addition of an overlayer. Requirements for valid testing results from a mechanistic viewpoint are analyzed using three-dimensional computational fracture mechanics. An initial test results is presented to demonstrate the feasibility of the approach.
adhesion; Combinatorial approach; edge delamination; finite element; fracture mechanics; interfacial debonding; thin film
Development of a meso-scale material model for ballistic fabric and its use in flexible-armor protection systems
Journal of Materials Engineering and Performance
19
1
22-39
2010
10.1007/s11665-009-9419-5
A meso-scale ballistic material model for a prototypical plain-woven single-ply flexible armor is developed and implemented in a material user subroutine for the use in commercial explicit finite element programs. The main intent of the model is to attain computational efficiency when calculating the mechanical response of the multi-ply fabric-based flexible-armor material during its impact with various projectiles without significantly sacrificing the key physical aspects of the fabric microstructure, architecture, and behavior. To validate the new model, a comparative finite element method analysis is carried out in which: (a) the plain- woven single-ply fabric is modeled using conventional shell elements and weaving is done in an explicit manner by snaking the yarns through the fabric and (b) the fabric is treated as a planar continuum surface composed of conventional shell elements to which the new meso-scale unit-cell based material model is assigned. The results obtained show that the material model provides a reasonably good description for the fabric deformation and fracture behavior under different combinations of fixed and free boundary con- ditions. Finally, the model is used in an investigation of the ability of a multi-ply soft-body armor vest to protect the wearer from impact by a 9-mm round nose projectile. The effects of inter-ply friction, projectile/ yarn friction, and the far-field boundary conditions are revealed and the results explained using simple wave mechanics principles, high-deformation rate material behavior, and the role of various energy- absorbing mechanisms in the fabric-based armor systems.
Ballistic performance; Flexible armor; High-performance fibers; Meso-scale unit-cell material model
Modeling the interfacial effect on the yield strength and flow stress of thin metal films on substrates
Mechanics Research Communications
35
1-2
65-72
2008
10.1016/j.mechrescom.2007.08.011
It is shown in this paper that interfacial effects have a profound impact on the scale-dependent yield strength and strain hardening rates (flow stress) of metallic thin films on elastic substrates. This is achieved by developing a higher-order strain gradient plasticity theory based on the principle of virtual power and the laws of thermodynamics. This theory enforces microscopic boundary conditions at interfaces which relate a microtraction stress to the interfacial energy at the interface. It is shown that the film bulk length scale controls the size effect if a rigid interface is assumed whereas the interfacial length scale dominates if a compliant interface is assumed. ?? 2007 Elsevier Ltd. All rights reserved.
Interfacial energy; Length scale; Nonlocal; Size effect; Thin films
Forward diffraction of Stokes waves by a thin wedge
Journal of Fluid Mechanics
99
33-52
1980
10.1017/S0022112080000481
The diffraction of a steady Stokes wave train by a thin wedge with vertical walls is studied when the incident wave is directed along the wedge axis (grazing incidence). Parabolic approximation applied recently by Mei and Tuck (1980) to linear diffraction is extended to this nonlinear case. Significant effects of nonlinearity are found numerically, in particular the sharp forward bending of wave crests near the wedge. The computed features are found to corroborate the existing experiments only qualitatively; the controlling factors in the latter being not completely understood. An analytical model of stationary shock is proposed to approximate the numerical results of Mach stems
diffraction, liquid waves
Visualization of avalanches in magnetic thin films: temporal processing
Journal of Statistical Mechanics: Theory and Experiment
2009
01
P01020
2009
10.1088/1742-5468/2009/01/P01020
Magneto-optical methods allow us to observe the dynamics of domain wall motion, but this is\r intrinsically a very noisy process. We discuss a new method allowing us to reduce the measurement\r noise, taking advantage of the acquisition of a whole temporal sequence of images.\r \r The resulting avalanche distributions give interesting hints as to the magnetization dynamics, but\r are strongly dependent on the size of the observation windows chosen. We investigate the effects of\r window size by studying finite-size scaling, and use this to extract the fractal dimension critical\r exponent 1/σν.
Fracture Mechanics: Fundamentals and Applications, Third Edition
Vasa
640
2005
10.1002/1521-3773(20010316)40:6<9823::AID-ANIE9823>3.3.CO;2-C
With its combination of practicality, readability, and rigor that is characteristic of any truly authoritative reference and text, Fracture Mechanics: Fundamentals and Applications quickly established itself as the most comprehensive guide to fracture mechanics available. It has been adopted by more than 100 universities and embraced by thousands of professional engineers worldwide. Now in its third edition, the book continues to raise the bar in both scope and coverage. It encompasses theory and applications, linear and nonlinear fracture mechanics, solid mechanics, and materials science with a unified, balanced, and in-depth approach.Reflecting the many advances made in the decade since the previous edition came about, this indispensable Third Edition now includes:A new chapter on environmental crackingExpanded coverage of weight functionsNew material on toughness test methodsNew problems at the end of the bookNew material on the failure assessment diagram (FAD) methodExpanded and updated coverage of crack closure and variable-amplitude fatigueUpdated solutions manualIn addition to these enhancements, Fracture Mechanics: Fundamentals and Applications, Third Edition also includes detailed mathematical derivations in appendices at the end of applicable chapters; recent developments in laboratory testing, application to structures, and computational methods; coverage of micromechanisms of fracture; and more than 400 illustrations. This reference continues to be a necessity on the desk of anyone involved with fracture mechanics.
Peel Mechanics for an Elastic-Plastic Adherend.
Journal of Applied Polymer Science
21
2817-2831
1977
10.1002/app.1977.070211018
The force required to propagate a 180 degree Cbend in an elastic-plastic strip has been calculated from elementary bending theory. Measured forces for Mylar strips of various thicknesses, bent to various degrees, were in good agreement with these calculated values. The corresponding additional stripping force in a peeling experiment will depend upon the thickness of the elastic-plastic adherend, becoming zero both for infinitesimally thin adherends and for those exceeding a critical thickness t//c and passing through a maximum value at intermediate thicknesses. Published data are in good agreement with these conclusions. For a strongly adhering strip, higher peel strengths are found for a peel angle of 180 degree , compared to 90 degree , and the effect is greater than can be accounted for solely by plastic yielding of the adherend. It is attributed in part to greater energy dissipation within the adhesive layer.
On the local and global buckling behaviour of angle, T-section and cruciform thin-walled members
Thin-Walled Structures
48
10-11
786-797
2010
10.1016/j.tws.2010.04.012
This paper reports the results of an investigation aimed at providing fresh insight on the mechanics underlying the local and global buckling behaviour of angle, T-section and cruciform thin-walled steel members (columns, beams and beam-columns). Due to the lack of primary warping resistance, members displaying these cross-section shapes possess a minute torsional stiffness and, therefore, are highly susceptible to buckling phenomena involving torsion – moreover, it is often hard to distinguish between torsion and local deformations. Almost all the numerical results presented are obtained by means of Generalised Beam Theory (GBT) analyses and, taking advantage of its unique modal features, it is possible to shed some new light on how to characterise and/or distinguish the local and global buckling modes of the above thin-walled members. Finally, some comments are made concerning the development of a rational and efficient (safe and economic) approach for their design.
Angle members; Buckling analysis; Cruciform members; Generalised Beam Theory (GBT); Local buckling; Thin-walled members; Torsional or flexural–torsional buckling; T-section members
Mechanical failure analysis of thin film transistor devices on steel and polyimide substrates for flexible display applications
Engineering Fracture Mechanics
77
4
660-670
2010
10.1016/j.engfracmech.2009.12.016
The crack onset strain (COS) of 4-level thin film transistor (TFT) devices on both steel foils and thin polyimide (PI) films was investigated using tensile experiments carried out in situ in an optical microscope. Cracks initiated first within the SiO2 insulator layer for both types of substrates. The COS was found to be equal to 1.15% and 0.24% for steel and PI, respectively. The influence of loading direction on failure of the TFT stack with anisotropic geometry was moreover found to be considerable, leading to recommendations for backplane design. The large difference in critical strain of the SiO2 layer on the two substrates was analyzed using an energy release rate approach, and found to result from differences in layer/substrate mechanical contrast and in internal stress state. Based on this analysis a correlation between layer/substrate elastic contrast and tensile failure behavior was devised. © 2010 Elsevier Ltd. All rights reserved.
Crack initiation; Electronics; Polyimide substrate; Steel substrate; Thin film transistor
Effect of temperature on the transverse cracking behavior of cross-ply composite laminates
Composites Part B: Engineering
28
419-424
1997
10.1016/S1359-8368(96)00062-5
This paper investigates temperature-dependent transverse cracking in cross-ply composite laminates over a wide range of service temperatures. The graphite-reinforced polymer-matrix composites considered are bismaleimide X5260/G40-800 (BASF) and Avimid K3B/IM7 (DuPont) materials. Fracture toughness is measured over a range of temperatures from − 50°C to 175°C and is found to be temperature dependent. Matrix cracking initiation is quantified experimentally using acoustic emission polar backscattering, ultrasonic inspection, and edge replication. Various modeling approaches are correlated with experimental results. It is found that the shearlag model and the energy release rate model provide upper and lower bounds on experimental results. The significance of including temperature-dependent properties is demonstrated.
On the stabilization of nonstationary parametric main resonance of a laminated angle-ply column
Computers & Structures
61
4
695-703
1996
10.1016/0045-7949(96)00048-X
The main resonance of a laminated angle-ply column subjected to nonstationary parametric excitations is studied using the asymptotic method. The nonstationary processes used are either linear or cyclic excitation frequency, i.e. Ω(t) = Ω0 + βt or Ω(t) = Ω0 + μ sin βt. The study includes the effects of geometrical nonlinearities, initial conditions and various sweep rates β. Effective and fast stabilization is observed. This is significant from the design and basic point of view. Separatrices (defined in the text) are also obtained for various sweep rates in the linear excitation frequency.
Effect of transverse cracks on the thermomechanical properties of cross-ply laminated composites
Composites Science and Technology
34
2
145-162
1989
http://dx.doi.org/10.1016/0266-3538(89)90102-4
The development of transverse cracks can be detrimental to the stiffness and dimensional stability of composite laminates. In this investigation, a modified shear lag analysis, taking into account the concept of interlaminar shear layer, is employed to evaluate the effect of transverse cracks on the stiffness reduction and change in the coefficient of thermal expansion in cross-ply laminated composites. This analysis involves the construction of admissible displacement fields which satisfy equilibrium and boundary conditions on the laminate and transverse crack surfaces. The present results represent well the dependence of the degradation of thermomechanical properties on the laminate configuration.
Dynamic response of antisymmetric cross-ply laminated composite beams with arbitrary boundary conditions
International Journal of Engineering Science
34
1
9-19
1996
10.1016/0020-7225(95)00080-1
An analytical solution of the classical, first- and third-order laminate beam theories is developed to study the transient response of antisymmetric cross-ply laminated beams with generalized boundary conditions and for arbitrary loadings. A general modal approach, utilizing the state form of the equations of motion and their biorthogonal eigenfunctions, is presented to solve the equations of motion of beams with arbitrary boundary conditions. The results obtained using the higher-order theory of Reddy (HOBT) are compared with those obtained by Timoshenko shear deformation beam theory (FOBT) as well as the Bernoulli-Euler theory (CBT).
An experimental investigation of the properties of cross-ply laminate used for manufacturing of small aircraft components
Composite Structures
75
93-99
2006
10.1016/j.compstruct.2006.04.080
This paper discusses the observations and results from an experimental investigation of cross ply laminates used to construct major structural components of a small aircraft manufactured in Australia. The static and fatigue experimental results are compared with established models in composites analysis and with the available data in composite databases. An analysis was done to statistically quantify any deviation of actual properties from the calculated values and investigate the differences in designed and actual capacities/operational life of the components made using this laminates. ?? 2006 Elsevier Ltd. All rights reserved.
Composites; Fatigue properties; Mechanical properties; Woven roving
Quantum mechanics: Entangled families.
Nature
455
7210
180-181
2008
10.1038/455180a
Quantum entanglement comes in a rich variety of types and families if more than two particles are involved. Experiments with photons are opening up fresh ways to systematically study multi-particle entanglement.
Interface Mechanics and Histology of Titanium and Hydroxylapatite- Coated Titanium for Dental Implant Applications
The International Journal of Oral & Maxillofacial Implants
2
1
15-22
1987
The interface mechanical characteristics and histology of CP titanium and hydroxylapatite (HA)-coated titanium were investigated. The HA-coated system developed five to eight times the mean interface strength of the uncoated, bead-blasted CP titanium system. Histologic evaluations in all cases revealed mineralization of interface bone directly onto the HA-coated implant surface, becoming part of the implant composite system. The uncoated implants had a thin fibrous interpositional layer present in most areas, with projections of bone in apposition to the implant surface in a limited number of locations. The results of this study indicate that the HA-coated titanium system may be attractive for use in endosseous dental implant applications.
Stress fields and energy release rates in cross-ply laminates
International Journal of Solids and Structures,
35
11
1025-1055
1998
10.1016/S0020-7683(97)00107-8
A method to model the thermoelastic response of flat laminated composites using a large radius axisymmetric hollow layered cylinder model is presented. An axisymmetric concentric cylinder model and a flat laminate model, each based on Reissner's variational principle with equilibrium stress fields, are compared. The stress components and the governing equations of the axisymmetric concentric cylinder formulation for a cylinder of infinite radius are shown analytically to be equivalent to the flat laminate formulation. Numerical results for the axisymmetric free edge stress field are shown to be nearly identical to the flat laminate free edge stress field solution. Selected results for the elastic stress fields and energy release rates in composite laminates with free edge and/or internal delaminations and transverse cracking are presented.
Adhesion mechanics of ivy nanoparticles
Journal of Colloid and Interface Science
344
2
533-540
2010
10.1016/j.jcis.2009.12.041
Adhesion mechanism of ivy has been of major research interest for its potential applications in high-strength materials. Recent experimental studies demonstrated that nanoparticles secreted from ivy tendrils play an important role in adhesion. In this work, we investigate how various factors such as van der Waals interaction, capillarity, and molecular cross-linking influence the adhesion mechanics of ivy nanoparticles. This paper provides guidelines in choosing different adhesive contact models. Understanding the mechanics of ivy adhesion could potentially inspire the design and fabrication of novel nano-bio-materials. ?? 2009 Elsevier Inc. All rights reserved.
Adhesion; Biological materials; Contact mechanics; Nanostructured materials
Thrust tectonics, thin skinned or thick skinned, and the continuation of thrusts to deep in the crust
Journal of Structural Geology
5
2
113-123
1983
10.1016/0191-8141(83)90037-8
The paper analyses the geometry of thin-skinned thrust zones, where the thrusts shallow out at depth and of thicker-skinned fault zones where much of the crust is involved and where the thrusts are frequently observed to become steeper downwards. In the interiors of many orogenic belts the steep dip of faults is not original but due to the folding above lower decoupling zones. The energy involved in the internal deformation of hanging-wall rocks may prohibit many faults becoming more shallow upwards. Such shallowing-upwards faults may occur in more ductile rocks to maintain compatibility between zones which have experienced different deformation intensities, but displacements on the faults are unlikely to be large. Another mechanism for producing faults which steepen downwards is proposed for the major thrusts which form the southern margin to the Himalayas. These carry large thicknesses (30 to 100 km) of crustal and upper mantle rocks to the south, causing flexuring and isostatic depression of the Indian plate. The steeply dipping thrusts are not footwall ramps; these may be some distance behind the steepened zone. This thrust-induced isostatic bending of the crust has important implications when considering regional seismic interpretations as well as thrust mechanics and kinematics.
A multi-scale computational strategy for structured thin sheets
International Journal of Material Forming
1
SUPPL. 1
61-64
2008
10.1007/s12289-008-0044-x
Engineering trends show an increasing use of multi-layered and structured thin sheets in innovative applications where the layer thickness approaches the microstructural scale. This paper presents a strategy to homogenize the actual three-dimensional heterogeneous sheet towards a shell continuum. Consistent scale transition relations are derived, providing the ability to solve the (generalized) stress-strain fields on both the microstructural and the engineering scale are obtained in a direct and coupled manner. © Springer/ESAFORM 2008.
Coarse graining; Computational homogenization; FE2; Multi-scale mechanics; Structural analysis; Structured thin sheets
Magnetoelasticity of highly deformable thin films: Theory and simulation
International Journal of Non-Linear Mechanics
47
2
185-196
2012
10.1016/j.ijnonlinmec.2011.05.004
Abstract A nonlinear two-dimensional theory is developed for thin magnetoelastic films capable of large deformations. This is derived directly from the three-dimensional theory. Significant simplifications emerge in the descent from three dimensions to two, permitting the self field generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers and numerical solutions are obtained to equilibrium boundary-value problems in which the membrane is subjected to lateral pressure and an applied magnetic field.
Dynamic relaxation; Magnetoelasticity; Thin films
An historical perspective on cell mechanics
Pflugers Archiv European Journal of Physiology
456
3-12
2008
10.1007/s00424-007-0405-1
The physical properties of the protoplasm have long been of interest, and today, several intricate methods, including atomic force microscopy, have been employed in studies of cellular mechanics. However, many current concepts and experimental approaches actually have their beginnings over 300 years ago. Unfortunately, these pioneering studies have been all but forgotten. In this paper, we have reviewed some of the early literature on cellular mechanics to place modern work within an historical framework. It is clear that with current nanoscience approaches, modern experiments employing cell indentation, manipulation, particle rheology and micro- or nano-needle poking are now quantifying mechanical properties which were only qualitatively described 100 years ago. Aside from the variety of approaches our predecessors have employed to understand cellular mechanics, we feel an understanding of the past will help to propel nanoscience into the future. As nanophysiology and nanomedicine are developing, we as a community should take time to consider the early roots of these fields.
aid of intricate appara-; atomic force microscopy; Atomic force microscopy; cell mechanics; Cell mechanics; elasticity; Elasticity; in so far as; it applies to; it is the latter; protoplasm; Protoplasm; successfully attacked without the; tus; type of research; viscoelasticity; Viscoelasticity; viscosity; Viscosity
On instability-induced debond initiation in thin film systems
Engineering Fracture Mechanics
77
8
1298-1313
2010
10.1016/j.engfracmech.2010.02.001
Thin films bonded to substrates are common in semiconductor dielectric stacks and in other applications. Often, in these systems, the mismatch in the Coefficient of Thermal Expansion between the films and the substrate result in significant compressive stresses during processing. These compressive stresses may lead to instabilities and possibly debonding. In the present study, we develop analytical descriptions of buckling and wrinkling-induced debonding by incorporating a cohesive zone model. The temperature excursion leading to buckling or wrinkling, the peak deflection values of the films, the wavelength of the wrinkling pattern, as well as the temperature excursion to the onset of damage are estimated analytically by minimizing the total energy of the combined film-cohesive zone system. Analytical estimates of cohesive stiffness and strength are provided based on (possibly experimentally) observed temperature excursions to the onset of instability and debonding. A non-dimensional grouping of parameters combining characteristics of film, cohesive zone and geometry is identified to be of importance in separating regimes with different debonding characteristics. Special conditions for the non-dimensional grouping emerge for film wrinkling to occur. Full-field simulations based on an incremental Spectral Method are presented to study wrinkling. This approach extends the applicability of the Spectral Method to phenomena involving non-linear foundations, non-monotonic and non-proportional loading. Results from numerical simulations using the incremental Spectral Method are compared with analytical estimates. The analytical derivation is found to provide reasonable estimates of wrinkling wavelength and amplitude but overestimates the cohesive strength. © 2010 Elsevier Ltd.
Buckling; Debond; Energy minimization; Incremental solution; Thin film; Wrinkling
Manufacturing technique and acoustic evaluation of sandwich laminates reinforced high-resilience inter/intra-ply hybrid composites
Fibers and Polymers
15
10
2201-2210
2014
10.1007/s12221-014-2201-9
This study focused on the fabrication and acoustic property evaluation of sandwich cover-ply-reinforced highresilience thermal-bonding nonwoven hybrid composites. P-phenyleneterephthalamides and bicomponent high-resilience bonding polyester intra-ply hybrid nonwoven fabrics were compounded with glass plain fabric to produce the high strength sandwich structural cover ply by means of needle punching and thermal bonding to reinforce the whole composites and dissipate energy when being impacted. Then, the acoustic absorption properties of the homogenous intra-ply hybrid meshwork layer were investigated before and after being reinforced with the aforementioned cover ply. The influencing factors, including areal density, fiber blending ratio, needle punching depth, and air cavity thickness between back plate of the impedance tube and composites, were comparatively investigated. Results revealed that hybrid composites exhibited exceedingly high acoustic absorption properties. Acoustic absorption coefficients were promoted with increases in areal densities and fiber blending ratio of 3D crimped hollow polyester, particularly at low-mid frequency range. In addition, needle punching depths and back air cavity thicknesses considerably affected the average absorption coefficients. The meshwork center layer reinforced with sandwich structural cover-ply perform high resilience properties.
Acoustic absorption; Air cavity; Hybrid composites; Porous materials; Thermal bonding
Effects of stress waveform and water absorption on the fatigue strength of angle-ply aramid fiber/epoxy composites
International Journal of Fatigue
24
2-4
339-348
2002
10.1016/S0142-1123(01)00089-5
The influences of stress waveform and water absorption on the tension–tension fatigue fracture behavior were investigated in ±45° angle-ply laminates of aramid fiber reinforced epoxy matrix composite. For dry specimens, the fatigue strength under negative pulse waveform was higher than that under the positive pulse waveform. Rotation of fibers to the longitudinal direction, which resulted from creep deformation caused by the cyclic loading superimposed on the maximum stress hold time, decreased the compliance, thereby increasing the fatigue life under the negative pulse waveform. Water absorption degraded the fiber/matrix interfacial strength and caused the swelling of the matrix, which resulted in decreases in the static tensile strength and fatigue strength. Although the strength under the negative pulse waveform was slightly higher than that under the positive one, the influence of stress waveform on fatigue strength was smaller in wet specimens.
Aramid fiber/epoxy matrix composites; Creep deformation; Fatigue strength; Interfacial debonding; Stress waveform; Water absorption
Reconstruction of Gaussian quantum mechanics from liouville mechanics with an epistemic restriction
Physical Review A - Atomic, Molecular, and Optical Physics
86
1
1-25
2012
10.1103/PhysRevA.86.012103
How would the world appear to us if its ontology was that of classical mechanics but every agent faced a restriction on how much they could come to know about the classical state? We show that in most respects it would appear to us as quantum. The statistical theory of classical mechanics, which specifies how probability distributions over phase space evolve under Hamiltonian evolution and under measurements, is typically called Liouville mechanics, so the theory we explore here is Liouville mechanics with an epistemic restriction. The particular epistemic restriction we posit as our foundational postulate specifies two constraints. The first constraint is a classical analog of Heisenberg's uncertainty principle; the second-order moments of position and momentum defined by the phase-space distribution that characterizes an agent's knowledge are required to satisfy the same constraints as are satisfied by the moments of position and momentum observables for a quantum state. The second constraint is that the distribution should have maximal entropy for the given moments. Starting from this postulate, we derive the allowed preparations, measurements, and transformations and demonstrate that they are isomorphic to those allowed in Gaussian quantum mechanics and generate the same experimental statistics. We argue that this reconstruction of Gaussian quantum mechanics constitutes additional evidence in favor of a research program wherein quantum states are interpreted as states of incomplete knowledge and that the phenomena that do not arise in Gaussian quantum mechanics provide the best clues for how one might reconstruct the full quantum theory.
Determination of interfacial fracture energy of PZT ferroelectric thin films by nano-scratch technique
Journal of Materials Science Letters
22
10
743-745
2003
10.1023/A:1023704026723
Generally, the PZT/Pt interface between the surface thin film and electrode is the poorest in multi-layer structure. The scratch models utilizing linear elatic fracture mechanics concept, in which delamination is modeled as bimaterial cracks, are characterized by the strain energy released per unit increae in delamination area and successfully applied to many practical test methods. This paper uses the nano-scratch test to assess the interfacial adhesion of Pb(Zr0.52Ti0.48)O3(PZT) ferroelectric thin films/substrate system.
Adhesion; Brittle fracture; Buckling; Buckling stress; Delamination; Ferroelectric materials; Ferroelectric thin film; Fracture mechanics; Indentation-induced stress; Interfaces (materials); Interfacial fracture energy; Linear elastic fracture mechanics; Mathematical models; Nano-scratch technique; Residual stresses; Semiconducting lead compounds; Shear stress; Strain; Strain energy release rate; Thin films
Statistical Mechanics of Learning
Quantum
5400
1-22
2001
10.1007/978-3-642-01805-3
The effort to build machines that are able to learn and undertake tasks such as datamining, image processing and pattern recognition has led to the development of artificial neural networks in which learning from examples may be described and understood. The contribution to this subject made over the past decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics, and include many examples and exercises.
Optimal design of composite laminated plates with the discreteness in ply angles and uncertainty in material properties considered
Computers & Structures
79
29-30
2501-2509
2001
10.1016/S0045-7949(01)00133-X
An algorithm is developed for optimizing laminated plate stacking sequences and determining thicknesses, which incorporates discrete ply angles and considers the uncertainties of material properties in a two-step optimization process. The branch and bound method was modified to handle discrete variables; and convex modeling was used to allow the consideration of variable material properties. The numerical results obtained show that the optimal stacking sequences are determined with fewer evaluations of the objective function than might be expected from considerations of the size of the design space. Our results also show that the optimal thickness increases when elastic moduli uncertainties are considered, which indicates that such uncertainties should not be ignored at the design stage.
Branch and bound method; Convex modeling; Stacking sequence optimization; Thickness minimization
Delamination location and size by modified acoustic emission on cross-ply CFRP laminates during compression-compression fatigue loading
17th International Conference on Composite Materials, ICCM-17, July 27, 2009 - July 31, 2009
Office of Naval Research Science and Technology (O
2009
The paper deals with location and size evaluation of delamination on cross-ply CFRP panels by modified acoustic emission system called VIGILANT. The system continuously monitored the specimens loaded in compression-compression fatigue loading. The modified acoustic emission system has proved its capability in locating delamination within a location error not exceeding 30mm. Besides, the mechanical noise generated by the universal testing machine and the fretting between the CFRP plate and the anti-buckling device was successfully filtered out by the VIGILANT system. The delamination size was also assessed within good agreement.
Acoustic emissions; Acoustic emission testing; Buckling; Composite materials; Delamination; Fatigue testing; Paper laminates; Steel sheet
Mode I stress intensity factor for cracked thin-walled open beams
Engineering Fracture Mechanics
110
249-257
2013
10.1016/j.engfracmech.2013.08.004
A general analytical method to determine the mode I stress intensity factor for thin-walled beams is presented. This method is based on the concept of crack surface widening energy release rate, which is expressed in terms of the G* integral and the thin-walled beam theory. A distinctive aspect of this technique is the incorporation of the warping effect, which is a common feature in thin-walled beams that significantly influences in the stress distribution. This characteristic gives generality to the method, allowing the analysis of crack scenarios that have not been yet considered by other authors. The results show a good agreement with shell finite element solutions and other results available in the literature.
Cracked thin-walled beams; Stress intensity factor; Warping effect
A Mathematical Model for the Mechanics of Saccular Aneurysms
Neurosurgery
17
2
291-295
1985
We constructed and discussed a mathematical model of intracranial saccular aneurysms based on the static mechanics of hollow vessels and were able to focus on three variables that are fundamental to the process of enlargement and rupture of these lesions. They are blood pressure (P), wall strength (sigma), and total wall substance (VT), which, if assigned values of 150 mm Hg, 10 MPa, and 1.0 mm3, lead to model-predicted values of 8 mm for the diameter and 40 micron for the wall thickness for the critical geometry of aneurysmal rupture. These are quantitatively similar to published measurements. The model is based on the assumption of a uniform thin spherical shell for the saccular aneurysm. The interrelationship of the variables, expressed in the equation for critical size at rupture (dc) (i.e., dc = [4 sigma VT/(pi P)]1/3), draws attention to the need for quantitative studies on aneurysmal geometry and on the stereology of the structural fraction of the aneurysmal wall. We concluded that tissue recruitment from around the initial site or hypertrophy of the wall tissue is commonly involved in the aneurysmal process. We identify the paradox of elastic stiffness and stability, which are characteristic of autopsy specimens in the laboratory, in contrast to plastic behavior and irreversible strain, which are essential to the natural process of enlargement of saccular aneurysms.
elasticity; enlargement; mechanics; model; saccular; size
Feynman’s simple quantum mechanics
AIP Conference Proceedings
399
1
1093-1100
1997
10.1063/1.53121
This sample class presents an alternative to the conventional introduction to quantum mechanics and describes its current use in a credit course. This alternative introduction rests on theory presented in professional and popular writings by Richard Feynman. Feynman showed that Nature gives a simple command to the electron: “Explore all paths.” All of nonrelativistic quantum mechanics, among other fundamental results, comes from this command. With a desktop computer the student points and clicks to tell a modeled electron which paths to follow. The computer then shows the results, which embody the elemental strangeness and paradoxical behaviors of the world of the very small. Feynman’s approach requires few equations and provides a largely non-mathematical introduction to the wave function of conventional quantum mechanics. Draft software and materials already used for two semesters in an e-mail computer conference credit university course show that Feynman’s approach works well with a variety of students. The sample class explores computer and written material and describes the next steps in its development.
Fluid Mechanics of a Shallow Fuel Layer Near a Burning Wick
Combustion Science and Technology
2
2-3
105-113
1970
10.1080/00102207008952239
Abstract Equations of the kind used in lubrication theory have been developed in order to examine the fluid mechanics of a thin layer of liquid fuel near a burning wick. Under the simplifying assumption made, the problem can be characterised by two dimensionless parameters. An extinction condition is defined and the relationship between the parameter at extinction is obtained. Some numerical solutions are presented for the variations of surface tension and fuel depth with distance from the wick.
Nonlinear Continuum Mechanics
October
1-34
2008
These notes are prepared for a class on an Introduction to Mathematical Modeling, designed to introduce CAM students to Area C of the CAM-CES Program. I view nonlinear continuum mechanics as a vital tool for mathematical modeling of many physical events - particularly for developing phenomenological models of thermomechanical behavior of solids and fluids. I attempt here to present an accelerated course on continuum mechanics accessible to students equipped with some knowledge of linear algebra, matrix theory, and vector calculus. I supply notes and exercises on these subjects as background material.
Observations and Simple Fracture-Mechanics Analysis of Indentation Fracture Delamination of Tin Films on Silicon
Journal of Adhesion Science and Technology
8
6
611-624
1994
Doi 10.1163/156856194x00375
Ultra micro- or nano-indentation is now widely used to determine the hardness and modulus of thin films on various substrates. In this paper, spherical tipped diamond indenters of small radii are used to investigate the fracture behaviour and delamination of thin TiN films on silicon. The observations clearly establish that the initial behaviour is elastic but at a critical load a sharp discontinuity occurs in the force-displacement curves at the onset of film fracture. Associated with this deformation, the underlying silicon material experiences a pressure-induced phase transformation and film delamination occurs about the contact site. A simple fracture mechanics analysis is presented to estimate the interfacial fracture toughness of the TiN film on the silicon.
adherence; fracture; interfacial toughness; spherical indentation; stressed thin-films; tin films
Geometrically frustrated antiferromagnets: statistical mechanics and dynamics
Introduction to Frustrated Magnetism
21
2009
These lecture notes are intended to provide a simple overview of the physics of geometrically frustrated magnets. The emphasis is on classical and semiclassical treatments of the statistical mechanics and dynamics of frustrated Heisenberg models, and on the ways in which the results provide an understanding of some of the main observed properties of these systems.
statistical mechanics; strongly correlated electrons
Proprioception: Sensational mechanics.
Nature reviews. Neuroscience
11
10
665
2010
10.1038/nrn2922
Research Highlight. Nature Reviews Neuroscience , doi : . Proprioception: Sensational mechanics. Katie Kingwell. Many senses that are based on mechanosensation, such as proprioception and touch, are known
Dynamic failure mechanics
International Journal of Solids and Structures
37
1-2
331-348
2000
10.1016/S0020-7683(99)00097-9
Advances in computing as well as measurement instrumentation have recently allowed for the investigation of a wider spectrum of physical phenomena in dynamic failure than previously possible. The current status and potential topics for research in dynamic failure mechanics are described in this article. These include basic research in dynamic crack initiation and growth in brittle materials, elastic–plastic solids, heterogeneous solids, such as layered materials and composites, and adiabatic shear banding in ductile materials. Research that would benefit and advance practical applications such as aircraft hardening, micrometeorite impact shielding and high speed machining is also outlined. For each of the topics, research needs in terms of theory, numerical simulation and validation as well as experimentation are described.
Adiabatic shear banding; Applications; Composites; Crack growth; Crack initiation; Dynamic failure; Elastic–plastic fracture; Layered materials
On Symplectic Reduction in Classical Mechanics
Physics
310
July
131
2005
10.1016/B978-044451560-5/50004-X
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light on philosophical issues about whether two apparently distinct but utterly indiscernible possibilities should be ruled to be one and the same. These issues are illustrated using ``relationist'' mechanics.
Modeling shear deformability of thin-walled composite beams with open cross-section
Mechanics Research Communications
37
3
320-325
2010
10.1016/j.mechrescom.2010.02.005
The present work formulates a one-dimensional kinematical model capable of assessing the statical behaviour of fibre-reinforced polymers (FRP) thin-walled beams with open cross-section. The proposed model accounts for the effects of shear deformability. Numerical results computed via finite element method (FEM) are provided and compared with the classical ones predicted by Vlasov’s theory. It is concluded that shear deformability can provoke deflections exceeding the values predicted by the classical thin-walled beam theory. Therefore, the proposed model seems to represent a viable alternative to assess the behaviour of such structures.
Composites; Finite element analysis; Shear deformability; Thin-walled beams
A simplified analysis on buckling of stressed and pressurized thin films on substrates
Archive of Applied Mechanics
84
2
149-157
2014
10.1007/s00419-013-0790-1
The buckling solutions for a stressed thin film deposited on a semi-infinite rigid substrate have been determined in the framework of the Foumlppl-von Karman's theory of thin plates and the perturbed bifurcation theory when pressures are applied onto the lower and upper free surfaces of the buckled film. It is found that the equilibrium solutions of the film are modified compared with the classical case of the Euler column, as well as the critical stress above which the film buckles.
Buckling; Explicit approximate solution; Mismatched pressure; Stability; Stressed thin film
Fracture mechanics of delamination defects in multilayer dielectric coatings.
Applied optics
52
32
7689-98
2013
10.1364/AO.52.007689
During the fabrication of multilayer-dielectric (MLD) thin-film-coated optics, such as the diffraction gratings used in OMEGA EP's pulse compressors, acid piranha cleaning can lead to the formation of chemically induced delamination defects. We investigate the causes of these defects and describe a mechanism for the deformation and failure of the MLD coating in response to hydrogen peroxide in the cleaning solution. A fracture mechanics model is developed and used to calculate the crack path that maximizes the energy-release rate, which is found to be consistent with the characteristic fracture pattern observed in MLD coating delamination defects.
Effects of Mode Ratio, Ply Orientation and Precracking on the Delamination Toughness of a Laminated Composite
Journal of Reinforced Plastics and Composites
15
2
141-173
1996
10.1177/073168449601500202
Results are presented from an investigation of the effects of mode ratio, interfacial ply orientation and precracking on the delamination toughness of a graphite/ epoxy composite. Delamination toughness tests were performed on specimens that exhibited growth at 00/00, 15{degrees}/15{degrees}, 15{degrees}/- 150, 30{degrees}/30{degrees} and 30{degrees}/-30{degrees} interfaces. Three mode ratios were considered. The double cantilever beam test was utilized for pure mode I, the end-notched flexure test was used for pure mode II, and the symmetrically delaminated single leg bending test was used for a mixed-mode condition, G,,IG, equal to approximately 0.4. All five interfaces were tested in both precracked and non-precracked conditions at each mode ratio. Also, for the 30{degrees}/30{degrees} and 30{degrees}/- 30{degrees} interfaces, two different stacking sequences were used to assess the effect of remote ply orientation on the perceived mode I and mode II toughness. For any mode ratio and interface angle, it was found that precracked toughness values were always lower than the corresponding nonprecracked result. No other consistent trends were observed in all of the data. For the mode I tests, the 30/30 interface exhibited the lowest toughness, for the mixed-mode tests, the 0/0 interface produced a minimum toughness, and for mode II no significant effect of interface angle on toughness was observed. These results are interpreted with the aid of recent three dimensional finite element analyses for energy release rate distributions along the delamination front for the different stacking sequences and test geometries. The accuracy of various data reduction techniques are also evaluated, and suggestions are made for future testing.
Vibration and stability of cross-ply laminated composite shallow shells subjected to in-plane stresses
Composite Structures
78
3
377-391
2007
10.1016/j.compstruct.2005.10.013
Natural frequencies and buckling stresses of cross-ply laminated composite shallow shells are analyzed by taking into account the effects of transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for rectangular laminated shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate theories which can take into account the complete effects of higher-order deformations such as shear deformations with thickness changes and rotatory inertia are applied to solve the vibration and stability problems of laminated composite shallow shells. Three types of simply supported shallow shells with positive, zero and negative Gaussian curvature are considered. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the lowest natural frequency for the fundamental mode r = s = 1 are examined in detail. Numerical results are compared with those of the published three-dimensional models and the extended two-dimensional model in which both in-plane and normal displacements are assumed to be C0 continuous in the continuity conditions at the interface between layers. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite shallow shells within small number of unknowns. ?? 2005 Elsevier Ltd. All rights reserved.
Buckling stress; Cross-ply laminated composite shallow shells; Global higher-order deformation theory; Interlaminar stresses; Natural frequency; Orthotropic materials
Computation in Classical Mechanics
American Journal of Physics
76
4
6
2007
10.1119/1.2870575
There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a dedicated course or program in computational physics. One way around this difficulty is to include computation in a standard upper-level physics course. An intermediate classical mechanics course is particularly well suited for including computation. We discuss the ways we have used computation in our classical mechanics courses, focusing on how computational work can improve students' understanding of physics as well as their computational skills. We present examples of computational problems that serve these two purposes. In addition, we provide information about resources for instructors who would like to include computation in their courses.
Photochemical ligand loss as a basis for imaging and microstructure formation in a thin polymeric film
Journal of the American Chemical Society
112
i
9490-9496
1990
Ligand loss photochem. occurs in thin polymeric films of ply[Ru(bpy)2(vpy)2]2+ (bpy is 2,2'-bipyridine, vpy is 4-vinylpyridine), poly[Ru(Me2bpy)2(vpy)2]2+ (Me2bpy is 4,4'-dimethyl-2,2'-bipyridine), and poly[Ru(Me4bpy)2(vpy)2]2+ (Me4bpy is 4,4',5,5'-tetramethyl-2,2'-bipyridine). These films were formed by reductive electropolymn. of the corresponding 4-vinylpyridine complexes on Pt disk electrodes. Upon photolysis, the ruthenium-pyridyl bonds were cleaved and the polymer was lost, exposing the underlying substrate. The photochem. reaction was used to transfer an image to the films by using masking techniques. In a subsequent step, poly[Os(vbpy)3]2+ (vbpy is 4-methyl-4'-vinyl-2,2'-bipyridine), which is photochem. stable, was formed selectively in the exposed regions of the electrode by reductive electropolymn. This procedure gave a laterally resolved, two-component, film-based structure in which there were discrete, spatially segregated regions of RuII and OsII. In a final step, the remaining film contg. RuII was removed by photolysis. This procedure left an image of the original mask in the poly[Os(vbpy)3]2+ that remained. [on SciFinder (R)]
Photoimaging compositions and processes (osmium an; photoimaging ruthenium osmium complex polymer; Photolysis (of polymeric polypyridyl complexes of; photolysis polypirydyl ruthenium complex polymer p; Polymerization (electrochem., of osmium and ruthen
Stress intensity factors for cracks in thin plates
Engineering Fracture Mechanics
69
13
1465-1486
2002
10.1016/S0013-7944(01)00136-9
This paper presents stress intensity factor solutions for several crack configurations in plates. The loadings considered include internal pressure, and also combined bending and tension. The dual boundary element method is used to model the plate and mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. Several cases including centre crack, edge crack and cracks emanating from a hole in finite width plates are presented. ?? 2002 Elsevier Science Ltd. All rights reserved.
2-D plane stress; Boundary element method; Plate bending; Stress intensity factors
Adhesive and Elastic Properties of Thin Gel Layers
Langmuir
15
15
4966-4974
1999
10.1021/la9810556
We employ linear elastic fracture mechanics to describe the adhesive and frictional properties of thin, elastic gel layers against a glass, hemispherical indenter. A triblock copolymer with poly (methyl methacrylate) endblocks and a poly (n-butyl acrylate) midblock is diluted with a selective solvent for the center block in order to form a low modulus, thermally reversible gel that behaves as an elastic solid at room temperature. Through simultaneous measurements of the circular contact area, normal displacement, and applied load, we show that the fracture mechanics expressions provide an accurate means to describe the adhesive behavior of the highly compliant polymer gels. By modifying the surface properties of the indenter, we show that the relationship between load and displacement is sensitive to the response of shear forces at the gel/indenter interface, whereas the relationship between the contact area and displacement is unaffected by this response. In addition, we demonstrate the utility of our methodology for quantifying adhesion in situations where the applied load cannot be measured directly.
Buckling of thin liquid jets
Journal of Fluid Mechanics
253
-1
593
1993
10.1017/S0022112093001910
The present work deals with the buckling phenomenon characteristic of highly viscous liquid jets slowly impinging upon a plate. The quasi-one-dimensional equations of the dynamics of thin liquid jets are used as the basis for the theoretical analysis of buckling. With the problem linearized, the characteristic equation is obtained. Its solutions show that instability (buckling) sets in only in the presence of axial compression in the jet, and when the distance between the nozzle exit and the plate exceeds some critical value. The latter is calculated. It is shown that buckling instability corresponds to the rectilinear jet/folding jet bifurcation point. The value of the folding frequency is calculated at the onset of buckling. The theoretical results are compared with Cruickshank & Munson's (1981) and Cruickshank's (1988) experimental data and the agreement is fairly good.
Bulk and thin film microstructures in untwinned martensites
Journal of the Mechanics and Physics of Solids
47
9
1917-1939
1999
10.1016/S0022-5096(98)00125-2
The microstructure in alloys for which the martensite phase is either the 9R or 18R long-period stacking order structure is investigated. A choice of a new unit cell to describe the lattice of the product phase is made, and it is found to give an exact austenite–martensite interface. A comparison with experimental observations for several different material systems supports this choice of unit cell, and the predictions of the shape strain and habit plane normal vectors are the same as those given by a phenomenological calculation. The approach followed here de-emphasizes the role of the internal defects within the unit cell of the martensite lattice in providing the mechanism by which compatibility between the phases is achieved. It is this reason that the name untwinned martensites is proposed to replace the older name faulted martensites. In addition, microstructures in thin film specimens of the alloys exhibiting the untwinned martensite are studied. In particular, a tent microstructure is constructed in a specially oriented film, and such microstructures have potential applications in micro-devices to act as either a pump or an actuator.
A Phase transformation; B Strain compatibility; Microstructure; Shape memory effect; Thin films
A finite element analysis of continuum damage mechanics for ductile fracture
International Journal of Fracture
102
2
83-102
1988
10.1007/BF00033000
A finite element formulation of an anisotropic theory of continuum damage mechanics for ductile fracture is presented. The formulation is based on a generalized model of anisotropic continuum damage mechanics of elasticity and plasticity proposed earlier by the authors. The validity of the proposed anisotropic damage model and finite element formulation is verified by comparing the predicted fracture load of center-cracked tension specimen made of thin aluminium alloy 2024-T3 with those determined experimentally and excellent agreement is achieved. The proposed finite element analysis can thus provide an important design tool to solve practical problems of engineering significance which may have hitherto been found difficult using the conventional fracture mechanics concept.
Some Open Points in Nonextensive Statistical Mechanics
Entropy
1
1
30
2011
10.1142/S0218127412300303
We present and discuss a list of some interesting points that are currently open in nonextensive statistical mechanics. Their analytical, numerical, experimental or observational advancement would naturally be very welcome.
Statistical Mechanics
Reprint of "Post-buckling analysis for the precisely controlled buckling of thin film encapsulated by elastomeric substrates" [In. J. Solids Struct. 45 (2008) 2014-2023]
International Journal of Solids and Structures
45
2008
3858-3867
2008
10.1016/S0020-7683(08)00168-6
The precisely controlled buckling of stiff thin films (e.g., Si or GaAs nano ribbons) on the patterned surface of elastomeric substrate (e.g., poly(dimethylsiloxane) (PDMS)) with periodic inactivated and activated regions was designed by Sun et al. [Sun, Y., Choi, W.M., Jiang, H., Huang, Y.Y., Rogers, J.A., 2006. Controlled buckling of semiconductor nanoribbons for stretchable electronics. Nature Nanotechnology 1, 201-207] for important applications of stretchable electronics. We have developed a post-buckling model based on the energy method for the precisely controlled buckling to study the system stretchability. The results agree with Sun et al.'s (2006) experiments without any parameter fitting, and the system can reach 120% stretchability. © 2007 Elsevier Ltd. All rights reserved.
Buckling; Mechanics; Stretchable electronics
Analysis of fracture in thin shells by overlapping paired elements
Computer Methods in Applied Mechanics and Engineering
195
5343-5360
2006
10.1016/j.cma.2005.10.024
A finite element methodology for evolution of cracks in thin shells using mid-surface displacement and director field discontinuities is presented. We enrich the mid-surface displacement and director fields of a discrete Kirchhoff-Love quadrilateral element using a piecewise decomposition of element kinematics, which leads to a basis that is a variant of the one used in the extended finite element method. This allows considerable simplifications in the inclusion of the shell director field. A cohesive law is employed to represent the progressive release of the fracture energy. In contrast with previous works, we retain the original quadrature points after the formation of a crack, which, in combination with an elasto-plastic multiplicative decomposition of the deformation gradient, avoids the previously required internal variable mapping during crack evolution. Results are presented for large strain elastic and elasto-plastic crack propagation. ?? 2005 Elsevier B.V. All rights reserved.
Elasto-plasticity; Extended finite element method; Fracture; Shell elements
An introduction to thermodynamics and statistical mechanics
North
534
2007
10.1017/CBO9780511801570
This introductory textbook for standard undergraduate courses in thermodynamics has been completely rewritten. Starting with an overview of important quantum behaviours, the book teaches students how to calculate probabilities, in order to provide a firm foundation for later chapters. It introduces the ideas of classical thermodynamics and explores them both in general and as they are applied to specific processes and interactions. The remainder of the book deals with statistical mechanics - the study of small systems interacting with huge reservoirs. The changes to this second edition have been made after more than 10 years classroom testing and student feedback. Each topic ends with a boxed summary of ideas and results, and every chapter contains numerous homework problems, covering a broad range of difficulties. Answers are given to odd numbered problems, and solutions to even problems are available to instructors at
On the thermodynamic foundations of non-linear solid mechanics
International Journal of Non-Linear Mechanics
7
3
237-254
1972
10.1016/0020-7462(72)90048-0
Non-equilibrium thermodynamics with internal variables governed by rate equations is explored as a foundation for non-linear solid mechanics. Rate equations are studied as to type, yielding descriptions of viscoelastic, viscoplastic, and plastic behavior. The special case of uncoupled instantaneous elasticity is considered, as well as materials exhibiting combined behavior.
Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites
Composites Science and Technology
65
7-8
1226-1236
2005
10.1016/j.compscitech.2004.12.027
This paper deals with the analysis of active constrained layer damping (ACLD) of laminated thin composite shells using piezoelectric fiber reinforced composite (PFRC) materials. The constraining layer of the ACLD treatment is considered to be made of the PFRC materials. A finite element model of the smart composite shells integrated with the patches of such ACLD treatment has been developed to demonstrate the performance of these patches on enhancing the damping characteristics of thin symmetric and antisymmetric cross-ply and anti-symmetric angle ply laminated composite shells. The effect of variation of piezoelectric fiber orientation in the constraining PFRC layer on the control authority of the patches has also been investigated. ?? 2005 Published by Elsevier Ltd.
Active; Composites; Constrained layer; Damping; Piezoelectric fiber; Reinforced
Research on conceptual understanding in mechanics
Physics Today
37
7
24-32
1984
10.1063/1.2916318
Recent investigations of the difficulties that students encounter in learning physics are beginning to provide a new resource for improving instruction.
In vivo finite element model-based image analysis of pacemaker lead mechanics.
Medical image analysis
5
4
255-70
2001
10.1016/S1361-8415(01)00041-X
BACKGROUND: Fractures of implanted pacemaker leads are currently identified by inspecting radiographic images without making full use of a priori known material and structural information. Moreover, lead designers are unable to incorporate clinical image data into analyses of lead mechanics.\n\nMETHODS: A novel finite element/active contour method was developed to quantify the in vivo mechanics of implanted leads by estimating the distributions of stress, strain, and traction using biplane videoradiographic images. The nonlinear equilibrium equations governing a thin elastic beam undergoing 3-D large rotation were solved using one-dimensional isoparametric finite elements. External forces based on local image greyscale values were computed from each pair of images using a perspective transformation governing the relationship between the image planes.\n\nRESULTS: Cantilever beam forward solution results were within 0.2% of the analytic solution for a wide range of applied loads. The finite element/active contour model was able to reproduce the principal curvatures of a synthetic helix within 3% of the analytic solution and estimates of the helix's geometric torsion were within 20% of the analytic solution. Applying the method to biplane videoradiographic images of a lead acutely implanted in an anesthetized dog resulted in expected variations in curvature and bending stress between compliant and rigid segments of the lead.\n\nCONCLUSIONS: By incorporating knowledge about lead geometric and material properties, the 3-D finite element/active contour method regularizes the image reconstruction problem and allows for more quantitative and automatic assessment of implanted lead mechanics.
Algorithms; Animals; Biomechanical Phenomena; Dogs; Finite Element Analysis; Heart Ventricles; Heart Ventricles: radiography; Image Processing, Computer-Assisted; Image Processing, Computer-Assisted: methods; Imaging, Three-Dimensional; Pacemaker, Artificial; Radiographic Image Enhancement
The Mechanics of Rock Cutting
International Journal of Rock Mechanics and Mining Sciences
9
2
261-270
1972
10.1016/0148-9062(72)90027-7
The failure process in rock cutting is observed and the formation of a recompacted crushed zone which sticks to the rake face of the cutting tool and acts as `the built-up edge' in metal cutting is described.\nBased on observation of the process of rock cutting and some simplifying assumptions a theory is developed on the mechanics of rock cutting. A formula for cutting force is proposed, which is similar to Merchant's well-known formula in metal cutting.\nSome experimental work was designed to cut plates of specimen rock, by an orthogonal cutting tool. The test results are compared with theory, and the parameters in the formula determined.
mechanics; rock cutting
Jordan canonical form solution for thermally induced deformations of cross-ply laminated composite beams
Journal of Thermal Stresses
22
3
331-346
1999
Thermal deformations in symmetric and antisymmetric cross-ply beams\nare investigated. The state-space approach in conjunction with the\nJordan canonical form is presented to obtain exact solutions for\nthe thermoelastic response of cross-ply composite beams for arbitrary\nboundary conditions and subjected to general temperature fields.\nThe classical, first-, second-, and third-order beam theories are\nused in the analysis. As a demonstrative example, deflections are\ncomputed for beams with various lamination schemes and boundary conditions\nundergoing linearly varying temperature through the thickness.
Material modeling for cross-ply ceramic matrix laminates with progressive damages and environmental degradation
American Society of Mechanical Engineers, Materials Division (Publication) MD
80
189-202
1997
A physically-based damage model has been developed to predict the nonlinear behavior of cross-ply ceramic matrix laminates due to progressive failures. It has been shown to model the nonlinear stress-strain response of chemical vapor infiltrated (CVI) SiC/SiC composites under tension loading accurately. This model utilizes a consistent set of measurable material parameters as inputs and shows good agreement with measured tensile stress-strain curves for a variety of ply thickness ratios. The material model is also utilized to characterize the environmentally induced property degradation in CMC's.
Ceramic matrix composites; Chemical vapor infiltration; Failure analysis; Laminated composites; Mathematical models; Silicon carbide; Strain; Stress analysis; Tensile properties; Weathering
Classical mechanics without determinism
Foundations of Physics Letters
72
6
11
2005
10.1007/s10702-006-1009-2
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical interpretation is sufficient to predict all measurable results of classical mechanics. In the classical case, the wave function that satisfies a linear equation is positive, which is the main source of the fundamental difference between classical and quantum mechanics.
A computational approach for analysis and optimal design of FRP beams
Comput Struct
70
2
169-183
1999
DOI: 10.1016/S0045-7949(98)00154-0
Fiber-reinforced plastic (FRP) beams are thin-walled or moderately\nthick-walled open or closed sections consisting of assemblies of\nflat panels. We present a computational approach with the computer\nprogram FRPBEAM (1994) for the response evaluation of pultruded FRP\nbeams in bending. This program combines micro/macro-mechanics analyses\nwith the Mechanics of Laminated composite Beams (MLB) model and an\nexplicit stability solution to analyze, design, and optimize FRP\nshapes. In FRPBEAM, the ply stiffnesses are predicted by micromechanics\nformulas, based on the fiber volume fraction of each lamina, and\nthe panel laminate properties are computed from the ply stiffnesses\nand macromechanics. The MLB model is used to analyze the overall\nresponse of FRP beams in bending, and the Tsai-Hill failure criterion\nis adopted to predict first-ply-failure loads. An example of a laminated\nbox beam is used to demonstrate the accuracy of the computer program\nfor predicting beam displacements and ply stresses in relation to\nfinite element analyses. A stability Rayleigh-Ritz method is included\nin the program and used to evaluate the critical buckling loads for\npultruded I-beams. Through parametric studies with FRPBEAM and a\nmultiobjective optimization scheme, the fiber architecture of an\nexisting I-beam is optimized, and based on a recommended practical\ndesign, the I-beam section is produced by pultrusion and subsequently\ntested in bending. The predicted response with FRPBEAM correlates\nwell with the experimental results. As illustrated by design analysis\nand optimization examples presented in this study, the experimentally\nand numerically verified computer program can be used to analyze\nexisting FRP shapes and develop new optimized shapes for the civil\nstructural market.
fiber-reinforced plastics beams
Influence of time-dependent damage on creep of multidirectional polymer composite laminates
Composites Part B: Engineering
42
3
489-498
2011
10.1016/j.compositesb.2010.12.003
An experimental study (Birur et al., 2006 [1]) on time-dependent evolution of various damage modes under constant load was extended; specifically, time-dependent evolution and influence of transverse cracks, in ??45?? and 90?? plies, on the creep of [??45/90\n 2]\n S multidirectional laminate of a polymer composite (Hexcel F263-7/Toho G30-500) was studied and modeled. The damage evolved with time in both ply groups sequentially and/or simultaneously depending on the test conditions. For the latter case, the two ply groups influenced each others damage evolution. The creep of the laminate was due to both the viscoelasticity of the plies and the time-dependent damage. A damaged ply was modeled using an equivalent undamaged ply with an apparent compliance, which was determined as a function of time-dependent transverse crack density. This was used along with a model frame work, based on lamination theory, to predict the creep compliance of the [??45/90\n 2]\n S laminate. The model predictions compared well with experimental results. ?? 2010 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Creep; C. Damage mechanics; Time-dependent damage
Free vibration of laminated cross-ply plates including shear deformation by spline method
International Journal of Mechanical Sciences
49
3
352-363
2007
10.1016/j.ijmecsci.2006.08.016
Spline function approximation technique is used to analyze the free vibration of symmetric and anti-symmetric cross-ply plates under shear deformation theory. The equations of motion of the plate are derived using YNS theory. A system of coupled differential equations in terms of displacement and rotational functions are obtained by assuming the solution in a separable form. These functions are approximated using Bickley-type splines of suitable orders. A generalized eigenvalue problem is obtained on applying the process of point collocation with suitable boundary conditions. Parametric studies have been made to investigate the frequency response of the plates with reference to the material properties, number of layers, fiber orientation, side-to-thickness ratio, aspect ratio and relative layer thickness. Some results are compared with existing solution obtained by FEM.
Anti-symmetric; Cross-ply; Free vibration; Shear deformation; Spline method; Symmetric
Nonlinear bending analysis of unsymmetric cross-ply laminated plates with piezoelectric actuators in thermal environments
Composite Structures
63
2
167-177
2004
10.1016/S0263-8223(03)00145-4
Nonlinear bending analysis is presented for a simply supported, shear deformable cross-ply laminated plate with piezoelectric actuators subjected to a transverse uniform or sinusoidal load combined with electrical loads and in thermal environments. The temperature field considered is assumed to be a uniform distribution over the plate surface and through the plate thickness and the electric field is assumed to be the transverse component EZ only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations of a laminated plate are based on a higher order shear deformation plate theory with a von K??rm??n-type of kinematic nonlinearity, and including thermo-piezoelectric effects. A perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending behavior of unsymmetric cross-ply laminated plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electrical loading conditions. The results presented show the effects of temperature rise and applied electric fields on the nonlinear bending behavior of the plate. ?? 2003 Elsevier Ltd. All rights reserved.
Higher order shear deformation plate theory; Hybrid laminated plate; Nonlinear bending; Perturbation technique; Thermo-piezoelectric effect
Thermal buckling of hybrid angle-ply laminated composite plates with a hole
Composites Science and Technology
65
11-12
1780-1790
2005
10.1016/j.compscitech.2005.03.007
In this paper, thermal buckling analysis of symmetric and antisymmetric laminated hybrid composite plates with a hole subjected to a uniform temperature rise for different boundary conditions is presented. The first-order shear deformation theory in conjunction with variational energy method is employed in mathematical formulation. The eight-node Lagrangian finite element technique is used for obtaining the thermal buckling temperatures of glass-epoxy/boron-epoxy hybrid laminates. The effects of hole size, lay-up sequences and boundary conditions on thermal buckling temperatures are investigated. The results are shown in graphical form for various boundary conditions. © 2005 Elsevier Ltd. All rights reserved.
Finite element method; Hybrid composite plates; Thermal buckling
Thermal postbuckling analysis of laminated cross-ply truncated circular conical shells
Composite Structures
71
1
101-114
2005
10.1016/j.compstruct.2004.09.030
In this work, thermoelastic postbuckling behavior of cross-ply laminated composite conical shells under presumed uniform temperature distribution is studied. The finite deflection analysis is carried out to determine the relationship between the maximum deflection and the temperature rise, and to evaluate the minimum temperature parameter that causes the bifurcation of shell deformation from axisymmetric deformation mode to asymmetric one. The formulation is based on first-order shear deformation theory that accounts for the transverse shear. The governing equations, derived using minimum total potential energy principle, are solved using semi-analytical finite element approach. The critical temperature parameter values corresponding to the onset of bifurcation are compared with those evaluated from linear eigenvalue analysis. The detailed study is carried out to highlight the influences of length-to-radius and radius-to-thickness ratios, semi-cone angle, number of layers and the boundary conditions on the nonlinear prebuckling/postbuckling thermoelastic response of the laminated circular conical shells. The participation of axisymmetric and asymmetric modes in the total response of the shells is also highlighted.
Bifurcation; Conical shell; Critical temperature; Cross-ply; Mode shape; Semi-analytical finite element; Thermal postbuckling
Postbuckling of shear deformable cross-ply laminated cylindrical shells under combined external pressure and axial compression
International Journal of Mechanical Sciences
43
11
2493-2523
2001
http://dx.doi.org/10.1016/S0020-7403(01)00058-3
A postbuckling analysis is presented for a shear deformable cross-ply laminated cylindrical shell of finite length subjected to combined loading of external pressure and axial compression. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán–Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under combined loading cases. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, antisymmetric and symmetric cross-ply laminated cylindrical shells for different values of load-proportional parameters.
Boundary layer theory of shell buckling; Composite laminated cylindrical shell; Higher order shear deformable shell theory; Postbuckling; Singular perturbation technique
Effect of warping on natural frequencies of symmetrical cross-ply laminated composite non-cylindrical helical springs
International Journal of Mechanical Sciences
74
65-72
2013
10.1016/j.ijmecsci.2013.04.010
Free vibration problem of symmetrical cross-ply laminated composite non-cylindrical helical springs with rectangular cross-section is investigated. The effect of the warping deformation of wire cross-section on natural frequencies is first considered in the formulation. The differential equations of motion for the springs, which consist of 14 first-order partial differential equations with variable coefficients, are derived using naturally curved and twisted anisotropic beam theory. The natural frequencies of the springs are found from improved Riccati transfer matrix by iteration. The element transfer matrix is calculated by the use of the Scaling and Squaring method and Pad´e approximations. Three examples are presented for different types of springs with rectangular cross-section under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FE-results using three-dimensional solid layered element (Solid 46) in ANSYS code. Numerical results reveal that the warping deformation has a significant influence on the natural frequencies, which should be considered in the free vibration analysis of the springs. Finally, the effects of various parameters and different stacking sequences on the natural frequencies for symmetrically laminated barrel springs with rectangular cross-section have also been studied.
Improved Riccati transfer matrix method; Natural frequency; Non-cylindrical helical spring; Symmetrical cross-ply laminated composite; Warping effect
Three-dimensional analysis of cross-ply laminated cylindrical panels with weak interfaces
International Journal of Solids and Structures
41
9-10
2429-2446
2004
10.1016/j.ijsolstr.2003.12.018
The bending and free vibration of a simply-supported, cross-ply laminated cylindrical panel with weak interfaces are investigated in this study. The problem is solved using three-dimensional state-space approach coupled with the layer-wise method, which turns the state equation with variable coefficients into one with constant coefficients. The weak interfaces are modeled as spring layers. Their effects on the integrity of the laminate panel are accounted for by integrating the so-called interfacial transfer matrices into the global transfer matrix. The cylindrical bending of the panel is also considered, and an exact static state-space solution is derived. Comprehensive numerical results are presented and some practical issues of importance to engineering applications are discussed. ?? 2004 Elsevier Ltd. All rights reserved.
Cross-ply laminate; Cylindrical panel; Spring-layer model; State-space approach; Weak interface
Tribological characteristics of thin films and applications of thin film technology for friction and wear reduction
Thin Solid Films
118
3
335-349
1984
10.1016/0040-6090(84)90204-9
Thin film deposition technologies based on chemical and physical vapor deposition are now well established to improve the wear resistance of cutting tools. Although severe tribological conditions occur here, coated tools perform exceptionally well. Despite this, the growth in use of thin film deposition technology is slow in the general mechanical industry. In part, this is due to lack of data on the tribological characteristics of bodies coated with thin films. In this paper, tribological test data gathered in a systematic program of sliding and rolling contact tests are presented to demonstrate the usefulness of thin film coatings for wear protection and friction reduction. Samples coated by reactive magnetron sputtering were tested in sliding and rolling contact tests at low and high speeds and at varying contact stresses. These results are presented and used to identify the primary consideration guiding the choice of coating materials, coating properties, film thickness needed etc. A newly developed film-to-substrate adhesion strength test is also briefly described and the results obtained are cited. It is shown that film material selection and coating process selection have a reasonable physical basis.
On cultural-selection mechanics
Current Anthropology
38
447
1997
10.1086/204630
Criticizes the report `Emergency Decisions, Cultural Selection Mechanics, and Group Selection,' by C. Boehm.
SOCIAL groups
Some elements of microstructural mechanics
Computational Materials Science
27
3
351-374
2003
10.1016/S0927-0256(03)00041-7
Microstructural mechanics combines the computational methods of structural mechanics and materials sciences. It is dedicated to the mechanics of heterogeneous materials. On the one hand, it can be used to compute industrial components for which the size of the heterogenities is of the order of magnitude of the size of the structure itself or of holes or notches. On the other hand, the computation of representative volume elements of heterogeneous materials enables one to predict the influence of phase morphology and distribution on the linear or non-linear effective properties, having in view microstructure optimization. Such computations provide the local stress-strain fields that can be used to predict damage or crack initiation. This work focuses on the modern tools available for reconstructing realistic three-dimensional microstructures and for computing them, including parallel computing. The choice of the local non-linear constitutive equations and the difficulty of identification of the corresponding parameters remain the weakest link in the methodology. The main example detailed in this work deals with polycrystalline plasticity and illustrates the tremendous heterogeneity of local stress and strain, and the effect of grain boundary or free surfaces. The computations are finally used to calibrate a simplified homogenization polycrystal model. © 2003 Elsevier Science B.V. All rights reserved.
Constitutive behaviour; Finite element; Materials; Microstructures; Parallel computing; Polycrystal; Structural mechanics; Viscoplasticity
A numerical investigation of surface crevasse propagation in glaciers using nonlocal continuum damage mechanics
Geophysical Research Letters
40
May
3064-3068
2013
10.1002/grl.50602
We use a nonlocal viscoelastic damage model to investigate the conditions that enable water-free surface crevasse propagation in grounded marine-terminating glaciers. Our simulations, on idealized rectangular ice slabs in contact with the ocean, show that crevasses propagate faster in thicker ice slabs. We find that: (1) the fraction of ice slab thickness penetrated by surface crevasses decreases with increasing seawater depth near the terminus; (2) a no-slip (fixed) basal boundary condition retards crevasse growth; and (3) crevasses form closer to the terminus when the seawater depth is larger or when the glacier base is fixed to the bedrock, which could lead to calving of smaller icebergs. However, water-free surface crevasses can penetrate (nearly) the entire ice thickness only in thicker ice slabs terminating in shallow seawater depths. This leads us to the conclusion that surface crevasses alone are not responsible for calving events in marine-terminating and thin glaciers. Key Points Nonlocal damage mechanics is well suited for studying fracture of glaciers Surface crevasse propagation is affected by basal boundary and seawater depth Through-penetrating surface crevasses are only observed in thicker glaciers ©2013. American Geophysical Union. All Rights Reserved.
calving; damage; glacier; sea level; simulation
Yield design of thin periodic plates by a homogenization technique and an application to masonry walls
Comptes Rendus - Mecanique
331
641-646
2003
10.1016/S1631-0721(03)00144-X
A homogenization method for determining overall yield strength properties of thin periodic plates from their local strength properties is proposed within the framework of the yield design theory. The proposed method is applied to the determination of the in-plane and out of plane strength criterion for masonry described as a regular assemblage of infinitely resistant bricks separated by Coulomb interfaces. ?? 2003 Acad??mie des sciences. Published by ??ditions scientifiques et m??dicales Elsevier SAS. All rights reserved.
Computational solid mechanics; Homogenization; Masonry; Out of plane; Plate; Yield design
Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement
COMPUTATIONAL MECHANICS
46
1
83-89
2010
10.1007/s00466-009-0426-z
Computation of incompressible flows in arterial fluid mechanics,\nespecially because it involves fluid-structure interaction, poses\nsignificant numerical challenges. Iterative solution of the fluid\nmechanics part of the equation systems involved is one of those\nchallenges, and we address that in this paper, with the added\ncomplication of having boundary layer mesh refinement with thin layers\nof elements near the arterial wall. As test case, we use matrix data\nfrom stabilized finite element computation of a bifurcating middle\ncerebral artery segment with aneurysm. It is well known that solving\nlinear systems that arise in incompressible flow computations consume\nmost of the time required by such simulations. For solving these large\nsparse nonsymmetric systems, we present effective preconditioning\ntechniques appropriate for different stages of the computation over a\ncardiac cycle.
Molecular Mechanics: The Art and Science of Parameterization
Reviews in Computational Chemistry
2
81-97
2007
10.1002/9780470125793.ch3
This chapter contains sections titled: Introduction Molecular Mechanics Theory History of Molecular Mechanics Formulation of Molecular Mechanics Heats of Formation Parameterization
Quantum statistical mechanics in a closed system
Physical Review A
43
4
2046-2049
1991
10.1103/PhysRevA.43.2046
A closed quantum-mechanical system with a large number of degrees of freedom does not necessarily give time averages in agreement with the microcanonical distribution. For systems where the different degrees of freedom are uncoupled, situations are discussed that show a violation of the usual statistical-mechanical rules. By adding a finite but very small perturbation in the form of a random matrix, it is shown that the results of quantum statistical mechanics are recovered. Expectation values in energy eigenstates for this perturbed system are also discussed, and deviations from the microcanonical result are shown to become exponentially small in the number of degrees of freedom.
Carbon composites based on multi-axial multi-ply stitched preforms - Part 6. Fatigue behaviour at low loads: Stiffness degradation and damage development
Composites Part A: Applied Science and Manufacturing
38
1633-1645
2007
10.1016/j.compositesa.2007.03.003
This article studies the fatigue properties of a carbon-fibre cross-ply non-crimp fabric reinforced epoxy composite. Tensile-tensile fatigue cycling was carried out at load levels corresponding to the onset of damage in a static tensile test, in machine, cross and bias direction. Specimens in machine and cross direction did not fail up to 106 cycles; specimens in bias direction had an average fatigue life Nmax of 3 × 105 cycles. Stiffness degradation in bias direction samples was found to be more severe than in machine or cross direction. Damage development in the samples was studied by means of X-ray photography and appears to show remarkable resemblance to the development under a static tensile test and can be qualitatively compared to the behaviour of non-stitched UD laminates. Post-fatigue tensile tests were done at various stages of the fatigue life. Small differences in damage onset strain level can be found. Failure strain of bias direction tested samples shows significant decrease upon cycling. © 2007 Elsevier Ltd. All rights reserved.
B. Fatigue; B. Mechanical properties; Non-crimp fabric composites
Several problems on dynamical systems and mechanics
Nonlinearity
21
9
T149-T155
2008
10.1088/0951-7715/21/9/T01
We discuss some open problems in the theory of dynamical systems, classical and quantum mechanics.
THE INEXTENSIONAL THEORY FOR THIN FLAT PLATES
The Quarterly Journal of Mechanics and Applied Mathematics
8
3
338-352
1955
10.1093/qjmam/8.3.338
This paper presents the inextensional theory for thin flat plates. The theory is applicable to cantilever and other plates subjected to a normal loading which is resisted primarily by the flexural rigidity of the plate rather than by the extensional rigidity. The middle surface of the plate is assumed to be inextensional so that the mode of deformation is a developable surface.
Problems on statistical mechanics
StatMechBook
vii, 284 p.
1999
10.1887/0750305215
A thorough understanding of statistical mechanics depends strongly on the insights and manipulative skills that are acquired through the solving of problems. Problems on Statistical Mechanics provides over 120 problems with model solutions, illustrating both basic principles and applications that range from solid-state physics to cosmology. An introductory chapter provides a summary of the basic concepts and results that are needed to tackle the problems, and also serves to establish the notation that is used throughout the book. The problems themselves occupy five chapters, progressing from the simpler aspects of thermodynamics and equilibrium statistical ensembles to the more challenging ideas associated with strongly interacting systems and nonequilibrium processes. Comprehensive solutions to all of the problems are designed to illustrate efficient and elegant problem-solving techniques. Where appropriate, the authors incorporate extended discussions of the points of principle that arise in the course of the solutions. The appendix provides useful mathematical formulae.
e-book CRC.; etc.; exercises; Statistical mechanics Problems
About the applicability of a simple model to predict the fatigue life and behavior of woven-ply thermoplastic laminates at T > Tg
Composites Part B: Engineering
61
181-190
2014
10.1016/j.compositesb.2014.01.050
Through the application of a simple model, the concept of damage accumulation has been used to predict the fatigue life of TP-based composite materials at a test temperature higher than its glass transition temperature. This work was aimed at studying the off-axis tension-tension fatigue behavior of woven-ply C/PPS laminates which consists of three primary stages: (i) In the initial phase of cyclic loading, damage accumulates rapidly along with a matrix plasticization under the form of intra-laminar cracking which may initiate in multiple locations, but preferably at the interfaces between fibers and matrix at the crimps - (ii) The second stage is characterized by a steady damage growth rate and little damage accumulation - (iii) Damage (mostly debonding and interlaminar cracks) generalizes rapidly during the last stage ultimately resulting in extensive delamination and fiber bundles pull-out. It also appears that the fatigue behavior is ascribed to the highly ductile and time-dependent behavior of matrix-rich regions due to the non-planar structure of woven plies. Finally, a simple analytical model was applied, and proved to be adequate to capture the different stages of damage scenario, with excellent correlation to the experimental data. © 2014 Elsevier Ltd. All rights reserved.
A. Fabrics/textiles; A. Thermoplastic resin; B. Fatigue; C. Analytical modeling
Study on a method for vibration control of the aeronautic thin-walled workpiece in high-speed milling process
2011 International Conference on Applied Mechanics, Materials and Manufacturing, ICAMMM 2011, November 18, 2011 - November 20, 2011
117-119
1851-1856
2012
10.4028/www.scientific.net/AMM.117-119.1851
A new method for vibration control of aeronautical thin-walled workpiece in high-speed milling progress using a dynamic vibration absorber is presented. First, the theoretical model of the method is established and studied. Then the effectiveness of this method is testified via the simulation based on FEM. Finally, the feasibility of this method is discussed. The result shows that this method for vibration control of the aeronautic thin-walled workpiece in high-speed milling progress is effective and practical. (2012) Trans Tech Publications.
Aerodynamics; Computational mechanics; Dynamics; Finite element method; Milling (machining); Thin walled structures; Vibration control
The wedge splitting test, a new method of performing stable fracture mechanics tests
Engineering Fracture Mechanics
35
1-3
117-125
1990
10.1016/0013-7944(90)90189-N
The wedge splitting test, a new method of performing stable fracture mechanics tests. E Bruehwiler, FH Wittmann Engineering Fracture Mechanics 35:11, 117-125, 1990. The wedge splitting test is
Effect of delamination on lamb wave velocity in cross-ply laminates
Journal of Materials Science Letters
21
24
1891-1893
2002
The effect of delamination on the stiffness and the S0 mode velocity in GFRP and CFRP cross-ply laminates was studied. The change of the stiffness and the S0 mode velocity as functions of the delamination length were obtained experimentally, and the results were in good agreement with those predicted for both laminates. In general, it was confirmed that measuring the S0 mode velocity is an excellent method of monitoring transverse cracks and delamination in cross-ply laminates.
Mechanical Performance of Composite Laminate with Oblique Splicing Ply
Proceedings of 2010 Asia-Pacific International Symposium on Aerospace Technology, Vol 1 and 2
856-859
2010
In order to cognition the mechanical performance of the composite laminate structures with ply splicing, the specific carbon/polyurethane composite laminate specimens has been designed to determine this material mechanical properties by means of the tension testing. The tensile elastic modulus and tensile strength are measured in the experiment. The breakage happened in place of splicing along the splicing line. The oblique ply splicing significantly influence the stiffness of the composite laminate, but the strength of the composite laminate with splicing ply is mainly determined by the continuous layers. The laminate fails in low load value. The numerical analyses using linear elastic and progressive damage approaches were conducted with the commercial FEM software (ABAQUS). The linear elastic finite element model is established to calculate the interlaminar stress of ply splicing in different layers angles. The progressive model, based on the damage mechanisms observed at the ply level and hypotheses regarding their effect on material stiffness, is used to predict the strength by means of numerical computation. There are three different criteria used here in the prediction. By combining the damage model with classical lamination theory, the behavior of laminates under plane stress loading is predicted. The capabilities of the proposed damage model are assessed based on comparison to experimental data.
composite laminate; FEM; ply splicing; tension strength
Dynamics of left ventricular wall and mitral valve mechanics--a model study.
Journal of biomechanics
22
3
261-271
1989
10.1016/0021-9290(89)90093-6
The relation between global left ventricular pumping characteristics and local cardiac muscle fiber mechanics is represented by a mathematical model of left ventricular mechanics in which the mitral valve papillary muscle system is incorporated. The wall of the left ventricle is simulated by a thick-walled cylinder. Transmural differences in fiber orientation are incorporated by changing the direction of material anisotropy across the wall. The cylinder is free to twist. The upper end of the cylinder is covered by a thin, flexible sheet, representing the base of the left ventricle. The mitral valve is incorporated in this sheet. The tips of the mitral leaflets are connected by chordae tendineae to the papillary muscles which are attached to the bottom of the cylinder. Canine cardiac cycles were simulated for various end-diastolic values of left ventricular volume (25-120 ml, control 60 ml), left atrial pressure (0-2.7 kPa, control 0.22 kPa) and aortic pressure (5-11 kPa, control 11 kPa). In this wide range of preload and afterload mechanical loading of the muscle fibers appeared to be distributed quite evenly (SD: +/- 5% of control value) over all muscular structures of the left ventricle, including the papillary muscles.
Buckling and post-buckling of long pressurized elastic thin-walled tubes under in-plane bending
International Journal of Non-Linear Mechanics
41
491-511
2006
10.1016/j.ijnonlinmec.2005.11.002
The present paper focuses on the structural stability of long uniformly pressurized thin elastic tubular shells subjected to in-plane bending. Using a special-purpose non-linear finite element technique, bifurcation on the pre-buckling ovalization equilibrium path is detected, and the post-buckling path is traced. Furthermore, the influence of pressure (internal and/or external) as well as the effects of radius-to-thickness ratio, initial curvature and initial ovality on the bifurcation moment, curvature and the corresponding wavelength, are examined. The local character of buckling in the circumferential direction is also demonstrated, especially for thin-walled tubes. This observation motivates the development of a simplified analytical formulation for tube bifurcation, which considers the presence of pressure, initial curvature and ovality, and results in closed-form expressions of very good accuracy, for tubes with relatively small initial curvature. Finally, aspects of tube bifurcation are illustrated using a simple mechanical model, which considers the ovalized pre-buckling state and the effects of pressure. ?? 2006 Elsevier Ltd. All rights reserved.
Bifurcation; Buckling; Cylindrical shell; Ovalization; Stability; Thin-walled; Tube
FINITE ELEMENT MODEL FOR ANALYSIS OF DEFORMATIONS OF BIAS-PLY MOTORCYCLE TIRES SUBJECT TO INFLATION PRESSURE.
Vehicle System Dynamics
13
3
113-128
1984
The finite element model previously formulated to represent a bias-ply motorcycle tire is improved for more accurate orthotropic stiffness values. Efforts are centered on accurate mapping of the cord angle from an actual tire to the finite element model. Using this improved finite element model, the deformations of the bias-ply motorcycle tire subject to inflation pressure are analyzed.
MATHEMATICAL TECHNIQUES - Finite Element Method; MOTOR CYCLES; PRESSURE EFFECTS - Analysis
Analytical mechanics of space systems
AIAA Education Series
11,34,37,112,113
2003
10.2514/4.861550
This book provides a comprehensive treatment of dynamics of space systems, starting with the fundamentals and covering topics from basic kinematics and dynamics to more advanced celestial mechanics. All material is presented in a consistent manner, and the reader is guided through the various derivations and proofs in a tutorial way. "Cookbook" formulas are avoided; instead, the reader is led to understand the principles underlying the equations at issue, and shown how to apply them to various dynamical systems. The book is divided into two parts. Part I covers analytical treatment of topics such as basic dynamic principles up to advanced energy concepts. Special attention is paid to the use of rotating reference frames that often occur in aerospace systems. Part II covers basic celestial mechanics, treating the two-body problem, restricted three-body problem, gravity field modeling, perturbation methods, spacecraft formation flying, and orbit transfers. MATLAB, Mat
Fatigue behavior of cross-ply glass-fiber composites based on epoxy resins of different toughnesses
Composites Science and Technology
61
1
157-163
2001
10.1016/S0266-3538(00)00205-0
The effect of matrix toughness on the fatigue behavior of cross-ply reinforced composites is discussed in this paper. Brittle and impact-modified epoxy resins containing commercial E-glass fibers with a good fiber matrix adhesion have been used. The fatigue behavior has been investigated by means of load-controlled tension-tension fatigue tests (R=0.1) and a frequency of 10 Hz with different applied max. loads between 150 and 330 MPa. The damage, as measured by stiffness reduction, was more significant for the composites with a brittle matrix. The energy loss was shown to be a sensitive tool for characterizing the nature of matrix toughness and is higher for impact-modified resins for a given strain amplitude. A non-linearity of the S/N curve was found for the impact-modified composites, while that for the brittle ones is linear on a semi log-scale. Furthermore, the brittle composites show an extensive region of final damage propagation, whereas the impact modified composites fail more in a sudden death manner.
a; b; c; damage mechanism; fatigue; polymer matrix composites; strain curves; stress; toughness
A finite element analysis of angle-ply laminate end-notched flexure specimens
Composite Structures
73
3
370-379
2006
10.1016/j.compstruct.2005.02.010
This paper deals with two and three-dimensional finite-element analysis of unidirectional and angle-ply laminate end-notched flexure specimens. Such laminates are for instance commonly used for deep sea applications and offer considerable advantage over their metal counterparts. Much work has recently been devoted to the failure mechanisms of composites. The area of delamination growth of composite laminates and shells is also a key issue for the structural performance and certification of underwate composite shells. In this study a geometric non-linear, two and three-dimensional finite element analysis of the end-notched flexure specimen, is performed to evaluate compliance and Mode-II strain energy release rate GII. Comparisons are made with experimental results and beam and plate theory solutions. ?? 2005 Elsevier Ltd. All rights reserved.
Composite material; Contact elements; Delamination; End-notched flexure specimen; Experiment; Fibre reinforced polymers; Finite element method
Static analysis of cross-ply laminated plates with integrated surface piezoelectric layers using differential quadrature
Composite Structures
88
3
342-353
2009
10.1016/j.compstruct.2008.04.018
The three-dimensional solution for static analysis of cross-ply rectangular plate imbedded in piezoelectric layers is presented using differential quadrature method (DQM) and Fourier series approach. The plate is assumed to be simply-supported at one pair of opposite edges and arbitrary conditions at the other pair. Applying the DQM to the governing differential equations and to the boundary conditions along the longitudinal or latitudinal directions, new state equations about state variables at discrete points are derived. The stress, displacement and electric potential distributions are obtained by solving these state equations. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers on the mechanical behavior of plate is studied. The method is validated by comparing numerical results for the plate without piezoelectric layers and simply-supported edges with that available in the literature. ?? 2008 Elsevier Ltd. All rights reserved.
Differential quadrature; Elasticity; Laminated plate; Piezoelectric; Static analysis
On the buckling behavior of cross-ply laminated composite plates due to circular/elliptical cutouts
Composite Structures
75
1-4
3-6
2006
10.1016/j.compstruct.2006.04.071
Cutouts are often found in composite structures. These are provided in structural components for ventilation and sometime to lighten the structure. In aircraft components (such as wing, spar, fuselage and ribs) cutouts are necessary for access, inspection, electric lines and fuel lines or to reduce the overall weight of the aircraft. This paper addresses the effects of a cutout on the buckling behavior of rectangular plates made of polymer matrix composites (PMC). The study is concentrated on the behavior of rectangular symmetric cross-ply laminates. The loaded while in order to study the effect of boundary condition, the unloaded edges are modeled in clamped and simply supported boundary condition. Finite element analysis is also performed to predict the effects of cutout on the buckling behavior of these plates. Several key findings and behavioral characteristics are discussed. These findings include the effects of cutout size, shape, plate aspect ratio and boundary conditions. Some overall important findings of these studies are that plates that have a cutout can buckle at loads higher than the buckling loads for corresponding plates without a cutout.
Buckling; Composite plate; Cutout; Finite element
The natural vibration of a symmetric cross-ply laminated composite conical-plate shell
Composite Structures
80
2
265-278
2007
10.1016/j.compstruct.2006.05.014
The feasibility of using the transfer matrix method to analyze a composite laminated conical-plate shell is explored theoretically. With the vibration theory and the transfer matrix method combined, the dynamic characteristics of a symmetric cross-ply laminated conical shell with an annular plate at the top end are investigated in detail. The governing equations of vibration for this system are expressed by the matrix differential equations, and the coefficient matrixes and joining matrix are derived. After the relationship between the transfer matrix and the coefficient matrix is established, the fourth order Runge–Kutta method is used numerically to solve the matrix equation. Once the transfer matrix of single component has been obtained, the product of each component matrix and the joining matrix can compose the matrix of entire structure. The frequency equations, mode shape and force vector are formulated in terms of the elements of the structural matrices. The 3D finite element numerical simulation has validated the present formulas of natural frequencies and mode shapes. The conclusions illustrate that this investigation will provide an important foundation for the advanced development of the laminated composite combination shells.
Composite laminated conical shells; Mode shape; Natural frequency; Numerical simulation
Planform effects upon the bistable response of cross-ply composite shells
Composites Part A: Applied Science and Manufacturing
42
7
825-833
2011
10.1016/j.compositesa.2011.03.012
This research aims at investigating the bistable characteristics of unsymmetric cross-ply laminates resulting from thermally induced stresses while curing. The bistable characteristics are examined with a focus on the change in geometry for a subset of configurations, namely, rectangular, trapezoidal and triangular. To this end, these geometries are systematically investigated leading to a set of non-dimensional parameters establishing the values required for bistable behavior. A new apparatus is designed to measure the magnitude of the force required for snap-through and snap-back. The influence of friction at the supports of the tested panels is minimized by utilizing air cushion for frictionless motion. Predictions from a nonlinear finite element based methodology using the ABAQUS??? code are validated through comparisons with test data. ?? 2011 Elsevier Ltd. All rights reserved.
B. Buckling; C. Finite element analysis (FEA); D. Mechanical Testing
Nonlinear thermoelastic stability characteristics of cross-ply laminated oval cylindrical/conical shells
Finite Elements in Analysis and Design
42
12
1061-1070
2006
10.1016/j.finel.2006.03.009
In this work, the thermoelastic stability characteristics of the cross-ply laminated oval cylindrical/conical shells subjected to uniform temperature rise are studied through nonlinear static analysis employing the finite element approach. Geometric nonlinearity is introduced in the formulation considering moderately large deformation effects. The study is carried out to highlight the influences of the noncircularity parameter, number of layers, material properties and semi-cone angle on the nonlinear thermoelastic response/stability characteristics of the laminated oval cylindrical/conical shells. It is brought out from the detailed studies that the circular shells exhibit distinct bifurcation point but the noncircular shells reveal smooth transition from the prebuckling to the postbuckling equilibrium path. The moderately noncircular shell response is found to be sensitive to the type of initial perturbation and the semi-cone angle whereas the highly noncircular shells are insensitive to the presence of small perturbation. It is also brought out that the linear eigenvalue buckling analysis approach may not be appropriate for the estimation of the critical temperature parameter of the highly noncircular shells.
Defect structures at thin film-substrate interfaces
Journal of the Mechanics and Physics of Solids
45
5
637-665
1997
10.1016/S0022-5096(96)00112-3
We consider the loss of lattice coherence at a planar interface between a thin film and substrate. Coherence is determined locally at the interface by a relative deformation gradient at the interface. We construct an interfacial free energy density fxs such that a fully coherent interface is a global minimizer fxs, and there are symmetry related local minima of fxs corresponding to line defects at the interface. By considering both the interfacial energy and the elastic energy of the film, we calculate equilibrium states as a function of film thickness to predict both the loss of coherence and the geometric pattern of interfacial defects.
a; b; c; interfaces; layered materials; phase transformations; variational calculus
A method for the estimation of the film thickness and plate tilt angle in thin film misaligned plate–plate rheometry
Journal of Non-Newtonian Fluid Mechanics
165
19-20
1419-1421
2010
10.1016/j.jnnfm.2010.07.004
This communication describes a general procedure for the estimation of the true gap and tilt angle in commercially available torsional flow plate–plate rheometers by simply measuring the torque and normal force acting on the plates when shearing a Newtonian fluid.
The ultrastructure and mechanics of elastic ligaments.
Advances in experimental medicine and biology
79
97-103
1977
10.1016/S0022-5320(77)90016-8
The major central part of elastic ligaments is constituted by longitudinally orientated elastic fibres, each surrounded by a sheath of spirally orientated collagen fibrils with an intervening thin layer of microfibrils. In the terminal region of such ligaments the orientation of the collagen fibrils is longitudinal and the elastic fibres end within the ligament without any attachment to bone. The ligament response to a first, unphysiologically high load produces a continuous stress-strain curve. On the other hand the curve becomes biphasic after repeated application of such loads. It is suggested that three factors are involved in this mechanical response, namely, frictional forces between elastic fibres and their sheaths, compressive forces exerted upon elastic fibres by their sheaths, and intre-sheath friction due to rearrangement of the constituent collagen fibrils.
An improved third order theory and assessment of efficient zigzag theory for angle-ply flat hybrid panels
Composite Structures
83
2
226-236
2008
10.1016/j.compstruct.2007.04.018
A new improved third order theory (ITOT) is presented for hybrid piezoelectric angle-ply flat panels under thermal loading. The transverse deflection is approximated nonuniformly to explicitly account for the transverse strain due to temperature and electric potential which are approximated as piecewise linear. The governing equations are derived using Hamilton’s principle. The ITOT and an existing efficient zigzag theory are assessed for simply-supported angle-ply flat hybrid panels for static loads and for natural frequencies by comparison with 2D solutions. The comparisons for test, composite and sandwich panels establish that for most cases the zigzag theory is very accurate and ITOT is an improvement over the third order theory (TOT) based on uniform approximation of deflection across the thickness.
A. Panels; B. Piezoelasticity; C. Zigzag theory; D. Third order theory
Wind Uplift Behavior of Mechanically Attached Single-Ply Roofing Systems: The Need for Correction Factors in Standardized Tests
Journal of Structural Engineering
134
3
489-498
2008
10.1061/(ASCE)0733-9445(2008)134:3(489)
In the United States, currently there are three consensus test methods for determining the wind uplift capacity of mechanically- attached single-ply roofing membrane systems. Each is based upon a specific specimen size and static loading regime. However, few studies have examined the relationship, if any, of failure loads among these methods. This study was conducted to determine the effects of varying specimen sizes on the static wind uplift performance or failure loads of mechanically-attached single-ply roofing membranes. Full-scale wind uplift pressure tests were performed in three phases, using six specimen sizes, and three membrane materials. The results were used to determine the minimum acceptable specimen sizes to be used for testing. In Phase 1, fastener failure loads were monitored, while in Phases 2 and 3, the failure experiments were repeated without measuring fastener loads. A significant difference in the apparent failure loads occurs among different specimen sizes for the same membrane materials. The results suggest that correction factors are necessary for comparing tests on different test beds and that the performance of membranes in the test chamber may not produce the same results on full scale structures
Distribution of dislocation source length and the size dependent yield strength in freestanding thin films
Journal of the Mechanics and Physics of Solids
58
5
678–695
2010
10.1016/j.jmps.2010.02.011
A method is proposed to estimate the size-dependent yield strength of columnar-grained freestanding thin films. The estimate relies on assuming a distribution of the size of Frank–Read sources, which is then translated into a log-normal distribution of the source strength, depending on film thickness, grain size and theoretical strength of the material, augmented with a single fit parameter. Two-dimensional discrete dislocation plasticity (DDP) simulations are carried out for two sets of Cu films and the fit parameter is determined from independent experiments. Subsequent {DDP} predictions of the stress–strain curves in comparison with the corresponding experimental data show excellent agreement of initial yield strength and hardening rate for films of varying film thickness and grain size. Having thus demonstrated the power of the proposed strength distribution, it is shown that the mode of this distribution governs the most effective source strength. This is then used to suggest a method to estimate the yield strength of thin films as a function of film thickness and grain size. Simple maps are presented that are in very good agreement with recent experimental results for Cu thin films.
Discrete dislocation plasticity (DDP); Frank–Read source; Plastic deformation; Size effects; Thin films
Modeling of wrinkling of thin circular sheets
International Journal of Non-Linear Mechanics
47
1
85-91
2012
10.1016/j.ijnonlinmec.2011.09.020
A version of the imperfection method is used to investigate the wrinkling (tension buckling) of thin, elastic, homogeneous, isotropic circular plates of uniform thickness undergoing small deflections without inplane twisting. A numerical procedure based on the finite difference approach is employed to quantitatively predict wrinkling loads and wrinkling patterns for three sets of support conditions. Representative numerical results are presented in tabular and graphical formats and used to illustrate interesting aspects of the predictions. ?? 2011 Elsevier Ltd. All rights reserved.
Circular sheets; Elastic stability; Plates; Tension buckling; Wrinkling
Contact mechanics of layered elastic materials: experiment and theory
Journal of Physics D: Applied Physics
40
19
5984-5994
2007
10.1088/0022-3727/40/19/031
This paper reports an experimental and theoretical investigation of the indentation of a layered elastic solid, with special reference to the surface force apparatus (SFA). The contacting surfaces of the SFA comprise a 3-layer material: a thin mica surface layer on a thicker epoxy layer supported by a thick silica substrate. An existing finite element analysis of the deformation of ideal mica/epoxy/silica surfaces used in the SFA is adapted to compare with the experimental measurements of the variation of contact size with load, both with and without adhesion at the interface. This is in marked difference to the Johnson, Kendall and Roberts (JKR) theory for homogeneous solids. Experiments and finite element calculations were also carried out on the elastic indentation of a thin (5.5 µm) layer of mica on a very thick layer of epoxy (>100 µm). As input data for the calculations, the elastic moduli of the mica and epoxy were measured in separate indentation experiments. The stiffness of a layered solid can be expressed by an 'effective modulus' , which has been deduced from the experimental measurements and compared with the theoretical values with fair success. The work of adhesion is commonly measured in the SFA by observing the 'pull-off force' to separate the surfaces. The theory shows that, for a layered solid, the pull-force can vary significantly from the JKR value for a homogeneous solid. In particular, it was found that the mica surface energy, γsv, measured by SFA experiments using crossed cylinders of mean radius R, where the materials are layered and the mica/mica adhesion is high, can vary with the pull-off force Fp according to Fp/4πR < γsv < Fp/2πR, and for this particular experiment was given as γsv = Fp/3.5 πR as compared with γsv = Fp/3πR for homogeneous materials.
Influences of roll-to-roll process and polymer substrate anisotropies on the tensile failure of thin oxide films
Thin Solid Films
518
23
6984-6992
2010
10.1016/j.tsf.2010.07.033
The influence of internal stress anisotropy resulting from anisotropic loading in a roll-to-roll (R2R) process, and polymer substrate anisotropy on the crack onset strain (COS) of thin oxide coatings was analyzed. Experimental data obtained for R2R processed films were compared with data obtained using an isotropic sheet-to-sheet (S2S) process with the same anisotropic substrate. In the R2R case the COS was found to increase by 20% between the transverse direction and the machine direction. In the S2S case the COS was found to be independent of orientation, except at a 45° in-plane orientation with respect to the machine direction, where it was 15% higher. The internal stress in the machine direction could not be determined, presumably due to deposition-induced curvature changes of the polymer substrate, and was therefore fitted to the COS data. Fracture mechanics analysis and finite element modeling of the experimental data showed that the influence of substrate anisotropy was marginal, and that it was the process-induced internal strain in the coating which controlled the COS. © 2010 Elsevier B.V.
Anisotropy; Failure; Internal stresses; Polymer substrates; Roll-to-roll processing
Impact dynamics of drops on thin films of viscoelastic wormlike micelle solutions
Journal of Non-Newtonian Fluid Mechanics
125
11-23
2005
10.1016/j.jnnfm.2004.08.012
The impact dynamics of water drops on thin films of viscoelastic wormlike micelle solutions is experimentally studied using a high-speed digital video camera at frame rates up to 4000 frame/s. The composition and thickness of the thin film is modified to investigate the effect of fluid rheology on the evolution of crown growth, the formation of satellite droplets and the formation of theWorthington jet. The experiments are performed using a series of wormlike micelle solutions composed of a surfactant, cetyltrimethylammonium bromide (CTAB), and a salt, sodium salicylate (NaSal), in deionized water. The linear viscoelastic shear rheology of the wormlike micelle solutions is well described by a Maxwell model with a single relaxation time while the steady shear rheology is found to shear thin quite heavily. In transient homogeneous uniaxial extension, the wormlike micelle solutions demonstrate significant strain hardening. The size and velocity of the impacting drop is varied to study the relative importance of Weber, Ohnesorge, and Deborah numbers on the impact dynamics. The addition of elasticity to the thin film fluid is found to suppress the crown growth and the formation of satellite drops with the largest effects observed at small film thicknesses. A new form of the splashing threshold is postulated which accounts for the effects of viscoelasticity and collapses the satellite droplet data onto a single master curve dependent only on dimensionless film thickness and the underlying surface roughness. Additionally, a plateau is observed in the growth of the maximum height of the Worthington jet height with increasing impact velocity. It is postulated that the complex behavior of the Worthington jet growth is the result of a dissipative mechanism stemming from the scission of wormlike micelles.
drop impact; satellite drop; surfactant solutions; viscoelastic; wormlike micelle solutions; worthington jet
Mechanisms of shear deformation in fiber-reinforced polymers: Experiments and simulations
International Journal of Fracture
158
2
197-209
2009
10.1007/s10704-009-9353-4
The mechanisms of in-plane shear deformation in a cross-ply glass fiber-epoxy laminate were studied through a combination of experiments and simulations. Shear deformation parallel and perpendicular to the fibers led to very different deformation and fracture patterns. Deformation was localized in a matrix shear band parallel to the fibers in the former, while fiber rotation and widespread plastic deformation in the matrix were dominant in the latter. The differences in the mechanical response between both orientations increased with the applied strain and it was shown that the cross-ply laminate response was given by the averaged contribution of both. The relevance of this behavior for the development of continuum damage mechanics models is noted.
Computational micromechanics; Fiber-reinforced polymers; Shear fracture
Introduction to Field Operators in Quantum Mechanics
American Journal of Physics
41
5
678
1973
10.1119/1.1987330
The equivalence of the field operator formulation of quantum mechanics and ordinary wave mechanics is proved in an efficient and elementary way. The discussion proceeds algebraically from the (anti-) commutation relations, which the field operators are defined to satisfy. Although the paper is introductory and presumes only a knowledge of elementary wave mechanics, it is intended to cover all of the essential elements of the subject in a rigorous way.
Three-dimensional crack front fields in a thin ductile plate
Journal of the Mechanics and Physics of Solids
38
6
787-812
1990
10.1016/0022-5096(90)90040-B
BASED on detailed finite element solutions, various aspects of the 3-D fields near a crack front in a thin ductile plate are analysed. In particular, the stress field in the immediate crack front vicinity is carefully investigated. The existence and size of local J-dominated fields are determined from a comparison of the complete near tip stress field with the plane strain HRR solutions using a dominance parameter. In conjunction with an estimated size of the finite deformation zone, the loss of HRR-dominance along the crack front is also studied. Physically, the loss of HRR-dominance at higher load occurs when the finite deformation region outgrows the (local) plane strain region, the size of which is essentially limited by the geometry of a thin plate. Alternatively. the existence (at the mid-plane) of plane strain HRR-dominance in a low hardening material under (in-plane) small scale yielding requires the thickness of a thin plate to exceed *0.5(K,/ug)‘, thus limiting the maximum in-plane extent of the plastic zone to a fraction of plate thickness. Furthermore, such a restriction on the plastic zone size precludes the coexistence of 1OCd plane strain and surrounding plane stress HRR-fields within a thin plate.
A new membrane model for the ballistic impact response and V50 performance of multi-ply fibrous systems
International Journal of Solids and Structures
40
24
6723-6765
2003
10.1016/S0020-7683(03)00329-9
This paper develops an analytical model for the ballistic impact response of fibrous materials of interest in body armor applications. It focuses on an un-tensioned 2D membrane impacted transversely by a blunt-nosed projectile, a problem that has remained unsolved for a half a century. Membrane properties are assumed characteristic of the best current body armor materials (Kevlar®, Spectra®, Zylon®, S2 glass), which have very high stiffness and strength per unit weight, and low strain-to-failure. Successful comparisons will be made with extensive experimental data on such material systems as reported by Cunniff [Decoupled response of textile body armor. Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999a, pp. 814–821; Vs–Vr relationships in textile system impact. Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999b; Dimensional parameters for optimization of textile-based body armor systems, Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999c, pp. 1303–1310]. Our mathematical formulation draws on the seminal work of Rakhmatulin and Dem’yanov [Strength Under High Transient Loads, 1961, pp. 94–152]. Under constant projectile velocity we first develop self-similar solution forms for the tensile ‘implosion’ wave and the curved cone wave that develops in its wake. Through matching boundary conditions at the cone wave front, we obtain an accurate approximate solution for the membrane response including cone wave speed and strain distribution. We then consider projectile deceleration due to membrane reactive forces, and obtain results on cone velocity, displacement and strain concentration versus time. Other results obtained are the membrane ballistic limit, or V50 velocity, and the residual velocity when penetrated above this limit. We then derive an exact functional representation of a V50 ‘master curve’ found empirically by Cunniff [ibid] to reduce data for a wide variety of fabric systems impacted by blunt cylindrical projectiles. This curve is given in terms two dimensionless parameters based only on fiber mechanical properties and the ratio of the fabric areal density to the projectile mass divided by its area of fabric contact. Our functional representation has no fitting parameters beyond one reflecting uncertainty in the effective diameter of the impact zone relative to the projectile diameter, and even then the values are consistent across several experimental systems. The extremely successful comparison of our analytical model to experimental results in the literature raises fundamental questions about many long-held views on fabric system impact behavior and parameters thought to be important.
Body armor; Fabric ballistic impact; V50 performance
Molecular mechanics parameters
Journal of Molecular Structure: THEOCHEM
312
1
69-83
1994
doi: 10.1016/s0166-1280(09)80008-0
A general scheme for choosing unknown parameters for use in the MM2 and MM3 force fields is discussed, and implemented in the form of a computer program.
dispersion; forcefields; rulebased
and Mechanics of Octopus Suckers
North
126-136
1990
10.2307/1541971
Page 1. Reference: Bid. Bull. 178: 126- 136. (April, 1990) WILLIAM M. KIER AND ANDREW M. SMITH*
Twin-rainbow metrology. I. Measurement of the thickness of a thin liquid film draining under gravity.
Applied optics
42
33
6584-6594
2003
10.1364/AO.42.006584
We describe twin-rainbow metrology, a new optical technique used to measure the thickness of thin films in a cylindrical geometry. We also present an application of the technique: measurement of the thickness of a Newtonian fluid draining under gravity. We compare these measurements with fluid mechanics models.
Mechanics of epidermal electronics
Journal of Applied Mechanics
79
3
31022
2012
10.1115/1.4005963
Epidermal electronic system (EES) is a class of integrated electronic systems that are ultrathin, soft, and lightweight, such that it could be mounted to the epidermis based on van der Waals interactions alone, yet provides robust, intimate contact to the skin. Recent advances on this technology will enable many medical applications such as to monitor brain or heart activities, to monitor premature babies, to enhance the control of prosthetics, or to realize human-machine interface. In particular, the contact between EES and the skin is key to high-performance functioning of the above applications and is studied in this paper. The mechanics concepts that lead to successful designs of EES are also discussed. The results, validated by finite element analysis and experimental observations, provide simple, analytical guidelines for design and optimization of EES with various possible functionalities. [DOI: 10.1115/1.4005963]
A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods
Journal of the Mechanics and Physics of Solids
48
6-7
1519–1540
2000
10.1016/S0022-5096(99)00091-5
We propose a scheme for the direct passage from atomic level to continuum level. The scheme is applicable to geometries, like films, rods and tubes, in which one or more dimensions are large relative to atomic scale but other dimensions may be of atomic scale. The atomic theory is assumed to be governed by a variational principle resting on the Born-Oppenheimer approximation. The atomic level energy is further assumed to satisfy certain decay properties when evaluated for disjoint sets of atoms. The scheme is based on two hypotheses: (1) distortions are limited, and (2) there are many atoms in certain directions. The scheme produces in a natural way the variables of the continuum theory. In the case of a film, the continuum theory that emerges is a Cosserat membrane theory with (v - 1) Cosserat vectors, v being the number of atomic layers in the film. The arguments presented are not mathematically rigorous. One difficulty is that it is not clear under which circumstances our decay hypothesis on interatomic interactions is consistent with quantum mechanics or density functional theory. (C) 2000 Elsevier Science Ltd. All rights reserved.
Emergent mechanics of biological structures
Mol Biol Cell
25
22
3461-3465
2014
10.1091/mbc.E14-03-0784
Mechanical force organizes life at all scales, from molecules to cells and tissues. Although we have made remarkable progress unraveling the mechanics of life's individual building blocks, our understanding of how they give rise to the mechanics of larger-scale biological structures is still poor. Unlike the engineered macroscopic structures that we commonly build, biological structures are dynamic and self-organize: they sculpt themselves and change their own architecture, and they have structural building blocks that generate force and constantly come on and off. A description of such structures defies current traditional mechanical frameworks. It requires approaches that account for active force-generating parts and for the formation of spatial and temporal patterns utilizing a diverse array of building blocks. In this Perspective, we term this framework "emergent mechanics." Through examples at molecular, cellular, and tissue scales, we highlight challenges and opportunities in quantitatively understanding the emergent mechanics of biological structures and the need for new conceptual frameworks and experimental tools on the way ahead.
An enhanced strain 3D element for large deformation elastoplastic thin-shell applications
Computational Mechanics
34
1
38-52
2004
10.1007/s00466-004-0551-7
In this work a previously proposed solid-shell finite element, entirely based on the Enhanced Assumed Strain (EAS) formulation, is extended in order to account for large deformation elastoplastic thin-shell problems. An optimal number of 12 enhanced (internal) variables is employed, leading to a computationally efficient perfor- mance when compared to other 3D or solid-shell enhanced elements. This low number of enhanced variables is suf- ficient to (directly) eliminate either volumetric and transverse shear lockings, the first one arising, for in- stance, in the fully plastic range, whilst the last appears for small thickness’ values. The enhanced formulation com- prises an additive split of the Green-Lagrange material strain tensor, turning the inclusion of nonlinear kine- matics a straightforward task. Finally, some shell-type numerical benchmarks are carried out with the present formulation, and good results are obtained, compared to well-established formulations in the literature.
characteristic of; enhanced strains; geometric and; lockings; material nonlinearities; shear locking effects; solid-shell elements; the first one is; thin shells; volumetric and transverse shear
Investigations of enzyme-catalysed reactions with combined quantum mechanics/molecular mechanics (QM/MM) methods
International Reviews in Physical Chemistry
29
1
65-133
2010
10.1080/01442350903495417
Combined quantum mechanics/molecular mechanics (QM/MM or QM-MM) methods are an excellent approach for modelling the mechanisms of enzyme-catalysed reactions. QM/MM methods allow detailed modelling of reactions in enzymes by coupling quantum chemical calculations on the active site with a simpler, empirical 'molecular mechanics' treatment of the rest of the protein. Possible reaction mechanisms can be compared and catalytic interactions analysed. QM/MM calculations can now be carried out for enzyme-catalysed reactions with quantum chemical methods of potentially very high accuracy. More approximate QM methods can allow extensive molecular simulations (e.g. molecular dynamics or Monte Carlo simulations). In this review, QM/MM techniques are outlined and some recent applications to enzyme-catalysed reactions are discussed.
ab-initio qm/mm; acid amide hydrolase; chorismate mutase; computational enzymology; cytochrome P450 compound I; density-functional theory; HIV; -lactamases; liver alcohol-dehydrogenase; lysozyme; molecular-mechanics; p-hydroxybenzoate hydroxylase; polarizable; potential-energy surface; quantum tunnelling; reaction; transform infrared-spectroscopy; transition-state stabilization
Mechanics. Vol. 1
Course of Theoretical Physics Ser Vol 1
1976
10.1016/j.jcis.2010.07.069
Annotation Devoted to the foundation of mechanics, namely classical Newtonian mechanics, the subject is based mainly on Galileo's principle of relativity and Hamilton's principle of least action. The exposition is simple and leads to the most complete direct means of solving problems in mechanics.The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.
Biofluid Mechanics: The Human Circulation (second edition)
Cardiovascular Engineering and Technology
3
4
351-352
2012
10.1007/s13239-012-0106-6
Designed for senior undergraduate or first-year graduate students in biomedical engineering, Biofluid Mechanics: The Human Circulation, Second Edition teaches students how fluid mechanics is applied to the study of the human circulatory system. Reflecting changes in the field since the publication of its predecessor, this second edition has been extensively revised and updated. New to the Second Edition Improved figures and additional examples More problems at the end of each chapter A chapter on the computational fluid dynamic analysis of the human circulation, which reflects the rapidly increasing use of computational simulations in research and clinical arenas Drawing on each author’s experience teaching courses on cardiovascular fluid mechanics, the book begins with introductory material on fluid and solid mechanics as well as a review of cardiovascular physiology pertinent to the topics covered in subsequent chapters. The authors then discuss fluid mechanics in the human circulation, primarily applied to blood flow at the arterial level. They also cover vascular implants and measurements in the cardiovascular system.
Material forces in micromorphic fracture mechanics
Journal of the Chinese Institute of Engineers
27
6
889-896
2004
The physical foundation, the balance laws and the constitutive relations of microcontinuum field theories are briefly reviewed. The concept of material forces, which may also be referred as Eshelbian mechanics, is extended to micromorphic theory. The balance law of pseudo-momentum is formulated. The detailed expressions of Eshelby stress tensor, pseudo-momentum, and material forces are derived. It is found that, for micromorphic thermoelastic solid, the material forces are due to (1) body force and body moment, (2) temperature gradient, and (3) the material inhomogeneities in density, microinertia, and elastic coefficients. It is shown that, at the crack front, material forces are reduced to generalized vectorial J-integral. The calculation of material forces, due to the presence of inhomogeneities or cracks, by finite element analysis and meshless analysis is discussed. Finite element analysis is performed for a multiphase material which is composed of randomly distributed and oriented grains and in between the grain boundaries in its amorphous phase. Each grain is modeled as a single crystal by specialized micromorphic theory. The grain boundaries are modeled with a thin and finite width by classical continuum mechanics. Numerical results, including Cauchy stresses, Eshelby stresses, and material forces, for a thin film of silicon subjected to thermal and/or mechanical loadings are obtained and discussed.
connecting molecular-dynamics; eshelbian mechanics; finite element; generalized vectorial j-integral; material forces; material inhomogenity; micromorphic theory; multiphase material; polycrystal
Electrohydrodynamic instability of a thin film of viscoelastic polymer underneath a lithographically manufactured mask
Journal of Non-Newtonian Fluid Mechanics
125
2-3
91-99
2005
10.1016/j.jnnfm.2004.09.008
The electrohydrodynamic instability of a thin film of initially static viscoelastic polymer under a mask is studied via a linear analysis. The conducting polymer film is separated from the mask by air. Under a normal electrical field, the initially flat polymer film self-assembles into well organized micro scale patterns. The driving force for the instability is an electrostatic force exerted on the free charges accumulated at the air–polymer interface. The electrical field is either applied externally or generated internally by the contact potentials at the interfaces of different materials. The system is unconditionally unstable. The elasticity of the polymer is found to destabilize the system. When the Deborah number is large enough, a resonant phenomenon appears as a result of the interaction between the two destabilizing mechanisms (the electrostatic force and the polymer elasticity). The resonance introduces two most unstable wave numbers, at which the growth rate of the disturbance is unbounded. The two most unstable wave numbers bifurcate at a minimum Deborah number, below which no resonance is found. The effects of the initial film thickness, the air gap thickness and the electrical properties of the conducting polymer on the instability are also investigated.
bifurcation; electrohydrodynamic instability; leaky dielectric model; non-newtonian; resonance; thin film; viscoelastic instability
A shear deformable plate element with an exact thin limit
Computer Methods in Applied Mechanics and Engineering
118
3-4
393-412
1994
10.1016/0045-7825(94)90009-4
We present a quadrilateral finite element developed within the framework of a shear deformable plate theory. The interpolation for the rotation takes advantage of internal rotational degrees of freedom (through the use of bubble functions), while the interpolation for the transverse displacement is linked to the nodal rotations. A careful study of the element behavior is performed using an extensive set of mixed patch tests; results from several numerical examples are also presented. The element has proper rank and excellent interpolating capacity. Moreover, without using any ad-hoc assumption (e.g., energy balancing schemes) the element presents no locking effects at all; in fact, the shear energy may be set identically equal to zero without introducing any ill-conditioning in the problem, thus recovering a proper thin plate limit.
A model for the weakening effect of very thin hard coatings
Wear
308
1-2
10-16
2013
10.1016/j.wear.2013.09.019
It was observed in several studies involving coated spherical contact, that very thin hard coatings may have a weakening effect of reducing the resistance to yield inception compared to an uncoated case. A numerical approach is utilized in this paper to study the effect of various mechanical properties of the substrate and the coating on the range of thicknesses where this weakening effect is encountered. A coating thickness associated with a maximum weakening is found and a universal dimensionless solution for the range of the detrimental coating thicknesses as well as for the maximum weakening thickness is presented. Good qualitative agreement is found between the model and a few published experimental results. ?? 2013 Elsevier B.V.
Contact mechanics; Hard coatings; Onset of plasticity; Weakening effect
Determinism beneath Quantum Mechanics
arXiv:quant-ph
12
2002
Contrary to common belief, it is not difficult to construct deterministic models where stochastic behavior is correctly described by quantum mechanical amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What is difficult however is to obtain a Hamiltonian that is bounded from below, and whose ground state is a vacuum that exhibits complicated vacuum fluctuations, as in the real world. Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. This may lead to a sufficiently complex vacuum state, and to an apparent non-locality in the relation between the deterministic ("ontological") states and the quantum states, of the kind needed to explain away the Bell inequalities. Theories of this kind would not only be appealing from a philosophical point of view, but may also be essential for understanding causality at Planckian distance scales.
Fracture mechanics of diamond-like carbon (DLC) films coated on flexible polymer substrates
Surface and Coatings Technology
201
14
6423-6430
2007
10.1016/j.surfcoat.2006.12.008
Diamond-like carbon (DLC) films have been widely used for many industrial applications due to their outstanding physical properties such as high hardness, wear resistance and biological compatibility. The DLC films coated on polymer substrates have also been extensively used and investigated because recently, quite a few applications for the use of these polymer-DLC composites have been proposed and actively discussed. The applications range from DLC-coated Polyethylene Terephthalate film (DLC-PET), through DLC-coated Polycarbonate (DLC-PC) to other DLC-coated rubbers. In this work, thin DLC films coated on several polymer substrates possessing different chemical structures and Young's moduli were introduced. The DLC-polymer films were stretched to different strains and the extended surface was investigated by optical microscopy and scanning electron microscopy (SEM) to study the fracture mechanics of the DLC-coated polymer films. Horizontally and vertically aligned micro-cracks and micro-buckling were observed, constructing periodic lattice-like fracture patterns on the surface of the extended DLC-polymer films. It was found that the lattice patterns were significantly influenced by Young's moduli of polymer substrates and DLC films, and that the patterns were also dependent on the adhesion between the DLC films and the polymers. © 2006 Elsevier B.V. All rights reserved.
Carbon films; Fracture surface; Polymers
A simple higher-order theory for laminated composite plates
Journal of Applied Mechanics
51
4
745-752
1984
10.1115/1.3167719
A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.
Long-Term Moisture Absorption in Graphite/Epoxy Angle-Ply Laminates
Journal of Composite Materials
18
1
32-46
1984
10.1177/002199838401800103
Angle-ply laminates of graphite/epoxy Fiberite T300/1034, Ciba-Geigy T300/920 and Ciba-Geigy T300/914 were exposed to moist air of different relative humidities for 400 days. Laminates of T300/1034 reach a first plateau after about 100 days and a se cond plateau of saturation after about 400 days. The plateau levels are functions of the relative humidity and also of the residual stresses in the laminate. Compressive residual stresses retard the diffusion and lower the plateau levels. Laminates of T300/920 and T300/914 show more rapid moisture absorption than laminates of T300/1034 but no clearly detectable saturation plateau. The shoulder of the moisture content vs. square root of time curve is over-estimated by the one-dimensional solution of Fick's equation of moisture diffusion. A three-dimensional solution is given and is shown to predict the moisture absorption better for specimens of small width to thickness ratio.
About the creep-fatigue interaction on the fatigue behaviour of off-axis woven-ply thermoplastic laminates at temperatures higher than Tg
Composites Part B: Engineering
58
478-486
2014
10.1016/j.compositesb.2013.11.005
The influence of plasticity and viscous effects on the fatigue behaviour of off-axis C/PPS laminates was investigated at temperatures higher than glass transition temperature. The obtained results clearly show that creep and fatigue are mutually influencing phenomena. Compared to the reference fatigue behaviour (with no prior loading), the fatigue life can be significantly extended with prior creep depending on loading conditions. Indeed, the strain accumulation seems to slow down after a long time creep preload, as if the time-dependent mechanisms were "evacuated" during this preload. The same conclusion can be drawn for the damage accumulation when the prior creep stresses are higher than the damage threshold or when the hold time is long enough, inducing significant plastic deformations. In angle-ply laminates, such deformations are associated with the reorientation of fibres. They contribute to the reduction of stress intensities, which results in increasing both fatigue life and maximum strain Émax at failure during fatigue loadings. © 2013 Elsevier Ltd. All rights reserved.
A. Fabric/textiles; A. Thermoplastic resin; B. Creep; B. Fatigue
Quantum mechanics of black holes.
Science (New York, N.Y.)
337
6094
538-40
2012
10.1126/science.1221693
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Statistical mechanics of money
European Physical Journal B
17
4
723-729
2000
10.1007/s100510070114
Abstract: In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann- Gibbs law characterized by an effective temperature equal to the average amount of ... \n
Economics; Model
Thermal expansion of unidirectional and cross-ply fibrous monoliths
Composites Science and Technology
62
7-8
967-976
2002
An investigation of the thermal expansion behavior of ceramic fibrous monoliths (FMs) is presented. The emphasis is on the development and validation of material models applicable to Si3N4/BN FMs in both unidirectional and cross-ply architectures. Approximate analytical models are developed for the coefficient of thermal expansion (CTE) based on the analysis of representative unit cells of the Si3N4 fibers and the surrounding BN interphase. The pertinent cell shapes are identified from quantitative measurements on real Si3N4/BN FMs. Corresponding finite element analyses are performed on the same unit cells for the purpose of validating the analytical models. Good agreement is obtained between the model predictions and experimental measurements of CTE. A rudimentary modification to the analytical model to account for texturing and anisotropy of the BN appears to yield adequate results. (C) 2002 Elsevier Science Ltd. All rights reserved.
ceramic matrix composites; ceramics; elastic properties; fibrous monoliths; finite element analysis (FEA); thermal properties
Problems in (nano)medical mechanics
International Journal of Non-Linear Mechanics
56
3-19
2013
10.1016/j.ijnonlinmec.2013.03.008
Three major biomedical problems in non-linear mechanics are stated, and several sub-problems are derived from simplifications that correspond to substituting model nanotechnology-based systems for their biological counterpart. Strategies for the solutions to these problems are briefly proposed. The medical implications of the solutions to the general and simplified problems are discussed, and perspectives on the deep transformation in health care these solutions would engender are presented. © 2013 Elsevier Ltd. All rights reserved.
Biobarriers; Biomedical mechanics; Environments; Mass transport through nanoscale; Mass transport through nanoscale environments; Nano delivery systems; Nanotechnology; Tumor targeting
Coupled bending and torsional vibration of nonsymmetrical axially loaded thin-walled Bernoulli-Euler beams
Mechanics Research Communications
31
6
697-711
2004
10.1016/j.mechrescom.2004.04.005
The dynamic transfer matrix is formulated for a straight uniform and axially loaded thin-walled Bernoulli-Euler beam element whose elastic and inertia axes are not coincident by directly solving the governing differential equations of motion of the beam element. Bernoulli-Euler beam theory is used, and the cross section of the beam does not have any symmetrical axes. The bending vibrations in two perpendicular directions are coupled with torsional vibration and the effect of warping stiffness is included. The dynamic transfer matrix method is used for calculation of exact natural frequencies and mode shapes of the nonsymmetrical thin-walled beams. Numerical results are given for a specific example of thin-walled beam under a variety of end conditions, and exact numerical solutions are tabulated for natural frequencies and solutions calculated by the other method are also tabulated for comparison. The effects of axial force and warping stiffness are also discussed. ?? 2004 Elsevier Ltd. All rights reserved.
Axial force; Bernoulli-Euler beams; Coupled bending-torsional vibrations; Dynamic transfer matrix; Nonsymmetrical thin-walled beams
Effect of rolling parameters on cold rolling of thin strip during work roll edge contact
Journal of Materials Processing Technology
140
1-3 SPEC.
535-541
2003
10.1016/S0924-0136(03)00783-0
In some cold rolling mills, a problem has been found that the sides of work rolls touch and deform when thin strip is rolled. The problem of work roll contact at the edges, which forms a new deformation feature in rolling, is analysed. In this paper, the authors focus on the research of the effects of rolling parameters on specific force such as rolling force, intermediate force, edge contact force and the profile of thin strip in cold rolling when the work roll edges contact. An influence function method is developed to simulate this special rolling process. Based on numerical simulation, the effects of the rolling parameters on the mechanics and deformation of the cold rolled thin strip are obtained. Numerical simulation tests have verified the validity of this developed method. ?? 2003 Elsevier B.V. All rights reserved.
Cold rolling of thin strip; Influence function method; Profile; Specific force; Work roll edge contact
Effect of stringer torsional rigidity on buckling na dintegrally stiffened angle ply plates
Fibre Science and Technology
16
1
39-43
1982
10.1016/0015-0568(82)90014-8
Buckling of laminated angle ply plates under axial compression is extended to integrally stringer reinforced laminated plates. Appropriate jump conditions are presented and it is found that stringer torsional rigidity plays a much more important role in raising the buckling load for plates with a large fibre angle than in those with a small fibre angle.
Simulation of progressive damage formation and failure during the loading of cross-ply composites
Composites
50
2001
The objective of this report is to summarise the current status of theoretical models and associated software that are designed to predict damage initiation and growth in cross-ply laminates to the point of failure. For the case of static loading to failure, the damage modes that are modelled are ply cracking in the 90o plies of the laminate, fibre failure in the 0o plies (using Monte Carlo methods), and fibre/matrix debonding associated with fibre fractures. Biaxial loading of the laminate is permitted, and account is taken of the effect of thermal residual stresses at both the fibre/matrix and ply levels. The computer application for the prediction of failure during static loading is known as STRENGTH. For the case of the environmental degradation of cross-ply laminates arising from exposure to aggressive environments, the principal damage mode is fibre failure arising from the operation of stress-corrosion mechanisms at the fibre defects. Ply cracking is not included in this model. A computer application known as RESIDUAL has been developed that predicts the lifetime, and time dependence of residual strength, for a cross-ply laminate subject to biaxial loading and thermal residual stresses in an aggressive environment. Descriptions are given of the physical basis of the models, and the associated assumptions. In addition a description is given of how to operate the software, and sample numerical outputs are given. These results can be used to confirm that the software has been installed correctly, and act as a record of software performance (for quality assurance purposes) for the current versions of the applications STRENGTH and RESIDUAL. High quality model validation data (obtained in collaboration with others) are presented that relate to model performance at the fibre/matrix level, and ply cracking level. The validation of the application software is an on-going activity that has not reached a state of maturity. This is particularly true for strength and environmental degradation predictions, which are very complex phenomena that are very difficult to model reliably. The current versions of the applications are regarded as the first useful steps.
Multipolar continuum mechanics
Archive for Rational Mechanics and Analysis
17
2
113-147
1964
10.1007/BF00253051
A general theory of multipolar displacement and velocity fields with corresponding multipolar body and surface forces and multipolar stresses is developed using an energy principle, an entropy production inequality and invariance conditions under superposed rigid body motions. Constitutive equations for the multipolar stresses are discussed and explicit results are given for an elastic medium. Work in a previous paper by the present authors (1964) is shown to be a special case of that given here. © 1964 Springer-Verlag.
Mechanics of upward propagation of cover-collapse sinkholes
Engineering Geology
52
23-33
1999
10.1016/S0013-7952(98)00051-9
Cover collapse sinkholes occur by failure of the walls of a soil void above cavernous bedrock. I examine conditions for failure in compression by crack propagation and coalescence, and for failure by sloughing in which pore water pressure produces a net tension perpendicular to the wall of the void. Compressive failure without relaxation of stress does not explain observed long-term stability of thick soils, nor failures in thin residual soils. If stress relaxation occurs with compressive failure, soil voids tend to stabilize and sinkholes are not predicted. Sloughing failure is not predicted for steady state pore pressure fields, even for a perched water table at the surface over a drained void. Transient pore pressure conditions that could produce sloughing may result from: (1) rapid drawdown causing soil consolidation and transient high pore pressure gradients; (2) approach of a wetting front in unsaturated soil, with high permeability behind the front; (3) dissolution of air from bubbles in the soil and exsolution near the void producing a low permeability zone near the void.
Finite element; Karst; Pore pressure; Sinkholes
Mechanics of Granular Materials: An Introduction
Fundamentals for Mechanics of Granular material
400
1999
This textbook compiles reports written by about 35 internationally recognized authorities, and covers a range of interests for geotechnical engineers. Topics include: fundamentals for mechanics of granular materials; continuum theory of granular materials; and discrete element approaches.
Ergodic theorem, ergodic theory, and statistical mechanics
Proceedings of the National Academy of Sciences
112
7
1907-1911
2015
10.1073/pnas.1421798112
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.
Mechanics of ciliary locomotion.
Biological reviews of the Cambridge Philosophical Society
49
1
85-125
1974
10.1111/j.1469-185X.1974.tb01299.x
The mechanics of ciliary motion have interested both zoologists and fluid mechani- cists for some years. Thus, both Gray (1928) in his book Ciliary Mowement and Prandtl (1952) in his book The Essentials of Fluid Dynamics expressed considerable interest in the fluid mechanics of ciliary movement. Biomechanics is a product of a modem development in scientific research where scientists with different back- grounds (biology and mathematics or physics) pool their knowledge in an attempt to understand a particular problem. Ciliary propulsion is one of the many interesting subjects in the new and rapidly developing field of biomechanics, requiring, in this case, an integration of information from studies in fluid mechanics and physiology.
The Nature of Information in Quantum Mechanics
American Journal of Physics
70
5
20
2002
A suitable unified statistical formulation of quantum and classical mechanics in a -algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer's information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with the projection postulate being a noncommutative generalization of conditional probability. This view clarifies many problems surrounding the interpretation of quantum mechanics, particularly problems relating to the measuring process.
Mindful universe: quantum mechanics and the participating observer
Choice: Current Reviews for Academic Libraries
45
6
1014
2008
10.1007/978-3-540-72414-8
The article reviews the book "Mindful universe: quantum mechanics and the participating observer," by Henry P. Stapp.
BOOKS -- Reviews; MINDFUL Universe: Quantum Mechanics & the Particip; NONFICTION; STAPP, Henry
Modeling of fault gouges with Cosserat Continuum Mechanics: Influence of thermal pressurization and chemical decomposition as coseismic weakening mechanisms
Journal of Structural Geology
38
254-264
2012
10.1016/j.jsg.2011.09.012
In this paper we study the impact of thermal pressurization and mineral decomposition reactions under seismic deformation conditions (e.g., slip rates of about 1 m/s) triggered by shear heating, to the stability of a saturated fault material. By using higher order continuum considerations, allowing for rotational degrees of freedom to the gouge material, we verify that the micro-inertia of the Cosserat Continuum may regularize the ill-posed problem of simple shear of a fault and that the thermal effects promote localization of deformation into ultra-thin shear bands. It is shown that the width of these structures depends on the parameters of the decomposition reaction considered, obtaining values as low as 100 ??m, in agreement with microstructural evidence from natural and artificial faults. ?? 2011 Elsevier Ltd.
Cosserat Continuum; Micro-inertia; Reaction kinetics; Shear heating; Undrained adiabatic shearing
Modeling of thin film lubrication
Tribology Transactions
38
1
108-118
1995
10.1080/10402009508983386
A rheological model is proposed which can be applied to boundary lubrication. The model satisfies the formal continuum mechanics considerations of material objectivity, i.e., it is indifferent to changes in coordinate system and reference frame. The model is applicable to thin films in which the molecular length scale is the same order as the film thickness, due to the use of ensemble, rather than spatial, averaging. The microstructure is described through the use of a director, a unit vector aligned with the molecular orientation. The model contains three material parameters, i.e., the conventional viscosity, a director viscosity which describes varying flow resistance depending on the director orientation, and an elastic modulus relating to moments required to change the director orientation. Typically, the directors are anchored to the boundary surfaces in a favored direction. Calculations are performed for mass velocity, director orientation, and stress in a contact. The lubricant exhibits nearly solid-like behavior near the surfaces, and nearly all sliding takes place across a thin shear layer. Predictions of friction and load are made.
Calculations; Continuum mechanics; Elastic moduli; Lubrication; Mathematical models; Microstructure; Molecular orientation; Rheology; Stresses; Surfaces; Thin films; Vectors; Viscosity
Fracture mechanics of bone.
Journal of biomechanical engineering
115
4B
549-54
1993
10.1115/1.2895538
This paper reviews the progress that has been made in applying the principles of fracture mechanics to the topic of fracture of long bones. Prediction of loading conditions which result in the propagation of fractures in bones has been of interest to the field of trauma biomechanics and orthopedics for over one hundred years. Independent verifications, by various investigators, of bone fracture mechanics parameters are reviewed and investigations of the effects of bone density and specimen thickness on the critical fracture mechanics parameters and of other factors such as critical crack length and plastic zone size in bovine femoral bone, and the effects of crack velocity on fracture mechanics parameters in bovine tibial bone are discussed. It took over ten years for the techniques of bone fracture mechanics to be applied to human compact bone, due primarily to geometric constraints from the smaller size of human bones. That work will be reviewed along with other continuing work to define the orientation dependence of the fracture mechanics parameters in bone and to refine the experimental techniques needed to overcome the geometric constraints of specimen size. A discussion is included of work still needed to determine fracture mechanics parameters for transverse and longitudinal crack propagation in human bone and to establish the effects of age on those parameters. Finally, a discussion will be given of how this knowledge needs to be extended to allow prediction of whole bone fracture from external loading to aid in the design of protective systems.
Animals; Biomechanics; Bone and Bones; Bone and Bones: physiology; Cattle; Fractures, Bone; Fractures, Bone: physiopathology; Humans; Stress, Mechanical
Interfacial stress analysis and prediction of debonding for a thin plate bonded to a curved substrate
International Journal of Non-Linear Mechanics
44
4
358-370
2009
10.1016/j.ijnonlinmec.2009.01.002
This paper focuses on the analytical and numerical modeling of the interface between a rigid substrate with simple constant curvature and a thin bonded plate. The interfacial behavior is modeled by independent cohesive laws in the normal and tangential directions, coupled with a mixed-mode fracture criterion. The newly developed analytical model determines the interfacial shear and normal stress distributions as functions of the substrate curvature, during the various behavioral stages of the interface prior to the initiation of debonding. The model is also able to predict the debonding load and the effective bond length. In the numerical model the interface is modeled by zero-thickness node-to-segment contact elements, in which both the geometrical relationships between the nodes of the discretized problem and the interface constitutive laws are suitably defined. Numerical results and comparisons between the predictions of the two models are presented.
Bond; Cohesive zone modeling; Contact mechanics; Curved substrate; Debonding; Fiber-reinforced polymer reinforcement; Finite element method; Interfacial stresses
Quantum mechanics, interference, and the brain
Journal of Mathematical Psychology
53
5
306-313
2009
10.1016/j.jmp.2009.03.005
In this paper we discuss the use of quantum mechanics to model psychological experiments, starting by sharply contrasting the need of these models to use quantum mechanical nonlocality instead of contextuality. We argue that contextuality, in the form of quantum interference, is the only relevant quantum feature used. Nonlocality does not play a role in those models. Since contextuality is also present in classical models, we propose that classical systems be used to reproduce the quantum models used. We also discuss how classical interference in the brain may lead to contextual processes, and what neural mechanisms may account for it.
Classical fields; Contextuality; Interference; Oscillators; Quantum mechanics
Wave mechanics for Ocean Engineering
Wave mechanics
496
2000
10.1007/s13398-014-0173-7.2
In a unitary way, this monograph deals with a wide range of subjects related to the mechanics of sea waves. The book highlights recent theoretical results on the dynamics of random wind-generated waves, on long-term wave statistics, and on beach planform evolution. A fresh approach is given to more traditional concepts. For example, new evidence from a recent series of small-scale field experiments is used to introduce some crucial topics like wave forces. Also, the book gives some worked examples for the design of offshore or coastal structures. An exciting subject dealt with in the book is the quasi-deterministic mechanics of three-dimensional wave groups in sea storms, and the loads exerted by these wave groups on offshore structures. The text is intended for researchers and graduate students in ocean engineering, but may also be understood by undergraduates. The more complex concepts are explained with examples or more extensive case studies.
Aluminum-GFRP hybrid square tube beam reinforced by a thin composite skin layer
Composites Part A: Applied Science and Manufacturing
40
10
1558-1565
2009
10.1016/j.compositesa.2009.06.015
Ultimate bending moments and energy-absorption capability of aluminum-glass fiber reinforced plastic (GFRP) hybrid tube beams were experimentally analyzed with particular focuses on effects of thin GFRP skin layer in relation to bending deformation behavior and fracture characteristics. Various hybrid tube beams were fabricated by inserting adhesive film between prepreg and metal layers and by aligning various composite ply angles. Under 3-point bending loads, aluminum-GFRP hybrid tube beams showed characteristic fracture processes according to the lay-up kinds of the skin layer in comparison to the virgin aluminum tube beams. In particular, the hybrid tube beams having a 0.5 mm thick [0??/90??]s skin layer showed the largest improvement in specific maximum moment (about 67%) and in specific energy-absorption (29%). Consequently, there was an optimal thickness and lay-up of the composite skin layer in creating the best performance of the hybrid tubes. ?? 2009 Elsevier Ltd. All rights reserved.
A. Hybrid; B. Buckling; B. Delamination; Energy-absorption
The aerodynamics of compliant membrane wings modeled on mammalian flight mechanics
36th AIAA Fluid Dynamics Conference and Exhibit, 5-8 June 2006, San Francisco, CA
June
2866
2006
10.2514/6.2006-2866
Mammalian flight is characterized by several features unique and distinct from the flight of both insects and birds. One such feature is the use of thin compliant wings as the lifting surface. Motivated by this, we present experimental results on the aerodynamics of compliant membrane wing models of low aspect ratio, performed at low Reynolds numbers, ranging from 30,000 to 100,000. Lift and Drag coefficients are measured over a range of angles of attack from -5 to 60 degrees. In addition the deformation of the wing due to aerodynamic loading is directly measured using a stereo photogrammetric method. Results indicate that the compliant wings' deformation increases with both angle of attack and that deformation scales with dynamic pressure until the onset of stall at which point inertial scaling fails. Stall on compliant wings occurs at higher angles of attack and is gentler than on a similar wing in which the membrane does not deform. Unsteady membrane vibrations are also measured and characterized. N
Development and verification of a meso-scale based dynamic material model for plain-woven single-ply ballistic fabric
Journal of Materials Science
43
18
6301-6323
2008
10.1007/s10853-008-2893-6
A meso-scale unit-cell based continuum material constitutive model has been developed for plain-woven single-ply ballistic fabric materials. This model, due to its computational efficiency, is suitable for use in computational analyses of the ballistic-protection performance of multi-layer body-armor vests. The model utilizes the continuum-level in-plane and out-of-plane deformation-state of the material, an energy minimization procedure and a simple account of yarn slip to update the structure/architecture of the fabric unit cell. Forces and moments developed within the structural components of the unit cell are then used to compute the continuum-level stress state at the material points associated with the unit cell in question. The model is implemented in a user-material subroutine suitable for use within commercial finite-element programs. To validate the model, a series of transient non-linear dynamic analyses of the impact of a square-shaped fabric patch with a spherical projectile is carried out and the computed results compared with their counterparts obtained using a more traditional finite-element approach within which yarns and yarn weaving are modeled explicitly. The results obtained show that the material model provides a reasonably good description for the fabric deformation and fracture behavior under a variety of boundary conditions applied to fabric edges and under varying fictional conditions present at the yarn/yarn and projectile/fabric interfaces. In addition, the overall ballistic energy absorption capacity of the fabric as well as its yarn-strain energy, yarn-kinetic energy, and frictional sliding contributions are predicted with reasonable accuracy by the proposed material model for fabric.
Experimental and numerical investigations on the time-dependent behavior of woven-ply PPS thermoplastic laminates at temperatures higher than glass transition temperature
Composites Part A
49
165-178
2013
10.1016/j.compositesa.2013.02.016
This study was aimed at investigating the time-dependent behavior of carbon woven-ply PPS laminates at temperatures higher than its Tg (95°C) when matrix viscoelasticity and viscoplasticity are prominent. Creep-recovery tensile tests were carried out on [(+45,−45)]7 laminates at 120°C in order to examine the contribution of these time-dependent effects to their mechanical response. A numerical modelling has been developed to account for these behaviors. For this purpose, a linear spectral viscoelastic model and a generalized Norton-type viscoplastic model have been implemented in the FE code Cast3m. Finally, validation tests were performed to determine the model’s ability to predict the laminates response to various loadings. The numerical simulations are in good agreement with the experimental responses even for structural testing as a creep test on a notched specimen.
a; A. Thermoplastic resin; B. Creep; C. Finite element analysis; D. Mechanical testing; thermoplastic resin
Mechanics of the arterial wall: Review and directions
Crit. Rev. Bio. Eng.
23
1-2
1-162
1995
The goals of this article are threefold: to briefly review the theory of finite elasticity and its application to arterial mechanics; to review what is known about the mechanical behavior of arteries in health and disease; and to review several clinically relevant aspects of arterial mechanics, as for example, aging, aneurysms, angioplasty, embolectomy, heat therapies, hypertension, trauma, and the disruption of atherosclerotic plaques. It is shown that, despite a huge literature on arterial mechanics, much remains unknown. In particular, a pressing need exists for detailed nonlinear three-dimensional constitutive relations for the passive and active arterial wall as a function of position along the arterial tree and disease. Arterial mechanics has, therefore, yet to reach its full potential as an important and consistent contributor to vascular medicine and surgery, but the possibilities remain great.
ACUTE MYOCARDIAL-INFARCTION; BALLOON EMBOLECTOMY CATHETERS; COMMON CAROTID-ARTERY; ELECTRON-MICROSCOPIC OBSERVATIONS; EXPERIMENTAL ARTERIOVENOUS-FISTULAS; INTRACRANIAL SACCULAR ANEURYSMS; TRANS-LUMINAL ANGIOPLASTY; UNSTABLE ANGINA-PECTORIS; VASCULAR SMOOTH-MUSCLE; ZERO-STRESS STATE
Stochastic mechanics and the Feynman integral
Journal of Mathematical Physics
41
9
6060
2000
10.1063/1.1286880
The Feynman integral is given a stochastic interpretation in the framework of Nelson’s stochastic mechanics employing a time-symmetric variant of Nelson’s kinematics recently developed by the author
Introduction to Continuum Damage Mechanics
Journal of Applied Mechanics
54
481
1987
10.1115/1.3173053
Introduction to Continuum Damage Mechanics . [Journal of Applied Mechanics 54, 481 (1987)]. LM Kachanov, Author, D. Krajcinovic, Reviewer. Abstract. Abstract not available.\n
Is Quantum Mechanics Falsifiable? A computational perspective on the foundations of Quantum Mechanics
arXiv preprint arXiv:1206.3686
1-12
2012
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regine by extending the usual scientific paradigm to indclude "interactive experiments".
Bohmian Mechanics versus Madelung Quantum Hydrodynamics
Foundations of Physics
June
1-5
2009
10.13140/RG.2.1.3663.8245
It is shown that the Bohmian mechanics and the Madelung quantum hydrodynamics are different theories and the latter is a better ontological interpretation of quantum mechanics. A new stochastic interpretation of quantum mechanics is proposed, which is the background of the Madelung quantum hydrodynamics. Its relation to the complex mechanics is also explored. A new complex hydrodynamics is proposed, which eliminates completely the Bohm quantum potential. It describes the quantum evolution of the probability density by a convective diffusion with imaginary transport coefficients.
Mechanics of Coastal Forms
Annual Review of Fluid Mechanics
33
1
339-370
2001
doi:10.1146/annurev.fluid.33.1.339
Recent studies of the morphodynamics of the coastal region are reviewed. Emphasis is given to idealized models that consider a morphological pattern in isolation from the others, to obtain indications on the physical processes controlling its appearance and development. In particular, attention focuses on morphodynamic stability analyses that allow understanding of the behavior of morphological features that are repetitive in both space and time. Indeed rhythmic patterns are commonly observed both in the continental shelf far from the coast and in the near-shore region.
Compression-after-impact response of woven fiber-reinforced composites
Composites Science and Technology
70
14
2128-2136
2010
10.1016/j.compscitech.2010.08.012
This manuscript investigates compression-after-impact failure in woven fiber-reinforced composites. Compression failure of composite structures previously damaged by an impact event is due to the propagation of impact-induced damage mechanisms such as interlaminar debonding, constituent (i.e., matrix and fiber) microcracking, sublaminate buckling, as well as the interactions between these mechanisms. The failure mechanisms within each ply are idealized based on a reduced order multiscale computational model, in which, the damage propagation in the matrix and fibers upon compression is explicitly modeled. Delamination along the ply interfaces is idealized using a cohesive surface model. The initial impact-induced damage within the microconstituents and interfaces are inferred from experimental observations. A suite of numerical simulations is conducted to understand the sublaminate buckling, propagation of delamination and constituent damage upon compression loading. The numerical investigations suggest extensive propagation of delamination with mode transition preceding sublaminate buckling. Initiation and propagation of matrix and fiber cracking, observed upon sublaminate buckling, is the cause of ultimate shear failure. ?? 2010 Elsevier Ltd.
B. Delamination; C. Damage mechanics; C. Finite element analysis; C. Multiscale modeling; Compression-after-impact
Depolarization fields in thin ferroelectric films
Journal of Applied Physics
44
8
3379-3385
1973
10.1063/1.1662770
A mechanism is proposed to explain depolarization phenomena that have been observed in thin ferroelectric film and related multilayer devices.
Size effects on the tensile and compressive failure of notched composite laminates
Composite Structures
96
736-744
2013
10.1016/j.compstruct.2012.10.004
An experimental and analytical investigation of the effect of size on the strength of composite laminates with central holes loaded in tension and compression is presented. Specimens with different hole sizes and with constant width-to-diameter ratios were tested in tension and compression under quasi-static loading and the strength reduction for increasing sizes was quantified for two lay-ups and for the two loading conditions. The first-ply failure load of the outer ply was identified using a new method that post-processes the displacement field obtained using the digital image correlation technique. The accuracy of the available strength prediction methods (point and average stress methods, inherent flaw model, semi-analytical cohesive zone model and finite fracture mechanics) to simulate the effect of size on the strength of notched composites is discussed. It is shown that the finite fracture mechanics model is the most accurate method.
Open-hole compression; Open-hole tension; Size effect
A New Technique for Ultrasonic-Nondestructive Evaluation of Thin Specimens
Experimental Mechanics
September
288-297
1988
Combining standard FFT methods with conventional ultrasonics, a method has been developed for measuring the phase velocity, the group velocity and the attenuation in ultra- thin specimens (submillimeter or subwavelength in thickness). A detailed description of this technique is given. The tech- nique was used on four disparate materials: aluminum, an epoxy, a particulate composite and a graphite-fiber/epoxy composite. The method works equally well for thin or thick specimens, and for dispersive as well as nondispersive media.
Precision tests of quantum mechanics
Physical Review Letters
62
5
485-488
1989
10.1103/PhysRevLett.62.485
It is proposed to set stringent limits on possible nonlinear corrections to ordinary quantum mechanics by searching for the detuning of resonant transitions. A suggested nonlinear generalization of quantum mechanics is used to show that such detuning would be expected in the rf transition in Be+ ions that is used to set frequency standards. Measurements at the National Bureau of Standards already set limits of order 10^{-21} on the fraction of the energy of the Be nucleus that could be due to nonlinear corrections to quantum mechanics, with good prospects of improving this by 2-3 orders of magnitude.
Thin, spray-on lining applications for rockburst, blast and fire damage mitigation
41st U.S. Rock Mechanics Symposium - ARMA's Golden Rocks 2006 - 50 Years of Rock Mechanics, June 17, 2006 - June 21, 2006
American Rock Mechanics Association
2006
Research has been undertaken to characterize the support capabilities of innovative spray-on lining materials, called TSLs, and to assess their capacity for inhibiting damage created by mining-induced rockbursts. A variety of TSLs and other spray support media were subjected to the effects of simulated rockbursting, through use of explosive detonation trials, to evaluate their damage mitigation value. The relative effectiveness of area support materials for suppressing dynamic rock fragmentation and support media damage was assessed using near- and far-field seismic monitoring and high-speed digital photographic analysis of repetitive blasting trials. The results of these trials have demonstrated that the majority of thin, spray-on lining products currently available are highly effective for mitigating rockburst damage in highly stressed mine environments. In civil engineering construction, the ability of TSLs to provide effective concrete structural reinforcement while providing resistance to environmental hazards, as with fires or dynamic failure events, may permit wider use of such products than is currently foreseen by the mining industry. Significant benefits for use of TSL materials in concrete liner rehabilitation and for concrete material protection have been assessed and will be presented. 2005, ARMA, American Rock Mechanics Association.
Civil engineering; Concrete products; Concretes; Damage detection; Explosives; Mining; Reinforcement; Rock bursts; Rock mechanics; Rocks; Safety engineering; Structural geology; Underground structures
The effect of ply drop-off regions on flow propagation and processing parameters during the resin transfer molding process
Bridging the Centuries with Sampe's Materials and Processes Technology, Vol 45, Books 1 and 2
746-760
2000
Historically, the Resin Transfer Molding (RTM) injection process has relied on trial and error, where the resin is injected into a fiber filled mold, difficulties and problems in impregnation are discovered, adjustments are made and the process is iterated. The science-based manufacturing can reduce the guesswork and allow for greater reliability in part outcome, One feature of a desired part is a tapered section, or one with a changing cross section. During the fabric lay-up these sections must be filled by ply drop-offs, where one layer of fabric overlays another. This feature can cause certain concerns during the filling stage. The resin will run down the ply drop-offs, and cause disturbances to a "natural" flow front propagation. This study will first explore the potential benefits of a converging and diverging flow. Also, once perimeter racetracking is introduced, the ply drops create a transverse racetracking channel, which can drastically alter the resin now pattern. This study will also examine the effect of different fabric stacking methods on the flow front pattern. Idealized upper and lower bound models will be introduced, and then the more practical middle bound models will be examined and their performance evaluated.
converging/diverging flow; permeability; ply drop-off; porous-media; racetracking
Nanoscale mechanics
Condensed Matter Physics
263
1
1-8
2003
The mechanical properties of very small systems are often strikingly different from the properties of everyday objects. As one considers ever smaller objects, thermal fluctuations, and then quantum fluctuations, start to be important. In this thesis I explain some unusual nanoscale mechanical effects, and predict some new effects. The bulk of the thesis is devoted to calculating the forces between bodies that are closely spaced, but not touching. These van der Waals forces have been studied in detail for bodies in thermal equilibrium. Most of the world is not in thermal equilibrium, and van der Waals forces in this regime are very different from their equilibrium cousins. In contrast to equilibrium forces, nonequilibrium forces are much stronger and may show chemical specificity. There is a friction associated with the van der Waals force between bodies in relative motion. When the bodies are at different temperatures, this friction may be negative. Intermolecular forces with one molecule excited are far stronger than ground-state forces and may be attractive or repulsive. Any optical effect in matter modifies the forces between the constituent molecules. The second part of this thesis is on solitonic kinks in fibrillar materials (e.g. polymers, actin bundles, microtubules, carbon nanotubes). All of these materials may support stable kinks, and these kinks play an important role in determining the mechanical properties; often more important than the detailed chemical makeup of the materials.
Tensile testing of thin films supported on compliant substrates
Mechanics of Materials
41
7
839-848
2009
10.1016/j.mechmat.2009.02.003
Elastic properties of thin films are routinely measured by straining them on a flexible carrier substrate. Stress-strain characteristics for the film/substrate composite strip are obtained and a simple mixture theory is used to extract the elastic properties of the film by assuming a uniform one-dimensional tensile stress distribution within the film thickness. In this paper, we examine the validity of using this simple theory by determining the three-dimensional elastic stress field in a composite strip. Three sample geometries and loading configurations are considered. In case A, the film is coated on one side of the carrier substrate while in case B, the carrier substrate is coated on both sides. For both case, the external load is applied only on the substrate. In case C, the geometry was the same as case A, but the external load was applied to both the film and the substrate. For film to substrate moduli ratios less than 5, the mixture theory provided adequate results with errors less than 10% for all cases considered. However, for case A, the rule of mixtures theory tends to significantly overestimate the tensile stress in the film for moduli ratio exceeding 5. An error analysis is also presented which provides guidance regarding the minimum film thickness necessary to attain results with a given accuracy. Overall the results presented in this paper provide researchers with rules to design the sample geometry and film thickness to accurately determine the elastic properties of thin films using the composite film/strip experiment. These rules are exemplified by measuring the elastic properties of a thin sputtered Al film and a hexagonal honeycomb structured Si/polymer composite film produced through an evaporation induced self-assembly process. In both cases, films are deposited on a flexible Kapton substrate and strained using a home-built film tester. ?? 2009 Elsevier Ltd. All rights reserved.
Pore size scaling for enhanced fracture resistance of nanoporous polymer thin films
Acta Materialia
56
20
5946-5953
2008
10.1016/j.actamat.2008.08.009
Poly(arylene) ether (PAE) polymer films containing controlled nanometer-sized pores are shown to exhibit increasing fracture resistance with porosity. Such surprising behavior is in stark contrast to widely reported behavior for the fracture toughness of porous solids, which decreases markedly with porosity. A ductile nano-void growth and coalescence fracture mechanics-based model is presented to rationalize the increase in fracture resistance of the voided polymer film. The model is shown to explain the behavior in terms of a specific scaling of the size of the pores with pore volume fraction. It is demonstrated that the pore size must increase with close to a linear dependence on the volume fraction in order to increase rather than decrease the fracture energy. Independent characterization of the pore size as a function of volume fraction is shown to confirm predictions made by the model. Implications for the optimum void size and volume fraction are considered for superior fracture resistance of the nanoporous films.
Fracture; Nanoporous; Thin-films
Fracture mechanics analysis of transverse cracks in thin coatings under spherical Indentation
ICF XI - 11th International Conference on Fracture
2005
The competition between transverse cracks originating from the surface and sub-surface of a thin, hard coating bonded by a delamination resistant adhesive to a polycarbonate substrate due to spherical indentation is investigated in real-time as a function of coating thickness and indenter radius. Fine (Y-TZP) and intermediate (alumina) size grain polycrystalline ceramics as well as pre-abraded amorphous glass are used for the coating. As the coating thickness is reduced, the familiar star-shape sub-surface damage is completely suppressed, leaving the surface ring crack to dominate the fracture. In the transition range, the sub-surface damage occurs as a set of off-axis circumferential cracks. This observation provides the basis for our simplified treatment of the sub-surface damage as a cylindrical crack. A linear fracture mechanics approach is used to predict the onset of transverse fracture in the coating. In consistency with the tests, the damage on the surface as well as the sub-surface of the coating is assumed as a cylindrical crack. The interactive effect of the coating thickness, indenter radius, crack length and contact radius is explored using a large-strain FEM contact code. In consistency with its polycrystalline nature, the coating is assumed to contain a distribution of cracks. The least fracture load among all permissible crack lengths that is obtained from the analysis is taken as the critical load. The numerical predictions from this analysis compare well with the tests results. The analysis also helps identify the applicability range of a relatively simple critical stress criterion in terms of the system parameters.
A computational model for the indentation and phase transformation of a martensitic thin film
Journal of the Mechanics and Physics of Solids
50
9
1789-1815
2002
10.1016/S0022-5096(02)00018-2
We propose a computational model for a stress-induced martensitic phase transformation of a single-crystal thin film by indentation and its reverse transformation to austenite by heating. Our model utilizes a surface energy that allows sharp interfaces with finite energy and a penalty that forces the film to lie above the indenter and undergo a stress-induced austenite-to-martensite phase transformation. We introduce a method to nucleate the martensite-to-austenite phase transformation since in our model the film would otherwise remain in the martensitic phase in a local minimum of the energy. © 2002 Elsevier Science Ltd. All rights reserved.
Austenite; B. Thin film; Martensite; Nucleation; Phase transformation
Thin film and substrate cracking under the influence of externally applied loads
Engineering Fracture Mechanics
72
1286-1298
2005
10.1016/j.engfracmech.2004.09.006
Cracking in thin film systems subject to residual tension is examined. The existing solution for the case of a crack tip in the substrate is modified to provide a solution of greater accuracy. The influence of external tensile loads on thin film and substrate cracking is examined. An approximate superposition scheme is presented for the determination of the energy release rate. Crack arrest is examined and parameters for determining the possibility of crack arrest are presented. For compliant films it was found that crack arrest does not occur when the substrate stress has the same magnitude as the residual stress. The influence of externally applied loads on crack channelling and conditions under which channelling will occur in the substrate are presented. ?? 2004 Elsevier Ltd. All rights reserved.
Noncommutative quantum mechanics
American Journal of Physics
72
5
608-612
2004
10.1119/1.1624116
We discuss the main features of noncommutative quantum mechanics, a version of nonrelativistic quantum mechanics that involves noncommuting coordinates. After finding a representation for the algebra obeyed by the coordinates and momenta, we analyze the changes due to the noncommutative nature of the coordinates. The noncommutative two-dimensional harmonic oscillator is discussed in detail. Under certain restrictions, the effect of the noncommutativity is found to be equivalent to a Landau interaction. The modifications produced by the noncommutativity on the thermodynamic functions of the oscillator also are studied.
A Method to Measure the Adhesion of Thin Glass Coatings on Polymer Films
The Journal of Adhesion
44
3
213-227
1994
10.1080/00218469408027078
A simple and reliable method to measure the adhesion of thin, hard coatings on polymer substrates is presented, based on the rupture mechanics of brittle films on ductile substrates. The regular fragmentation pattern of the coating obtained after straining specimens under uniaxial tension is analyzed through a classical shear-lag analysis at the coating/substrate interface. The model links the mean crack spacing measured on strained specimens to the interfacial shear strength and the reversible adhesion energy. Fragmentation tests were carried out on a PET film coated on both sides by SiO<sub>2</sub> layers (24 nm on the thick side, and 6nm on the thin side). The interfacial shear strength was found to be close to 100 MPa for both coatings and the adhesion energy of SiO<sub>2</sub> on PET was found to be of the order of 230 mJ m<sup>2</sup>, both values being slightly higher for the thin coating side.
Co-rotational formulation for geometric nonlinear analysis of doubly symmetric thin-walled beams
Computer Methods in Applied Mechanics and Engineering
190
45
6023-6052
2001
10.1016/S0045-7825(01)00212-2
A doubly symmetric thin-walled beam element with open section is derived using co-rotational (CR) total Lagrangian (TL) formulation. The effects of deformation-dependent third-order terms of element nodal forces on the buckling load and post-buckling behavior are investigated. All coupling among bending, twisting, and stretching deformations for beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, all third-order terms of nodal forces, which are relevant to the twist rate, rate of twist rate and curvature of the beam axis are also considered. An incremental-iterative method based on the Newton-Raphson method combined with constant are length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. A parabolic interpolation method of the arc length is used to find the buckling load. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed element and to investigate the effect of third-order terms of element nodal forces on the buckling load and post-buckling behavior of doubly symmetric thin-walled beams. ?? 2001 Elsevier Science B.V. All rights reserved.
Buckling; Co-rotational formulation; Geometric nonlinearity; Postbuckling; Thin-walled beam
Effects of In-plane Elastic Stress and Normal External Stress on Viscoelastic Thin Film Stability
Mathematical Modelling of Natural Phenomena
7
4
6-19
2012
10.1051/mmnp/20127402
Motivated by recent experiments on the electro-hydrodynamic instability of spincast polymer films, we study the undulation instability of a thin viscoelastic polymer film under in-plane stress and in the presence of either a close by contactor or an electric field, both inducing a normal stress on the film surface. We find that the in-plane stress affects both the typical timescale of the instability and the unstable wavelengths. The film stability is also sensitive to the boundary conditions used at the film-substrate interface. We have considered two conditions, either rigidly attaching the film to the substrate or allowing for slip.
74b20; 74d10; 74f15; 74h55; 74k35; 76e17; and phrases; elasticity; in-; instability; mathematics subject classification; mechanics; polymers; residual stress; ternal; thin films; visco
Myocardial Mechanics in Cardiomyopathies
Progress in Cardiovascular Diseases
57
1
111-124
2014
10.1016/j.pcad.2014.03.003
Cardiomyopathies are a heterogeneous group of diseases that can be phenotypically recognized by specific patterns of ventricular morphology and function. The authors summarize recent clinical observations that mechanistically link the multidirectional components of left ventricular (LV) deformation with morphological phenotypes of cardiomyopathies for offering key insights into the transmural heterogeneity of myocardial function. Subendocardial dysfunction predominantly alters LV longitudinal shortening, lengthening and suction performance and contributes to the phenotypic patterns of heart failure (HF) with preserved ejection fraction (EF) seen with hypertrophic and restrictive patterns of cardiomyopathy. On the other hand, a more progressive transmural disease results in reduction of LV circumferential and twist mechanics leading to the phenotypic pattern of dilated cardiomyopathy and the clinical syndrome of HF with reduced (EF). A proper characterization of LV transmural mechanics, energetics, and space-time distributions of pressure and shear stress may allow recognition of early functional changes that can forecast progression or reversal of LV remodeling. Furthermore, the interactions between LV muscle and fluid mechanics hold the promise for offering newer mechanistic insights and tracking impact of novel therapies. © 2014 Elsevier Inc.
Cardiac dysfunction; Cardiac mechanics; Cardiomyopathy; Heart failure
Off-specular X-ray scattering studies of the morphology of thin films
Physica A: Statistical Mechanics and its Applications
231
1-3
99-110
1996
10.1016/0378-4371(96)00085-4
We discuss the scattering of X-rays from thin films at a surface or interface decorated with a morphology of islands and how these effects manifest themselves in the specular reflectivity and the diffuse (off-specular) scattering. We show how this technique has been used to study block copolymer films decorated with islands on the surface and the development of electrochemically induced pitting on a Cu electrode in an electrolyte solution.
A large displacement and finite rotation thin-walled beam formulation including cross-section deformation
Computer Methods in Applied Mechanics and Engineering
199
23-24
1627-1643
2010
10.1016/j.cma.2010.01.006
This paper presents a new formulation for thin-walled beams that includes cross-section deformation. The kinematic description of the beam emanates from the geometrically exact Reissner-Simo beam theory and is enriched with arbitrary cross-section deformation modes complying with Kirchhoff's assumption. The inclusion of these deformation modes makes it possible to capture the cross-section in-plane distortion, wall (plate) transverse bending and out-of-plane (warping), which leads to a computationally efficient numerical implementation. Several illustrative numerical examples are presented and discussed, showing that the resulting beam finite element leads to solutions that are in very good agreement with those obtained with standard shell finite elements, albeit involving much less degrees-of-freedom. © 2010 Elsevier B.V.
Beam finite elements; Finite rotations; Large displacements; Thin-walled members
Randomness in Classical Mechanics and Quantum Mechanics
Journal of Statistical Physics
68
1-2
12
2009
10.1007/s10701-010-9450-2
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations, i.e. the uncertainty (errors of observation) in the determination of coordinate and momentum is always positive (non zero). A "functional" formulation of classical mechanics was suggested. The fundamental equation of the microscopic dynamics in the functional approach is not the Newton equation but the Liouville equation for the distribution function of the single particle. Solutions of the Liouville equation have the property of delocalization which accounts for irreversibility. The Newton equation in this approach appears as an approximate equation describing the dynamics of the average values of the position and momenta for not too long time intervals. Corrections to the Newton trajectories are computed. An interpretation of quantum mechanics is attempted in which both classical and quantum mechanics contain fundamental randomness. Instead of an ensemble of events one introduces an ensemble of observers.
Continuum Mechanics and Theory of Materials
Applied Mechanics Reviews
55
B23
2002
10.1115/1.1451084
This treatise attempts to portray the ideas and general principles of the theory of materials within the framework of phenomenological continuum mechanics. It is a well-written mathematical introduction to classical continuum mechanics and deals with concepts such as elasticity, plasticity, viscoelasticity and viscoplasticity in nonlinear materials. The aim of a general theory of material behaviour is to provide a classified range of possibilities from which a user can select the constitutive model that applies best. The book will be invaluable to graduate students of materials science in engineering and in physics. The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.
A one field full discontinuous Galerkin method for Kirchhoff-Love shells applied to fracture mechanics
Computer Methods in Applied Mechanics and Engineering
200
45-46
3223-3241
2011
10.1016/j.cma.2011.07.008
In order to model fracture, the cohesive zone method can be coupled in a very efficient way with the finite element method. Nevertheless, there are some drawbacks with the classical insertion of cohesive elements. It is well known that, on one the hand, if these elements are present before fracture there is a modification of the structure stiffness, and that, on the other hand, their insertion during the simulation requires very complex implementation, especially with parallel codes. These drawbacks can be avoided by combining the cohesive method with the use of a discontinuous Galerkin formulation. In such a formulation, all the elements are discontinuous and the continuity is weakly ensured in a stable and consistent way by inserting extra terms on the boundary of elements. The recourse to interface elements allows to substitute them by cohesive elements at the onset of fracture.The purpose of this paper is to develop this formulation for Kirchhoff-Love plates and shells. It is achieved by the establishment of a full DG formulation of shell combined with a cohesive model, which is adapted to the special thickness discretization of the shell formulation. In fact, this cohesive model is applied on resulting reduced stresses which are the basis of thin structures formulations. Finally, numerical examples demonstrate the efficiency of the method. ?? 2011 Elsevier B.V.
Cohesive element; Discontinuous Galerkin method; Finite-elements; Fracture mechanics; Kirchhoff-Love; Shells
Statistical mechanics of voting
Physical review letters
81
8
9
1998
10.1103/PhysRevLett.81.1718
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system from the agents' preferences and a voting rule. The dynamics form a one dimensional statistical mechanics model; this suggests the use of the topological entropy to quantify the complexity of the system. We formulate natural political/social questions about the expected complexity of a voting rule and degree of cohesion/diversity among agents in terms of random matrix models--ensembles of statistical mechanics models--and compute quantitative answers in some representative cases.
arrow; chaotic dynamical system; condorcet cycle; political cohesion; random matrix model; social diversity; s theorem; topological en-; tropy
Quantum Mechanics, Special Chapters
Zeitschrift für Physikalische Chemie
213
Part_2
223-225
1999
10.1524/zpch.1999.213.Part_2.223
Quantum Mechanics -- Special Chapters is an important additional course for third-year students. Starting with the quantization of a free electromagnetic field and its interaction with matter, it discusses second quantization and interacting quantum fields. After re-normalization problems and a general treatment of nonrelativistic quantum field theory, these methods are applied to problems from solid-state physics and plasma physics: quantum gas, superfluidity, plasmons, and photons. The book concludes with an introduction to quantum statistics, the structure of atoms and molecules, and the Schrödinger wave equation formulated by Feynman path integrals. 72 fully and carefully worked examples and problems consolidate the material.
Mechanics of breathing in man.
Journal of applied physiology (Bethesda, Md. : 1985)
2
11
592-607
1950
The mechanical work done by the respiratory muscles in producing the movements of breathing has been studied relatively little by physiologists. Although most text books of physiology give values for the work done by the heart, similar estimates for the work of breathing are lacking. The classic contributions of Rohrer(1-3) lay the foundation for this subject, but only a few pertinent papers, notably those of Neergaard and Wirz(5), Vuilleumier(5), Bayliss and Robertson(6) and Dean and Visscher(7), have since appeared. The material presented below, although based on data which are neither sufficiently precise nore extensive enough to furnish an exact description of the mechanics of breathing, constitutes an approximate analysis, which we have found valuable as a way of thinking about certain respiratory problems.
RESPIRATION
The primary electroviscous effect in a suspension of spheres with thin double layers
Journal of Fluid Mechanics
132
-1
337
1983
10.1017/S0022112083001640
Previous studies of the distortion of the electric double layer around a charged sphere have assumed that the electric stresses are small compared with the viscous stresses. The flow around the particle is therefore changed only slightly by the presence of the charge cloud. This change is measured by the Hartmann number, and in § 6 we remove the restriction that it should be small. It is found that the previous linearized theory is sufficiently accurate for typical experimental values of the Hartmann number. Previous studies have also assumed that the potential at the surface of the particle is small. This assumption is removed in § 7 of this paper. For values of the non-dimensional surface potential smaller than 2 the predictions are altered by less than 10 %. For higher values the differences between linear and nonlinear theory are not negligible, especially when the charge cloud is thin compared with the radius of the charged sphere.
I-Band Titin in Cardiac Muscle Is a Three-Element Molecular Spring and Is Critical for Maintaining Thin Filament Structure
The Journal of Cell Biology
146
3
631-644
1999
10.1083/jcb.146.3.631
In cardiac muscle, the giant protein titin exists in different length isoforms expressed in the molecule's I-band region. Both isoforms, termed N2-A and N2-B, comprise stretches of Ig-like modules separated by the PEVK domain. Central I-band titin also contains isoform-specific Ig-motifs and nonmodular sequences, notably a longer insertion in N2-B. We investigated the elastic behavior of the I-band isoforms by using single-myofibril mechanics, immunofluorescence microscopy, and immunoelectron microscopy of rabbit cardiac sarcomeres stained with sequence-assigned antibodies. Moreover, we overexpressed constructs from the N2-B region in chick cardiac cells to search for possible structural properties of this cardiac-specific segment. We found that cardiac titin contains three distinct elastic elements: poly-Ig regions, the PEVK domain, and the N2-B sequence insertion, which extends [~]60 nm at high physiological stretch. Recruitment of all three elements allows cardiac titin to extend fully reversibly at physiological sarcomere lengths, without the need to unfold Ig domains. Overexpressing the entire N2-B region or its NH2 terminus in cardiac myocytes greatly disrupted thin filament, but not thick filament structure. Our results strongly suggest that the NH2-terminal N2-B domains are necessary to stabilize thin filament integrity. N2-B-titin emerges as a unique region critical for both reversible extensibility and structural maintenance of cardiac myofibrils.
Numerical simulations of impact behaviour of thin steel plates subjected to cylindrical, conical and hemispherical non-deformable projectiles
Engineering Fracture Mechanics
75
1635-1656
2008
10.1016/j.engfracmech.2007.06.005
In this paper, a numerical study of normal perforation of thin steel plates impacted by different projectile shapes is reported. The numerical simulations of this problem have been performed using a finite element code, ABAQUS-Explicit with a fixed and an adaptive mesh for the plate. To define the thermoviscoplastic behaviour of the material constituting the plate, the Johnson-Cook model has been used. This homogeneous behaviour has been coupled with the Johnson-Cook fracture criterion to predict completely the perforation process. Three kinds of projectile shape (blunt, conical and hemispherical) have been simulated with a large range of impact velocities from 190 to 600 m/s. The analysis considers the influence of adiabatic shear bands, plastic work and the gradient of temperature generated in the plate. The numerical results predict correctly the behaviour projectile-plate in agreement with experimental data published by other authors. © 2007 Elsevier Ltd. All rights reserved.
Adaptive mesh; Ballistic limits; Ductile fracture; Numerical simulation; Perforation
Physics of Thin Films
Journal of The Electrochemical Society
111
85C
1964
10.1149/1.2426128
Lecture notes (TU Vienna) for deposition methodes, theory of thin film condensation and thin film characterization
Ag-Coated Fe 3 O 4 @SiO 2 Three-Ply Composite Microspheres: Synthesis, Characterization, and Application in Detecting Melamine with Their Surface-Enhanced Raman Scattering
The Journal of Physical Chemistry C
114
17
7738-7742
2010
10.1021/jp100141c
Ag nanoparticles with average sizes of 20 nm were well-dispersed on the surfaces of Fe3O4@SiO2 composite microspheres through a simple wet-chemical method employing the Ag-mirror reaction. The as-synthesized Ag-coated Fe3O4@SiO2 three-ply composite microspheres are monodisperse and bifunctional, with ferromagnetic and surface-enhanced Raman scattering (SERS) properties. The products were characterized by means of X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy dispersive X-ray analysis (EDX). SERS signals of typical analytes such as rhodamine 6G (Rh 6G) were observed on Ag nanoparticles from the Ag-coated Fe3O4@SiO2 microspheres, even though the concentration of the analyte was as low as 1 ? 10?15 M (Rh 6G). The Ag-coated Fe3O4@SiO2 microspheres were applied to detecting melamine, and strong SERS signals were obtained with melamine concentration of 1 ? 10?6 M. This work may provide a potential and unique technique to detect melamine.\nAg nanoparticles with average sizes of 20 nm were well-dispersed on the surfaces of Fe3O4@SiO2 composite microspheres through a simple wet-chemical method employing the Ag-mirror reaction. The as-synthesized Ag-coated Fe3O4@SiO2 three-ply composite microspheres are monodisperse and bifunctional, with ferromagnetic and surface-enhanced Raman scattering (SERS) properties. The products were characterized by means of X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy dispersive X-ray analysis (EDX). SERS signals of typical analytes such as rhodamine 6G (Rh 6G) were observed on Ag nanoparticles from the Ag-coated Fe3O4@SiO2 microspheres, even though the concentration of the analyte was as low as 1 ? 10?15 M (Rh 6G). The Ag-coated Fe3O4@SiO2 microspheres were applied to detecting melamine, and strong SERS signals were obtained with melamine concentration of 1 ? 10?6 M. This work may provide a potential and unique technique to detect melamine.
MaxEnt Mechanics
Physics
17
January
12
2007
This paper shows that: (a) given a mechanical system described by a set of independent coordinates in configuration space, (b) given an initial state of specified initial coordinates, and (c) given a situation in which the system can follow any one of a set of different possible paths with a pertinent probability pi, then the average path (defined as the weighted average positions and corresponding times) will obey Lagranges' equations iff the Shannon information defined by the distribution of probabilities is an extreme (maximum) compared to any imaginable other distribution. Moreover, the resulting action function is proportional to this Shannon information.
05; 20; 45; 70h03; 94a17; entropy; jj statistical mehanics; lagrange; lagrangian hamiltonian mechanics; lagrangian mechanics; least action principle; maxent; measures information; msc 2000 codes; pacs codes; s equations; y
Size and rate dependent necking in thin metallic films
Journal of the Mechanics and Physics of Solids
62
1
81-98
2014
10.1016/j.jmps.2013.09.006
The control of the ductility of thin metallic films is a major issue in a variety of technologies involving flexible electronics, MEMS and deformable coatings. An enhanced closed form 1D imperfection based localization analysis is developed in order to investigate the mechanics of diffuse necking in metallic films. The model relies on a description of the localization process in a finite length specimen using either a 2- or 3-zone model, under plane stress or plane strain tension conditions. A strain gradient plasticity contribution to the stabilization of the localization process is taken into account in the hardening response through a simple estimate of the deformation gradient inside the necking zone. The model, with gradient plasticity effects, is validated towards 2D finite element simulations. The response of the material involves both strain-hardening and rate sensitivity, as well as possible creep relaxation. The plastic flow parameters are related to the grain size and film thickness. The model shows, in agreement with experiments, that the ductility can either drop to small values for very small grain sizes and/or film thickness due to the high strength and to the presence of imperfections, or can remain constant or even increase owing to an increased rate sensitivity resulting from thermally activated mechanisms. This last stabilization effect can be reinforced by gradient plasticity effects if allowed by the dominant deformation mechanism. ?? 2013 Elsevier Ltd. All rights reserved.
Creep; Ductility; Elastic-plastic material; Strain gradient plasticity; Thin films; Viscoplastic material
Active constrained layer damping of geometrically nonlinear transient vibrations of composite plates using piezoelectric fiber-reinforced composite
Thin-Walled Structures
47
2
178-189
2009
http://dx.doi.org/10.1016/j.tws.2008.05.011
This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated thin composite plates using piezoelectric fiber-reinforced composite (PFRC) materials. The constraining layer of the ACLD treatment is considered to be made of the PFRC materials. The Golla–Hughes–McTavish (GHM) method has been used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. A finite element model has been developed for the cross-ply and antisymmetric angle-ply plates integrated with the patches of ACLD treatment undergoing geometrically nonlinear vibrations. The Von Ka`rma`n-type nonlinear strain displacement relations and the first-order shear deformation theory (FSDT) are used for deriving this coupled electromechanical nonlinear finite element model. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the cross-ply and antisymmetric angle-ply plates for suppressing the geometrically nonlinear transient vibrations of the plates. Emphasis has also been placed on investigating the effect of variation of fiber orientation in the PFRC material on the control authority of the ACLD patches.
Active damping; Geometrically nonlinear; Laminated plates; Piezocomposites; Smart structures
Pulmonary mechanics during mechanical ventilation
Respiratory Physiology & Neurobiology
180
2-3
162-172
2012
10.1016/j.resp.2011.11.014
The use of mechanical ventilation has become widespread in the management of hypoxic respiratory failure. Investigations of pulmonary mechanics in this clinical scenario have demonstrated that there are significant differences in compliance, resistance and gas flow when compared with normal subjects. This paper will review the mechanisms by which pulmonary mechanics are assessed in mechanically ventilated patients and will review how the data can be used for investigative research purposes as well as to inform rational ventilator management.
acute respiratory syndrome; mechanical ventilation
Quantum Mechanics of Black Holes
Science
337
6094
538-540
2012
10.1126/science.1221693
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Estimation of the 90° ply strength distribution and shear lag parameter from multiple transverse cracking in graphite-epoxy cross-ply laminates
Materials Science and Engineering: A
158
1
65-70
1992
A method to estimate the Weibull parameters for the strength distribution of a transverse ply and the shear lag parameter (the ratio of the shear modulus G to the thickness b of the shear transfer region) in cross-ply 02/904/02, 02/906/02 and 02/9012/02 graphite-epoxy laminates from multiple transverse cracking was proposed and applied to experimental results. The estimated values of the Weibull parameters were essentially the same as those estimated by the Peters method. The value of the shear lag parameter G/b was found to be 50-100 MPa [mu]m-1 for 02/904/02 and 02/906/02 laminates. On the contrary, the experimental results on the multiple cracking of the 90° ply in a 02/9012/02 laminate at high applied stresses could not be described by the value of G/b = 50-100 MPa [mu]m-1, possibly owing to the occurrence of plastic deformation and/or shear failure in the 0°-90° interface.
Classical mechanics as nonlinear quantum mechanics
Physics
7
2007
10.1063/1.2827300
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.
Testing Water Vapour Permeability of Sawdust and Banana Peels Ply Board as Non-Veneer Panel
International Journal of Construction Engineering and Management
2
2
33-37
2013
10.5923/j.ijcem.20130202.01
This experimental study aimed to measure the moisture performance of sawdust and banana peels ply board as non-veneer panel for construction projects. The goal was to measure the vapour permeability values of sawdust and banana peels ply board, compare the results with those done for oriented strand board and to investigate the efficiency of structures through these panel products. Structures made of different materials have different drying efficiencies under high relative humidity conditions that are representative of their application as non-veneer panel in cold climates
Banana Peels; Construction Materials; Ply Board; Sawdust
Rheological properties and adhesive failure of thin viscoelastic layers
Journal of Rheology
46
1
273
2002
10.1122/1.1428316
Methods have been developed for measuring the linear viscoelastic properties of thin adhesive layers, and for determining the stress intensity factor characterizing the driving force for adhesive failure. Both methods involve bringing a hemispherical indenter in contact with the adhesive layer while simultaneously monitoring the load, displacement, and radius of contact between the indenter and the adhesive. Dynamic moduli for the adhesive layer are obtained by oscillating the indenter, and the adhesive properties are obtained by pulling the indenter completely out of contact with the adhesive layer. Existing theories of viscoelastic contact mechanics were extended to account for the fact that the adhesive layer thickness is not substantially larger than the contact radius, as is generally assumed. A variety of correction factors were introduced that depend on the ratio of the contact radius to the adhesive layer thickness. These methods were applied to a model adhesive based on an acrylic triblock copolymer. Determination of the time-dependent creep and relaxation functions for this material was simplified by the power-law frequency response of the dynamic moduli. The large stress intensity factors observed were related to a Dugdale model of the cohesive zone at the contact edge.
Computational dynamic fracture mechanics
International Journal of Fracture
86
1
127-159
1997
10.1023/A:1007376924191
This paper provides a review on the state of the art in computational dynamic fracture mechanics. The following important essential ingredients in computational dynamic fracture mechanics are included: (i) fundamental aspects of dynamic fracture mechanics, (ii) types of fracture simulation, (iii) computational models of dynamic crack propagation, and (iv) use of dynamic J-integral in computational models. In item (i), special attention is focused on the asymptotic eigen fields for various states of dynamic crack tips, which provide the foundation of dynamic fracture mechanics asWilliams asymptotic eigen solutions provided the foundation of static linear fracturemechanics. In item(ii), a new concept ofmixed-phase simulation is presented for general nonself-similar crack propagation, in addition to the generation-phase and application-phase simulations. A comprehensive summary of computational models for dynamic crack propagation is given in item (iii). Finally, in item (iv), several attractive features of the dynamic J-integral are presented.
asymptotic eigen field; compu; dynamic crack propagation; dynamic fracture; dynamic j integral; finite element method; numerical simulation; tational modeling
Progressive failure of laminated composites with a hole under compressive loading based on micro-mechanics
Advanced Composite Materials
1-14
2014
10.1080/09243046.2014.915105
This paper deals with progressive failure analysis of composites structure on the basis of the theory of micro-mechanics of failure (MMF). The MMF theory includes micro-scale stress amplification within each constituent material (fiber and matrix) and failure criteria for the judgment of the constituent failure. The unit cell model with the face-centered array distribution of carbon fibers is constructed to analyze the micro-scale stress amplification factors in the fiber and matrix. Noninteractive failure criteria are proposed to judge the failure of the fiber and matrix. During the process of loading, the constituents? failure can be identified by the MMF failure criteria, and then the material properties degradation scheme is evaluated according to the failure modes of constituents and applied for each element to continue the progressive failure analysis for the composite materials. The user-defined material subroutine for the micro-scale stress amplification in the constituents, failure judgment of the constituents, and degradation of ply properties is developed using the Abaqus Fortran scripts. Micro-scale stress of the constituents is visualized for detailed analysis. The initial failure, subsequent propagation, final failure, and the strength of open-hole compression (OHC) structure of the carbon fiber-reinforced polymer composites are studied based on MMF theory. The ultimate load and failure behavior of the OHC structure obtained from both theoretical analysis and tests are compared and analyzed. This paper deals with progressive failure analysis of composites structure on the basis of the theory of micro-mechanics of failure (MMF). The MMF theory includes micro-scale stress amplification within each constituent material (fiber and matrix) and failure criteria for the judgment of the constituent failure. The unit cell model with the face-centered array distribution of carbon fibers is constructed to analyze the micro-scale stress amplification factors in the fiber and matrix. Noninteractive failure criteria are proposed to judge the failure of the fiber and matrix. During the process of loading, the constituents? failure can be identified by the MMF failure criteria, and then the material properties degradation scheme is evaluated according to the failure modes of constituents and applied for each element to continue the progressive failure analysis for the composite materials. The user-defined material subroutine for the micro-scale stress amplification in the constituents, failure judgment of the constituents, and degradation of ply properties is developed using the Abaqus Fortran scripts. Micro-scale stress of the constituents is visualized for detailed analysis. The initial failure, subsequent propagation, final failure, and the strength of open-hole compression (OHC) structure of the carbon fiber-reinforced polymer composites are studied based on MMF theory. The ultimate load and failure behavior of the OHC structure obtained from both theoretical analysis and tests are compared and analyzed.
Qubit quantum mechanics with correlated-photon experiments
American Journal of Physics
78
5
510
2010
10.1119/1.3337692
A matrix-based formalism is used to explain the results of undergraduate level quantum mechanics experiments with correlated photons. The article includes new variations of experiments and new results. A discussion of our experience with a correlated-photon laboratory component for an undergraduate course on quantum mechanics is presented.
Thermal Response of Symmetric Cross-Ply Laminated Plates Subjected to Linear and Non-Linear Thermo-Mechanical Loads
Journal of Thermal Stresses
36
5
466-479
2013
10.1080/01495739.2013.770664
The flexural response of symmetric cross-ply laminated plates subjected to uniformly distributed linear and non-linear thermo-mechanical loads is presented using trigonometric shear deformation theory. The in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The theory satisfies the shear stress-free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Thermal stresses and displacements for three-layer symmetric square cross-ply laminated plates subjected to uniform linear and nonlinear and thermo-mechanical loads are obtained. The results of present theory are compared with those of classical plate theory, first-order shear deformation theory and higher-order shear deformation theory. The flexural response of symmetric cross-ply laminated plates subjected to uniformly distributed linear and non-linear thermo-mechanical loads is presented using trigonometric shear deformation theory. The in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The theory satisfies the shear stress-free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Thermal stresses and displacements for three-layer symmetric square cross-ply laminated plates subjected to uniform linear and nonlinear and thermo-mechanical loads are obtained. The results of present theory are compared with those of classical plate theory, first-order shear deformation theory and higher-order shear deformation theory.
Fracture mechanics
Applied Mechanics Reviews
38
10
1271-1275
1985
10.1115/1.3143689
Fracture mechanics is an active research field that is currently advancing on many fronts. This appraisal of research trends and opportunities notes the promising developments of nonlinear fracture mechanics in recent years and cites some of the challenges in dealing with topics such as ductile-brittle transitions, failure under substantial plasticity or creep, crack tip processes under fatigue loading, and the need for new methodologies for effective fracture analysis of composite materials. Continued focus on microscale fracture processes by work at the interface of solid mechanics and materials science holds promise for understanding the atomistics of brittle vs ductile response and the mechanisms of microvoid nucleation and growth in various materials. Critical experiments to characterize crack tip processes and separation mechanisms are a pervasive need. Fracture phenomena in the contexts of geotechnology and earthquake fault dynamics also provide important research challenges.
The mechanics of frost heaving
Journal of Geology
38
4
303-317
1930
The old theory that frost heaving is due to change in volume of water frozen was based on experiments with closed systems. Field observations and recent experiments indicate that soils, when subjected to freezing under normal conditions, usually behaven as open systems. When the freezing of saturated soils results in little or no heaving, part of the water is forced through the soil voids below the zone of freezing, compressing ,or expelling air. Excessive heaving results when water is pulled through the soil to build up layers of segregated ice. These ice layers grow in thickness because water molecules are pulled into the thin film that separates the growing ice crystals from underlying les. Since heavy surface loads may be heaved and much force is required to pull water through impervious clay, the water is put under high tension.
force of crystallization; frost heave
Use of Solid-State Transducers in Mechanics and Acoustics
Journal of the Audio Engineering Society
17
5
506-511
1969
10.1109/TAU.1971.1162153
Solid state devices have been used extensively to measure and generate\nstresses and stress waves in solids, liquids, and gases. Strain gages\nhaving gage factors of 175 can be constructed from silicon. By using\np-n junctions and transistors in their amplifying phases, very sensitive\ndevices are obtained. Thin films have been used for transducers and\nmonolithic crystal filters. (14 References)
Mechanic; pn junctions; Silicon; stress; thin films; transducer; transducers
Mechanics Tissue
Mechanical Engineering
2006
10.1159/000086197
Tissue Mechanics, Second Edition is about the mechanics of tissues for use at the advanced undergraduate level or above. Tissues transmit mechanical loads just like bridges and building structures. Not only do they transmit loads, but also they adapt their own structures so that the structures will transmit the mechanical loads more effectively, unlike bridges and building structures. The structures of living tissues are continually changing due to growth and response to the tissue environment, including the mechanical environment. The objective of this text is to describe the nature of the composite components of a tissue, the cellular processes that produce these constituents, the assembly of the constituents into a hierarchical structure, and the behavior of the tissues composite structure in the adaptation to its mechanical environment. A tissues mechanical environment is the history of mechanical loading experienced by the tissue in some reference time period, like a day. The most important features of the textbook are its middle level, neither too advanced nor too elementary, its fresh perspective on older material issues, and the inclusion of new research results carefully crafted onto this intermediate base of mechanics. Key Features: An introductory chapter on the structure of tissues and the fascinating unresolved problems concerning how biological tissues are formed and constructed. Detailed illustrations and included (with book/author watermark) on CD for tutorial instructional use Example problems to provide the student with hands-on experience with concepts Extensive appendices and tutorial materials on new developments including expanded treatment of ceramic materials and implants Detailed references for further reading Solutions Manual on CD for Bona Fide Instructors (separate entity; top secret sales code) As in TM, 1E a website (http://tissue-mechanics.com/) that has been established to provide supplemental material for the book. On this website is posted downloadable additional chapters on specific tissues, downloadable PowerPoint presentations of all the book's chapters, corrections to the published volume and additional exercises and examples for the existing chapters.
Elasticity solution for cross-ply composite and sandwich laminates
Composite Structures
83
1
13-24
2008
10.1016/j.compstruct.2007.03.003
A novel semi-analytical model is presented here for accurate estimation of stresses and displacements in composite and sandwich laminates. Displacements and corresponding transverse stresses are considered as primary variables of interest. Formulation is based on solution of a two-point boundary value problem (BVP) governed by a set of linear first-order ordinary differential equations (ODEs) through the thickness of a laminate. These first-order ODEs are numerically integrated by using fourth-order Runge-Kutta-Gill routine. Present model is free from any simplifying assumptions and also satisfies the continuity requirements of displacements and interlaminar transverse stresses at the laminae interfaces. Solutions for a wide range of composite and sandwich laminates are obtained to validate the present formulation. Results obtained through this technique are seen to compare well with the available three dimensional (3D) elasticity and other two dimensional (2D) analytical and 2D/3D finite element (FE) solutions. Few new benchmark solutions are also presented for future reference. ?? 2007 Elsevier Ltd. All rights reserved.
Composites; Laminate; Numerical integration; Runge-Kutta-Gill algorithm; Sandwich; Semi-analytical method
Model and experimental analysis of oblique incident ultrasound in a tissue layer using doublet mechanics theory.
The Journal of the Acoustical Society of America
130
6
4117-25
2011
10.1121/1.3658471
The fundamental framework of doublet mechanics (DM) is used to analyze high-frequency ultrasound wave propagation in materials with discrete microstructure. Ultrasonic reflection coefficients were measured from a thin layer of tissue embedded between two glass substrates at oblique incidence. Theoretical calculations for the reflection coefficients of a multi-layered system at oblique angles are performed using both DM theory and the classical continuum mechanics theory (CCM). For example, at the frequency of 10 MHz at incident angle 8° in sample with 30 μm thickness, the discrepancy in the magnitude of the reflection coefficient between experimental results and theoretical prediction is 15.8% for DM but 79.0% for CCM; similar results at other frequencies and incident angle in the samples with 30 and 60 μm thickness have also been obtained, which demonstrates that the DM theory can better describe the wave propagation in tissue. The influence of the incident angles and tissue thickness are also discussed in this paper.
Applicability of Fracture Mechanics on Brittle Delamination of Nanoscale Film Edge.
Transactions of the Japan Society of Mechanical Engineers Series A
69
677
187-194
2003
10.1299/kikaia.69.187
The stress concentration near the interface edge of a film/substrate, which dominates the delamination, is analyzed by molecular dynamics (MD) analysis. Here, the film thickness is on the nanoscale and the interatomic interaction is simulated by Morse-type model potentials. Three types of load are applied to the film/substrate to examine the effect of the stress-concentrated region on the delamination at the interface edge. At lower applied load, the stress distribution along the interface near the edge in the MD simulation coincides well with that obtained by linear elastic analysis (FEM: Finite Element Method). However, after the stress near the edge reaches the ideal strength of the interface, it deviates from the FEM result. The delamination crack is initiated from the free edge when the stress at y < 1 nm (y: distance from the edge) reaches the ideal interface strength. This signifies the criterion of interface toughness that the delamination is governed by the stress in the region (process zone). This also suggests the limit of applicability of linear elastic fracture mechanics on the nanoscale components.
crack initiation; delamination; fracture mechanics; interface edge; molecular dynamics; nanomechanics; stress concentra-; thin film; tion
Nonconservative Lagrangian and Hamiltonian mechanics
Physical Review E
53
2
1890-1899
1996
10.1103/PhysRevE.53.1890
Traditional Lagrangian and Hamiltonian mechanics cannot be used with nonconservative forces such as friction. A method is proposed that uses a Lagrangian containing derivatives of fractional order. A direct calculation gives an Euler-Lagrange equation of motion for nonconservative forces. Conjugate momenta are defined and Hamilton's equations are derived using generalized classical mechanics with fractional and higher-order derivatives. The method is applied to the case of a classical frictional force proportional to velocity.
On a nonlinear thermocapillary effect in thin liquid layers
Journal of Fluid Mechanics
273
-1
361
2006
10.1017/S0022112094001977
\nDilute aqueous solutions of long alcohol chains were recently found to \ncause a quadratic dependence of surface tension on the temperature without \naffecting other bulk properties of the liquid: sigma = sigma 0+ alpha \nQ(T-T0)2, alpha Q>0. The impact of such Marangoni instability on the \nbehaviour of a thin liquid layer is studied in this work. We derive an \nequation describing a nonlinear spatiotemporal evolution of a thin film. \nThe behaviour of the perturbed film in the absence of gravity, critically \ndepends on whether the temperature T0, yielding a minimal surface tension, \nis attained on the surface of the film. When this is the case, a \nqualitatively new behaviour is observed: perturbations of the film \ninterface may evolve into continuous steady patterns that do not rupture. \nOtherwise, the observed patterns due to the linear and quadratic Marangoni \neffects are qualitatively similar and result in the rupture of the film \ninto separate drops.
Determination of elastic moduli of thin layers of soft material using the atomic force microscope
Biophys J
82
5
2798-2810
2002
10.1016/S0006-3495(02)75620-8
We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels
Afm; Atomic force; atomic force microscope; Atomic-force-microscope; Cantilever; Cells; Contact; Elastic-modulus; Errors; films; force; Force microscope; gel; Gels; Indentation; Layer; Layers; materials; measurements; Mechanical-properties; Mechanics; Microscope; microsphere; Microspheres; Model; Modulus; Poly(vinyl alcohol); probe; Probes; Samples; Scale; Sensitivity; Soft; Strain; Substrate; Tests; Thin; Thin-layers; Tip
Models of mechanics
Models of Mechanics
138
1-213
2006
10.1007/1-4020-4835-1
This textbook on models and modeling in mechanics introduces a new unifying approach to applied mechanics: through the concept of the open scheme, a step-by-step approach to modeling evolves. The unifying approach enables a very large scope on relatively few pages: the book treats theories of mass points and rigid bodies, continuum models of solids and fluids, as well as traditional engineering mechanics of beams, cables, pipe flow and wave propagation. Models of Mechanics complements existing books that deal with continuum mechanics, offering a setting that is broad enough to encompass also the mechanics of mass points, and theories of beams and other intrinsically one-dimensional bodies. An obtained knowledge of the unifying approach can be a base for advanced studies of fluid and solid mechanics, as well as specializations in mechatronics, control and structural optimization. The book is ideal for use in conjunction with equation-based finite element programs like FEMLAB and FlexPDE. It provides tools for organizing and structuring the broad discipline of mechanics, as well as a platform for deriving new models of applied use. © 2006 Springer. All Rights Reserved.
Is quantum mechanics equivalent to a classical stochastic process?
Physical Review A
19
6
2440-2445
1979
10.1103/PhysRevA.19.2440
The authors analyze the connection between the theory of stochastic processes and quantum mechanics. It is shown that quantum mechanics is not equivalent to a Markovian diffusion process as claimed in recent papers. The origin of a possible confusion about this question is clarified. The authors further demonstrate that there does not even exist a non-Markovian process equivalent to quantum mechanics.
Response of mode II interlaminar fracture toughness of composite laminates with carbon nanotubes interlayer
Proceedings of SPIE
6423
642351-642351-7
2007
10.1117/12.780319
Aggregation is usually unavoidable for the carbon nanotubes due to the high surface free energy. In this paper, an attempt was carried out to investigate the effects of the nanotube's films as ply interfaces on the mode II interlaminar fracture toughness. The nanotubes were distributed into absolute ethyl alcohol solvent and acted as core solutions. A polymer, Poly(methylmethacrylate)(PMMA), was dissolved in solvent and acted as shell solutions. Then, the core and shell solutions were electrospun into compound nanofibers by use of a co-axial electrospinning to obtain a second distribution for the carbon nanotubes. The compound nanofibers were collected as thin films in a reasonable thickness and were inserted into the middle interface of a composite laminate. For comparison, the core solutions were sprayed directly onto the surface of the middle ply of the preformed laminates. End notched flexure (ENF) test was applied to investigate the effect of the nanotubes in different forms on the interlaminar fracture toughness of the cured laminates. Scanning electronic microscope (SEM) was used to analyze the fracture mechanics of the ENF specimens. Testing results have shown that the nanotubes have significant reinforcement effect on the interlaminar fracture toughness for those studied cases in this research. SEM analysis of the fracture surface of the ENF specimens has indicated that the polymer nanofibers and nanotubes have a good consistency with the matrix resin of the laminates.
Statistical mechanics in closed systems
Physical Review A
43
2046
1991
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
bla
Draining of liquid from thin axially symmetric films
Journal of Applied Mechanics and Technical Physics
16
2
217-222
1976
10.1007/BF00858916
The problem of the movement of liquid in a thin film under the effect of forces of capillary pressure when one or both film surfaces are retarded is analyzed by the iteration method. The results obtained allow one to trace the evolution of the film, i.e., to construct its profiles at different times and to find the law of its thinning. A comparison is made with experimental data.
Molecular Mechanics Force Fields for Modeling Inorganic and Organometallic Compounds
Reviews in Computational Chemistry
6
73-148
2007
10.1002/9780470125830.ch2
This chapter contains sections titled: Introduction Molecular Mechanics Force Fields and Inorganic Problems Applications of Molecular Mechanics to Transition Metal Complexes Main Group Molecular Mechanics
Electrically driven cracks in piezoelectric ceramics: experiments and fracture mechanics analysis
Journal of the Mechanics and Physics of Solids
50
11
2333-2353
2002
10.1016/S0022-5096(02)00030-3
Piezoelectric systems like multilayer actuators are susceptible to damage by crack propagation induced by strain incompatibilities. These can arise under electric fields for example between the electroded and external regions. Such incompatibilities have been realised in thin rectangular model specimens from PZT-piezoelectric ceramics with top and bottom electrodes only close to one edge. Under an electric field, controlled crack propagation has been observed in situ in an optical microscope. The crack paths are reproducible with very high accuracy. Small electrode widths lead to straight cracks with two transitions between stable and unstable crack growth regions, while large electrode widths result in curved cracks with four transitions. Fracture mechanics analysis is able to explain the different crack paths. An iteration method is developed to simulate the curved crack propagation also for strong curvature of the crack paths using the finite element method. The computed crack contours exhibit excellent quantitative agreement with the experiment with respect to their shape, the Stages of stable and unstable crack propagation and the transitions between them. Finally, also the crack length as a function of the electric field can be predicted. (C) 2002 Elsevier Science Ltd. All rights reserved.
crack propagation and arrest; delamination; finite elements; multilayer actuators; piezoelectric material; strain compatibility
Trends in Nanoscale Mechanics
Trends in Nanoscale Mechanics: Mechanics of Carbon Nanotubes, Graphene, Nanocomposites and Molecular Dynamics
213-222
2014
10.1007/978-94-017-9263-9
This part of the edited volume highlights trends in recent publications by providing examples of important research papers in different areas of nanoscale mechanics. Research papers on novel applications of carbon nanotubes, nanocomposites, nanodevices, quantum anti-dots, and other nanostructures are noted.
Thin-layer electrodeposition of Zn in the agar gel medium
Physica A: Statistical Mechanics and its Applications
387
16-17
4007-4014
2008
10.1016/j.physa.2008.02.074
The preparation of Zn deposits has been performed by thin-layer electrodeposition in acidic zinc sulphate solution with and without agar, respectively. The morphological and structural characteristics of the deposits have been investigated by scanning electron microscopy (SEM) and X-ray diffraction (XRD). The study shows that the presence of agar has a significant influence on the morphology of the Zn deposits. Under the chosen conditions and without agar, the deposit shows a dendritic morphology, which is made of orderly arranged grains with a preferred orientation in [0001]. In the presence of agar, the deposit shows a dense branch morphology, which has a randomly oriented grain texture and diminished grain size in comparison with that of the dendritic morphology. This work contributes to understanding the influence of agar gel on the pattern formation in thin-layer electrodeposition. ?? 2008 Elsevier Ltd. All rights reserved.
Dendritic; Dense branch morphology; Thin-layer electrodeposition
Nanoscale mechanics of solid-supported multilayered lipid films by force measurement
Thin Solid Films
516
15
5039-5045
2008
10.1016/j.tsf.2008.02.023
Using atomic force microscopy and molecular force probe, we have studied the structure and nanomechanical response to nano-indentation of multilayered films of dioleoylphosphatidylcholine films prepared by solution spreading, spin-coating, and capillary methods. The influence of the film thickness on the apparent elastic (Young's) modulus is investigated. Young's moduli of samples prepared by the different methods were found to be similar for sufficiently thick films. An ostensible influence of substrate coupling on the apparent Young's modulus is observed for thinner lipid films. The results are discussed in comparison with previously reported estimates for supported lipid bilayers (membranes) and cells. ?? 2008 Elsevier B.V. All rights reserved.
Atomic force microscopy (AFM); Bilayer membrane; Lipid films; Nanomechanics; Solution spreading; Spin-coating; Structure and elastic properties; Young's modulus
A combined texture and FEM study of strain states during roll-cladding of five-ply stainless steel/aluminum composites
Materials Science and Engineering: A
453
347-358
2007
10.1016/j.msea.2006.10.130
Two composites of five plies of STS/Al/Al/Al/STS and STS/Al/STS/Al/STS were produced from ferritic stainless steel (STS 430) and aluminum alloy (AA 3003) sheets by roll-cladding at elevated temperature. In order to analyze the strain states during roll-cladding, the evolution of crystallographic textures at different through-thickness positions in the roll-clad composites was investigated. The finite element method (FEM) was employed to simulate the co-deformation of the different sheets and to determine the stresses and strains acting in the five-ply composites during roll-cladding. The strain states derived from the FEM simulations were used to model the texture evolution in the individual sheets of the roll-clad composites. Friction conditions were determined in a parametric study by fitting the overall thickness strains and modeled textures to the results obtained experimentally.
finite element method; roll-cladding; rolling texture; shear texture; strain state
Static and dynamic thermo-electro-mechanical analysis of angle-ply hybrid piezoelectric beams using an efficient coupled zigzag theory
Composites Science and Technology
64
16
2463-2475
2004
10.1016/j.compscitech.2004.05.012
This work presents static and dynamic electro-thermo-mechanical analysis of angle-ply hybrid piezoelectric beams using a recently developed efficient coupled zigzag theory. In this theory, the displacement approximations account for the thermoelectric strain in the thickness direction and the shear traction-free conditions at the top and the bottom of the beam and the shear continuity conditions at the layer interfaces are exactly satisfied. The theory is assessed against two-dimensional exact piezo-thermo-elasticity solution and compared with the first and third order shear deformation theories. The effect of the span-to-thickness ratio, type of loading and the orientation of the angle-plys on the accuracy of the theories is investigated. It has been concluded that, in general, the new zigzag theory is more accurate than the other theories considered.
A. Layered structures; A. Smart materials; B. Interface; B. Thermo-mechanical properties; C. Laminate theory
Bending of cross-ply laminated composites: An accurate and efficient plate theory based upon models of Lekhnitskii and Ren
Composite Structures
93
3
1078-1088
2011
10.1016/j.compstruct.2010.09.020
Bending laminated composites results in a distinctive zig-zag shaped deformation pattern, accordingly jumping transverse shear strains at layer interfaces, but continuous courses of transverse shear stresses there. An accurate representation of this laminate-specific mechanical behavior in terms of plate theories is challenging, even more if computational efficiency is aimed for. Here, an axiomatic equivalent single layer plate theory for cross-ply laminated composites is presented, which is based on the work of Lekhnitskii and Ren and delivers accurate deformation and stress prognoses at the cost of six solution variables. Fulfilling transverse stress continuity, the infinitesimal equilibrium equations are considered in order to derive an appropriate ansatz for the transverse shear stresses including the influence of all plane stress reduced stiffness components. However, the effect of the normal stress σzz is neglected, and deflection w is assumed constant across the plate thickness. The equilibrium equations and corresponding boundary conditions of the plate theory are derived by application of the principle of virtual displacements. Numerical results for symmetrical and non-symmetrical composites as well as for typical sandwich plates obtained by the present theory show good agreement with corresponding exact elasticity solutions given by Pagano, even for thick plates. © 2010 Elsevier Ltd.
Advanced plate theory; Cross laminated timber; Laminated composite plates; Navier solution; Shear deformations
Fabrication of active thin films for vibration damping in MEMS devices for the next generation army munition systems
Transformational Science and Technology for the Current and Future Force
42
251-+
2006
Doi 10.1142/9789812772572_0032
This research combined continuum mechanics modeling, materials design, materials fabrication/processing, and experimental testing/characterization to promote a materials solution for passive damping of undesirable extrinsic vibrations in microelectromechanical-systems-based devices. Shape memory alloy, nickel titanium (NiTi) thin films were deposited by an in-situ reactive DC magnetron sputtering process and piezoelectric, barium strontium titanate (Ba0.80Sr0.20TiO3) were fabricated using pulsed laser deposition and metal organic solution deposition techniques. These films were integrated as a bi-layer structure on n+ platinum silicon substrates to form a vibration-damping pedestal module known as "active materials". The optimized post deposition annealing temperatures for the shape memory alloy, and piezoelectric thin films were determined to be 500 and 750 degrees C, respectively. Crystalline, pinhole-free, and crack-free films of 250-400 nm thickness were fabricated. The surface roughness of the films was around 2.2 nm with average grain size of approximately 50 nm. Cross-sectional microscopy affirmed the dense and uniform microstructure. The bilayer pedestal design concept offers a solution for passive damping.
deposition; temperature
An approach for reliability-based robust design optimisation of angle-ply composites
Composite Structures
90
1
53-59
2009
10.1016/j.compstruct.2009.01.008
Variations of manufacturing process parameters and environmental aspects may affect the quality and performance of composite materials, which consequently affects their structural behaviour. Reliability-based design optimisation (RBDO) and robust design optimisation (RDO) searches for safe structural systems with minimal variability of response when subjected to uncertainties in material design parameters. An approach that simultaneously considers reliability and robustness is proposed in this paper. Depending on a given reliability index imposed on composite structures, a trade-off is established between the performance targets and robustness. Robustness is expressed in terms of the coefficient of variation of the constrained structural response weighted by its nominal value. The Pareto normed front is built and the nearest point to the origin is estimated as the best solution of the bi-objective optimisation problem. © 2009 Elsevier Ltd. All rights reserved.
Bi-objective optimisation; Composite structures; Reliability; Robust design
Analysis of Local Delaminations Caused by Angle Ply Matrix Cracks
Journal of Composite Materials
30
4
418-440
1996
10.1177/002199839603000401
Two different families of graphite/epoxy laminates with similar layups but different stacking sequences, (0θ/-θ) s and (-θ/θ/0) s , laminates, were analyzed using three-dimensional finite element analysis for 0 = 15 and 30 degrees. Delaminations were modeled in the -θ/θ interface, bounded by a matrix crack and the stress free edge. The total strain energy release rate, G, along the delamination front was computed using three different techniques: the virtual crack closure technique (VCCI), the equivalent domain integral (EDI) technique, and a global energy balance technique. The opening fracture mode component of the strain energy release rate, G1, along the delamination front was also computed for various delamination lengths using VCCT. Although the finite element model did not have an orthogonal mesh, VCCT still yielded accurate results which were in agreement with the global energy balance and yielded similar G distributions across the delamination front as the EDI technique. For both layups analyzed, the matrix crack length influenced the magnitude of G for delamination. Furthermore, the opening mode, G., was greatest near the matrix crack and decreased near the free edge. The laminate stacking sequences with a matrix crack in the surface angle ply had a greater GI value than the laminate stacking sequences with an angle ply matrix crack in the interior of the specimen thickness. This is consistent with test results in the literature that show delamination occurs earlier in the fatigue life of laminates with matrix cracks in the surface plies than in the interior plies.
A Continuous Transition Between Quantum and Classical Mechanics . I
Foundations
32
6
871-892
2002
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical mechanics which provides a continuous transition to quantum mechanics via environment-induced decoherence.
classical mechanics; decoherence; quantum mechanics
An enhanced single-layer variational formulation for the effect of transverse shear on laminated orthotropic plates
European Journal of Mechanics - A/Solids
29
4
567-590
2010
http://dx.doi.org/10.1016/j.euromechsol.2009.12.004
A novel mixed formulation is derived by means of Reissner's variational approach-based on Castigliano's principle of least work in conjunction with a Lagrange multiplier method for the calculus of variations. The governing equations present an alternative theory for modeling the important three-dimensional structural aspects of plates in a two-dimensional form. By integrating the classical Cauchy's equilibrium equations with respect to the thickness co-ordinate, and enforcing continuity of shear and normal stresses at each ply interface, condenses the effect of the thickness. A reduced system of partial differential equations of sixth-order in one variable, is also proposed, which contains differential correction factors that formally modify the classical constitutive equations for composite laminates. The theory degenerates to classical composite plate analysis for thin configurations. Significant deviations from classical plate theory are observed when the thickness becomes comparable with the in-plane dimensions. A variety of case studies are presented and solutions are compared with other models available in the literature and with finite element analysis.
Castigliano's theorem; Mixed formulatio; Variational approach
A Rate Dependent Constitutive Model for Carbon-Fiber Reinforced Plastic Woven Fabrics
Mechanics of Advanced Materials and Structures
14
8
619-631
2007
10.1080/15376490701672443
This paper deals with the modelling until rupture of composite\nstructures made of carbon-fiber/epoxy-resin woven fabrics submitted to\ndynamic loadings. The model is built at the mesoscale of the elementary\nply. It takes into account the slightly nonlinear brittle behavior of\nthe fibers under tensile solicitations, their nonlinear behavior in\ncompression as well as the strongly nonlinear and irreversible behavior\nof the ply in shear. Strain rate effects are also introduced and\nspecial attention is paid to the objectivity of the model in the\ncontext of finite element calculation. Therefore the choice of a\ndelayed damage mesomodel coupled with viscoplasticity is made. In order\nto identify the values of the parameters of the model, an optimization\nprocedure based on a gradient-free direct search method has been\ndeveloped. As a logical procedure to this study, the models ability to\navoid strain localization and mesh dependence is then checked on simple\nuniaxial examples. The last part of this paper is devoted to structural\ncalculation. The results of the simulations of both the impact on\ncomposite plate and the crushing of thin-walled tube demonstrate the\ncapability of the model to reproduce observed physical phenomena.
composite woven fabrics; delayed damage mesomodel; direct search method; dy-; identification; viscoplasticity
Axial capacity and crushing of thin-walled metal, fibre-epoxy and composite metal-fibre tubes
Thin-Walled Structures
48
6
440-452
2010
10.1016/j.tws.2010.01.006
Recent investigations of square hollow section (SHS) metal tubes with externally bonded carbon fibres have shown significant increases in the axial capacity and mean crushing load, compared with the metal SHS. The composite metal-fibre tubes employed carbon fibre reinforced polymer (CFRP) matrix layouts of two and four layers of carbon fibres. In this paper the same sized two and four layer CFRP SHS were manufactured independent of the metal SHS, and the axial capacity and crushing behaviour were determined experimentally. Four different tube sizes were tested, resulting in tube width to thickness ratios between 32 and 144. A photogrammetry system was employed to accurately determine the buckling and post-buckling behaviour. It is shown that the capacity and mean crush load of the composite metal-CFRP SHS exceed the sum of those for the individual metal SHS and CFRP SHS, by up to 1.8 times. This composite action results from the bond between the metal and the carbon fibres, and the mechanics with respect to buckling, capacity and crushing is discussed. The strength of metal, composite metal-CFRP and CFRP tube walls are determined using the effective width approach, and are shown to compare well with the experimental results. ?? 2010 Elsevier Ltd. All rights reserved.
Buckling; Carbon fibre reinforced polymer (CFRP); Composite tubes; Crushing; Energy absorption; Metal-fibre composites
Quantitative Interfacial Energy Measurements of Adhesion-Promoted Thin Copper Films by Supercritical Fluid Deposition on Barrier Layers
Journal of Engineering Materials and Technology
132
April 2010
021014
2010
10.1115/1.4000283
A fivefold increase in adhesion energy is observed for poly(acrylic acid) (PAA) modified Cu/TaN interfaces in which the thin copper films are deposited by the hydrogen assisted reduction of bis(2,2,7-trimethyloctane-3,5-dionato) copper in supercritical carbon dioxide. The PAA adhesion layer is sacrificial at the reaction conditions used, and X-ray photoelectron spectroscopy has shown that the Cu/TaN interface is free of contamination following deposition. The resulting average interfacial adhesion energy is just above 5 J/m(2), which meets adhesion requirements for integration in Cu interconnects. The adhesion measurements are performed with a custom built four-point bend fracture mechanics testing system. Comparison of the copper film thickness to the measured adhesion energy indicated that there is no effect on the adhesion energy as the film thickness changes.
adhesion; fracture mechanics; supercritical fluid deposition
Rolling stones: The motion of a sphere down an inclined plane coated with a thin liquid film
Physics of Fluids
21
8
1-8
2009
10.1063/1.3207884
A spherical bead deposited on a smooth tilted dry plane wall rolls down the slope under the uniform acceleration of gravity. We describe an analogous experiment conducted using a plane wall that is coated with a thin layer (of order 50–100 μm) of a viscous liquid. The steady motion of the sphere under gravity involves a combination of rotation and sliding. We examine the dependence of the experimentally observed steady translational and rotational speeds on the physical parameters in the system. In particular, the interplay between viscous forces and interfacial forces leads to nontrivial exponents for the scaling of the speeds with the characteristics of the sphere and the viscous liquid. The overhang situation, in which the sphere rolls down the underside of an inclined lubricated plane, is also examined. In this case, the steady motion is still observed for a certain range of angles and bead sizes; that is, the sphere does not always detach from the surface. The adhesive force arises dynamically from the motion of the sphere and can exceed classical quasistatic capillary forces. Such a force should also play a role in other problems of lubrication mechanics such as humid granular flows.
Fluid Mechanics
Comparative biochemistry and physiology Toxicology pharmacology CBP
80
1
766
2002
For many researchers, next generation sequencing data holds the key to answering a category of questions previously unassailable. One of the important and challenging steps in achieving these goals is accurately assembling the massive quantity of short sequencing reads into full nucleic acid sequences. For research groups working with non-model or wild systems, short read assembly can pose a significant challenge due to the lack of pre-existing EST or genome reference libraries. While many publications describe the overall process of sequencing and assembly, few address the topic of how many and what types of reads are best for assembly. The goal of this project was use real world data to explore the effects of read quantity and short read quality scores on the resulting de novo assemblies. Using several samples of short reads of various sizes and qualities we produced many assemblies in an automated manner. We observe how the properties of read length, read quality, and read quantity affect the resulting assemblies and provide some general recommendations based on our real-world data set.
Prediction of the fatigue life of slender web plates using fracture mechanics concepts
Thin-Walled Structures
35
2
81-100
1999
10.1016/S0263-8231(99)00025-7
The results of a series of fatigue tests, on slender plate girders subjected to repeated shear loading, are summarized and used to establish a lower bound fatigue strength curve for the welded web boundary, based on geometric or principal surface stress ranges. The propagation of a semi-elliptical surface crack, through the thickness of a plate, is studied using fracture mechanics concepts. An extensive parametric study indicates that the initial crack size and aspect ratio, the geometric stress concentration at the weld toe, and the plate thickness, all have a significant influence on fatigue strength. It is concluded that the fracture mechanics approach requires specification of a number of parameters which are difficult to determine in practice. However, having specified a realistic crack size and aspect ratio and an approximate stress concentration at the weld toe, the solution can be calibrated against available experimental fatigue strength curves.
fatigue; fracture mechanics; plate girder; shear buckling; welding
Evaluation of modeling techniques for a type III hydrogen pressure vessel (70 MPa) made of an aluminum liner and a thick carbon/epoxy composite for fuel cell vehicles
International Journal of Hydrogen Energy
37
3
2353-2369
2012
10.1016/j.ijhydene.2011.11.001
Stress distributions in the composite layers of a Type III hydrogen pressure vessel composed of a thin aluminum liner (5 mm) and a thick composite laminate (45 mm) were calculated by using three different modeling techniques. The results were analyzed and compared with the plausible stress distribution calculated by a full ply-based modeling technique. A laminate-based modeling technique underestimated the generated stresses especially at the border between the cylinder and dome parts. A hybrid modeling technique combining a laminate-based modeling for the dome part with a ply-based modeling for the cylinder part was also tried, but it overestimated the generated stresses at the border. In order for the ply-based modeling technique to carry out precise analysis, a fiber trajectory function for the dome part was derived and the composite thickness variation was also considered.
Anisotropic property; Laminates; Ply; Type III hydrogen pressure vessels; Winding angle
Frontal accretion along the western Mediterranean Ridge: the effect of Messinian evaporites on wedge mechanics and structural style
Marine Geology
186
59-82
2002
10.1016/S0025-3227(02)00173-1
In the context of the IMERSE project, several crossings of the deformation front of the western Mediterranean Ridge were made in the region of the Sirte Abyssal Plain, the Messina Abyssal Plain and the intervening region. In this paper, we present seismic images and interpretations across the deformation front, with particular emphasis on the role the Messinian evaporites have played in controlling the accretionary tectonics of the thin frontal portion of the wedge. The seismic images show that the basal detachment generally is located at the base of the evaporites. From a consideration of the mechanics of the wedge, for both Coulomb and plastic rheologies, we show that the low wedge taper (c. 2< degrees >) requires that the detachment is characterised by extreme fluid overpressuring (within 2% of lithostatic in places) and that the basal yield stress (less than 1 MPa) is lower than that of a wet salt decollement zone. This supports the seismic interpretation that the detachment occurs in overpressured sediments beneath the impermeable evaporites. Lateral variations in the accretionary style can be related to lateral variations in evaporite thickness, the effectiveness of the evaporite as an impermeable seal and to local relief on the subducting plate; these factors control the escape of fluids from beneath the evaporites and hence fluid pressure and basal yield stresses. < copyright > 2002 Elsevier Science B.V. All rights reserved.
accretionary wedges; basal detachment; mediterranean ridge; messinian; uid pressure
Strain measurement in the wavy-ply region of an externally pressurized cross-ply composite ring
Journal of Engineering Materials and Technology-Transactions of the Asme
118
3
325-329
1996
Doi 10.1115/1.2806813
Ply-level strains are determined in the cross-section of an externally pressurized cross-ply (3:1 circumferential to axial fiber ratio) graphite-epoxy ring containing ara isolated circumferential wavy region. A special test fixture was used which permitted measuring orthogonal displacement components in the wavy area using moire interferometry as the pressure was increased. Strain components were determined at selected locations in the wavy area up to approximately 90 percent of failure pressure. The study shows: (1) Large interlaminar shear strains, which are non-existent in the ''perfect'' ring, are present near the wave inflection points: (2) The wavy plies generate increased interlaminar normal compressive strains in both circumferential and axial plies along a radial line coinciding with maximum wave amplitude; and (3) Nonlinear strain response begins at approximately 60 percent of failure pressure.
hydrostatically loaded cylinders; layer waviness; stress state
Effect of tube geometry and ply-angle on energy absorption of a circular glass/epoxy crush tube - A numerical study
Composites Part B: Engineering
43
2960-2967
2012
10.1016/j.compositesb.2012.05.040
The superior specific energy absorption characteristics of long fiber composite structures as compared to aluminum and steel are well established. Due to cost and time involved in testing of composites, it is imperative to develop numerical solution of the crushing phenomenon. The work presented here reports work to better understand the energy absorption characteristics of glass-fiber circular crush tubes. The effect of tube diameter and ply orientation on the energy absorption has been extensively investigated. Numerical results are compared with experiments performed elsewhere and the correlation between the two is encouraging. ?? 2011 Elsevier Ltd. All rights reserved.
A. Glass fibers; A. Polymer-matrix composites; B. Directional orientation; B. Energy absorption; B. Impact behavior
New Double Indentation Technique for Measurement of the Elasticity Modulus of Thin Objects
Experimental Mechanics
51
1
85-95
2010
10.1007/s11340-010-9340-8
The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, sodalime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the loaddisplacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.
double indentation; elasticity modulus; fe modelling; measurement method; middle ear ossicle bone; thin objects
An aeroelastic model for composite rotor blades with straight and swept tips. Part I: Aeroelastic stability in hover
International Journal of Non-Linear Mechanics
37
4-5
967-986
2002
10.1016/S0020-7462(01)00109-3
An analytical model for predicting the aeroelastic behavior of composite rotor blades with straight and swept tips is presented. The blade is modeled by beam type finite elements along the elastic axis. A single finite element is used to model the swept tip. The non-linear equations of motion for the finite element model are derived using Hamilton's principle and based on a moderate deflection theory and accounts for: arbitrary cross-sectional shape, pretwist, generally anisotropic material behavior, transverse shears and out-of-plane warping. Numerical results illustrating the effects of tip sweep, anhedral and composite ply orientation on blade aeroelastic behavior are presented. It is shown that composite ply orientation has a substantial effect on blade stability. At low thrust conditions, certain ply orientations can cause instability in the lag mode. The flap-torsion coupling associated with tip sweep can also induce aeroelastic instability in the blade. This instability can be removed by appropriate ply orientation in the composite construction. © 2002 Published by Elsevier Science Ltd.
Fibrin clot structure and mechanics associated with specific oxidation of methionine residues in fibrinogen
Biophysical Journal
103
11
2399-2407
2012
10.1016/j.bpj.2012.10.036
Using a combination of structural and mechanical characterization, we examine the effect of fibrinogen oxidation on the formation of fibrin clots. We find that treatment with hypochlorous acid preferentially oxidizes specific methionine residues on the ??, ??, and ?? chains of fibrinogen. Oxidation is associated with the formation of a dense network of thin fibers after activation by thrombin. Additionally, both the linear and nonlinear mechanical properties of oxidized fibrin gels are found to be altered with oxidation. Finally, the structural modifications induced by oxidation are associated with delayed fibrin lysis via plasminogen and tissue plasminogen activator. Based on these results, we speculate that methionine oxidation of specific residues may be related to hindered lateral aggregation of protofibrils in fibrin gels. ?? 2012 Biophysical Society.
Probability theory in quantum mechanics
American Journal of Physics
54
10
883
1986
10.1119/1.14783
The abstract theory of probability and its interpretation are briefly reviewed, and it is explicitly demonstrated that the formalism of quantum mechanics satisfies the axioms of probability theory. This refutes the suggestions which have occasionally been made that ‘‘classical’’ probability theory does not apply to quantum mechanics. Several erroneous applications of probability theory to quantum mechanics are examined, and the nature of the errors are exposed. It is urged that more attention be given to probability theory in the physics curriculum.
Dynamic response of single-ply membrane roofing systems
Journal of Wind Engineering and Industrial Aerodynamics
42
1-3
1525-1536
1992
10.1016/0167-6105(92)90161-3
The use of a servo system, able to reproduce measured time-varying wind pressures on areas of cladding at full scale, has shown the dynamic response of some porous and flexible claddings systems to be non-linear and frequency-dependent, indicating that static proof testing methods may be inappropriate.
Quantum mechanics: Hidden context
Nature
1-2
2009
10.1038/460464a
The idea that physical phenomena might be described by a more down- to-earth theory than quantum physics has met with resistance from many physicists. Indeed, it seems that nature is not as simple as we would like.
Statistical Mechanics
Distribution
8
5
519-521
1987
10.1017/CBO9780511815836
Unlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition.
Measurements of Piezoelectric Coefficient d 33 of Lead Zirconate Titanate Thin Films Using a Mini Force Hammer
Journal of Vibration and Acoustics
135
1
011003
2013
10.1115/1.4006881
Lead zirconate titanate (PbZrxTi1-xO3, or PZT) is a piezoelectric material widely used as sensors and actuators. For microactuators, PZT often appears in the form of thin films to maintain proper aspect ratios. One major challenge encountered is accurate measure- ment of piezoelectric coefficients of PZT thin films. In this paper, we present a simple, low-cost, and effective method to measure piezoelectric coefficient d33 of PZT thin films through use of basic principles in mechanics of vibration. A small impact hammer with a tiny tip acts perpendicularly to the PZT thin-film surface to generate an impulsive force. In the meantime, a load cell at the hammer tip measures the impulsive force and a charge amplifier measures the responding charge of the PZT thin film. Then the piezoelectric coefficient d33 is obtained from the measured force and charge based on piezoelectricity and a finite element modeling. We also conduct a thorough parametric study to under- stand the sensitivity of this method on various parameters, such as substrate material, boundary conditions, specimen size, specimen thickness, thickness ratio, and PZT thin- film material. Two rounds of experiments are conducted to demonstrate the feasibility and accuracy of this new method. The first experiment is to measure d33 of a PZT disk resonator whose d33 is known. Experimental results show that d33 measured via this method is as accurate as that from the manufacturer’s specifications within its tolerance. The second experiment is to measure d33 of PZT thin films deposited on silicon substrates. With the measured d33, we predict the displacement of PZT thin-film membrane microac- tuators. In the meantime, the actuator displacement is measured via a laser Doppler vibrometer. The predicted and measured displacements agree very well validating the accuracy of this new method.
On the breakup of a thin liquid film subject to interfacial shear
Journal of Fluid Mechanics
500
113-133
2004
10.1017/S0022112003007080
The breakup of a thin non-evaporating liquid film that is either flowing down or climbing on a vertical or inclined surface and subject to cocurrent or countercurrent interfacial shear (or gas flow) is investigated analytically. Analytical expressions for the dimensionless liquid film thickness, $\Delta_{\hbox{\scriptsize\it min}}$, and wetting rate, $\Gamma_{\hbox{\scriptsize\it min}}$, at breakup are derived based on the minimization of the total energy of a stable rivulet, formed following the film breakup. For a downflowing liquid film, increasing the cocurrent interfacial shear (or gas velocity) or decreasing the equilibrium contact angle, $\theta_{o}$, decreases both $\Delta_{\hbox{\scriptsize\it min}}$ and $\Gamma _{\hbox{\scriptsize\it min}}$, below their values with zero interfacial shear. Conversely, increasing the countercurrent interfacial shear or $\theta_{o}$, increases both $\Delta_{\hbox{\scriptsize\it min}}$ and $\Gamma_{\hbox{\scriptsize\it min}}$, above their values with zero interfacial shear. The predictions of $\Delta _{\hbox{\scriptsize\it min}}$ and $\Gamma _{\hbox{\scriptsize\it min}}$ for a climbing water film on a vertical surface are in good agreement with reported experimental data for a wide range of cocurrent gas velocities.
Mechanics of low density materials
Journal of the Mechanics and Physics of Solids
34
6
563-578
1986
10.1016/0022-5096(86)90037-2
Mechanics analyses are used to derive the effective elastic moduli for low density materials. Both open cell and closed cell geometric models are employed in the case of isotropic media. The five independent effective moduli are derived for a low density transversely isotropic medium. Compressive strength, as defined by elastic stability, is also derived for open cell and closed cell isotropic materials. The theoretical results are compared with some experimental results, and also are assessed with respect to previous work.
Mesofracture mechanics: a necessary link
Theoretical and Applied Fracture Mechanics
37
1-3
371-395
2001
10.1016/S0167-8442(01)00081-7
Classical fracture mechanics is based on the premise that small scale features could be averaged to give a larger scale property such that the assumption of material homogeneity would hold. Involvement of the material microstructure,...
A Field Guide to Recent Work on the Foundations of Statistical Mechanics
The Ashgate Companion to Contemporary Philosophy of Physics
99-196
2008
This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility, ergodicity, mixing, coarse graining, past hypothesis, reductionism, phase average, thermodynamic limit, interventionism, entropy.
Structure and Mechanics of woven Fabrics
New York
1-316
2004
10.1533/9781845690403
Fabric mechanics are fundamental to the way textiles are designed, tested and manufactured and underpin the way woven fabrics are used in the modern world. With fully comprehensive coverage of all aspects of fabric anisotropy, stress-strain relationships and fabric drape modelling and testing, structure and mechanics of woven fabrics, discusses and exemplifies all major aspects of fabric mechanics and their relevance to every stage of the contemporary textile industry. ??After a general introduction illustrating the role and study of woven fabric mechanics, the first group of chapters examines the structural, tensile, bending and shear properties of woven fabrics. Sections cover the general behaviour of these properties, how they are modelled and their anisotropy. Drape deformation modelling is covered extensively, one chapter detailing theory and a second, computation and simulation. The properties of fabrics with seams and fabric complex deformation analysis and simulation are also detailed. ??Structure and mechanics of woven fabrics is an essential reference for all textile academics, students, researchers, technicians, engineers and technologists, covering all areas of textile material applications, from composites and geotextiles, to medical textiles and biotextiles.
The spreading of a thin drop by gravity and capillarity
Quarterly Journal of Mechanics and Applied Mathematics
36
1
55-69
1983
10.1093/qjmam/36.1.55
Solutions are given for the spreading of a thin drop using lubrication theory. The relative importance of gravity to capillarity in the spreading is measured by the Bond number and all values of this number are covered. As usual when a moving contact line is present, a slip boundary condition is applied. For moderate and low Bond numbers the solution is found by matching three asymptotic expansions, and numerical results are given for the rate of spread as a function of the radius. A very simple solution is obtained in the special case of zero Bond number, when the spreading is by capillarity alone. When the Bond number is large, a similarity solution exists for the drop as a whole, but it fails near the edge of the drop and when the drop is close to its equilibrium position. It is shown here that the similarity solution can be completed by a solution valid near the edge and the approach to equilibrium is also discussed.
Fracture Mechanics: Fundamentals and Applications
Aerospace Engineering
2
688
1995
With its combination of practicality, readability, and rigor that is characteristic of any truly authoritative reference and text, Fracture Mechanics: Fundamentals and Applications quickly established itself as the most comprehensive guide to fracture mechanics available. It has been adopted by more than 100 universities and embraced by thousands of professional engineers worldwide. Now in its third edition, the book continues to raise the bar in both scope and coverage. It encompasses theory and applications, linear and nonlinear fracture mechanics, solid mechanics, and materials science with a unified, balanced, and in-depth approach.Reflecting the many advances made in the decade since the previous edition came about, this indispensable Third Edition now includes: A new chapter on environmental cracking Expanded coverage of weight functions New material on toughness test methods New problems at the end of the book New material on the failure assessment diagram (FAD) method Expanded and updated coverage of crack closure and variable-amplitude fatigue Updated solutions manualIn addition to these enhancements, Fracture Mechanics: Fundamentals and Applications, Third Edition also includes detailed mathematical derivations in appendices at the end of applicable chapters; recent developments in laboratory testing, application to structures, and computational methods; coverage of micromechanisms of fracture; and more than 400 illustrations. This reference continues to be a necessity on the desk of anyone involved with fracture mechanics.
A survey of Bohmian mechanics
Il Nuovo Cimento B
110
5-6
737-750
1995
10.1007/BF02741477
Bohmian mechanics is the most naively obvious embedding imaginable of Schr\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function $\psi$ its configuration is typically random, with probability density $\rho$ given by $|\psi|^2$, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, is a consequence of Bohmian mechanics.
01.30.Cc; 03.65.Bz; Conference proceedings; Foundations; miscellaneous theories; theory of measurement
The stability of thin, stretched and twisted elastic rods
International Journal of Non-Linear Mechanics
68
96-100
2015
10.1016/j.ijnonlinmec.2014.05.018
The stability of thin elastic rods that have been stretched and twisted is considered. Two general stability criteria are proposed. The first is appropriate when both the axial stretch and the torsional twist are prescribed and it is based on the elegant method of Gent for the formulation of a knot in twisting. The second criterion is valid when the axial force and the moment about the axis of the rod are prescribed. Both criteria are valid for all thin elastic rods, being independent of the modelling approach adopted. The criteria are illustrated with specific examples of the phenomenological approach to the modelling of thin, elastic, incompressible rods in tension and torsion.
Elastic rods; Stability; Thin; Torsion and extension
P. A. M. Dirac and the discovery of quantum mechanics
American Journal of Physics
79
3
261
2011
10.1119/1.3536639
Dirac’s contributions to the discovery of nonrelativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described.
Comparative study on the behavior of woven-ply reinforced thermoplastic or thermosetting laminates under severe environmental conditions
Materials and Design
35
707-719
2012
10.1016/j.matdes.2011.10.037
This work aims at determining whether thermoplastic-based composites can be used in secondary aircraft structures to replace thermosetting-based composites or not. In order to answer this question, the mechanical behaviors of carbon fiber fabric reinforced thermoplastic (PPS or PEEK) and thermosetting (epoxy) laminates subjected to different stress states under severe environmental conditions (120??C after hygrothermal aging) have been compared. In addition to usual mechanical tests (tensile, open hole tensile), single-bolt double lap joint and single-bolt single lap joint tests were also performed. Severe conditions help enhance the ductile behavior of the epoxy matrix, but degrade the fiber/matrix interface, resulting in lower stiffness and strength of laminates with a quasi-isotropic lay-up. In thermoplastic-based laminates, the degree of retention of mechanical properties is quite high even for PPS-based laminates when T>Tg. In laminates with a [45]7 lay-up, severe conditions adversely affect the mechanical properties of the three composite systems. However, the combination of matrix ductile behavior, and the strain gradient near the hole, lead to an extensive plastic deformation along the ??45?? oriented fibers bundles in notched A-P laminates. It results in decreasing significantly the hole-sensitivity of C/PPS and C/Epoxy under severe conditions. In bolted joints, a severe environment has a limited impact on the bearing strength of epoxy-based laminates. In the case of thermoplastic-based laminates, it increases the strength of double lap joints, but is detrimental to the strength of single lap joints. ?? 2011 Elsevier Ltd.
A. Polymers; D. Mechanical fastening; E. Environmental performance
New Foundations for Classical Mechanics
American Journal of Physics
58
703
1990
10.1119/1.16386
This study evaluates the effect of whole blood storage on common coagulation parameters in order to confirm or revise acceptable storage limits as defined by current guidelines and diverse study reports. Aliquots were taken from the citrated whole blood of inpatients and outpatients (n = 147) within 4 h after blood withdrawal and after extended storage of whole blood for 8 and 24 h at ambient temperature. Aliquots were centrifuged and analyzed for prothrombin time (PT), activated partial thromboplastin time (APTT), fibrinogen (Fbg), antithrombin (AT), thrombin time (TT) and D-dimer. For each parameter, samples from 33-56 patients were investigated covering a wide range of normal and pathological values. Samples from patients receiving heparin were excluded from analyses of APTT and TT. All assays were performed using reagents and an analyzer from Siemens Healthcare Diagnostics Products GmbH. The mean percentage change after 8 and 24-h storage was below 10% for all parameters. Considering the changes in individual samples, all parameters can be reliably tested after 8-h storage, since less than 15% of the samples demonstrated individual changes of above 10%. The acceptable storage time can be extended to 24 h for PT, TT and D-dimer. Clinically relevant changes were detected after 24-h storage for APTT: 41% of the investigated samples demonstrated changes of above 10%. After 24-h storage, changes for Fbg and AT values were more than 15% in five out of 49 and in three out of 45 samples, respectively. This sporadic increase of values is clinically acceptable except for borderline samples.
Mesh-independent modeling and moiré interferometry studies of damage accumulation in open-hole composite laminates
Mechanics of Composite Materials
40
5
419-427
2004
10.1023/B:MOCM.0000047232.60559.27
A three-dimensional ply-level modeling of multiple matrix cracking near an open hole in a quasi-isotropic composite laminate was performed. A mesh-independent displacement discontinuity modeling method based on higher-order shape functions was constructed for this purpose. The mesh configuration is dictated by the boundaries of a specimen, such as the presence of a hole, whereas the matrix cracking surfaces are aligned with the fiber direction in a given ply. The surface of the displacement jump associated with matrix cracking was defined in terms of the domain Heaviside function approximated by using higher-order polynomial B-splines. Several matrix cracks in each ply of a [0/45/90/–45]s composite were modeled, and their effect on the fiber-direction stress magnitude in the 0? ply was examined. Up to 35% relaxation of the fiber-direction strain amplitude due to matrix cracking (splitting) in the 0? ply was predicted. The moiré interferometry was used to experimentally determine the strain and displacement fields in the surface layer of the same composite, previously prestressed beyond the damage initiation load. A good correlation between the experimental data and the stress redistribution predicted by the mesh-independent damage modeling technique was observed.
composite laminates; moiré interferometry; numerical B-spline analysis; strength
Design and Potentiality of an Apparatus for Measuring Yarn/Yarn and Fabric/Fabric Friction
Experimental Mechanics
52
8
1123-1136
2012
10.1007/s11340-011-9566-0
The market demand for thicker complex shaped structural composite parts is increasing. Processes of the Liquid Composite Moulding (LCM) family, such as Resin Transfer Moulding (RTM) are considered to manufacture such parts. The first stage of the RTM process consists in the preforming of the part. During the pre-forming of multilayered reinforcements, frictions between the plies occur and need to be taken into account for the forming simulation. An experimental device designed to analyse the ply/ply and ply/tool frictions has been set up. The different set up steps of the device are described. First results are presented, which show the ply/ply friction behaviour for a glass plain weave fabric. A specific contact behaviour has been observed for dry reinforcement fabric in comparison to non-technical textiles. A honing effect classically observed in dry fabric testing has also been pointed out through cyclic experiments. It can be attributed to both fibre material abrasion and fibre reorganisation inside the yarn.
Contact; Fabrics; Friction; Friction measurements; RTM; Textiles; Tribology; Woven reinforcement
A first-ply failure analysis of composite laminates
Computers and Structures
25
3
371-393
1987
A finite-element computational procedure is developed for the first-ply failure analysis of laminated composite plates. The procedure is based on the first-order shear deformation theory and a tensor polynomial failure criterion that contains the maximum stress, maximum strain, the Hill, Tsai-Wu and Hoffman failure criteria as special cases. By specifying the desired criterion, a first-ply failure analysis of composite laminates subjected to in-plane and/or bending loads can be achieved. A number of problems are presented to evaluate these failure criteria when applied to laminates subjected to in-plane and/or bending loads
bending; elastic deformation; failure (mechanical); finite element analysis; laminates; mechanical engineering computing
A partitioned fluid-structure algorithm for elastic thin valves with contact
Computer Methods in Applied Mechanics and Engineering
197
1750-1761
2008
10.1016/j.cma.2007.03.019
We present a numerical method to simulate the movements of a thin valve immersed in an incompressible viscous fluid. The fluid and structure meshes are not matching: the kinematic continuity is imposed using Lagrange multipliers. The method therefore belongs to the "Fictitious Domain" (FD) family. This approach allows very large displacements. We propose a partitioned fluid-structure algorithm which keeps the fluid and structure solvers independent and which is able to manage contact without assuming that the structure solvers include contact capabilities. Various numerical tests are proposed. In particular, when the displacement is moderate, we show that the results are in good agreement with Arbitrary Lagrangian Eulerian (ALE) simulations. We then present results with contact on a rigid wall. Finally we show that the proposed approach can be mixed with ALE when the wall is elastic. ?? 2007 Elsevier B.V. All rights reserved.
ALE; Contact; Fictitious domains; Valves
Fracture Mechanics of Bond Failure in the “Pure Shear” Test Piece
Rubber Chemistry and Technology
76
2
483-494
2003
10.5254/1.3547755
The "pure shear" test piece consists of a thin, rectangular strip of rubber held by or bonded to rigid grips along its long edges. When the grips are pulled apart, the rubber in the center of the test piece is in a deformed state close to pure shear. This test piece is commonly used for studies of fracture in rubber (rubber tear) because it is amenable to simple fracture mechanics analyses. The "pure shear" test piece may also be used for study of failure at the rubber-to-metal bond. Its geometry and manner of loading make it especially useful for study of long-term durability of bonds in corrosive environments such as in a salt fog chamber. This paper discusses non-linear finite element analysis results for failure at the bond of the "pure shear" test piece. Results are compared with well-known results for analogous cases in rubber tear. Short and long cracks located in the center and at the free edges are considered.
A first-ply failure analysis of composite laminates
Computers & Structures
25
3
371-393
1987
10.1016/0045-7949(87)90130-1
A finite-element computational procedure is developed for the first-ply failure analysis of laminated composite plates. The procedure is based on the first-order shear deformation theory and a tensor polynomial failure criterion that contains the maximum stress, maximum strain, the Hill, Tsai-Wu and Hoffman failure criteria as special cases. By specifying the desired criterion, a first-ply failure analysis of composite laminates subjected to in-plane and/or bending loads can be achieved. A number of problems are presented to evaluate these failure criteria when applied to laminates subjected to in-plane and or bending loads.
Measurements of Deflection and Residual Stress in Thin Films Utilizing Coherent Light Reflection/Projection Moir, Interferometry
EXPERIMENTAL MECHANICS
53
6
977-987
2013
10.1007/s11340-012-9699-9
Thin film technology is an area of great importance in current applications of opto-electronics, electronics, MEMS and computer technology. A critical issue in thin film technology is residual stresses that arise when the coating is deposited onto a substrate. Residual stresses can be very large in magnitude and have detrimental effects on the role that the thin film must play. To save development time on coating deposition processes it is important to perform accurate residual stresses measurements in situ in real time where the deposition is made. A novel optical set up is developed in this study to measure deflections and residual stresses generated in coated specimens that can be applied directly in the reactor utilized in the deposition process. Experimental results are in good agreement with other measurements carried out independently and other data reported in literature for thin films like those tested in the experiments.
Numerical analysis of a model for ferromagnetic shape memory thin films
Computer Methods in Applied Mechanics and Engineering
196
3759-3770
2007
10.1016/j.cma.2006.10.039
We give a model for the deformation and magnetization of a single crystal ferromagnetic shape memory thin film under the influence of an applied magnetic field. The energy is nonconvex since it models multiple phases and symmetry-related variants of the crystal structure. Nonconvexity is also presented by the magnetic saturation condition which requires the magnetization to have a constant magnitude. We propose a class of finite element methods and prove a rate of convergence for the minimum thin film energy. In addition to the challenge of analyzing a nonconvex energy, the analysis overcomes the challenge presented by contributions to the energy that are naturally defined in the reference configuration for the elastic energy and in the spatial frame for the magnetic energy. We present numerical computations for the deformation and magnetization of a Ni2MnGa thin film that exhibit the convergence rate given by analysis. ?? 2007 Elsevier B.V. All rights reserved.
Ferromagnetic; Phase transformation; Shape memory; Thin film
Microscopic mechanics of fiber networks
Journal of Applied Physics
75
5
2383-2392
1994
10.1063/1.356259
Studies the microscopic mechanics of fiber networks. Challenges of\nelastic deformation and fracture in disordered fiber networks; Model\nof the fiber network; Stress variation along a fiber.
Fluid mechanics for engineers: A graduate textbook
Fluid Mechanics for Engineers: A Graduate Textbook
1-504
2010
10.1007/978-3-642-11594-3
The contents of this book covers the material required in the Fluid Mechanics Graduate Core Course (MEEN-621) and in Advanced Fluid Mechanics, a Ph.D-level ...
Equilibrium and nonequilibrium statistical mechanics
NASA STI/Recon Technical Report A
76
32809
1975
The general concepts of statistical mechanics are examined, taking into account Hamiltonian dynamics, statistical ensembles, and reduced distribution functions. Equilibrium statistical mechanics are considered, giving attention to equilibrium ensembles and thermodynamics, equilibrium properties of ideal systems, slightly nonideal systems in equilibrium, reduced distribution functions in equilibrium, dense fluids in equilibrium, phase transitions, and modern theories of critical phenomena. Discussed subjects of nonequilibrium statistical mechanics include an intuitive treatment of nonequilibrium phenomena, kinetic equations and hydrodynamics, eigenvalues of the kinetic equations and the theory of transport coefficients, and the evolution in time of weakly coupled gases
Classical Mechanics; Distribution Functions; Dynamic Characteristics; Eigenvalues; Equilibrium Equations; Hamiltonian Functions; Hydrodynamics; Kinetic Equations; Kinetic Theory; Nonequilibrium Conditions; Phase Transformations; Quantum Mechanics; Statistical Distributions; Statistical Mechanics; Steady State; Thermodynamic Equilibrium; Transport Theory
Fluid Mechanics in Disks Around Young Stars*
Annual Review of Fluid Mechanics
41
1
283-315
2009
10.1146/annurev.fluid.010908.165144
This article reviews hydrodynamic and magnetohydrodynamic processes in disks around young stars, encompassing the epochs of molecular-cloud turbulence, dense core collapse, disk formation, disk evolution, and planetesimal formation.
accretion disks; astrophysical fluid dynamics; planetesimal formation; protoplanetary disks
A Reconstruction of Quantum Mechanics
Foundations of Physics
45
5
557-590
2015
10.1007/s10701-015-9886-5
We show that exactly the same intuitively plausible definitions of state, observable, symmetry, dynamics, and compound systems of the classical Boolean structure of intrinsic properties of systems lead, when applied to the structure of extrinsic, relational quantum properties, to the standard quantum formalism, including the Schrödinger equation and the von Neumann–Lüders Projection Rule. This approach is then applied to resolving the paradoxes and difficulties of the orthodox interpretation.
First order analysis of thin plate deformable mirrors
Journal of the Korean Physical Society
44
6
757-764
2003
10.1117/12.459743
Continuous thin-plate deformable mirrors with discrete actuators are widely used as adaptive mirrors. The performance of a thin-plate deformable mirror can be characterized by the influence functions and the layout of the actuators. This paper first derives equations that model the influence functions of thin-plate deformable mirrors based on an analytic calculation and a finite- element analysis; then, it presents a performance analysis for the cases of triangular, rectangular, and hexagonal patterned-actuators. The results from this study may be used for first-order design and analysis of thin-plate deformable mirrors.
adaptive optics; deformable mirror; opto-mechanics
Micro- and Nanoscale Fluid Mechanics
Chemistry & …
536
2010
10.1017/CBO9780511760723
This text focuses on the physics of fluid transport in micro- and nanofabricated liquid-phase systems, with consideration of gas bubbles, solid particles, and macromolecules. This text was designed with the goal of bringing together several areas that are often taught separately - namely, fluid mechanics, electrodynamics, and interfacial chemistry and electrochemistry - with a focused goal of preparing the modern microfluidics researcher to analyse and model continuum fluid mechanical systems encountered when working with micro- and nanofabricated devices. This text serves as a useful reference for practising researchers but is designed primarily for classroom instruction. Worked sample problems are included throughout to assist the student, and exercises at the end of each chapter help facilitate class learning.
On optimum design in fluid mechanics
Journal of Fluid Mechanics
64
97
1974
10.1017/S0022112074002023
In this paper, the change in energy dissipation due to a small hump on a body in a uniform steady flow is calculated. The result is used in conjunction with the variational methods of optimal control to obtain the optimality conditions for four minimum-drag problems of fluid mechanics. These conditions imply that the unit-area profile of smallest drag has a front end shaped like a wedge of angle 90".
Analysis of thin plates by the element-free Galerkin method
Computational Mechanics
17
1-2
26-35
1995
10.1007/BF00356476
A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into ''finite elements''. The satisfaction of the C-1 continuity requirements are easily met by EFG since it requires only C-1 weights; therefore, it is not necessary to resort to Mindlin-Reissner theory or to devices such as discrete Kirchhoff theory. The requirements of consistency are met by the use of a quadratic polynomial basis. A subdivision similar to finite elements is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers. It is shown, that high accuracy can be achieved for arbitrary grid geometries, for damped and simply-supported edge conditions, and for regular and irregular grids. Numerical studies are presented which show that the optimal support is about 3.9 node spacings, and that high-order quadrature is required.
An analytical model of intervertebral disc mechanics
Journal of Biomechanics
28
1
53-68
1995
10.1016/0021-9290(95)80007-7
The intervertebral disc is a complex mechanical structure, and it is important to understand the loading of specific structures which might cause damage leading to failure or mechanical impairment. At present it is only possible to model such internal loadings owing to the extreme technical difficulties involved in experimental measurement. The simple analytical model described in this paper makes exact predictions of the loads carried by fibres and also their path within the annulus fibrosus, without pre-defining the fibre configuration. The disc is modelled as an axially symmetric structure comprising a fluid filled centre, retained by a thin, doubly curved, fibre-reinforced membrane under tensile stress. The annulus is taken to consist of two lamellae reinforced by oppositely oriented collagen fibres that are free to follow paths defined by one of two geometrical rules. The predictive power and possible uses of the model are illustrated using boundary conditions experimentally determined from a typical young disc. The model was used to calculate the shape of the membrane surface, fibre path, volume of disc, area of annulus, length of fibre bundle and tension at a point along length of fibre. Equatorial fibre angle could be approximately predicted (to about 5??), since there was only a small range of valid solutions to the model. The predicted surface profiles, fibre loads and angles were found to be in reasonable agreement with published experimental studies. Two examples of how the static model might be used to calculate changes in disc morphology and loading are included to demonstrate how a wide range of experimental data and theoretical behavior might be incorporated. This analytical model is important since it enables exact solutions to be calculated for the forces acting at any point along a fibre, their paths and also the surface geometry, from a small number of physical measurements without the need to estimate the mechanical properties of individual areas of the disc. It facilitates the prediction of the behaviour of the disc under varying load by providing a framework that can be further developed using a wide range and combination of experimental conditions and theoretical relationships.
Why Classical Mechanics Cannot Naturally Accommodate Consciousness But Quantum Mechanics Can.
Arxiv preprint quant-ph/9502012
25
1995
It is argued on the basis of certain mathematical characteristics that classical mechanics is not constitutionally suited to accomodate consciousness, whereas quantum mechanics is. These mathematical characteristics pertain to the nature of the information represented in the state of the brain, and the way this information enters into the dynamics.
Shape optimization of a sheet swimming over a thin liquid layer
JOURNAL OF FLUID MECHANICS
601
25-61
2008
10.1017/S0022112008000384
Motivated by the propulsion mechanisms adopted by gastropods, annelids\nand other invertebrates, we consider shape optimization of a flexible\nsheet that moves by propagating deformation waves along its body. The\nself-propelled sheet is separated from a rigid substrate by a thin\nlayer of viscous Newtonian fluid. We use a lubrication approximation to\nmodel the dynamics and derive the relevant Euler-Lagrange equations to\nsimultaneously optimize swimming speed, efficiency and fluid loss. We\nfind that as the parameters controlling these quantities approach\ncritical values, the optimal solutions become singular in a\nself-similar fashion and sometimes leave the realm of validity of the\nlubrication model. We explore these singular limits by computing\nhigher-order corrections to the zeroth order theory and find that wave\nprofiles that develop cusp-like singularities are appropriately\npenalized, yielding non-singular optimal solutions. These corrections\nare themselves validated by comparison with finite element solutions of\nthe full Stokes equations, and, to the extent possible, using recent\nrigorous a priori error bounds.
What are game mechanics?
Lostgarden
1-11
2006
The phrase “game mechanics” sends a pleasant shiver down my spine. At the heart of every game are these mysterious whirring clicking mechanisms that deliver to the player pleasure and thrills. We use them, we build them, but I’ve never seen a good unified definition of game mechanics that gives us a practical base upon which to build great games. Here is one. It is clobbered together from a variety of influences though many of you will recognize some central tenets from ‘A Theory of Fun’ by Raph Koster. Game mechanics are rule based systems / simulations that facilitate and encourage a user to explore and learn the properties of their possibility space through the use of feedback mechanisms. It is a simple definition, but it offers a good amount of insight into why games work and how we can make them better. Feedback
Fluid Mechanics
Course of Theoretical Physics
6
539
1987
10.1007/b138775
Mjog god kennslubok. Agaet fyrir byrjendur sem og lengra komna
Lecture notes on fracture mechanics
Cornell University
14853
607
2007
Fracture mechanics is a vast and growing field. A search of the Cornell\nLibrary in winter 2006\n\nuncovered over 181 entries containing ”fracture mechanics” in the\nsubject heading and 10,000\n\nentries in a relevance keyword search. This book is written for students\nwho want to prepare to\n\nbe able to read some of this vast literature and for those who want\nto apply fracture mechanics to\n\nreal world problems. It is assumed the reader is familiar with the\ntheory of linear elasticity, vector\n\ncalculus, linear algebra and indicial notation. As much as possible\nI proceed in a linear fashion,\n\nbut the reader may find that some backtracking is needed. These notes\nare used in a one semester\n\ncourse at Cornell.\n\nThere are many approaches to teaching fracture. Here the emphasis\nis on mechanics models\n\nfor crack tip fields and energy flows with discussion of how these\nresults affect observed fracture\n\nbehavior. A brief discussion of computational fracture methods is\ngiven along with additional\n\npractical aspects such as fracture toughness testing and fracture\ncriteria. The notes do not contain\n\nmuch on the understanding of material behavior or on fracture at the\nmicromechanical level. Both\n\nthe mechanics and the materials sides of fracture should be studied\nin order to obtain a balanced\n\nand more complete picture of the field.\n\nThese notes grow out of my experience teaching fracture at Cornell\nand taking fracture mechanics\n\nin graduate school at Caltech with Ares Rosakis. Textbooks consulted\ninclude Hutchinson’s\n\nnotes on nonlinear fracture [1], Lawn’s book on the fracture of brittle\nmaterials [2], Suresh on fatigue\n\n[3] and texts by Janssen [4], Anderson [5], Sanford [6] and Hellan\n[7].\n\nTopics that could be added include interface fracture, better coverage\nof computational methods,\n\nviscoelastic fracture and more discussion of the physical aspects\nof fracture. Topics that I hope to\n\nwork on but have yet to start include: computational cohesive zone,\nfatigue crack growth model\n\nand fracture of plates and shells.
Noether's theorem in classical mechanics revisited
European Journal of Physics
28
1
37-43
2007
10.1088/0143-0807/28/1/004
A didatic approach to Noether's theorem in classical mechanics is derived and used to obtain the laws of conservation.
Analysis of the nonlinear dynamic response of viscoelastic symmetric cross-ply laminated plates with transverse matrix crack
Composite Structures
72
4
469-476
2006
http://dx.doi.org/10.1016/j.compstruct.2005.01.016
Based on the Schapery’s 3-D constitutive relationship and the Von Karman’s plate theory, the constitutive equations and the nonlinear dynamic governing equations for viscoelastic symmetric cross-ply laminated plates with transverse matrix cracks are derived. By using the finite difference method and Newmark-β scheme, the unknown functions are separated and these equations are iterated to seek solutions. Numerical calculating results show that the effect of damage on the nonlinear dynamic responses of structures is significant.
Damage; Laminated plates; Nonlinear dynamic response; Viscoelastic
Elastic and initial flexural failure analysis of unsymmetrically laminated cross-ply strips
Composites Part B: Engineering
27
96
505-518
1996
10.1016/1359-8368(96)00031-5
A finite difference version of the Dynamic Relaxation (DR) method is used to generate elastic solutions of the small and the large deflection Mindlin plate equations for unsymmetrically laminated cross-ply strips subjected to uniform lateral pressure. The Maximum Stress (Independent) and Tsai-Hill failure criteria are combined with these solutions to produce initial failure analyses. It is shown that coupling between bending and stretching due to the B11 stiffness term can cause a considerable increase or decrease in the flexural stiffness of simply supported in-plane fixed strips relative to the equivalent orthotropic strips but not necessarily in the corresponding failure pressures. It is also found that the predictions of the two failure criteria are in close agreement. Copyright ?? 1996 Elsevier Science Limited.
Composites; Failure; Flexure; Laminates; Strips
Consistent higher-order analysis on shock response of cross-ply curved panels
Composites Engineering
5
3
297-311
1995
10.1016/0961-9526(94)00098-T
A consistent higher-order analysis is presented for the shock response of doubly-curved cross-ply laminated thick panels simply supported on four edges. Emphasis is laid on consistency with the three-dimensional boundary conditions and interlaminar stress continuity, respectively. In each layer, a three-dimensional dynamic displacement field is assumed in terms of in-plane double Fourier series and cubic polynomials in the thickness direction. A system of modified Lagrange equations is derived via an energy variational approach with all surface conditions, and interlaminar continuity included. Modal analysis is performed for the shock response using a modified exponential decay overpressure. Three-dimensional displacements and stresses can be found any time throughout the panels. Present results, including frequency spectra of σ33, are perfectly consistent with existing wave theory without prior assumption of wave motion.
Vibration and stability analyses of cross-ply laminated circular cylindrical shells
Journal of Sound and Vibration
157
1
139-159
1992
10.1016/0022-460X(92)90571-E
An improved analytical procedure is introduced in the context of free vibration and stability problems of cross-ply laminated circular cylindrical shells. The Donnell shear-deformation type theory and Donnell's classical theory are used to illustrate the procedure. Numerical results are presented for shells with a variety of boundary conditions. Special attention is given to the axisymmetric problems and new results, not yet found in the literature, for stability and vibration are reported. It is recommended that the new technique be used for generating the Lévy-type solutions in vibration and stability problems of laminated shell panels and plates when the number and order of equations are higher than those of the classical theories.
Mechanics of rupture of cerebral saccular aneurysms
Journal of Biomechanics
8
6
385-392
1975
10.1016/0021-9290(75)90074-3
ost saccular aneurysms initiate in human intracranial arteries in and about the circle of Willis. Rupture of an aneurysm causes subarachnoid hemorrhage which seriously endangers the patient’s life. To study the possible cause of rupture, a dynamic analysis is performed. A thin-shell theory is applied to a spherical model subjected to time-dependent internal pressure and boundary conditions. The fundamental strain-displacement differential equations relations, and stress-strain are found by combining the equations relations. of motion, The solution involves Legendre functions of the first kind. Natural frequencies of aneurysms of different sizes and closing angles are determined as functions of the elastic properties. These properties are investigated by using data from the literature. It is found that the natural frequencies of certain types of aneurysms fall within the range of bruit that commonly accompany aneurysms. Resonance and consequently frequencies rupture is then expected when the bruit frequency is the same as the natural frequency of the aneurysm. Critical aneurysm sizes, for various closing angles, are predicted.
Continuum Mechanics: Concise Theory and Problems
Continuum Mechanics: Concise Theory and Problems
20
1998
Written in response to the dearth of practical and meaningful textbooks in the field of fundamental continuum mechanics, this comprehensive treatment offers students and instructors an immensely useful tool. Its 115 solved problems and exercises not only provide essential practice but also systematically advance the understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. Readers follow clear, formally precise steps through the central ideas of classical and modern continuum mechanics, expressed in a common, efficient notation that fosters quick comprehension and renders these concepts familiar when they reappear in other contexts. Completion of this brief course results in a unified basis for work in fluid dynamics and the mechanics of solid materials, a foundation of particular value to students of mathematics and physics, those studying continuum mechanics at an intermediate or advanced level, and postgraduate students in the applied sciences. "Should be excellent in its intended function as a problem book to accompany a lecture course." — Quarterly of Applied Math.
Time-symmetric quantum mechanics
Foundations of Physics
37
159-168
2007
10.1007/s10701-006-9089-1
A time-symmetric formulation of nonrelativistic quantum mechanics is developed by applying two consecutive boundary conditions onto solutions of a time- symmetrized wave equation. From known probabilities in ordinary quantum mechanics, a time-symmetric parameter P0 is then derived that properly weights the likelihood of any complete sequence of measurement outcomes on a quan- tum system. The results appear to match standard quantum mechanics, but do so without requiring a time-asymmetric collapse of the wavefunction upon measurement, thereby realigning quantum mechanics with an important fundamental symmetry.
Quantum mechanics; Time reversal operator; Time reversal symmetry
The physics and micro-mechanics of nano-voids and nano-particles in polymer combinations
Polymer (United Kingdom)
54
13
3131-3144
2013
10.1016/j.polymer.2013.03.035
In this article the role of voids or particulate inclusions of different sizes on mechanical properties and particularly on toughness in several polymers is discussed. With decreasing void sizes and intervoid distances, the influence of the interphase material around the voids becomes more important and characteristic changes in the nano- and micro-deformation mechanisms appear. These mechanisms are revealed by several techniques of electron microscopy within rubber modified polymers, nanocomposites and nanofibres respectively. Three nanoscopic toughness enhancing mechanisms are described in detail: thin layer yielding, nanovoid-modulated craze-formation, and the core flattening mechanism. The action of these mechanisms constitutes a distinct advantage of nanovoids over microvoids. ?? 2013 Elsevier Ltd. All rights reserved.
Electron microscopy; Nano-/micromechanics; Polymer combinations; Polymer nano-composites
The self-assembly, elasticity, and dynamics of cardiac thin filaments.
Biophysical journal
94
6
2170-2178
2008
10.1529/biophysj.107.116087
Solutions of intact cardiac thin filaments were examined with transmission electron microscopy, dynamic light scattering (DLS), and particle-tracking microrheology. The filaments self-assembled in solution with a bell-shaped distribution of contour lengths that contained a population of filaments of much greater length than the in vivo sarcomere size ( approximately 1 mum) due to a one-dimensional annealing process. Dynamic semiflexible modes were found in DLS measurements at fast timescales (12.5 ns-0.0001 s). The bending modulus of the fibers is found to be in the range 4.5-16 x 10(-27) Jm and is weakly dependent on calcium concentration (with Ca2+ > or = without Ca2+). Good quantitative agreement was found for the values of the fiber diameter calculated from transmission electron microscopy and from the initial decay of DLS correlation functions: 9.9 nm and 9.7 nm with and without Ca2+, respectively. In contrast, at slower timescales and high polymer concentrations, microrheology indicates that the cardiac filaments act as short rods in solution according to the predictions of the Doi-Edwards chopsticks model (viscosity, eta approximately c(3), where c is the polymer concentration). This differs from the semiflexible behavior of long synthetic actin filaments at comparable polymer concentrations and timescales (elastic shear modulus, G' approximately c(1.4), tightly entangled) and is due to the relative ratio of the contour lengths ( approximately 30). The scaling dependence of the elastic shear modulus on the frequency (omega) for cardiac thin filaments is G' approximately omega(3/4 +/- 0.03), which is thought to arise from flexural modes of the filaments.
On study of nonclassical problems of fracture and failure mechanics and related mechanisms
International Applied Mechanics
45
1
1-31
2009
10.1007/s10778-009-0168-9
Some nonclassical problems of fracture mechanics that have been analyzed by the author and his collaborators at the Institute of Mechanics (Kiev) during the past thirty years are considered in brief
Cracked materials; Dynamic brittle fracture mechanics; Fracture and failure mechanics; Fracture of composites; Nonclassical problems
Practical Quantum Mechanics
American Journal of Physics
41
1
140
1973
10.1119/1.1987153
From the reviews: "Anyone who has taught a course of quantum mechanics knows the difficulty of providing practical examples which are within the mathematical competence of the students and can be completed in a reasonable time. In this book will be found 219 problems, together with their solutions, which will greatly extend the repertoire. (...) The first volume deals exclusively with one-body problems without spin. (...) In the second volume the problems cover a wider range and include illustrations of the introduction of spin, the interactions between two and three particles, quantum statistics and the Dirac relativistic equation with shorter sections on non-stationary problems and radiation theory. (...)" Nature, Sept. 10, 1971. "The student who can master these problems will have a good grasp of the practical applications of quantum theory and, therefore, of the basic concepts as well. I recommend the book unreservedly." The Australian Physicist, May 1972.
Inorganic Molecular Mechanics
Journal of Chemical Education
73
2
108
1996
10.1021/ed073p108
The use of inorganic molecular mechanics has increased dramatically in the last decade. In this article we review some of the main differences between inorganic molecular mechanics and organic molecular mechanics, and highlight some common errors that can be made.\nThe use of inorganic molecular mechanics has increased dramatically in the last decade. In this article we review some of the main differences between inorganic molecular mechanics and organic molecular mechanics, and highlight some common errors that can be made.
Junction Conditions for Cracked Elastic Thin Solids Under Bending and Shear
Quarterly Journal of Mechanics & Applied Mathematics
62
4
481-494
2009
10.1093/qjmam/hbp017
The paper presents an asymptotic model of the spring-like behaviour of small elastic junctions within two-dimensional thin solids subjected to a flexural or shearing load. The approach employs the method of compound asymptotic expansions. It is shown that the flexural stiffness increases quadratically with the increase of the thin ligament length, whereas the shear stiffness is relatively high and it is less sensitive to the change of the thickness of the thin ligament within the junction region. The expressions for the effective junction conditions agree well with the independent numerical simulations for test configurations. In addition to the junction conditions, our model also provides a uniform asymptotic approximation of elastic displacements within a thin solid containing surface breaking cracks separated by a thin bridge. [ABSTRACT FROM PUBLISHER] Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
ELASTICITY; SHEAR (Mechanics); STIFFNESS (Mechanics); SURFACE chemistry; THIN films
Granular element method for computational particle mechanics
Computer Methods in Applied Mechanics and Engineering
241-244
262-274
2012
10.1016/j.cma.2012.06.012
This paper presents a method within the family of the discrete element method (DEM) capable of accurately capturing grain shape by using Non-Uniform Rational Basis-Splines (NURBS). The new method, called GEM, bypasses one of the current bottlenecks in computational discrete mechanics of granular materials by allowing discrete elements to take realistic and complex granular shapes encountered in engineering and science (e.g., sand grains). More than a new method, this paper presents a new concept for DEM: using NURBS to seamlessly transition from advanced visualization tools (e.g., X-ray CT) to physics-based computational models where particle shape is realistically modeled. It is expected that, with the rapid advancement of computational power, combining high-fidelity characterization with physics-based computations will lead to more predictive modeling approaches. The granular element method may help transition from characterization to modeling and could lead to more realistic predictions at the grain scale. © 2012 Elsevier B.V.
Discrete element method; Multiscale analysis; NURBS; Particle mechanics
Theoretical study of mechanical behavior of thin circular film adhered to a flat punch
International Journal of Mechanical Sciences
51
6
481-489
2009
10.1016/j.ijmecsci.2009.04.003
In this paper we present a theoretical study of the cylindrical punch test where a thin circular film clamped at the periphery is adhered to the planar surface of a rigid cylindrical punch, and an external tensile load is applied to the punch causing the film to delaminate from the substrate. We obtain analytical solutions to the deflection of the membrane in the asymptotic limit of large or small loads, and then combine the bending and stretching effects using a lumped parameter force–deflection model. An equilibrium theory of delamination mechanics is derived based on energy balance. The cases of initially stress-free and prestressed film are analyzed, which ought to have significant implications in many technological situations.
Adhesion; Energy release rate; Large deflection; Plate; Residual stress
Effects of Ply Stacking Sequence in 3D Fiber Reinforced Foam Core Sandwich Structures with Defects
55th AIAA/ASMe/ASCE/AHS/SC Structures, Structural Dynamics, and Materials Conference
1-10
2014
10.2514/6.2014-0504
Foam core sandwich composites are widely used in primary structural components of launch vehicles and spacecraft. These structures exhibit complex failure modes and are highly sensitive to butt-joints, core mismatches, impact damage, voids, and facesheet delaminations. 3D Fiber Reinforced Foam Cores (3DFRFC) represent a new class of core material designed to replace standard foam core in future aerospace structures. An analysis program is being developed to investigate the effect of ply stacking sequence on debond buckling in 3DFRFC structures with defects. The detailed microstructure is modeled using the embedded element method to investigate the local interaction between the facesheet and the core. Linear and nonlinear buckling analysis was used to understand the sensitivity of the predicted buckling load to the ply stacking sequence. Preliminary results show that the effect of ply stacking sequence on the buckling load is consistent across variations to the core types, modeling methods, and defect sizes investigated.
Adapting ply drop positions for compensating fabric changesApplication to swimming monofins
Finite Elements in Analysis and Design
46
10
930-935
2010
10.1016/j.finel.2010.06.007
Composite structures manufactures sometimes have to change their material, either in an attempt to reduce their costs, or because of their provider's policies. If the structure's behavior has to stay constant, some re-design is necessary to compensate for material variations. In tapered composite structures, ply drop positions can be moved for such purpose. The present article describes an application to swimming monofins. The intuitive concepts used by swimmers to characterize monofins are translated here into two criteria: the deflection under static loading and the natural frequencies. The ply drop positions with the thicker prepeg are optimized, so that the deformed configuration and natural frequencies are as close as possible to those of the reference monofin. Numerical simulations based on the finite element method provide the deflections and natural frequencies of the various models. The optimization problem is solved with the Globalized and Bounded NelderMead (GBNM) algorithm (Luersen et al. (2004) [1]). The ply drop positions identifications of two monofins with different characteristics are carried out and the results are discussed. ?? 2010 Elsevier B.V.
Laminate composite materials; Optimization; Swimming monofin design
Hole flanging with ironing of two-ply thick sheet metals(1999).pdf
Journal of Materials Processing Technology
89-90
51-57
1999
Two-ply sheet metals are used in the manufacturing of electronic equipment, chemical instruments, transportation works and so on. Two-ply sheet metals are generally composed of metals that have different mechanical properties. Thus the forming process of these materials is complicated. The forming characteristics in hole flanging with ironing for two-ply sheet metals were studied. An explosively welded Al/Cu bi-metallic sheet metal was used as a model material throughout the experiments. The thickness of the matrix A1 was 2.20 mm and that of the cladding Cu was 0.83 mm. A number of experiments were performed using a conical punch with a cone angle of 45. The experimental results were compared with FEM-simulated results, from which it was demonstrated that the rigid-plastic FEM can be used effectively for predicting the forming process and the finished shape of bi-metallic sheet metals.
Experimental studies of light-weight woodframe shear walls with ply-bamboo sheathing panels
Jianzhu Jiegou Xuebao/Journal of Building Structures
34
9
142-149
2013
In order to promote the application of bamboo materials in construction industry, this paper reports lateral loading test results of lightweight woodframe shear walls with ply-bamboo sheathing panels. ASTM E2126-09 was selected as the experimental guideline for the monotonic and cyclic tests of eight shear walls. Two types of shear walls were made using two different nails, 51 mm long nail-gun driven nails and 51 mm long nail staples. The bearing capacity is 5.2 kN/m and 6.2 kN/m respectively. Shear walls keep its integrity and most of its bearing capacity when the lateral displacement is below 100 mm. Test results show that the application of ply-bamboo sheathing panel can satisfy the bearing capacity requirements of shear walls designed as structural elements, according to current codes for timber structures.
Lightweight woodframe; Nails; Ply-bamboo sheathing panel; Quasi-static test; Seismic performance; Shear wall; Static test
Obtaining 3D PLY Part from DEM Surface Data for Terrain Modeling by Additive Fabrication
International Journal of Engineering Science and Technology, Vol 6, Iss 4, Pp 177-187 (2014)
2014
Physical modeling of the earth’s terrain has been gaining popularity among architects and land-use planners in the last few years. It is partly because of the limitations with the cartographic maps and virtual reality techniques and partly because of availability of rapid manufacturing processes to produce physical models of terrain with accurate freeform surfaces. Recently many researchers have employed Additive Manufacturing (AM) processes to fabricate physical scale models of the terrains. However, they got a physical model in several steps. They used more than one software package to translate surface DEM data into faceted models, leading to loss of data in intermediate file format conversion. This paper presents a methodology which can convert surface DEM data directly into PLY format in single step. This work also eliminates the data loss associated with translation of data into intermediate file formats. In this paper two data formats: DEM ASCII XYZ and Surfer Grid have been directly converted into PLY format. The results of the program are verified and validated with the help of sample data files as well as real world DEM data.
Additive Manufacturing; Dem Ascii Xyz Format; Digital Elevation Model; Faceted Model; Ply Format; Surfer Grid Format.
Transient piezothermoelastic analysis of a cross-ply laminated cylindrical panel bonded to a piezoelectric actuator
Applied Mathematical Modelling
29
4
321-339
2005
10.1016/j.apm.2004.09.006
In this study, the theoretical treatment of transient piezothermoelastic problem is developed for a cross-ply laminated cylindrical panel bonded to a piezoelectric actuator due to nonuniform heat supply. By using the exact solutions for cross-ply laminate and piezoelectric layer of crystal class mm2, the theoretical analysis of a transient piezothermoelasticity is developed for a simple supported cylindrical composite panel under the state of plane strain. Analysis of a piezothermoelastic problem leads to an appropriate electric potential applied to the piezoelectric layer which suppresses the induced thermoelastic displacement in the radial direction at the midpoint on the free surface of the cross-ply laminate. Some numerical results for the temperature change, the displacement, the stress in a transient state when the transient thermoelastic displacement is controlled are shown in figures.
Cylindrical composite panel; Displacement control; Piezothermoelasticity; Plane strain problem; Transient state
Influence of matrix toughness and ductility on the compression-after-impact behavior of woven-ply thermoplastic- and thermosetting-composites: A comparative study
Composite Structures
110
207-218
2014
10.1016/j.compstruct.2013.12.008
This study was aimed at comparing the residual compressive strength and behavior of TS-based (epoxy) and TP-based (PPS or PEEK) laminates initially subjected to low velocity impacts. Provided that the impact energy is not too low, the permanent indentation is instrumental in initiating laminates local buckling under compressive loadings. CAI tests revealed that matrix toughness is not the primary parameter ruling the damage tolerance of the studied materials. However, matrix ductility seems to slow down the propagation of transverse cracks during compression thanks to plastic micro-buckling which preferentially takes place at the crimps in woven-ply laminates. It could therefore justify why the matrix toughness of TP-based laminates does not result in significantly higher CAI residual strengths. Finally, the compressive failure mechanisms of impacted laminates are discussed depending on matrix nature, with a particular attention paid to the damage scenario (buckling and propagation of 0° fibers failure).
Impact behavior; Polymer–matrix composites; Residual properties; Woven fabrics
An introduction to chaos in nonequilibrium statistical mechanics
Physics Today
54
3
287
1999
10.1063/1.1366071
Introduction to applications and techniques in non-equilibrium statistical mechanics of chaotic dynamics.
Mechanical response of PHB- and cellulose acetate natural fiber-reinforced composites for construction applications
Composites Part B: Engineering
42
7
1920-1928
2011
10.1016/j.compositesb.2011.05.039
Biobased composites are being evaluated for construction applications where wood or petroleum-based composites are currently used. The biobased composites studied are made from biopolymers and plant-based fibers and have been demonstrated to rapidly biodegrade in anaerobic conditions to methane thereby reducing construction-related landfill waste and producing a useful end product, namely fuel for energy or feedstock to grow more biopolymer. Mechanical properties are evaluated for hemp fabric/cellulose acetate and hemp fabric/poly(hydroxybutyrate) (PHB) composites. The composites have comparable strength to structural lumber and engineered wood products, with stiffness comparable to most engineered wood products. Classical laminate plate theory sufficiently predicts initial laminate behavior from ply-level experimental data. Simple nonlinear models using laminate plate theory and uncoupled ply-level experimental constitutive response are evaluated.
A. Polymer–matrix composites; Biobased composite; B. Mechanical properties; C. Laminate mechanics; E. Lay-up (manual)
Fluorescence detection by intensity changes for high-performance thin-layer chromatography separation of lipids using automated multiple development.
Journal of chromatography. A
1218
19
2668-75
2011
10.1016/j.chroma.2010.11.033
Changes in emission of berberine cation, induced by non-covalent interactions with lipids on silica gel plates, can be used for detecting and quantifying lipids using fluorescence scanning densitometry in HPTLC analysis. This procedure, referred to as fluorescence detection by intensity changes (FDIC) has been used here in combination with automated multiple development (HPTLC/AMD), a gradient-based separation HPTLC technique, for separating, detecting and quantifying lipids from different families. Three different HPTLC/AMD gradient schemes have been developed for separating: neutral lipid families and steryl glycosides; different sphingolipids; and sphingosine-sphinganine mixtures. Fluorescent molar responses of studied lipids, and differences in response among different lipid families have been rationalized in the light of a previously proposed model of FDIC response, which is based on ion-induced dipole interactions between the fluorophore and the analyte. Likewise, computational calculations using molecular mechanics have also been a complementary useful tool to explain high FDIC responses of cholesteryl and steryl-derivatives, and moderate responses of sphingolipids. An explanation for the high FDIC response of cholesterol, whose limit of detection (LOD) is 5 ng, has been proposed. Advantages and limitations of FDIC application have also been discussed.
Berberine; Cholesterol; Chromatography, High Pressure Liquid; Chromatography, High Pressure Liquid: methods; Chromatography, Thin Layer; Chromatography, Thin Layer: methods; Densitometry; Densitometry: methods; Lipids; Lipids: chemistry; Lipids: isolation & purification; Sensitivity and Specificity; Spectrometry, Fluorescence; Spectrometry, Fluorescence: methods
Mechanics of intracellular stress fibers: A short review
Japanese Journal of Applied Physics
50
8 PART 4
2011
10.1143/JJAP.50.08LA04
The mechanical response of living cells against external stimuli depends\nlargely on the physical and biochemical properties of an intracellular\nstructure called cytoskeleton. Three main kinds of filamentous protein\nstructures, namely, microtubules, intermediate filaments, and actin thin\nfilaments comprise the cytoskeleton. In the case of cells cultured on an\nadhesive substrate, the development of actin-based cytoskeleton,\nespecially linearly bundled actin filaments called stress fibers (SFs),\nis well established. SFs are formed close to the cell membrane with one\nor both of their ends associated with the transmembrane structure called\nthe focal adhesion (FA). In this article, we review some fundamental\nfacts about SFs in live cells starting from the early description of the\nbundled filaments as observed under optical and electron microscopies.\nThe morphology, chemical components, and biological functions of SFs,\nand recent work on the mechanical nature of SFs are reviewed. (C) 2011\nThe Japan Society of Applied Physics
The effect of width on the mechanical properties of angle-ply laminates
Composites Science and Technology
58
3-4
497-504
1998
10.1016/S0266-3538(97)00154-1
It has recently been shown that wide specimens of angle-ply laminates\nare much stronger than expected on the basis of the Tsai-Hill theory\nor the maximum-stress theory. This paper extends the work to investigate\nthe effect of test specimen width on the strength of ±45 ° balanced\nangle-ply laminates. In addition, the relative stiffness has been\nestimated from the crosshead movement, and the previous results for\nstiffness of wide test specimens are re-examined. It is shown that\nspecimen strength increases monotonically with specimen width. The\nstiffness, on the other hand, is approximately constant up to a width\nof 30 mm, and then increases. With respect to the strength, these\nresults confirm that the earlier theories were relevant only to edge\neffects, and not to most real structures. The earlier stiffness results,\ntogether with the present result, suggest that laminate theory for\nelastic constants may also be influenced by edge effects. It is shown\nthat the earlier results fit the standard laminate equations only\nif the shear modulus of the laminae are 10 GPa for glass-fibre and\n30 GPa for carbon-fibre laminates. If these results are verified,\nthe way is open for much greater use of angle-ply laminates. They\nmay be an order of magnitude stiffer and stronger than expected.\nResults with filament-wound tubes lend strong independent support\nto the work.
b; strength
Some general properties of stress-driven surface evolution in a heteroepitaxial thin film structure
Journal of the Mechanics and Physics of Solids
42
5
741-772
1994
10.1016/0022-5096(94)90041-8
Heteroepitaxial thin films are subjected to very large stresses, typically in the giga-Pascal range, due to lattice mismatch. Their applications in microelectronic devices have drawn a growing research effort which involves, in part, a better understanding of the processes by which defects such as cracks and dislocations are nucleated in a thin layer structure. One of the possible defect mechanisms is related to a stress-induced morphological instability which tends to roughen the film surface by mass diffusion during film growth or annealing. A major objective of this paper is to show that a few invariance properties of the strain energy density and the chemical potential in a heteroepitaxial structure can be utilized to obtain some valuable information concerning the equilibrium profile, the stress concentration and the formation of cusp-like stress singularities without having to resort to full-scale numerical studies. The process of cusp-formation requires a critical film thickness Hcr which is independent of the Matthews critical thickness herfor misfit dislocation formation by propagation of threading dislocations within the film. Calculations show that Hcr is significantly larger than hcr for a wide range of misfit strain, suggesting that nucleation of threading dislocations via cusp-formation could be critical in the overall process of strain relaxation in this type of film. Finally, a “phase” diagram is constructed to categorize important consequences of the surface evolution based on the instability wavelength and average film thickness.
Discrete quantum mechanics
Nuclear Physics B
225
1
1-52
1983
10.1016/0550-3213(83)90011-1
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solution spaces of the Schrödinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schrödinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, and the infinite families of new orthogonal (the exceptional) polynomials. Two new infinite families of orthogonal polynomials, the Xℓ Meixner–Pollaczek and the Xℓ Meixner polynomials, are reported.
Mechanics of cell growth
Mechanics Research Communications
42
118-125
2012
10.1016/j.mechrescom.2012.01.010
Cell growth describes an essential feature of biological tissues. This growth process may be modeled by using a set of relatively simple governing equations based on the axioms of mass and momentum balance, and using a continuum framework that describes cells and tissues as mixtures of a solid matrix, a solvent and multiple solutes. In this model the mechanics of cell growth is driven by osmotic effects, regulated by the cells' active uptake of solutes and passive uptake of solvent. By accounting for the anisotropy of the cells' cytoskeletal structures or extracellular matrix, as well as external constraints, a wide variety of growing shapes may be produced as illustrated in various examples. © 2012 Elsevier Ltd. All rights reserved.
Cell division; Cell growth; Interstitial growth; Mixture theory
On the principles of elementary quantum mechanics
Physica
12
7
405-460
1946
10.1016/S0031-8914(46)80059-4
Our problems are about α the correspondence a ↔ a between physicial quantities a and quantum operators a (quantization) and β the possibility of understanding the statistical character of quantum mechanics by averaging over uniquely determined processes as in classical statistical mechanics (interpretation). α and β are closely connected. Their meaning depends on the notion of observability. We have tried to put these problems in a form which is fit for discussion. We could not bring them to an issue. (We are inclined to restrict the meaning of α to the trivial correspondence a → a (for lim ħ → 0) and to deny the possibility suggested in β). Meanwhile special attention has been paid to the measuring process (coupling, entanglement; ignoration, infringement; selection, measurement). For the sake of simplicity the discussion has been confined to elementary non-relativistic quantum mechanics of scalar (spinless) systems with one linear degree of freedom without exchange. Exact mathematical rigour has not been aimed at.
Confining thin elastic sheets and folding paper
Archive for Rational Mechanics and Analysis
187
1-48
2008
10.1007/s00205-007-0076-2
Abstract Crumpling a sheet of paper leads to the formation of complex folding patterns over several length scales. This can be understood on the basis of the interplay of a nonconvex elastic energy, which favors locally isometric deformations, and a small singular perturbation, which penalizes high curvature. Based on three-dimensional nonlinear elasticity and by using a combination of explicit constructions and general results from differential geometry, we prove that, in agreement with previous heuristic results in the physics literature, the total energy per unit thickness of such folding patterns scales at most as the thickness of the sheet to the power 5/3. For the case of a single fold we also obtain a corresponding lower bound.
A Stochastic Model for the Growth of Matrix Cracks in Composite Laminates
Journal of Composite Materials
18
3
239-254
1984
10.1177/002199838401800304
This paper presents a stochastic simulation model for the growth of multiple matrix cracks in composite laminates subjected to both static and fatigue loads. Working within the premise of ply-elasticity, a new concept of effective flaws is introduced which replaces the conventional constant ply strength criterion. Thus, the model con sists of an application of fracture mechanics and a rational representation of material flaw distributions. Simulation examples are presented on [02/902]s and [0 2/903]s graphite-epoxy laminates which undergo characteristic transverse cracking under uniaxial tension.
Elastic and viscoelastic contact mechanics of coating/substrate composites in axisymmetric indentation
Philosophical Magazine
86
February 2012
5607-5624
2006
10.1080/14786430600891345
Indentation contact mechanics of coating/substrate composites is addressed in elastic and viscoelastic regimes. An analytical solution for the elastic Boussinesq problems is examined first using an appropriate contact pressure distribution. The analytical expression for the elastic modulus less than or equal i>E less than or equal /i> less than or equal sub>eff less than or equal /sub> of layered composites is then converted to the corresponding stress relaxation modulus less than or equal i>Y less than or equal / i> less than or equal sub>eff less than or equal /sub> is a member of the set of ( less than or equal i>t less than or equal /i>) using the correspondence principle of linear elastic and linear viscoelastic deformations. Several numerical simulations for the stress relaxation behaviour of layered composites, i.e., a viscoelastic coating on an elastic substrate, an elastic coating on a viscoelastic substrate, etc., are demonstrated to obtain rheological insights into the contact behaviour of coating/substrate composites for flat-ended cylindrical indentation. The assumptions and approximations included in the theoretical considerations are carefully addressed. The viscous squeezing flow, in a thin coating film, out of the geometrically constrained space beneath the indenter is also examined.
Mode II edge delamination of compressed thin films
Journal of Applied Mechanics-Transactions of the Asme
68
5
725-730
2001
Doi 10.1115/1.1388012
Ceramic coatings deposited on metal substrates generally develop significant compressive stresses when cooled from the temperature at which they are processed as a result of.. thermal expansion mismatch. One of the main failure modes for these coatings is edge delamination. For an ideally brittle interface, the edge delamination of a compressed thin film involves mode II interface cracking. The crack faces are in contact with normal stress acting across the faces behind the advancing tip. Frictional shielding of the crack tip has been shown to increase the apparent fracture toughness. Roughness effects associated with the separating faces can also contribute to the apparent toughness. A model of mode II steady-state edge delamination that incorporates combined friction and roughness effects between the delaminated film and substrate is proposed and analyzed. This model is used to assess whether frictional shielding and surface roughness effects are sufficient to explain the large apparent mode II fracture toughness values observed in experiments.
Bohmian mechanics and quantum field theory
Physical Review Letters
93
9
1-4
2004
10.1103/PhysRevLett.93.090402
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Nose-Hoover Nonequilibrium Dynamics and Statistical Mechanics
Molecular Simulation
33
13-19
2007
10.1080/08927020601059869
At equilibrium Nose's 1984 revolutionary thermostat idea linked Newton's mechanics with Gibbs' statistical mechanics. His work expanded the scope of isothermal and isobaric simulations. Nose-Hoover dynamics has subsequently facilitated the simulation and detailed understanding of nonequilibrium problems. The fractal phase-space distributions, and their close link to the Lyapunov spectrum, provide a novel explanation of irreversibility and a rich field for exploration.
fractals; irreversibility; molecular dynamics; thermostats
{"Einstein's} Dream" - Quantum Mechanics as Theory of Classical Random Fields
arXiv:1204.5172
2012
This is an introductory chapter of the book in progress on quantum foundations and incompleteness of quantum mechanics. Quantum mechanics is represented as statistical mechanics of classical fields.
Quantum Physics
Mechanics of ventricular torsion
Journal of Biomechanics
29
6
745-752
1996
10.1016/0021-9290(95)00129-8
Recent research suggests that left ventricular torsion is an important indicator of cardiac function. We used two theoretical models to study the mechanics of this phenomenon: a compressible cylinder and an incompressible ellipsoid of revolution. The analyses of both models account for large- strain passive and active material behavior, with a muscle fiber angle that varies linearly from endocardium to epicardium. Relative to the end- diastolic configuration, the predicted torsion exhibits several experimentally observed features, including a peak near end systole, rapid untwisting during isovolumic relaxation, and increased twist near the apex. The magnitude of the twist is sensitive to the fiber architecture, the ventricular geometry, and the compressibility and contractility of the myocardium. In particular, the model predicts that the systolic twist increases with increasing compressibility, contractility, and wall thickness, while it decreases with increasing cavity volume. The peak twist approximately doubles (from about 0.02 to 0.04 rad cm-1) with a doubling of myocardial compressibility or with a change in the endocardial/epicardial muscle fiber angles from 90/-90?? to 60/-60??. The twist is less sensitive to changes in contractility and ventricular geometry. These findings provide a basis for interpreting measurements of ventricular torsion in the clinical setting.
Cardiac mechanics; Heart; Torsion; Twist; Ventricle
Nonlinear continuum mechanics and large inelastic deformations
Solid Mechanics and its Applications
174
1-745
2011
10.1007/978-94-007-0034-5_1
The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form.The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations.The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc.The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.
Games for Learning Institute White Paper: Learning Mechanics and Assessment Mechanics for Games for Learning
Games for Learning Institute Manuscripts
1-19
2011
In this paper, we will discuss the approach for assessment of learning and related learner variables taken by the Games for Learning Institute (G4LI). We will first describe game mechanics in general, and then introduce the concepts of learning mechanics and assessment mechanics and describe criteria for their design and requirements of how they can inform the design of related game mechanics.
(R)Thin-film piezoelectric-on-silicon resonators for high-frequency reference oscillator applications.
IEEE transactions on ultrasonics, ferroelectrics, and frequency control
55
12
2596-606
2008
10.1109/TUFFC.2008.976
This paper studies the application of lateral bulk acoustic thin-film piezoelectric-on-substrate (TPoS) resonators in high-frequency reference oscillators. Low-motional-impedance TPoS resonators are designed and fabricated in 2 classes--high-order and coupled-array. Devices of each class are used to assemble reference oscillators and the performance characteristics of the oscillators are measured and discussed. Since the motional impedance of these devices is small, the transimpedance amplifier (TIA) in the oscillator loop can be reduced to a single transistor and 3 resistors, a format that is very power-efficient. The lowest reported power consumption is approximately 350 microW for an oscillator operating at approximately 106 MHz. A passive temperature compensation method is also utilized by including the buried oxide layer of the silicon-on-insulator (SOI) substrate in the structural resonant body of the device, and a very small (-2.4 ppm/ degrees C) temperature coefficient of frequency is obtained for an 82-MHz oscillator.
Acoustics; Acoustics: instrumentation; Algorithms; Electric Impedance; Electrochemistry; Electrochemistry: instrumentation; Electronic; Electronics; Electronics: instrumentation; Equipment Design; Mechanics; Microelectrodes; Micromanipulation; Nonlinear Dynamics; Oscillometry; Oscillometry: instrumentation; Oxides; Oxides: chemistry; Silicon; Silicon: chemistry; Temperature; Transistors
What Connects Different Interpretations of Quantum Mechanics ?
Quo Vadis Quantum Mechanics?
10
2004
In this paper, we investigate the idea that different interpretations of quan- tum mechanics can be seen as restrictions of the consistent (or decoherent) histories quantum mechanics of closed systems to particular classes of his- tories, together with the approximations and descriptions of these histories that the restrictions permit.
Development of novel cost effective hybrid ply carbon-fibre composites
Composites Science and Technology
56
9
1047-1054
1996
10.1016/0266-3538(96)00064-4
A carbon-fibre/epoxy hybrid material has been developed which comprises ultra-high-performance fibres in the principal load-bearing direction and standard carbon fibres in the secondary orientations. The effect of stacking sequence on mechanical properties, including impact damage tolerance, has been studied and the results compared with non-hybrid data. By optimising the stacking sequence the hybrid material exhibited a mechanical performance similar to that of the ultra-high-performance material and a performance superior to the standard material. The energy absorbed during low velocity impact was analysed in terms of an initiation and propagation energy. The energy absorbed through delamination initiation was increased by placing 45?? fibres in the surface plies and by placing ultra-high-performance fibres in the 0?? plies. The energy absorbed during delamination growth was independent of the fibre type and determined solely by the matrix material. On the basis of current pre-preg prices the hybrid material corresponds to a significant cost saving of 12% through the use of lower cost standard fibres in the secondary stressed layers. ?? 1996 Published by Elsevier Science Limited.
Carbon fibre; Composites; Hybrids; Impact; Lay-up
Mode I interlaminar fracture of symmetrical cross-ply composites
Composites Science and Technology
41
2
147-164
1991
10.1016/0266-3538(91)90025-K
The composite material structures commonly used in the aeronautical industry are designed with lay-ups of the type [±θ]. By contrast with what happens in a unidirectional composite, a delamination defect can exist and propagate between the differently-oriented laminae in a ±θ composite. Consequently, the strain and stress fields, and also the fracture mechanisms, become more complex. An experimental method and analysis has been used on double-cantilever beam (DCB) specimens of a carbon-epoxy laminate, using strain gauges and acoustic emission to detect the appearance of microcracking at the crack tip and the onset of delamination growth. Experimentally, the strain energy release rates for the initiation cracks and the delamination growth, GIC and GIP, respectively, are very different according to whether the defect is situated between the [0/0], [0/90] or [90/90] layers. Microfractographic analysis shows and explains why the [0/90] and [90/90] layers have higher strain energy release rates than that of the unidirectional [0/0] layers.
Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions
Journal of Engineering Mechanics
133
3
308-319
2007
10.1061/(ASCE)0733-9399(2007)133:3(308)
... doi: 10.1061 /( ASCE ) 0733 - 9399 ( 2007 ) 133 : 3 ( 308 ). TECHNICAL PAPERS. Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions. Article History. ... Permalink: http://dx.doi.org/ 10.1061 /( ASCE ) 0733 - 9399 ( 2007 ) 133 : 3 ( 308 ). ... \n
Introduction to advanced mechanics
Solid Mechanics and its Applications
141
95-167
2006
This chapter serves as a brief guide and introduction of the basics of mechanics needed for the mechanics analysis in microelectronics. Theory of stress and strain, thermal stress and strain, and the fundamental principles and equations of thermal mechanics are presented first. Several common nonlinear constitutive laws of materials such as hyperelasticity, plasticity and creep are introduced. Failure criteria for static loading and cyclic loading are described. Then, the fundamentals of fracture mechanics including linear fracture mechanics, mixed-mode fracture, and elasto-plastic fracture mechanics are presented. Interface fracture mechanics is also discussed. In the part of computational mechanics, the basics of finite element theory and numerical implementation are briefed and the focus is on the advanced topics such as the treatment of geometric and material nonlinearity in finite element implementation, extraction of fracture parameters, sub-structural and sub-modelling methods, and adaptive meshing and element birth and death.
Tensorial description of quantum mechanics
Phys. Scripta
T153
014012
2013
10.1088/0031-8949/2013/T153/014012
Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.
A review of cetacean lung morphology and mechanics
Journal of Morphology
274
12
1425-1440
2013
10.1002/jmor.20192
Cetaceans possess diverse adaptations in respiratory structure and mechanics that are highly specialized for an array of surfacing and diving behaviors. Some of these adaptations and air management strategies are still not completely understood despite over a century of study. We have compiled the historical and contemporary knowledge of cetacean lung anatomy and mechanics in regards to normal lung function during ventilation and air management while diving. New techniques are emerging utilizing pulmonary mechanics to measure lung function in live cetaceans. Given the diversity of respiratory adaptations in cetaceans, interpretations of these results should consider species-specific anatomy, mechanics, and behavior.
Cetacean; Lung mechanics; Myoelastic sphincters; Respiratory anatomy
Crack initiation at free edge of interface between thin films in advanced LSI
Engineering Fracture Mechanics
69
12
1289-1299
2002
10.1016/S0013-7944(02)00009-7
Since electronic devices are made of multi-layered sub-micron films, delamination along the interface is one of the major failure mechanisms. This paper aims to develop a method for evaluating the mechanical criterion of interface cracking between thin films on a substrate. The focus is put on crack initiation from the free edge of the interface where the stress concentrates due to the mismatch of elastic deformation. In the evaluation, it is important to exclude plastic deformation and fracture of the thin metal film, because they bring about ambiguity on the measured magnitude of interface strength. In this study, an experimental method is proposed on the basis of fracture mechanics concepts, and the validity is examined by tests on Cu (conductor metal)/TaN (barrier metal) interface in a large-scale integrated circuit. The critical stress intensity at delamination crack initiation is successfully analyzed by the boundary element method. © 2002 Elsevier Science Ltd. All rights reserved.
Fracture toughness; Free edge effect; Interface strength; LSI; Thin film
Numerical investigations in penetration mechanics
International Journal of Engineering Science
16
11
859-869
1978
10.1016/0020-7225(78)90071-X
Computational techniques have been employed to investigate a variety of phenomena associated with the penetration process including cratering in thick targets and the perforation of thin targets. The dependency of these phenomena on impact velocity, material properties and projectile-target configurations are investigated for a variety of impact situations. Comparisons of the computational results with experimental data are made for those cases for which such data are available; agreement between theory and experiment is quite good.
Effective conductivities of thin-interphase composites
Journal of the Mechanics and Physics of Solids
61
12
2680-2691
2013
10.1016/j.jmps.2013.08.022
A method is presented for approximating the effective conductivity of composite media with thin interphase regions, which is exact to first order in the interphase thickness. The approximations are computationally efficient in the sense the fields need to be computed only in a reference composite in which the interphases have been replaced by perfect interfaces. The results apply whether any two phases of the composite are separated by a single interphase or multiple interphases, whether the conductivities of the composite phases are isotropic or anisotropic, and whether the thickness of an interphase is uniform or varies as a function of position. It is assumed that the conductivities of the interphase materials have intermediate values as opposed to very high or very low conductivities. © 2013 Elsevier Ltd. All rights reserved.
Effective conductivity; Multiphase composites; Thin interphases
Influence of active stiffening on dynamic behaviour of piezo-hygro-thermo-elastic composite plates and shells
Journal of Sound and Vibration
278
257-283
2004
10.1016/j.jsv.2003.10.002
The active stiffening and active compensation analyses are carried out to present the influence of active stiffness on the dynamic behaviour of piezo-hygro-thermo-elastic laminates. A coupled piezoelectric finite element formulation involving a hygrothermal strain field is derived using the virtual work principle and is employed in a nine-noded field consistent Lagrangian element. The closed-loop system is modelled with elastic stiffness, active stiffness introduced by isotropic actuator lamina and geometric stiffness due to stresses developed by hygrothermal strain. Through a parametric study, the influence of active stiffening and active compensation effects on the dynamics of cross-ply and angle-ply laminated plates and shells are highlighted. The active stiffening on thin shells is significantly influenced by boundary effects and the actuator efficiency further decreases with increase in curvature. The reduction in natural frequencies of cross-ply laminates due to hygrothermal strain is actively compensated by active stiffening; however, it is observed that the actuator performance reduces significantly with increase in curvature particularly in angle-ply laminates, which demands the use of directional actuators. The active stiffening and active compensation effects are low in moderately thick piezo-hygro-thermo-elastic plates and shells, which are less influenced by boundary conditions. ?? 2003 Elsevier Ltd. All rights reserved.
Numerical methods in rock mechanics
International Journal of Rock Mechanics and Mining Sciences
39
409-427
2002
10.1016/S1365-1609(02)00065-5
The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures built on and in rock masses, and hence for supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating couplings between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized. Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference list, ‘significant’ references are asterisked and ‘very significant’ references are doubly asterisked.
coupled processes; design; numerical modelling; outstanding issues; review; rock mechanics
Limit loads and fracture mechanics parameters for thick-walled pipes
International Journal of Pressure Vessels and Piping
88
10
403-414
2011
10.1016/j.ijpvp.2011.07.005
In this paper, information on plastic limit loads and both elastic and elastic-plastic fracture mechanics parameters is given for cracked thick-walled pipes with mean radius-to-thickness ratios ranging from two to five. It is found that existing limit load expressions for thin-walled pipes can be applied to thick-walled pipes, provided that they are normalized with respect to the corresponding un-cracked thick-walled pipe values. For elastic fracture mechanics parameters, FE values of the influence functions for the stress intensity factor and the crack opening displacement are tabulated. For elastic-plastic J, it is shown that existing reference stress based J estimates can be applied, provided that a proper limit load for thick-walled pipes is used.
Crack opening displacement; J-integral estimates; Limit load; Stress intensity factor; Thick-walled pipe
Statistical mechanics of glass
Journal of Non-Crystalline Solids
396-397
41-53
2014
10.1016/j.jnoncrysol.2014.04.009
The field of glass science is quickly maturing from a purely empirical science to one built upon rigorous fundamental physics. These advancements offer an unprecedented level of understanding of the glass transition and the glassy state, as well as the ability to design new glass compositions starting at the atomic level. As a nonequilibrium material, the structure and properties of glass depend not only on its composition, but also on its thermal and pressure histories. Since glass is thermodynamically unstable, it is continually relaxing toward the metastable supercooled liquid state. Owing to this time dependence of glass properties and microstructure, traditional reversible thermodynamics cannot be directly applied to study the glassy state. While some nonequilibrium aspects of the glassy state can be estimated using irreversible thermodynamics, this approach has no microscopic basis and hence cannot offer a rigorous physical description of either the glass transition or glass itself. Alternatively, nonequilibrium statistical mechanics offers a framework in which the macroscopic properties of a glass can be rigorously calculated from its microscopic structure. As such, statistical mechanics has many practical applications in glass science and technology. The objective of this article is to provide an overview of various statistical mechanical descriptions of the glassy state and their practical use in understanding glass physics and in the design of new glass compositions. The relationship among these various descriptions is emphasized to build a single unified picture of glass statistical mechanics synthesizing these various approaches. © 2014 The Authors. Published by Elsevier B.V.
Constraint theory; Glass; Glass transition; Relaxation; Statistical mechanics; Theory
Bohmian Mechanics and the Quantum Revolution
arXiv.org
1-20
1995
10.1007/s10701-009-9319-4
it would be natural to suppose that the two books with which I shall be concerned in this essay, The Undivided Universe by Bohm and Basil J. Hiley, which is a presentation of Bohm’s 1952 theory incorpo- rating some later developments, many of which represent joint work with Bohm’s long-time collaborator Hiley, and Bell’s Speakable and Unspeakable in Quantum Me- chanics, which collects all of Bell’s work, up to 1987, on the foundations of quantum mechanics, are in diametric opposition, with the former defending hidden variables and the latter defending quantum orthodoxy. This, however, is not so; in fact, Bell provides a far stronger argument against the orthodox Copenhagen interpretation of quantum mechanics and, indeed, in favor of what have been called (absurdly, according to Bell) hidden variables theories than do Bohm and Hiley
Bohmian mechanics; Copenhagen interpretation; Quantum mechanics
Effect of electrode size and silicon residue on piezoelectric thin-film membrane actuators
Sensors and Actuators, A: Physical
147
1
279-285
2008
10.1016/j.sna.2008.04.015
Piezoelectric micro-electromechanical systems (MEMS) often adopt a membrane structure to facilitate sensing or actuation. Design parameters, such as membrane size, thickness of the piezoelectric thin film, and electrode types, have been studied to maximize actuation, sensitivity, or coupling coefficient. This paper is to demonstrate numerically and experimentally that the size of silicon residue and its relative size to the top electrode are two critical yet unrecognized parameters in maximizing the actuation displacement of PZT thin-film membrane actuators. To study effects of the silicon residue, we have developed a finite element model using ANSYS. The model consists of five components: a square passive silicon membrane, a silicon substrate, a PZT thin film, a square top electrode, and a silicon residue region. In particular, the silicon residue has a circular inner diameter and a square outer perimeter with a trapezoidal cross section. Predictions of the finite element model lead to several major results. First, when the silicon residue is present, there exists an optimal size of the top electrode maximizing the actuator displacement. Second, the optimal electrode size is roughly 50-60% of the inner diameters of the silicon residue. The displacement of the membrane actuator declines significantly as the electrode overlaps with the silicon residue. Third, the maximal actuator displacement decreases as the inner diameter of the silicon residue decreases. Aside from the finite element analysis, a mechanics-of-material model is also developed to predict the electrode size that maximizes the actuator displacement. To verify the simulation results, eight PZT thin-film membrane actuators with progressive electrode sizes are fabricated. These actuators all have a square membrane of 800 ??m ?? 800 ??m with the inner diameter of the silicon residue controlled between 500 and 750 ??m. A laser Doppler vibrometer is used to measure the actuator displacements. The experimental measurements confirm that there exists an optimal size of the top electrode maximizing the actuator displacement. ?? 2008 Elsevier B.V. All rights reserved.
Electrode size; Finite element analysis; Membrane actuators; PZT thin films; Silicon residue
A closed-form structural model of planar fibrous tissue mechanics
Journal of Biomechanics
42
10
1424-1428
2009
10.1016/j.jbiomech.2009.04.005
Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite-element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress-strain law. ?? 2009 Elsevier Ltd. All rights reserved.
Soft-tissue mechanics
Three-dimensional transient piezothermoelasticity for a rectangular composite plate composed of cross-ply and piezoelectric laminae
International Journal of Engineering Science
38
1
47-71
2000
10.1016/S0020-7225(99)00019-1
In this study, the theoretical analysis of three-dimensional transient piezothermoelasticity is developed for a rectangular composite plate composed of cross-ply laminae and piezoelectric material of crystal class mm2, subject to partial heat supply. We obtain the exact solutions for the three-dimensional temperature change in a transient state, and three-dimensional transient piezothermoelasticity of a simply supported combined plate. As an example, numerical calculations are carried out for a cross-ply laminated rectangular plate made of alumina fiber-reinforced aluminum composite, associated with a piezoelectric plate of a cadmium selenide solid. Some numerical results for temperature change, displacement, stress, electric potential, and electric displacement distributions in a transient state are shown in figures. Furthermore, the influence of thickness of the piezoelectric plate on thermal stress or electric field are investigated.
Influence of mechanical and probabilistic models on the reliability estimates of fibre-reinforced cross-ply laminates
Structural Safety
51
35-46
2014
10.1016/j.strusafe.2014.06.001
Numerous methodologies for estimating the reliability of fibre-reinforced plastics have been published in the past few decades. Several of these methodologies use different mechanical and probabilistic models, each one based on a number of assumptions and approximations. The objective of this study is to assess common assumptions and approximations made on mechanical and probabilistic models used in reliability analyses of fibre-reinforced plastic laminates. The assessment consists of two parts: a theoretical overview of the models and their justification, and an investigation of the quantitative influence of the models on the reliability estimates of a group of fibre-reinforced cross-ply laminates. The reliability estimates are calculated through Monte Carlo simulations using different mechanical and probabilistic models. This study concludes that both mechanical and probabilistic models can significantly influence the reliability estimations. For the mechanical models, the factor with the greatest influence is the definition and modelling of matrix cracking. While, for the probabilistic models, the choice of probability distribution for modelling ply property variability has the greatest influence.
Fibre-reinforced plastics; Mechanical modelling; Probabilistic modelling; Structural reliability
Low velocity impact behavior of glass/epoxy cross-ply laminates with different fiber treatments
Polymer Composites
20
2
269-278
1999
This paper deals with the influence of the fiber/matrix adhesion quality on the impact behavior of cross-ply glass/epoxy laminates. Glass fibers with two different treatments (one to promote and one to prevent adhesion to the matrix) were embedded in epoxy matrix systems and subjected to low velocity impacts at energies below perforation energy. It will be shown that the laminates with good fiber/matrix adhesion are significantly more damage resistant than the plates with poor adhesion. It will be pointed out that the composites with the more brittle matrix system show the lower damage resistance. For all materials, the absorbed energy correlates well with the amount of impact induced damage. Furthermore, an experimental/mathematical model is introduced that gives the possibility of predicting the maximum deflection and maximum force for any given impact energy. Only one experiment is needed for each material to identify the model parameters. These parameters describe the real material behavior and can be used as characteristic values to classify materials with respect to their impact stiffness and damage resistance.
Adhesion; Brittle matrix system; Brittleness; Damage resistance; Energy absorption; Epoxy resins; Glass epoxy cross ply laminates; Glass fibers; Impact resistance; Impact testing; Laminated composites; Low velocity impact behavior; Mathematical models; Velocity
First ply failure analysis of stiffened panels – a finite element approach
Composite Structures
51
1
73-81
2001
10.1016/S0263-8223(00)00126-4
A first-ply failure analysis method has been developed for predicting the failure load on the laminated composite stiffened panels under various loading conditions. The present finite element formulation is generalised to analyse both laminated bare/stiffened plate and shell panels elegantly. Eight noded isoparametric quadratic elements for shell and three noded curved beam elements for the stiffener are used for the analysis of stiffened panel. The stiffness matrix of the stiffener is computed independently and then transferred to that of the shell. The formulation eliminates the restriction on the location and orientation of the stiffener within the shell element. Several prominent failure theories have been considered in the present work for the prediction of failure load. The results obtained by the present formulation have been compared with those available in literature and some parametric study has also been performed on the basis of variety in shell geometry.
finite element method; First ply failure load; Isoparametric shell element; Laminated stiffened panels
Analytical piezoelasticity solution for vibration of piezoelectric laminated angle-ply circular cylindrical panels
Journal of Sound and Vibration
324
3-5
832-849
2009
10.1016/j.jsv.2009.02.035
An exact two-dimensional (2D) piezoelasticity solution is presented for free vibration and steady-state forced response of simply supported piezoelectric angle-ply laminated circular cylindrical panels in cylindrical bending under harmonic electromechanical load, with and without damping. The piezoelectric layers are polarized along radial direction to induce extension actuation/sensing mechanism. The variables are expanded layerwise in Fourier series to satisfy the boundary conditions at the simply supported ends. The governing equations get reduced to ordinary differential equations in thickness direction with variable coefficients and these are solved by the modified Frobenius method. The unknown coefficients of the solution are obtained using the transfer matrix method. Results for the natural frequency and its variation with ply angle and for steady-state response due to harmonic electromechanical excitation are presented for single layer piezoelectric panel, and hybrid multilayered inhomogeneous test, composite and sandwich panels. The numerical results presented in tabular form would serve as useful benchmark for assessing one-dimensional (1D) panel theories for free vibration and harmonic response of hybrid cylindrical panels. (C) 2009 Elsevier Ltd. All rights reserved.
icle in press
Fatigue hysteresis behavior of cross-ply C/SiC ceramic matrix composites at room and elevated temperatures
Materials Science and Engineering A
586
160-170
2013
10.1016/j.msea.2013.08.017
The tensile fatigue hysteresis behavior of cross-ply C/SiC composites at room and elevated temperatures in air atmosphere has been investigated in present analysis. The hysteresis modulus and hysteresis loss energy corresponding to different cycles have been analyzed. Based on damage mechanisms of fiber sliding relative to matrix in fiber/matrix interface debonded region upon unloading and subsequent reloading, the hysteresis loops models considering different matrix cracking modes have been developed. The hysteresis loss energy for strain energy lost per volume during corresponding cycle is formulated in terms of fiber/matrix interface shear stress. By comparing experimental hysteresis loss energy with computational values, fiber/matrix interface shear stress of cross-ply C/SiC composites at room and elevated temperatures has been estimated. ?? 2013 Elsevier B.V.
Ceramic-matrix composites (CMCs); Fatigue; Hysteresis loops; Interface
Natural vibration of unsymmetric cross-ply laminates
Journal of Sound and Vibration
330
20
4764-4779
2011
10.1016/j.jsv.2011.03.014
This study considers the linear vibration characteristics of square [0 \n n/90\n n]\n T laminates relative to their room-temperature static equilibrium configurations. A RayleighRitz approach combined with Hamilton's principle is used to provide approximate solutions to this vibration problem. The vibration mode shapes are assumed to have the same spatial dependence as used in past investigations to study the room-temperature configurations of these laminates, and are thus assumed to be perturbations on the static equilibrium configurations. Hamilton's principle then results in the so-called zero- and first-order equations. The zero-order equations lead to the classic static equilibrium results of past investigations, presented here in nondimensional form with analytical solutions at the bifurcation point. The first-order equations, combined with zero-order results, lead to the vibration characteristics for each zero-order static configuration. Interest centers on the lowest natural frequency and the associated mode shape for laminates clamped at their midpoints, with special attention as to how these vibration characteristics depend on the laminate side-length-to-thickness ratio. With an imaginary-valued frequency, the static saddle configuration for side-length-to-thickness ratios larger than the critical value is correctly assessed as unstable. A finite element model is also used to study the vibration characteristics and to compare with the findings for the developed analysis. The qualitative comparisons between the developed analysis and the finite element model are generally good, and the quantitative comparisons are also satisfactory. ?? 2011 Elsevier Ltd. All rights reserved.
Causality and Nonlocality as Axioms for Quantum Mechanics
Arxiv Preprints
9
1997
Quantum mechanics permits nonlocality - both nonlocal correlations and nonlocal equations of motion - while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality: "superquantum" correlations, and nonlocal "jamming" of correlations. These models are consistent with some definitions of nonlocality and causality.
Microscopic description of elementary growth processes and classification of structural defects in pentacene thin films.
The journal of physical chemistry. B
111
1
139-50
2007
10.1021/jp0653003
Elementary growth processes such as kink initiation, adding a molecule to a kink, and adding a molecule between two neighboring kinks and between two grains are theoretically studied in pentacene films by adding one molecule at a time to a predefined aggregate. For each molecule, the potential energy surface is calculated using the MM3 molecular mechanics force field, which allowed one to identify useful parameters like the energy barrier for diffusion and the energy to create kinks, as well as defect configurations. Depending on the properties of the potential energy surface and the resulting growth-condition-dependent probabilities of initiating defect configurations in the film, three types of pentacene defects are identified: a thermally activated defect, an intrinsic defect, and a kinetic defect. Upon film growth, most defects relax into the ideal crystal configuration. Bulk defects that resist relaxation have densities lower than 10(16) defects/cm3 at typical growth conditions. Grain boundary defects, on the other hand, are very stable. Moreover, interstitial molecules at grain boundaries are identified as a source of compressive stress.
Molecular Mechanics (PART 1)
Chemistry 380.37
May
1-7
2013
In this assignment, you will perform some molecular mechanics calculations using the Avogadro software package. One of the objectives of this assignment is to explore the ability of molecular mechanics force fields to adequately represent the energies of molecules as their geometries are varied. Another objective is to learn how to extract information about force field parameters from calculations. In addition, the use of Avogadro to build simple organic molecules and perform equilibrium geometry and energy calculations will be illustrated.
A continuum model for the flow of thin liquid films over intermittently chemically patterned surfaces
The European Physical Journal Special Topics
166
1
159-163
2009
10.1140/epjst/e2009-00899-5
It is known from both experiments and molecular dynamics simulations that chemically patterning a solid surface has an effect on the flow of an adjacent liquid. This fact is in stark contrast with predictions of classical fluid mechanics where the no-slip boundary condition is insensitive to the chemistry of the solid substrate. It has been shown that the influence on the flow caused by a steep change in the wettability of the solid substrate can be described in the framework of continuum mechanics using the interface formation theory. The present work extends this study to the case of intermittent patterning. Results show that variations in wettability of the substrate can significantly affect the flow, especially of thin films, which may have applications to the design of microfluidic devices.
On Randomness in Quantum Mechanics
European Journal of Physics
29
3
567-575
2007
10.1088/0143-0807/29/3/016
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
Bending of sandwich plates with anti-symmetric angle-ply face sheets - Analytical evaluation of higher order refined computational models
Composite Structures
75
1-4
114-120
2006
10.1016/j.compstruct.2006.04.007
The aim of the present study is to assess the accuracy of the few computational models based on various shear deformation theories in predicting the bending behaviour of sandwich plates with anti-symmetric angle-ply face sheets under static loading. Five two-dimensional models available in the literature are used for the present evaluation. The performance of the various models is evaluated on a simply supported laminated plate under sinusoidal loading. The equations of equilibrium are derived using the principle of minimum potential energy (PMPE). Analytical solution method using double Fourier series approach is used in conjunction with the admissible boundary conditions. The accuracy of each model is established by comparing the results of composite plates with the exact solutions already available in the literature. After establishing the correctness of the theoretical formulations and the solution method, benchmark results for transverse displacement, in-plane stresses, moment and shear stress resultants are presented for the multilayer sandwich plates. ?? 2006 Elsevier Ltd. All rights reserved.
Analytical solutions; Flexural; Higher-order theory; Sandwich plates; Shear deformation
Crush behaviour of carbon fibre angle-ply reinforcement and the effect of interlaminar shear strength on energy absorption capability
Composites Part B: Engineering
31
5
435-440
2000
10.1016/S1359-8368(00)00026-3
A series of carbon fibre epoxy laminates have been prepared with a range of fibre orientations. The laminates have been tested under compression loading conditions to measure the specific energy absorption in crushing. A relationship has been identified between the specific sustained crushing stress and the interlaminar shear stress of the materials. This relationship mirrors a similar trend identified for glass fibre composites in an earlier programme.
a; b; carbon fibre; e; fracture; lay-up; plate-crushing test; prepreg
The nonlinear growth of surface-tension-driven instabilities of a thin annular film
Journal of Fluid Mechanics
233
141–156
1991
10.1017/S0022112091000423
The stability and initial growth rate of disturbances on an annular film lining a cylindrical tube have been the focus of several previous works. The further development of thsse disturbances as they grow to form stable unduloids or liquid bridges is investigated by means of a thin-film integral model. The model is compared both with perturbation theories for early times, and a numerical solution of the exact equations (NEKTON) for later times. The thin-film model gave results that were in good agreement with solutions of the exact equations. The results show that linear perturbation theory can be used to give good estimates of the times for unduloid and liquid bridge formation. The success of the model derives from the dominant influence of narrow draining regions that feed into the growing unduloid, and these regions remain essentially one-dimensional throughout the growth of the instability. The model is used to analyse the evolution of the liquid layer lining the small airways of the lung during a single breath. The timescales for formation of unduloids and liquid bridges are found to be short enough for the liquid layer to be in a virtually quasi-equilibrium state throughout the breathing cycle. This conclusion is only tentative, however, because the model assumes that the surface tension of the airway liquid lining does not change with changes in interfacial area despite the known presence of pulmonary surfactant.
Quantum Will: Determinism meets Quantum Mechanics
Euresis Journal
5
1-16
2013
We present a brief non-technical introduction to the standing discussion on the relation between Quan- tum Mechanics and Determinism. Quantum Mechanics inherent randomness in the measurement pro- cess is sometimes presented as a door to explain free will. We argue against this interpretation. The possibility that Quantum Mechanics provides just an effective description of Nature which is only valid at our low-energy scales is also discussed.
Quantum mechanics: the truth about reality.
Nature
445
7129
723-724
2007
10.1038/445723a
Hopes of keeping quantum mechanics real have been dashed by new measurements of neutrons quantum behaviour. Despite what our classical sensibilities require, the world is indeed fundamentally random.
Computational mechanics at the mesoscale
Acta Materialia
48
1
105-124
2000
10.1016/S1359-6454(99)00290-6
Conventional continuum mechanics models of inelastic deformation processes are size scale independent. In contrast, there is considerable experimental evidence that plastic flow in crystalline solids is inherently size dependent over a size scale that ranges from a fraction of a micrometer to 100 mu m or so. It is over this mesoscale size range that key deformation and fracture processes in a variety of structural and electronic materials take place. Computational studies play a central role in the development of a mesoscale theoretical Framework because size dependent phenomena come into play when there are gradients of deformation and stress, so that numerical methods are usually needed to obtain solutions. Three mesoscale continuum formulations are discussed, each involving a length scale and each having a different character: (i) discrete dislocation plasticity, (ii) nonlocal plasticity and (iii) the coupling of matter diffusion and deformation. The main focus is on illustrating the capability of such frameworks to elucidate aspects of material behavior that are not amenable either to a direct atomistic analysis or to a size independent continuum analysis. Numerical implementation issues are also discussed. (C) 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.
2 DIMENSIONS; COMPUTER-SIMULATION; constitutive equations; DEPENDENCE; DISCRETE DISLOCATION; FINITE-ELEMENT ANALYSIS; LENGTH SCALE; LOCALIZATION; MATERIAL RATE; mechanical properties; modeling; plastic flow; SCALE MOLECULAR-DYNAMICS; SINGLE-CRYSTALS; STRAIN GRADIENT PLASTICITY; theory and
Mechanics of Materials
Mechanics of Materials
6636
10
6636-6636
2010
10.1115/1.1470679
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
Quaternionic quantum mechanics is consistent with complex quantum mechanics
International Journal of Theoretical Physics
31
6
965-981
1992
10.1007/BF00675088
Quaternionic quantum mechanics is investigated in the light of the great success of complex quantum mechanics. It is shown that to reproduce the results of complex quantum mechanics, quaternionic quantum mechanics must contain complex quantum mechanics.
Mode I stress intensity factor for cracked thin-walled composite beams
Theoretical and Applied Fracture Mechanics
67-68
38-45
2013
10.1016/j.tafmec.2013.10.002
In this paper, we present an analytical method to determine the mode I stress intensity factor for thin-walled beams made of laminated composites. The technique relies on the concept of crack surface widening energy release rate, which is expressed in terms of the G* integral and thin-walled beam theory. In the vicinity of the crack tip, a solution of the G* integral is obtained employing stress and displacement fields derived for materials with general orthotropy. The effect of warping is taken into account. This is a common feature in thin-walled beams which cannot be neglected, especially when flexural–torsional loads are present. The model shows a good agreement with finite element results. It is shown that, although the approaches developed for isotropic materials may be useful in the treatment of orthotropic problems, they may not yield good results for some typical lamination sequences.
Fiber reinforced composite; Fracture mechanics; G* integral; Stress intensity factor; Thin-walled beam
Error Bounds in Equilibrium Statistical Mechanics
Journal of Mathematical Physics
9
5
655
1968
10.1063/1.1664624
A new method is presented for the calculation of thermodynamic properties from equilibrium statistical mechanics. Starting from the high‐temperature expansion coefficients for the canonical partition function, error bounds are obtained, which are both rigorous and optimal.
Ultrasonic monitoring of ply crack and delamination formation in compositetube under torsion load
Proceedings - IEEE Ultrasonics Symposium
595-598
2010
10.1109/ULTSYM.2010.5935887
As a simple model of a rotor spar, a circular graphite-epoxy composite laminate cylinder was subjected to cyclic torsional load. The test section of the cylindrical specimen varied from four to six plies of ±45° fibers, due to intentional ply overlaps and gaps. A layer of 13-μm Teflon film was inserted between plies at three locations to serve as delamination initiators. A commercial X-Y scanner was mounted to the load frame to enable ultrasonic inspection without removing the specimen. A focused immersion probe was mounted in a captive water column with a rugged Nitrile membrane tip, which was coupled to the cylinder using a mist of soapy water. The transducer was aligned normal to the cylinder surface using the X-axis. Scanning was performed along the length of the specimen with the Y-axis and the specimen was incrementally rotated by the torsion head of the load frame. After 350k cycles of torsion, several linear 45° diagonal indications appeared as 5–40% attenuation of the back wall echo, with no apparent echoes from the interior of the composite, suggesting through-ply cracks in the innermost ply. Crack indications grew and new cracks appeared as torsion cycling continued. Internal reflections from delaminations associated with the growing ply cracks appeared after 500k cycles. Three areas of extensive multi-layer delaminations appeared after 1150k cycles. Failure of the specimen occurred at 1600k cycles. The observed progressive damage was not associated with the Teflon inclusions. Concurrent thermographic measurements provided lower-resolution confirmation of the damage observed.
composites; in situ; ultrasonic
Surface processes and phase transitions from ab initio atomistic thermodynamics and statistical mechanics
Catalysis Today
105
1 SPEC. ISS.
17-35
2005
10.1016/j.cattod.2005.04.015
Knowledge of the surface composition and atomic geometry is a prerequisite for understanding the physical and chemical properties of modern materials such as those used in, for example, heterogeneous catalysis, corrosion resistance, sensors, and fuel cells. To understand the function of surfaces under realistic conditions, it is crucial to take into account the influence of environmental gas at finite (possibly high) temperatures and pressures. Recent experimental and theoretical studies have shown that when transition metal surfaces are exposed to high oxygen pressures, thin oxide-like structures can form which may have little similarity to the bulk oxides, and thus possess unique chemical and physical properties. Given that technological oxidation catalysis typically involves oxygen-rich conditions, such structures may be present, and in fact be the active material for the reaction, as opposed to the traditionally believed pure metal. Using the approach of ab initio atomistic thermodynamics, free energy phase-diagrams for oxygen/transition metal systems in (T, p)-space ranging from ultra-high vacuum to technically relevant pressures, p, and temperatures, T, are discussed. In addition, results of ab initio statistical mechanical schemes, namely, the Lattice-gas Hamiltonian plus Monte Carlo (MC) simulations, are presented for oxygen/transition metal and alkali-atom/metal systems, where for the latter, the recently introduced "Wang-Landau" algorithm is employed, which affords an accurate estimation of the density of (configurational) states, therefore allowing a direct determination of all major thermodynamic functions. © 2005 Published by Elsevier B.V.
Atomistic thermodynamics; Phase transition; Surface
Thin film delamination: A discrete dislocation analysis
Journal of the Mechanics and Physics of Solids
54
10
2214-2234
2006
10.1016/j.jmps.2006.02.008
Interface delamination during indentation of micron-scale ceramic coatings on metal substrates is modeled using discrete dislocation (DD) plasticity to elucidate the relationships between delamination, substrate plasticity, interface adhesion, elastic mismatch, and film thickness. In the DD method, plasticity in the metal substrate occurs directly via the motion of dislocations, which are governed by a set of physically based constitutive rules for nucleation, motion and annihilation. A cohesive law with peak stress over(σ, ^) characterizes the traction-separation response of the metal/ceramic interface. The indenter is a rigid flat punch and plane strain deformation is assumed. A continuum plasticity model of the same problem is studied for comparison. For low interface strengths (e.g. over(σ, ^) < σy), DD and continuum plasticity results are quantitatively similar, with delamination being nearly independent of interface strength, and easier for thinner, lower-modulus films. For higher interface strengths (over(σ, ^) / σy > 2), continuum plasticity predicts no delamination up to very high loads while the DD model shows a smooth increase in the critical indentation force for delamination with increasing interface strength. Tensile delamination in the DD model is driven by the accumulation of dislocations, and their associated high stresses, at the interface upon unloading. The DD model is thus capable of predicting the nucleation of cracks, and its dependence on material parameters, in realms of realistic constitutive behavior and/or small length scales where conventional continuum plasticity fails. © 2006 Elsevier Ltd. All rights reserved.
Delamination; Dislocations; Finite elements; Fracture mechanics
Non-linear stability analysis of imperfect thin-walled composite beams
International Journal of Non-Linear Mechanics
45
2
100-110
2010
10.1016/j.ijnonlinmec.2009.09.006
The static nonlinear behavior of thin-walled composite beams is analyzed\nconsidering the effect of initial imperfections. A simple approach\nis used for determining the influence of imperfection on the buckling,\nprebuckling and postbuckling behavior of thin-walled composite beams.\nThe fundamental and secondary equilibrium paths of perfect and imperfect\nsystems corresponding to a major imperfection are analyzed for the\ncase where the perfect system has a stable symmetric bifurcation\npoint. A geometrically nonlinear theory is formulated in the context\nof large displacements and rotations, through the adoption of a shear\ndeformable displacement field. An initial displacement, either in\nvertical or horizontal plane, is considered in presence of initial\ngeometric imperfection. Ritz's method is applied in order to discretize\nthe nonlinear differential system and the resultant algebraic equations\nare solved by means of an incremental Newton-Rapshon method. The\nnumerical results are presented for a simply supported beam subjected\nto axial or lateral load. It is shown in the examples that a major\nimperfection reduces the load-carrying capacity of thin-walled beams.\nThe influence of this effect is analyzed for different fiber orientation\nangle of a symmetric balanced lamination. In addition, the postbuckling\nresponse obtained with the present beam model is compared with the\nresults obtained with a shell finite element model (Abaqus).
A theoretical study of a thin-film delamination using shaft-loaded blister test: Constitutive relation without delamination
Journal of the Mechanics and Physics of Solids
56
9
2815-2831
2008
10.1016/j.jmps.2008.04.009
This paper presents exact solutions for nonlinear large deflection of thin circular membrane loaded by a central point force using blister test with two types of boundary conditions and with or without residual stress cases. A comparison with existing solutions is presented, and a geometrically nonlinear finite element analysis (FEA) is conducted to verify our analytical solutions.
Adhesion and adhesives; Analytical solutions; Delamination; Residual stress; Shells and membranes
Mathematical treatment of stability problems for thin shallow elastic shells of revolution
International Journal of Non-Linear Mechanics
29
4
587-601
1994
http://dx.doi.org/10.1016/0020-7462(94)90025-6
This paper presents a review of investigations on non-linear stabilities of thin shallow elastic shells of revolution, beginning with von Kármán's original 1910 paper on the subject. Altogether 83 papers were reviewed. The theoretical foundations and the new methods and new concepts that were introduced over the years are discussed. Most of the work is not well known outside the People's Republic of China.
Tissue mechanics and fibrosis.
Biochimica et biophysica acta
1832
7
884-90
2013
10.1016/j.bbadis.2013.02.007
Mechanical forces are essential to the development and progression of fibrosis, and are likely to be as important as soluble factors. These forces regulate the phenotype and proliferation of myofibroblasts and other cells in damaged tissues, the activation of growth factors, the structure and mechanics of the matrix, and, potentially, tissue patterning. Better understanding of the variety and magnitude of forces, the characteristics of those forces in biological tissues, and their impact on fibrosis in multiple tissues is needed and may lead to identification of important new therapeutic targets. This article is part of a Special Issue entitled: Fibrosis: Translation of basic research to human disease.
Hydrostatic pressure; Myofibroblast; Shear; Stretch; Tension; Tissue stiffness
The failure of thin-walled lipped channel compression members due to coupled local-distortional interactions and material yielding
Thin-Walled Structures
61
14-21
2012
10.1016/j.tws.2012.03.025
This paper details appropriate finite element modelling strategies and procedures for the determination of the coupled local-distortional interactive response of thin-walled lipped channel sections. The modelling procedures are able to describe the complete loading history of the compression members from the onset of local buckling through post-local buckling behaviour leading to local-distortional interaction including material yielding and yield propagation to ultimate conditions and then to elasto-plastic unloading. The numerical simulations take due account of the influence of geometrical imperfections on the compressive ultimate failures of the sections and the results from the finite element models are shown to agree favourably with the ultimate loads and failure mechanisms from experimental tests on steel lipped channel sections exhibiting local-distortional interaction.
Coupled buckling; Distortional buckling; Failure mechanics; Finite element simulation; Geometric imperfections; Global flexural buckling; Lipped channel columns; Local buckling; Local-distortional interaction; Material yielding; Post-local buckling
An evaluation of factors influencing pore pressure in accretionary complexes: Implications for taper angle and wedge mechanics
Journal of Geophysical Research: Solid Earth
111
4
1-21
2006
10.1029/2005JB003990
At many subduction zones, accretionary complexes form as sediment is off-scraped from the subducting plate. Mechanical models that treat accretionary complexes as critically tapered wedges of sediment demonstrate that pore pressure controls their taper angle by modifying basal and internal shear strength. Here, we combine a numerical model of groundwater flow with critical taper theory to quantify the effects of sediment and décollement permeability, sediment thickness, sediment partitioning between accretion and underthrusting, and plate convergence rate on steady state pore pressure. Our results show that pore pressure in accretionary wedges can be viewed as a dynamically maintained response to factors which drive pore pressure (source terms) and those that limit flow (permeability and drainage path length). We find that sediment permeability and incoming sediment thickness are the most important factors, whereas fault permeability and the partitioning of sediment have a small effect. For our base case model scenario, as sediment permeability is increased, pore pressure decreases from near-lithostatic to hydrostatic values and allows stable taper angles to increase from ∼2.5° to 8°–12.5°. With increased sediment thickness in our models (from 100 to 8000 m), increased pore pressure drives a decrease in stable taper angle from 8.4°–12.5° to <2.5–5°. In general, low-permeability and thick incoming sediment sustain high pore pressures consistent with shallowly tapered geometry, whereas high-permeability and thin incoming sediment should result in steep geometry. Our model results compare favorably with available data from active accretionary complexes. Active margins characterized by a significant proportion of fine-grained sediment within the incoming section, such as northern Antilles and eastern Nankai, exhibit thin taper angles, whereas those characterized by a higher proportion of sandy turbidites, such as Cascadia, Chile, and Mexico, have steep taper angles. Observations from active margins also indicate a strong trend of decreasing taper angle (from >15° to <4°) with increased sediment thickness (from <1 to 7 km). One key implication is that hydrologic properties may strongly influence the strength of the crust in a wide range of geologic settings.
http://dx.doi.org/10.1029/2005JB003990, doi:10.102
Optimum design of fiber-reinforced composite cylindrical skirts for solid rocket cases subjected to buckling and overstressing constraints
Composites Part B: Engineering
34
273-284
2003
10.1016/S1359-8368(02)00104-X
In order to increase the flight range of aerospace vehicles and the efficiency of solid rocket motors, designers attempt to reduce the weight of solid rocket motors. A skirt is a potential element for weight reduction in rocket motors as it leads to reduction of the total weight of solid rocket motor. Due to its significance for solid rocket motors, the objective of this paper is to investigate the optimal design of a fiber-reinforced composite cylindrical skirt subjected to a buckling strength constraint and an overstressing strength constraint under aerodynamic torque and axial thrust. The present optimal design problem involve in determining the best laminate configuration to minimize the weight of the cylindrical skirt. To find the optimal solution accurately and quickly, the hybrid genetic algorithm (HGA) is employed in this work. Buckling strength and overstressing strength of the fiber-reinforced composite cylindrical skirt are analyzed using classical laminate theory and elastic stability theory of thin shells. The Tsai-Wu failure criterion is employed to assess the first ply failure, and an overstressing load level factor is introduced to describe the failure strength. In addition, a buckling load factor is introduced to describe the buckling strength. Due to the critical issue of buckling strength, the effects of the design parameters on the buckling strength are investigated in this work. Finally, a practical design example of the proposed fiber-reinforced composite cylindrical skirt is investigated using the present analysis procedure. Results reveal that the fiber-reinforced composite cylindrical skirt laminated symmetrically with both cross-ply layers [0/90°] and angle-ply layers [+45/ - 45°] can sustain a great buckling load. Furthermore, the buckling strength of the skirt shell laminated with equal-hybrid between the angle-ply layers and the cross-ply layers is greater than that of the skirt shell laminated with over-weighted hybrid between the angle-ply layers and the cross-ply layers. Results provide a valuable reference for designers of aerospace vehicles. © 2003 Elsevier Science Ltd. All rights reserved.
Angle-ply; Buckling; Cross-ply; Fiber-reinforced; Overstressing; Skirt
Some problems in statistical mechanics that I would like to see solved
Physica A: Statistical Mechanics and its Applications
263
1–4
491-499
1999
10.1016/S0378-4371(98)00517-2
Some reflections about open problems in statistical mechanics are offered on the occasion of the award of the IUPAP Boltzmann medal.
Analysis of thin film cracking and buckling on compliant substrate by fragmentation test
Advances in Fracture and Damage Mechanics VI
348-349
329-332
2007
10.4028/www.scientific.net/KEM.348-349.329
Application of coating fragmentation test for determination of coating properties is considered. A probabilistic model of coating fragmentation under uniaxial tensile loading is applied for coating and interface property identification of thin brittle coating/polymer substrate system. A finite element model is developed to simulate the process of buckle formation in coating strips during fragmentation test. The measured buckle geometry parameters and buckle density evolution as a function of the applied strain is used to estimate the interface toughness.
Passive respiratory mechanics: The occlusion techniques
European Respiratory Journal
17
141-148
2001
10.1183/09031936.01.17101410
The aim of this position paper is to define quality control and acceptance criteria for measuring passive respiratory mechanics in infants using the occlusion techniques to ensure that valid results are obtained. These guidelines cover numerous aspects including: 1) terminology and definitions; 2) equipment; 3) data acquisition; 4) data handling and analysis; 5) reporting of results. Adherence to these guidelines should ensure that measurement of passive respiratory mechanics in infants in different lung function laboratories could be performed with an acceptable degree of safety, precision, and reproducibility. This will facilitate multi-centre collection of data and performance of clinical investigations.
Infant; Occlusion techniques; Passive respiratory mechanics; Respiratory function tests; Respiratory mechanics; Standardization
Vibration of a thin rectangular plate subjected to series of moving inertial loads
Mechanics Research Communications
55
105-113
2014
10.1016/j.mechrescom.2013.10.009
In this article, the resonance of a rectangular plate due to multiple traveling masses is studied. Two series of moving inertial loads traversing the plate surface along parallel rectilinear trajectories with opposite directions are considered. This investigation is of significance in engineering mechanics dealing with the vibration of two-lane slab-type bridges under the moving vehicles. The peak values of DAF (dynamic amplification factor) are determined with respect to the variation of loads velocity and inertia as well as their spacing.
Moving inertial loads; Thin rectangular plates; Transverse vibration; Two-lane slab-type bridges
Micron-scale channel formation by the release and bond-back of pre-stressed thin films: A finite element analysis
Journal of the Mechanics and Physics of Solids
58
4
447-465
2010
10.1016/j.jmps.2010.02.004
Buckling of thin films on a rigid substrate during use or fabrication is a well-known but unwanted phenomenon. However, this phenomenon can also be exploited to generate well-controlled patterns at the micro and nano-scale. These patterned surfaces find various technological applications such as optical gratings or micro/nano-fluidic channels. In this article, we present a numerical model that accounts for the buckling-up of pre-strained thin films by a reduction of the interface toughness and the subsequent bond-back. Channels are formed whose dimensions can be controlled by tuning the film dimensions, film thickness and stiffness, the eigenstrain in the film and the cohesive interface energy between the film and the substrate. We will show how the buckling-up and draping back processes can be captured in terms of a limited set of dimensionless parameters, providing quantitative insight on how these parameters should be tuned to generate a specified channel geometry. © 2010 Elsevier Ltd. All rights reserved.
Buckle-driven delamination; Channel formation; Cha; Buckling; Fluidic devices; Steel sheet; Thin film; Finite element method
COPULATORY MECHANICS IN THE FUNNEL-WEB SPIDERS HISTOPONA-TORPIDA AND TEXTRIX-DENTICULATA (AGELENIDAE, ARANEAE)
Acta Zoologica
75
4
379-384
1994
The functional morphology of the copulatory organs of Histopona torpida (C. L. Koch, 1834) and Textrix denticulata (Olivier, 1789), investigated by semi-thin serial sectioning after freeze- fixation of the animals in copula, is described. In H. torpida, the long embolus runs through a precisely defined course in the membraneous genital pouch of the female vulva. The patellar apophysis locks the pedipalp in the female epigastric furrow. In T. denticulata this is accomplished by the retrolateral tibial apophysis that gets hold at the female scape. In both species the conductor has a locking as well as a guiding function for the embolus. A comparison with previously investigated agelenids shows a surprising diversity in the function of the retrolateral tibial apophysis.
Philosophy of Quantum Mechanics
The Ashgate Companion to the New Philosophy of Physics
July
16-98
2008
This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation.
Molecular mechanics of smooth muscle contractile proteins in airway hyperresponsiveness and asthma.
Proceedings of the American Thoracic Society
5
23
40-46
2008
10.1513/pats.200704-053VS
Airway hyperresponsiveness (AH) is a hallmark of asthma. The dynamics of the airway smooth muscle (SM) contraction, rather than its force-generating capacity, have been postulated to be key features of AH. Two mechanisms were proposed whereby an increased velocity of shortening (Vmax) of the airway SM leads to excessive bronchoconstriction. The first mechanism involves a greater Vmax during the initial portion of contraction, whereas the second mechanism implicates a greater Vmax after muscle stretches, such as after each tidal breath. This review focuses on the components of the contractile apparatus that have so far been reported to enhance the mechanics of the myosin molecular motor, thus leading to a greater Vmax. A greater activation of myosin, via increased phosphorylation of its regulatory light chain (LC20) by myosin light chain kinase, correlates with an increased Vmax in models of AH and in human asthmatic bronchial SM cells. However, poor correlations between these two parameters have also been reported in other models. A greater expression of the fast SM myosin heavy chain isoform [(+)insert or SM-B] also correlates with the greater Vmax measured in models of AH and in human asthmatic bronchial SM cells. However, the (+)insert isoform can only explain a twofold increase in Vmax, as extrapolated from its velocity of actin filament propulsion in the in vitro motility assay. Further considerations are given to the combination of these two factors with other components of the contractile machinery, thereby leading to the enhancement of airway SM function.
1; 2; 3; accepted that its function; actin; asthmatic airways exhibit two; be; but it is widely; distinctive abnormalities that can; in normal airways is; is altered in asthma; muscle; myosin; not clear; phosphorylation; sm; the role of smooth; thick filament; thin filament
The mechanics of the adhesive locomotion of terrestrial gastropods.
The Journal of experimental biology
213
Pt 22
3920-3933
2010
10.1242/jeb.046706
Research on the adhesive locomotion of terrestrial gastropods is gaining renewed interest as it provides a source of guidance for the design of soft biomimetic robots that can perform functions currently not achievable by conventional rigid vehicles. The locomotion of terrestrial gastropods is driven by a train of periodic muscle contractions (pedal waves) and relaxations (interwaves) that propagate from their tails to their heads. These ventral waves interact with a thin layer of mucus secreted by the animal that transmits propulsive forces to the ground. The exact mechanism by which these propulsive forces are generated is still a matter of controversy. Specifically, the exact role played by the complex rheological and adhesive properties of the mucus is not clear. To provide quantitative data that could shed light on this question, we use a newly developed technique to measure, with high temporal and spatial resolution, the propulsive forces that terrestrial gastropods generate while crawling on smooth flat surfaces. The traction force measurements demonstrate the importance of the finite yield stress of the mucus in generating thrust and are consistent with the surface of the ventral foot being lifted with the passage of each pedal wave. We also show that a forward propulsive force is generated beneath each stationary interwave and that this net forward component is balanced by the resistance caused by the outer rim of the ventral foot, which slides at the speed of the center of mass of the animal. Simultaneously, the animal pulls the rim laterally inward. Analysis of the traction forces reveals that the kinematics of the pedal waves is far more complex than previously thought, showing significant spatial variation (acceleration/deceleration) as the waves move from the tail to the head of the animal.
adhesive locomotion; invertebrate; propulsive force
Designing cold-formed steel sheets for composite slabs: An experimentally validated FEM approach to slip failure mechanics
Thin-Walled Structures
44
12
1261-1271
2006
10.1016/j.tws.2007.01.010
The aim is to understand the steel–concrete slip mechanisms and its dependence on geometrical and physical parameters, in order to improve designs for steel decking for composite slabs. A new methodology to build 3D non-linear FEM models has been developed to simulate the longitudinal slip mechanics of composite slabs in ‘‘pull-out’’ tests. Sensibility of shear resistance is analysed in relation to: friction coefficient, embossing depth and slope, sheet thickness, inclination, length, width and spacing of embossments and profiling angle of rib shape. A new steel sheet design has been developed and optimised. On the other hand, several pull-out tests as well as reduced ‘‘m–k’’ shear-bond bending tests have been carried out in order to corroborate and validate FEM results, as well as to evaluate some other aspects. This paper summarizes the conclusions regarding to design recommendations and general slip behaviour matters. Several parameters, such as the embossing slope, the retention angle, the surface friction conditions, etc., have shown to be very significant in slip resistance.
ANSYS; Cold-formed steel sheet; Embossment; Friction; Longitudinal slip; Non-linear 3D finite elements; Pull-out test; Shear transfer; Steel–concrete composite slabs
Multimedia fluid mechanics
Choice: Current Reviews for Academic Libraries
46
6
1132
2009
The article reviews the DVD-ROM "Multimedia Fluid Mechanics," edited by G.M. Homsy.
Mechanical response of linear viscoelastic composite laminates incorporating non-isothermal physical aging effects
Composites Science and Technology
59
9
1411-1427
1999
10.1016/S0266-3538(98)00179-1
This paper presents a method of predicting the mechanical response of composite laminates including the effects of linear viscoelasticity and physical aging. Effective-time theory has been used to characterize the physical aging behavior of each linear viscoelastic lamina. In accordance with experimental findings, the aging behavior of each lamina is allowed to differ in the shear and transverse directions. The mechanical loading is restricted to the linear range, which decouples the aging and load behavior. A recursive algorithm has been used to solve the hereditary convolution integral that governs the response of each ply. Classical thin-laminate theory is then used to assemble the individual ply response equations and determine the overall laminate response to general in-plane force and moment loading. The method automatically recovers the ply-level stresses and strains, which are often critical to strength and durability predictions. The model can use either lamina compliance or modulus properties as its basis. Several illustrative examples of long-term laminate response to variable loading are presented and the impact of physical aging is explored. It is shown that for multidirectional laminates, the stiffness of the lamina in the fiber directions can allow simplifications of the model.
Practical fracture mechanics in design
Mechanical engineering
183
xiv, 525 p.
2005
10.1243/147509005X10459
Theoretical treatments of fracture mechanics abound in the literature. Among the first books to address this vital topic from an applied standpoint was the first edition of Practical Fracture Mechanics in Design. Completely updated and expanded to reflect recent developments in the field, the second edition of this valuable reference concisely reviews all of the fracture modes and design methodologies needed for control and prevention of structural failures in mechanical components. Practical Fracture Mechanics in Design, Second Edition begins with the historical development of the field, which is critical in understanding the origins and purpose of the various methodologies and equations. The book goes on to provide the fundamentals, basic formulas, elementary worked examples, and references with an emphasis on linear elastic fracture mechanics (LEFM). The author also includes case studies and design problems to clarify the concepts and explain their application. New chapters cover experimental methods in fracture, fracture of composite materials, dynamic fracture, and post mortem analysis of fracture surfaces. Providing much more than a simple introduction to fracture mechanics, this critical, authoritative guide supplies easy-to-use and understand tools based on hands-on experience in design, emphasizing practical applications over heavily theoretical, rigorous mathematical derivations.
Engineering design.; Fracture mechanics.
Local thin plate spline collocation for free vibration analysis of laminated composite plates
European Journal of Mechanics - A/Solids
33
24-30
2012
10.1016/j.euromechsol.2011.11.004
This paper focuses for the first time on free vibration analysis of laminated composite plates by a meshless local collocation method based on thin plate spline radial basis function. This method approximates the governing equations using the nodes in the support domain of any data center. Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, material properties, and lamination schemes are computed by present method. The choice of shape parameter, effect of dimensionless sizes of the support domain on accuracy, convergence characteristics are studied by several numerical examples. The results are compared with available published results which demonstrate the accuracy and efficiency of present method.
Free vibration; Laminated composite plates; Meshless local collocation method; Radial basis function; Thin plate spline
Thin-walled multicell beam analysis for coupled torsion, distortion, and warping deformations
Journal of Applied Mechanics, Transactions ASME
68
2
260-269
2001
10.1115/1.1357166
Due to the complicated deformations occurring in thin-walled multicell beams, no satisfactory one-dimensional beam theory useful for general quadrilateral multicells appears available. In this paper, we present a new systematic approach to analyze the coupled deformations of torsion, distortion, and the related warping. To develop a one-dimensional thin-walled multicell beam theory, the method to determine the section deformation functions associated with distortion and distortional warping is newly developed. In order to guarantee the singlevaluedness of the distortional warping function in multicells, distortional shear flows have been utilized. The superior result by the present one-dimensional theory is demonstrated with various examples.
Fracture and buckling of thin panels with edge crack in tension
Theoretical and Applied Fracture Mechanics
36
1
57-60
2001
10.1016/S0167-8442(01)00056-8
This study is concerned with the buckling and/or cracking of thin aluminium panels with an edge crack in tension. Two types of end conditions are considered. In the first case, the ends of the panel are clamped such that they would extend in parallel. In the second case, the ends are permitted to rotate when extended in tension. The cracked edge would open while the smooth edge is compressed that could lead to out-of-plane deflection if the panels are sufficiently thin. An empirical relation is obtained for the critical tensile stress. Relations among the geometrical parameters for which buckling occurs are also derived. ?? 2001 Elsevier Science Ltd. All rights reserved.
Thin films of molybdenum and tungsten disulphides by metal organic chemical vapour deposition
Journal of Materials Science
23
11
3981-3986
1988
10.1007/BF01106824
Thin films of MoS2 and WS2 have been prepared on various substrates (glass, quartz, LiF, MgO, mica, molybdenum, gold, platinum, aluminium, copper, steel, graphite, MoSe2) by metal-organic chemical vapour deposition using sulphur or hydrogen sulphide and the hexacarbonyls of the transition metals as volatile components. The deposition technique is described here. The thin layers have been examined by X-ray powder diffraction and scanning electron microscopy. Time-resolved microwave conductivity measurements were used to detect the photoactivity of these materials.
A variational approach to the fracture of brittle thin films subject to out-of-plane loading
Journal of the Mechanics and Physics of Solids
61
11
2360-2379
2013
10.1016/j.jmps.2013.05.001
We address the problem of fracture in homogenous linear elastic thin films using a variational model. We restrict our attention to quasi-static problems assuming that kinetic effects are minimal. We focus on out-of-plane displacement of the film and investigate the effect of bending on fracture. Our analysis is based on a two-dimensional model where the thickness of the film does not need to be resolved. We derive this model through a formal asymptotic analysis. We present numerical simulations in a highly idealized setting for the purpose of verification, as well as more realistic micro-indentation experiments. ?? 2013 Elsevier Ltd.
Brittle fracture; Dimension reduction; Thin films; Variational approach to fracture
Direct approach to elastic deformations and stability of thin-walled rods of open profile
Acta Mechanica
200
3-4
167-176
2008
10.1007/s00707-008-0026-6
A new geometrically nonlinear theory of thin-walled rods of open profile\naccounting for warping and bi-moment is developed. The direct approach\nwe employ is based on the principles of Lagrangean mechanics. Linear\nequations for small deformations in the vicinity of a pre-stressed\nstate are derived. These equations can be used in particular for\nstability analysis. Stability of a beam subjected to axial or transversal\nloading is considered as an example. Solutions with coupled bending\nand twisting mode of buckling are compared with the classical Euler's\nsolution, existing results for thin-walled rods and numerical solutions\nfor a shell model.
Use of capacitance to measure surface forces. 2. Application to the study of contact mechanics
Langmuir
13
22
5957-5961
1997
10.1021/la9702650
We performed capacitance measurements between silver layers on the back side of thin (<1 mu m) mica substrates in surface force apparatus to determine the contact area with very high precision (<0.1% of the total area) and at a rate that is faster (similar to 1 kHz) than that in more traditional methods based on interferometry. To demonstrate the capabilities of the technique, we measured the adhesion and adhesion hysteresis between two mica surfaces. A peculiar discontinuous decrease in contact area, with decreasing load, between two dry mica surfaces is observed. We also studied the possible effect of shear forces on the value of the contact area due to adhesive forces, as in JKR theory.
Study of size effects in thin films by means of a crystal plasticity theory based on DiFT
Journal of the Mechanics and Physics of Solids
56
11
3304-3314
2008
10.1016/j.jmps.2008.06.004
In a recent publication, we derived the mesoscale continuum theory of plasticity for multiple-slip systems of parallel edge dislocations, motivated by the statistical-based nonlocal continuum crystal plasticity theory for single-glide given by Yefimov et al. [2004b. A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity simulations. J. Mech. Phys. Solids 52, 279-300]. In this dislocation field theory (DiFT) the transport equations for both the total dislocation density and geometrically necessary dislocation (GND) density on each slip system were obtained from the Peach-Koehler interactions through both single and pair dislocation correlations. The effect of pair correlation interactions manifested itself in the form of a back stress in addition to the external shear and the self-consistent internal stress. We here present the study of size effects in single crystalline thin films with symmetric double slip using the novel continuum theory. Two boundary value problems are analyzed: (1) stress relaxation in thin films on substrates subject to thermal loading, and (2) simple shear in constrained films. In these problems, earlier discrete dislocation simulations had shown that size effects are born out of layers of dislocations developing near constrained interfaces. These boundary layers depend on slip orientations and applied loading but are insensitive to the film thickness. We investigate the stress response to changes in controlled parameters in both problems. Comparisons with previous discrete dislocation simulations are discussed. (c) 2008 Elsevier Ltd. All rights reserved.
A Novel Attempt to Produce Three Ply Yarns from the Short Staple Ring Frame using Long Staple Core
Institution of Engineers (India)
89
30-34
2008
Attempts have been made continuously to produce the value added products with the existing machinery set up in the short staple spinning system that include siro spinning, production of three ply yarns directly from the ring frame. In the present work, an attempt has been made to produce three ply yarns, directly, from the short staple ring frame using long staple fibres as core and cotton fibres as sheath. The samples produced in this process were evaluated for the physical properties like, appearance, unevenness, hairiness, moisture and tensile properties. Majority of the properties were appeared to be influenced by the cotton fibres due to higher proportion in the final yarn structure.
core; long staple fibre; sheath; short staple ring frame; three ply yarn
Statistical Mechanics Approaches to Socioeconomic Behavior
NBER Working Paper
No. 203
37
1996
SERIES STATISTICAL MECHANICS APPROACHES TO SOCIOECONOMIC BEHAVIOR Steven N. Technical Working raised in this paper as well as Lawrence , Kim-Sau
Biaxial strength of cross-ply carbon fiber-reinforced composite laminates fabricated by lapped molding technique
Materials Science and Engineering A
271
1-2
496-502
1999
10.1016/S0921-5093(99)00496-7
A failure criterion must be considered for each failure mode and parameters of the model determined in each case. In this study, a failure criterion was developed by introducing the notion of equivalent biaxial strength under biaxial loading of tension and torsion. The experimental results showed that the equivalent biaxial strength has a power-type relation to a parameter, cos ??. The failure strength under biaxial loading can be predicted as a function of tensile strength, torsional strength and biaxial ratio. Scattering of the experimental data can be predicted using a Weibull distribution function and the concept of equivalent biaxial strength. The model should accurately predict the biaxial strength of general laminated composite materials.
Biaxial loading; Equivalent biaxial strength; Failure index; Fiber reinforced plastics (FRP); Weibull distribution
Microstructural Randomness and Scaling in Mechanics of Materials
CRC seriesmodern mechanics and mathematics
471
2008
10.1080/00107510903282572
An area at the intersection of solid mechanics, materials science, and stochastic mathematics, mechanics of materials often necessitates a stochastic approach to grasp the effects of spatial randomness. Using this approach, Microstructural Randomness and Scaling in Mechanics of Materials explores numerous stochastic models and methods used in the mechanics of random media and illustrates these in a variety of applications. The book first offers a refresher in several tools used in stochastic mechanics, followed by two chapters that outline periodic and disordered planar lattice (spring) networks. Subsequent chapters discuss stress invariance in classical planar and micropolar elasticity and cover several topics not yet collected in book form, including the passage of a microstructure to an effective micropolar continuum. After forming this foundation in various methods of stochastic mechanics, the book focuses on problems of microstructural randomness and scaling. It examines both representative and statistical volume elements (RVEs/SVEs) as well as micromechanically based stochastic finite elements (SFEs). The author also studies nonlinear elastic and inelastic materials, the stochastic formulation of thermomechanics with internal variables, and wave propagation in random media. The concepts discussed in this comprehensive book can be applied to many situations, from micro and nanoelectromechanical systems (MEMS/NEMS) to geophysics.
Elasticity in engineering mechanics
Canadian Journal of Civil Engineering
1989
10.1139/l89-067
Elasticity in Engineering Mechanics has been prized by many aspiring and practicing engineers as an easy-to-navigate guide to an area of engineering science that is fundamental to aeronautical, civil, and mechanical engineering, and to other branches of engineering. With its focus not only on elasticity theory, including nano- and biomechanics, but also on concrete applications in real engineering situations, this acclaimed work is a core text in a spectrum of courses at both the undergraduate and graduate levels, and a superior reference for engineering professionals.
Lipophilicity of vinpocetine and related compounds characterized by reversed-phase thin-layer chromatography.
Journal of chromatography. A
996
1-2
195-203
2003
10.1016/s0021-9673(03)00617-4
A reversed-phase thin-layer chromatographic method was developed and applied to quantitate the lipophilicity of sparingly water-soluble eburnane alkaloids of therapeutic interest. Our method development included calibration, optimization and validation procedures, using also sets of auxiliary compounds. The log P(TLC) values of five relatively hydrophilic eburnanes were verified by stir-flask studies. The alkaloids were found to have lipophilicity values in the 2.9-4.8 log P(TLC) range. Conclusions on structure-lipophilicity relationships were drawn in terms of ring anellation, character and length of side chain, conformational preferences and moiety-solvent interactions, also supported by molecular mechanics studies.
Calibration; Chemistry, Physical; Chromatography, High Pressure Liquid; Chromatography, High Pressure Liquid: methods; Chromatography, Thin Layer; Chromatography, Thin Layer: methods; Lipids; Lipids: chemistry; Molecular Conformation; Physicochemical Phenomena; Quantitative Structure-Activity Relationship; Solubility; Solvents; Solvents: chemistry; Vinca Alkaloids; Vinca Alkaloids: chemistry; Vincamine; Vincamine: chemistry
Molecular mechanics force-field parameterization procedures
Journal of Computational Chemistry
5
5
486-499
1984
10.1002/jcc.540050510
A set of procedures and guidelines are presented for the estimation of bond length, bond angle, and torsional potential constants for molecular mechanics force fields. The force field constants are ultimately derived by “subtracting” nonbonded molecular mechanics energies from corresponding molecular orbital energies using a model compound containing the chemical structure to be parameterized. Case study examples of bond length, bond angle, and torsional rotation force field parameterizations are presented. A general discussion of molecular mechanics force field parameterization strategy is included for reference and completeness. Finally, a curve-fitting program to generate force field parameters from raw data is given in Appendix I.
Crashworthy characteristics of axially statically compressed thin-walled square CFRP composite tubes: Experimental
Composite Structures
63
3-4
347-360
2004
10.1016/S0263-8223(03)00183-1
In this paper the results of experimental works pertaining to the crash behaviour, collapse modes and crashworthiness characteristics of carbon fibre reinforced plastic (CFRP) tubes that were subjected to static axial compressive loading are presented in detail. The tested specimens were featured by a material combination of carbon fibres in the form of reinforcing woven fabric in thermosetting epoxy resin, and they were cut at various lengths from three CFRP tubes of the same square cross-section but different thickness, laminate stacking sequence and fibre volume content. CFRP tubes were compressed in a hydraulic press of 1000 kN loading capacity at very low-strain rate typical for static testing. The influence of the most important specimen geometric features such as the tube axial length, aspect ratio and wall thickness on the compressive response and collapse modes of the tested tubes is thoroughly analysed. In addition, the effect of the laminate material properties such as the fibre volume content and stacking sequence on the energy absorbing capability of the thin-wall tubes is also examined. Particular attention is paid on the analysis of the mechanics of the tube axial collapse modes from macroscopic and microscopic point of view, emphasizing on the mechanisms related to the crash energy absorption during the compression of the composite tubes. ?? 2003 Elsevier Ltd. All rights reserved.
Axial compression; Carbon fabric; CFRP; Composite tubes; Crashworthiness; Square cross-section
Optimal design of hybrid laminates with discrete ply angles for maximum buckling load and minimum cost
Composite Structures
32
1-4
409-415
1995
10.1016/0263-8223(95)00067-4
The design of hybrid symmetric laminated plates consisting of high-stiffness surface and low-stiffness core layers is presented. In the first problem the maximization of buckling load is carried out over a discrete set of ply angles. In the second problem the minimum number of high-stiffness plies is determined for a given buckling load to minimize the material cost. Boolean variables are introduced to specify stacking sequence. Solution of the linear optimization problem yields an optimal stacking sequence. The effect of hybridization is investigated for various problem parameters such as the aspect ratio of the laminate and the number of plies. The optimal designs are obtained with upper bound constraints on the effect of bending-twisting coupling stiffnesses. Results are given for hybrid graphite-epoxy/glass-epoxy laminates under both uniaxial and biaxial loadings.
Potassium channel mechanics
Neuron
32
4
555-556
2001
10.1016/S0896-6273(01)00509-8
What is the moving part that switches an ion channel's current on and off? In this issue of Neuron, del Camino and Yellen (2001) exploit scanning cysteine mutagenesis and sulfhydryl reagents to show that the intracellular end of the S6 helices forms a mechanical gate for the Shaker potassium channel.
Vibrations of rotating cross-ply laminated circular cylindrical shells with stringer and ring stiffeners
International Journal of Solids and Structures
39
2
529-545
2002
10.1016/S0020-7683(01)00194-9
In this paper, the vibration analysis of simply supported rotating cross-ply laminated cylindrical shells with axial and circumferential stiffeners, i.e., stringers and rings, is presented using an energy approach. The effects of these stiffeners are evaluated via two methods, namely: by a variational formulation with individual stiffeners treated as discrete elements; and by an averaging method whereby the properties of the stiffeners are averaged over the shell surface. The effects of initial hoop tension, centrifugal and Coriolis forces due to the rotation are considered in the present formulation. Also, stiffener eccentricity is accounted for. The present formulation is verified by comparison with experimental and numerical results available in open literature. Excellent agreement is observed and a new range of results is presented for rotating shells which can be used as a benchmark to approximate solutions. Detailed studies on the depth- to-width ratios of the stiffeners on the forward and backward frequencies were conducted for the transverse, circumferential and longitudinal modes. © 2001 Published by Elsevier Science Ltd.
Energy method; Free vibration; Frequencies; Laminated composites; Rings (components); Rotating composite laminated cylindrical shells; Rotation; Shells (structures); Stiffeners; Stringer/ring stiffeners; Variational formulation; vibration; Vibration measurement
Evaluation of in-plane ply shear properties from unidirectional plate torsion tests
Composites Part A: Applied Science and Manufacturing
53
168-175
2013
10.1016/j.compositesa.2013.06.012
Torsion tests were conducted on unidirectional carbon/epoxy laminated plates. Preliminary finite element analyses showed that the specimen geometry selected avoided pronounced geometric non-linearity and ensured that a significant volume of material would be under a high fraction of the maximum shear stress. Furthermore, the clear prevalence of in-plane shear stresses allowed the development of a simplified data analysis model. Calculated shear-stress strain curves were consistent with the results of tensile tests on angle-ply coupons, despite lower failure stresses that may have been caused by surface defects or by spurious transverse tensile stresses. Nevertheless, the unidirectional plate torsion test is worthy of further research, given the structural relevance of torsional loads and the problems of in-plane shear tests methods. © 2013 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Mechanical properties; C. Finite element analysis (FEA); D. Mechanical testing
Free vibration of cross-ply piezoelectric laminates in cylindrical bending with arbitrary edges
Composite Structures
87
1
93-100
2009
10.1016/j.compstruct.2008.01.002
Based on the piezoelasticity equations for two-dimensional problems, a recently proposed approach, which combines the state-space method and the differential quadrature method, is employed and extended to analyze the free vibration of piezoelectric laminates in cylindrical bending. The application of differential quadrature method to the state equation to approximate the derivatives with respect to the in-plane direction yields a state equation valid at discrete points along that direction. No assumption on deformations and stresses along the thickness direction is introduced, so that the present analysis is very suitable to the analysis of piezoelectric laminates with arbitrary layer-up and thickness. The direct incorporation of standard boundary conditions that are consistent with the basic equations at the two ends into the formulations also avoids the approximation usually introduced if Saint-Venant's principle is employed. The approach is verified by comparing the results with the exact solution of laminates with simple supports. © 2008 Elsevier Ltd. All rights reserved.
Cross-ply piezoelectric laminate; Differential quadrature method; Free vibration; State-space method
Mapping mechanical properties of organic thin films by force-modulation microscopy in aqueous media.
Beilstein journal of nanotechnology
3
464-74
2012
10.3762/bjnano.3.53
The mechanical properties of organic and biomolecular thin films on surfaces play an important role in a broad range of applications. Although force-modulation microscopy (FMM) is used to map the apparent elastic properties of such films with high lateral resolution in air, it has rarely been applied in aqueous media. In this letter we describe the use of FMM to map the apparent elastic properties of self-assembled monolayers and end-tethered protein thin films in aqueous media. Furthermore, we describe a simple analysis of the contact mechanics that enables the selection of FMM imaging parameters and thus yields a reliable interpretation of the FMM image contrast.
acoustic atomic force microscopy; biomolecules; elastic modulus; mapping; nanomechanical characterization; self-assembled
Geometric Aspects of Quantum Mechanics and Quantum Entanglement
Journal of Physics: Conference Series
30
9-16
2006
10.1088/1742-6596/30/1/002
It is shown that the standard non-relativistic Quantum Mechanics gives rise to elegant and rich geometrical structures. The space of quantum states is endowed with nontrivial Fubini-Study metric which is responsible for the “peculiarities” of the quantum world. We show that there is also intricate connection between geometrical structures and quantum entanglement.
Cellular and biomolecular mechanics and mechanobiology
Computer Methods in Biomechanics and Biomedical Engineering
1-1
2012
10.1080/10255842.2012.705081
This book describes these exciting new developments, and presents experimental and computational findings that altogether describe the frontier of knowledge in cellular and biomolecular mechanics, and the biological implications, in health and disease. The book is written for bioengineers with interest in cellular mechanics, for biophysicists, biochemists, medical researchers and all other professionals with interest in how cells produce and respond to mechanical loads.
Escherichia coli peptidoglycan structure and mechanics as predicted by atomic-scale simulations.
PLoS computational biology
10
2
e1003475
2014
10.1371/journal.pcbi.1003475
Bacteria face the challenging requirement to maintain their shape and avoid rupture due to the high internal turgor pressure, but simultaneously permit the import and export of nutrients, chemical signals, and virulence factors. The bacterial cell wall, a mesh-like structure composed of cross-linked strands of peptidoglycan, fulfills both needs by being semi-rigid, yet sufficiently porous to allow diffusion through it. How the mechanical properties of the cell wall are determined by the molecular features and the spatial arrangement of the relatively thin strands in the larger cellular-scale structure is not known. To examine this issue, we have developed and simulated atomic-scale models of Escherichia coli cell walls in a disordered circumferential arrangement. The cell-wall models are found to possess an anisotropic elasticity, as known experimentally, arising from the orthogonal orientation of the glycan strands and of the peptide cross-links. Other features such as thickness, pore size, and disorder are also found to generally agree with experiments, further supporting the disordered circumferential model of peptidoglycan. The validated constructs illustrate how mesoscopic structure and behavior emerge naturally from the underlying atomic-scale properties and, furthermore, demonstrate the ability of all-atom simulations to reproduce a range of macroscopic observables for extended polymer meshes.
A multiscale molecular dynamics approach to contact mechanics.
The European physical journal. E, Soft matter
19
1
47-58
2006
10.1140/epje/e2006-00004-9
The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without adhesion. The calculations are compared with analytical contact mechanics models based on continuum mechanics.
On Quantum Mechanics
American Journal of Physics
64
4
42
2004
We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization.
Measurement of the Interfacial Mechanical-Properties of a Thin Ceramic Coating on Ductile Substrates
Thin Solid Films
306
1
124-129
1997
10.1016/S0040-6090(97)00259-9
The interfacial mechanical properties of two systems, SiOx/Au and SiOx/Cu, were measured by a modified periodic cracking method. The state of stress in the SiOx-coated metal wires with cylindrical symmetry were analyzed using a classic model of continuum elasticity. Experimentally, the measurement was carried out by a uniaxial tensile test. Specimens for the tensile test were prepared by depositing a thin layer of SiOx on the metal wires by a plasma enhanced chemical vapor deposition (PECVD) technique. After tensile loading, it was found that the fracture morphology of the SiOx coating depended upon the bonding strength of the interfaces. For a weak interface such as SiOx/Au with a measured bonding strength of 0.230 MPa, debonding at the interface prevailed and most of the cracks in the SiOx coating were inclined to the tensile axis by 45 degrees. In contrast, cracks in the coating of a strong interface such as SiOx/Cu showed periodicity and were perpendicular to the tensile axis. The bonding strength of the interface was estimated to be, at least, 0.885 MPa, while the ultimate shear strength was measured to be 49.5 MPa. (C) 1997 Elsevier Science S.A.
Chemical Vapor Deposition (CVD)/Copper/Gold/Silico
Free vibration and dynamic stability of rotating thin-walled composite beams
European Journal of Mechanics, A/Solids
30
3
432-441
2011
10.1016/j.euromechsol.2010.12.015
The dynamic stability behavior of thin-walled rotating composite beams is studied by means of the finite element method. The analysis is based on Bolotin's work on parametric instability for an axial periodic load. The influence of fiber orientation and rotating speeds on the natural frequencies and the unstable regions is studied for symmetrically balanced laminates. The regions of instability are obtained and expressed in non-dimensional terms. The "modal interchange" phenomenon arising in rotating beams is described. The dynamic stability problem is formulated by means of linearizing a geometrically nonlinear total Lagrangian finite element with seven degrees of freedom per node. This finite element formulation is based on a thin-walled beam theory that takes into account several non-classical effects such as anisotropy, shear flexibility and warping inhibition. © 2010 Elsevier Masson SAS. All rights reserved.
Composite; Finite elements; Parametric resonance; Thin-walled rotating beams
Computational cardiovascular mechanics: Modeling and applications in heart failure
Computational Cardiovascular Mechanics: Modeling and Applications in Heart Failure
1-320
2010
10.1007/978-1-4419-0730-1
Computational Cardiovascular Mechanics provides a cohesive guide to creating mathematical models for the mechanics of diseased hearts to simulate the effects of current treatments for heart failure. Clearly organized in a two part structure, this volume discusses various areas of computational modeling of cardiovascular mechanics (finite element modeling of ventricular mechanics, fluid dynamics) in addition to a description an analysis of the current applications used (solid FE modeling, CFD). Edited by experts in the field, researchers involved with biomedical and mechanical engineering will find Computational Cardiovascular Mechanics a valuable reference.
Thermomechanical Behavior of Thin Metal Films under Different Ambient Conditions
AIP Conference Proceedings
817
2006
98-103
2006
10.1063/1.2173537
We present measurements on the thermomechanical properties of thin copper and gold films on substrates tested under vacuum and in a nitrogen flow ambient. The differences observed can be attributed to a native oxide layer on the copper surface that is removed under vacuum conditions but is present during experiments in inert atmosphere. This result hints to the importance of surface properties for thin film mechanics. © 2006 American Institute of Physics.
Copper; Diffusion; Oxide; Substrate curvature; Surface; Thin film
FEM model for analysis of RC prestressed thin-walled beams
Fracture Mechanics of Concrete and Concrete Structures, Vols 1-3
1-3
819-826\n1886
2007
This paper deals with service behavior of prestressed cracked thin-walled beams. A non linear finite element model for thin-walled beams has been developed. Deflections in the non-linear range are obtained by adopting a smeared crack model for concrete in tension. Contribution of steel bars in reducing deformation has been considered. An example of a thin-walled prestressed girder is presented.
finite-element; section
Quantum mechanics: The usefulness of uselessness
Nature
466
7310
1053-1054
2010
doi: 10.1038/4661053a
A game for three or more players called 'guess your neighbour's input' reveals common ground between classical and quantum physics  at the expense of more exotic, super-quantum, theories of nature.
quantum_mechanics
Effects of interface dislocations on properties of ferroelectric thin films
Journal of the Mechanics and Physics of Solids
55
8
1661-1676
2007
10.1016/j.jmps.2007.01.011
Effects of interfacial dislocations on properties of thin-film ferroelectric materials, such as the self-polarization distribution, Curie temperature, dielectric constant and the switching behaviors, are investigated via the system dynamics based on the Landau-Devonshire functional. Dislocation generation in the film is found to reduce the overall self-polarization and the Curie temperature. The spatial variations are both very strong, particularly in the immediate neighborhood of the dislocation cores. In agreement with previous results based on a stationary model, a dead layer exists near the film/substrate interface, in which the average self-polarization is much reduced. Moreover, it is evident from our results that interface dislocations play an important role in suppressing the remnant polarization and the coercive field of the polarization. (C) 2007 Elsevier Ltd. All rights reserved.
852 2362 8439; 852 2766 6646; ã corresponding author; b; c; chung; cn; coercive field; edu; e-mail addresses; fax; ferroelectric thin film; h; hit; interface dislocations; polyu; remnant polarization; self polarization; stdwangb; tel; wang; woo; y; yuezheng; zheng; zsu
The mechanics of amphibian locomotion.
The Journal of experimental biology
23
2
177-203
1946
1. A new type of apparatus is described for measuring the forces exerted on the ground by tetrapods in three orthologonal axes simultaneously.2. From results obtained with toads and newts an analysis of the mechanics of normal amphibian walking is carried out and several features of Gray's (1944) analysis of the mechanics of the tetrapod skeleton are confirmed.3. The introduction into the stride of periods of instability is shown to be related to an increase of the length of the stride and is an adaptation to faster movement.4. The pattern of couples exerted on the limbs by the extrinsic muscles is calculated for the toad and newt. This is found to be basically the same as that in the cat and in man is shown to be, in several important respects, the most efficient possible.5. The internal mechanics of the toad forelimb is discussed. It is basically similar to that of both fore- and hindlimbs of the newt. The operation of this type of limb is compared to that of a crank' mechanism and differs in important respects from that of the mammals.
LOCOMOTION
Numerical investigation of deformation mechanics in fold-and-thrust belts: Influence of rheology of single and multiple décollements
Tectonics
31
3
1-23
2012
10.1029/2011TC003047
Thin-skinned fold-and-thrust belts related to convergence tectonics develop by scraping off a rock sequence along a weaker basal décollement often formed by water-saturated shale layers or low-viscosity salt horizons. A two-dimensional finite element model with a viscoelastoplastic rheology is used to investigate the structural evolution of fold-and-thrust belts overlying different types of décollements. In addition, the influence of multiple weak layers in the stratigraphic column is studied. Model shale décollements are frictional, with lower friction angles as the cover sequence. Model salt layers behave linear viscous, due to a lower viscosity as the cover sequence, or with a power law rheology. Single viscous décollement simulations have been compared to an analytical solution concerning faulting versus folding. Results show that fold-and-thrust belts with a single frictional basal décollement generate thrust systems ramping from the décollement to the surface. Spacing between thrust ramps depends on the thickness of the cover sequence. The structural evolution of simulations with an additional low-frictional layer depends on the strength relationship between the basal and the intersequential décollement. Tectonic underplating and antiformal stacking occur if the within-sequence décollement is weaker. In the frontal part of models, deformation is restricted to the upper part and imbrication occurs with a wavelength depending on the depth of the intermediate weak layer. “Salt” décollement with a viscosity of 1018 Pa⋅s leads to isolated box folds (detachment folds). Multiple salt layers (1018 Pa⋅s) result in long-wavelength folding. Our results for both frictional and viscous décollements are in bulk agreement with the Mohr-Coulomb type, critical wedge theory.
0545 Computational Geophysics: Modeling (1952; 4255; 4316); 8108 Tectonophysics: Continental tectonics: compr; 8118 Tectonophysics: Dynamics and mechanics of fa; accretionary wedge; fold-and-thrust belt; numerical modeling; salt rheology; shale rheology
Analysis of electromagnetic propagation in birefringent thin film
SCIENCE IN CHINA SERIES G-PHYSICS MECHANICS & ASTRONOMY
48
5
513-520
2005
10.1360/142004-53
In general, the propagating behavior of extraordinary wave in\nanisotropic materials is different from that in isotropic materials.\nWith the tangential continuity of Maxwell's equations, the\nelectromagnetic propagating behaviors have been investigated at the\nincident and exit interfaces of the uniaxial anisotropic thin film. The\nemphasis was placed on two interesting optical phenomena such as\nhomolateral refraction behavior and wide-angle Brewster's phenomenon,\nwhich occurred at the interfaces of uniaxial anisotropic thin film.
birefringent thin film; interface; homolateral ref
Quantum Mechanics as a Principle Theory
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
31
1
75-94
2000
http://dx.doi.org/10.1016/S1355-2198(99)00032-5
I show how quantum mechanics, like the theory of relativity, can be understood as a ‘principle theory’ in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World.
Decoherence.; Entangled States; Interpretation of Quantum Mechanics; Principle Theory; Teleportation
Low phase-noise UHF thin-film piezoelectric-on-substrate LBAR oscillators
21st IEEE International Conference on Micro Electro Mechanical Systems, MEMS 2008 Tucson, January 13, 2008 - January 17, 2008
1012-1015
2008
10.1109/MEMSYS.2008.4443830
This paper reports on the first demonstration of a low phase-noise 467MHz temperature-compensated oscillator based on a ZnO-on-nanocrystalline diamond lateral bulk acoustic resonator (LBAR). The temperature compensation is achieved by using a thin silicon-dioxide buffer layer on the surface of the diamond film. The oscillator performance is compared with an uncompensated 496MHz AlN-on-silicon oscillator. The sustaining circuitry is comprised of a 9.4mW tunable transimpedance amplifier (TIA) in 0.18m CMOS. The phase-noise is measured below ?80dBc/Hz at 1kHz offset with temperature drift of ?4ppm/C from -5C to 90C. 2008 IEEE.
Amplifiers (electronic); Composite micromechanics; Diamond films; Diamonds; Differential amplifiers; Mechanical engineering; Mechanics; Mechatronics; MEMS; Microelectromechanical devices; Nonmetals; Oscillators (electronic); Reactive ion etching; Silicon; Zinc oxide
Failure mechanics of organic–inorganic multilayer permeation barriers in flexible electronics
Composites Science and Technology
71
3
365-372
2011
10.1016/j.compscitech.2010.12.003
Organic-inorganic multilayer permeation barriers are emerging as a promising solution to the stringent barrier requirement of flexible electronics. Yet the mechanical failure of the multilayer permeation barriers could be fatal to their barrier performance. We study two co-evolving failure mechanisms of the multilayer permeation barriers under tension, namely, the cracking of the inorganic oxide layer and the delamination along the oxide-organic interface, using computational modeling. An effective driving force for the oxide layer cracking is determined, which decreases as the oxide-organic interfacial adhesion increases. Emerging from the study is a simple but effective design to enhance the deformability of multilayer permeation barriers by applying a thin protective coating. Further studies show that strong adhesion of the coating-oxide interface is crucial for the coating performance. The results from this study provide quantitative guidance for the material selection and structural optimization of organic-inorganic multilayer permeation barriers of high mechanical durability. ?? 2010 Elsevier Ltd.
A. Flexible composites; A. Layered structures; B. Delamination; B. Fracture; Permeation barriers
Experimental Modeling of Thin-Skinned Shortening around Magmatic Intrusions
Bulletin of Volcanology
57
1
33-43
1995
Magmatic intrusions can trigger thin-skinned compression of the adjacent sedimentary cover by three processes: (a) gravity gliding away from the topographic dome resulting from the ascending magma; (b) fluid push from the rear resulting from forceful intrusion then lateral spreading of the magma; and (c) increased loading by volcanic accumulation. The applicability of the first two mechanisms, gravity gliding and fluid push, was tested using dynamically scaled experiments. Model results help to elucidate the kinematics and structural evolution of thrusts and folds formed by such processes and determine which geological parameters control the deformation style. The results show that the presence of a weak layer within the sedimentary overburden is essential to form thrust and fold belts around the intrusion. Experiments suggest that although gravity gliding can dominate the early stages of deformation, most of the deformation is caused by lateral spreading of the fluid magma pushing the adjacent sedimentary rocks. Models also suggest that true laccoliths can form only if the sedimentary section comprises a basal low-viscosity stratum. Comparison with natural examples allows the evaluation of the applicability of experimental results.
decollement; experimental modeling; failure; fluid push; growth; henry mountains; laccolith; laccolithic intrusions; magmatic intrusions; mechanics; scaling; thin-skinned thrusting; utah
Fire performance of composite laminates embedded with multi-ply carbon nanofiber sheets
Composites Part B: Engineering
41
2
176-181
2010
10.1016/j.compositesb.2009.08.001
In this study, free-standing carbon nanofiber sheets (CNS) were incorporated into glass fiber reinforced polyester composites through resin transfer molding (RTM) process. These sheets were made of vapor grown carbon nanofibers. The composite laminates consisted of eight plies of CNS and eight plies of glass fiber mats. The fire retarding performance of the laminates was evaluated with cone calorimeter tests with an external radiated heat flux of 50 kW / m\n 2. The test results indicated that there was significant improvement in the fire retardancy of composite laminates due to the incorporation of CNS. It was found that the CNS plies survived the test except the one on the top surface of the laminates. The formation of compact char materials was observed on the surface of the CNS residues. The improvement in fire retarding performance was achieved through the barrier and insulator effects of the CNS and charred materials by restricting the migration of flammable products to the top surface of the laminates and preventing the transmission of external heat to the underlying polyester resin. ?? 2009 Elsevier Ltd.
A. Nano-structures; B. High-temperature properties; C. Hybrid
Continuum Damage Mechanics and Creep Life Analysis
Journal of Applied Mechanics
67
March
193-196
2000
10.1115/1.321163
It is shown that the original continuum damage mechanics model of Kachanov is better suited for creep life analysis of creep-brittle solids and structures than continuum damage mechanics models that take into account damage-induced softening. [S0021-8936(00)03001-4].
An orthotropic active–strain model for the myocardium mechanics and its numerical approximation
European Journal of Mechanics - A/Solids
48
83-96
2014
10.1016/j.euromechsol.2014.03.006
In the wide literature devoted to the cardiac structural mechanics, the strain energy proposed by Holzapfel and Ogden exhibits a number of interesting features: it has suitable mathematical properties and it is based on few material parameters that can, in principle, be identified by standard laboratory tests. In this work we illustrate the implementation of a numerical solver based on such a model for both the passive and active mechanics of the heart. Moreover we discuss its performance on a few tests that can be regarded as preliminary to the adoption of the Holzapfel–Ogden model for a real cardiac simulation. While the passive behavior of the cardiac muscle is modeled as an orthotropic hyperelastic material, the active contraction is here accounted for a multiplicative decomposition of the deformation gradient, yielding the so–called “active strain” approach, a formulation that automatically preserves the ellipticity of the stress tensor and introduces just one extra parameter in the model. We adopt the usual volumetric–isochoric decomposition of the stress tensor to obtain a mathematically consistent quasi–incompressible version of the material, then the numerical approximation applies to a classical Hu–Washizu three fields formulation. After introduction of the tangent problem, we select suitable finite element spaces for the representation of the physical fields. Boundary conditions are prescribed by introduction of a Lagrange multiplier. The robustness and performance of the numerical solver are tested versus a novel benchmark test, for which an exact solution is provided. The curvature data obtained from the free contraction of muscular thin films are used to fit the active contraction parameter.
Active strain; Cardiac mechanics; Numerical simulation
Predictive Statistical Mechanics
Frontiers of Nonequilibrium Statistical Physics
33-55
1986
This workshop is concerned with two topics, foundations of quantum theory and of irreversible statistical mechanics, which might appear quite different. Yet the current problems in both fields are basically the same, two different aspects of a deep conceptual hangup that permeates not only physics, but all fields that use probability theory. A different way of thinking about these problems is expounded, which has had useful results recently in statistical mechanics and more general problems of inference, and which we hope may prove useful in quantum theory. An adequate account of all the technical details alluded to in the writer's five talks would require a volume in itself, but much of this is now in print or in the publication pipeline. Therefore we try to explain here the original motivation in quantum theory, the formalism that evolved from it, and some recent applications, with references to further details.
Tissue mechanics.
Physics in medicine and biology
20
3
699-717
1975
10.1243/EMED_JOUR_1978_007_005_02
The human body and its components are subjected to awide variety of loads, which are either externally imposedor originate internally due to muscle actions. In additionabnormal loads may be produced for example, duringplastic surgery by the production or rotation of skinflaps, or by the forces at the interface between thesupport and the skin of a patient in bed or a wheelchair.The investigation of the mechanical properties of skinand other soft connective tissues was started at the BioengineeringDepartment in an attempt to understand theway in which the tissues transmit and withstand theseloads, how alterations in the tissue may make themmore liable to mechanical damage, and the underlyingmechanisms producing tissue damage
17_Cited_17_from_2007_Mechanics of thin-walled curved beams made of composite materials, allowing for shear deformability
Thin-Walled Structures
45
9
759-789
2007
10.1016/j.tws.2007.06.005
In this paper, a new theoretical model is developed for the generalized linear analysis of composite thin-walled curved beams with open and closed cross-sections. In the present model two important concepts concerning to composite thin-walled curved beams are addressed. The first one is the incorporation in the model of what is called full shear deformability, i.e. shear flexibility due to both bending and non-uniform warping is considered. The second feature is connected with the constitutive aspects, and it contemplates the use of different hypotheses that can be adopted in the formulation. These topics are treated in a straightforward way by means of the Linearized Principle of Virtual Work. In order to obtain the motion equations of the model a non-linear displacement field, whose rotations are formulated by means of the rule of semitangential transformation, is employed. This model allows the study of many problems of statics, free and forced vibrations with arbitrary initial stresses and linear stability of composite thin-walled curved beams with general cross-sections. A discussion about the constitutive equations is performed in order to explain characteristic features of the effects included in the theory. This paper presents the theoretical formulation together with finite element procedures that are developed to obtain the numerical approximations to the general equations of thin-walled shear-deformable composite curved beams. For this kind of structural member, iso-parametric finite elements are introduced. Numerical examples are carried out in several topics of statics, dynamics and buckling problems, focusing attention in the validation of the theory with respect to experimental data and with 2D and 3D computational approaches. Also, new parametric studies are performed in order to show the influence of shear deformability on the mechanics of the thin-walled composite curved-beams with open and closed cross-sections as well as to illustrate the utility of the model.
Anisotropy; Composites; Shear flexibility; Thin-walled curved beams
Edge Effects in Angle-Ply Composite Laminates
Journal of Composite Materials
11
October
422-428
1977
This paper presents the results of a zeroth-order solution for edge effects in angle-ply composite laminates obtained using perturbation techniques and a limiting free body approach. The general solution for [±&thetas;] laminates is applied to the special case of a [s ±45]graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness-to-width ratio h/b and compared to finite difference results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress &z,sigma; and provides mathematical evidence for singular interlaminar shear stresses &x tazu; and &y tazu; in [±45] graphite/epoxy laminates.
Influence of conical projectile diameter on perpendicular impact of thin steel plate
Engineering Fracture Mechanics
75
2946-2967
2008
10.1016/j.engfracmech.2008.01.011
A numerical study of conical projectiles for perpendicular impact on a thin steel plate is reported. The target material considered, Weldox 460 E steel, is frequently used for this kind of application and several results of experiments are available in the international literature to verify numerical simulations. The Johnson-Cook constitutive relation coupled with the Johnson-Cook failure criterion have been applied to analyse penetration of the target and also the failure process. The analysis has been focussed on the influence of the projectile diameter on the perforation process, assuming the same projectile mass. The aim was to preserve the same initial kinetic energy and identical nose angle. The goal is to estimate the ballistic limit, the residual velocity, the plastic work, and the temperature levels produced during the penetration process. The analysis has shown a linear increase of the ballistic limit with the projectile diameter. © 2008 Elsevier Ltd. All rights reserved.
Ductile failure; Dynamic behaviour; Numerical simulation; Perforation
A theoretical and numerical study of thin film delamination using the pull-off test
International Journal of Solids and Structures
41
3-4
717-730
2004
10.1016/j.ijsolstr.2003.09.027
An accurate closed-form analytical solution for the strain energy release rate for a thin rectangular film loaded by a central line force using the pull-off test is derived in the presence of a tensile residual stress. The theoretical constitutive relation and the strain energy release rate agree very well with two-dimensional nonlinear finite element analysis for the entire deformation regime ranging from bending plate to stretching membrane. Fracture modes for this pull-off test are also investigated based upon the finite element analysis, offering additional insights to the interfacial delamination. (C) 2003 Elsevier Ltd. All rights reserved.
adhesion test; adhesive; blister test; coating delamination; coatings; efficiency; element analysis; energy-release rates; finite; fracture; fracture-mechanics; membrane behavior; peel-test; pull-off test; residual stress; residual-stress; strain energy release rate; transition; V-peel test
Mechanics of disordered solids. III. Fracture properties
Physical Review B
47
2
713-722
1993
10.1103/PhysRevB.47.713
Brittle fracture of disordered media are studied using Monte Carlo simulations in both two and three dimensions (3D). Elastic and superelastic percolation networks with central and bond-bending forces are used as models of disordered media. We find that the distribution of fracture strength in a solid with broadly distributed microscopic heterogeneities, and in randomly reinforced materials, is adequately described by the classical Weibull distribution, rather than the recently proposed Gumbel distribution. System-size dependence of the external stress F for fracture is also studied. We find that, contrary to recent claims, for a d-dimensional system of size L, F is given by F∼Ld-1/(lnL)ψ, where 0≤ψ≤0.5. The fractal dimension of the cracks is found to be about 1.7 in 2D, close to that of fracture surfaces of natural rocks at small scales. The scaling of the fracture stress σf near the percolation threshold pc is found to obey, σf∼(p-pc)fT, where p is the fraction of intact springs (or the damage level$)— and, Tf≃2.42 in 2D and Tf≃2.64 in 3D. The 2D result is in agreement with the experimental estimate of Tf for fracture of thin perforated metal foils. These values are also close to the lower bound, Tf≥f-νdmin, where f is the critical exponent of the elastic moduli of the system, ν the correlation-length exponent of percolation, and dmin the fractal dimension of the shortest paths on a percolation cluster. Finally, we study the similarities and differences between fractured and percolation networks.
Simulation of the ductile tearing for two grades of 2024 aluminum alloy thin sheets
Engineering Fracture Mechanics
73
1531-1552
2006
10.1016/j.engfracmech.2006.01.024
The purpose of this work is to develop a finite-element simulation of ductile tearing tests carried out on aerospace aluminum alloys using continuum damage mechanics. The model is applied to two similar 2024 alloy thin sheets containing different amounts of intermetallic particles. The materials are characterized using small specimens (smooth and notched bars, Kahn specimens) and large M(T) panels. Observations show that, in severely notched samples, crack initiation is "flat" whereas crack propagation is "slanted". The simulation is based on an extension of the Rousselier model which includes the description of plastic anisotropy and void nucleation around second phase particles. The model parameters are adjusted in the case of the material containing the lowest amount of intermetallic particles to represent continued crack propagation as well as the overall plastic behavior, without modeling the fact that the crack is slanted. The model is adjusted on small specimens and the transferability of the model is checked on M(T) panels. It is shown that such large panels present a certain amount of buckling despite the use of an anti-buckling device. Apart from buckling, prediction of load and crack advance is good. The transfer of the model parameters to the material containing the highest amount of particles is made by modifying the mesh size according to the ratio of the particle mean spacing as the materials have very similar behaviors. This methodology is shown to be satisfactory. Finally, the model is used as a numerical tool to investigate the effects of plastic hardening, prestraining and plastic anisotropy on crack growth resistance. ?? 2006 Elsevier Ltd. All rights reserved.
2024 Aluminum alloy; Ductile rupture; Finite-element simulation; Tearing resistance
Influence of fibre reinforcement and peel ply surface treatment towards adhesion of composite surfaces
International Journal of Adhesion and Adhesives
25
404-409
2005
10.1016/j.ijadhadh.2004.11.006
The mechanisms governing adhesion are often complicated as adhesion properties depend on several physical and chemical parameters. Owing to the growing importance of adhesion in several fields of research, there are an increasing number of studies in the hope to bring a better understanding of these phenomena. The aim of the present paper is to show the correlation between the surface characteristics of composite materials and adhesion performances of corresponding surfaces assemblies. To this purpose, surface free energy assessment, roughness measurement, scanning electron microscopy (SEM) analysis, and infra-red Fourier transform (IRFT) coupled with microscopic study have been performed. Relationships between carbon/epoxy and glass/epoxy composite surface characteristics and results from single lap shear tests are established. Conclusions clearly show the importance of considering a polymer composite surface not only as a polymer entity, but also as a fibre/polymer unit. © 2005 Elsevier Ltd. All rights reserved.
Composites; Contact angle; Epoxide; Lap shear tests; Surface roughness
Inelastic mechanics of sticky biopolymer networks
New Journal of Physics
12
0-17
2010
10.1088/1367-2630/12/5/053024
We propose a physical model for the nonlinear inelastic mechanics of sticky biopolymer networks with potential applications to inelastic cell mechanics. It consists in a minimal extension of the glassy wormlike chain (GWLC) model, which has recently been highly successful as a quantitative mathematical description of the viscoelastic properties of biopolymer networks and cells. To extend its scope to nonequilibrium situations, where the thermodynamic state variables may evolve dynamically, the GWLC is furnished with an explicit representation of the kinetics of breaking and reforming sticky bonds. In spite of its simplicity the model exhibits many experimentally established non-trivial features such as power-law rheology, stress stiffening, fluidization, and cyclic softening effects.
Dynamic analysis of thin-walled members using Generalised Beam Theory (GBT)
Thin-Walled Structures
72
188-205
2013
10.1016/j.tws.2013.07.004
This paper presents the main steps and procedures involved in the development of a Generalised Beam Theory (GBT) formulation to perform dynamic analyses of thin-walled members subjected to initial perturbations or acting loads. It combines (i) the GBT modal discretisation of the cross-section deformation with (ii) the commonly adopted vibration mode superposition approach - this combination leads to an original "doubly modal" representation of the displacement field, which (i) provides deep insight into the mechanics involved in the dynamic response under consideration and, moreover, (ii) makes it possible to obtain accurate results with surprisingly low degree of freedom numbers. The application and potential of the formulation is illustrated by presenting and discussing numerical results concerning the dynamic responses of cold-formed steel lipped channel beam in several situations, namely (i) the damped oscillations following the release from a deformed configuration, (ii) the action of uniformly distributed loads with periodic (sinusoidal and square-wave) and impulsive (rectangular) time variations, and (iii) the effect of a point load moving along the span with constant speed. For validation purposes, the GBT-based results are compared with values yielded by Ansys shell finite element analyses - the total number of degrees of freedom involved in the GBT analyses was significantly lower. © 2013 Elsevier Ltd.
Dynamic analysis; Generalised Beam Theory (GBT); Local and global dynamic responses; Mode superposition principle; Thin-walled members
Analysis of plasma-induced morphological changes in sputtered thin films over compliant elastomer
Journal of Physics D: Applied Physics
47
10
105401
2014
10.1088/0022-3727/47/10/105401
Flexible electronics and other polymer-based devices demand effective metallization of thin metal films over soft substrates. However, metallization of thin films over soft elastomers such as polydimethylsiloxane (PDMS) often leads to crack formation and morphological changes in the film as well as over the elastomeric surface offering limited applications in the development of biomedical microdevices. In the present study, optimized sputtering conditions like variations in base vacuum, working pressure, sputtering power and time required for crack-free uniform deposition of nichrome thin film over a PDMS surface are discussed. Analysis of film buckling and cracking under optimized and non-optimized conditions is performed through study of plasma colour, optical microphotographs and scanning electron microscopy images. The Young's modulus of an oxidized PDMS surface under no-crack conditions is estimated through the buckling mechanics of thin films and is found to vary with deposition conditions. The present investigation establishes that interaction of a PDMS surface with plasma modifies the surface properties to the extent that its mechanical properties either become compliant to the overlying deposited film, forming buckles, or become noncompliant, leading to cracked films. Fabrication of microheaters on crack-free nichrome thin film under optimized conditions was carried out to explore its suitability in flexible electronics.
cracking; flexible electronics; pdms elastomer; scanning electron; sputtering
Orientation-Preserving Rod Elements for Real-Time Thin-Shell Simulation
IEEE Transactions on Visualization and Computer Graphics
17
6
822-835
2011
10.1109/TVCG.2010.92
We propose a new computation model for simulating elastic thin shells at interactive rates. Existing graphical simulation methods are mostly based on dihedral angle energy functions, which need to compute the first order and second order partial derivatives with respect to current vertex positions as bending forces and stiffness matrices. The symbolic derivatives are complicated in nonisometric element deformations. To simplify computing the derivatives, instead of directly constructing the dihedral angle energy, we use the orientation change energy of mesh edges. A continuum-mechanics-based orientation-preserving rod element model is developed to provide the bending forces. The advantage of our method is simple bending force and stiffness matrix computation, since in the rod model, we apply a novel incremental construction of the deformation gradient tensor to linearize both tensile and orientation deformations. Consequently, our model is efficient, easy to implement, and supports both quadrilateral and triangle meshes. It also treats shells and plates uniformly.
Computational mechanics of materials and structures
Engineering Structures
31
6
1288-1297
2009
10.1016/j.engstruct.2009.01.005
Mechanics of Materials and Structures has become a popular new name of former Institutes for Strength of Materials and/or Structural Analysis at European Universities of Technology. This designation stands for a scientific program aimed at a symbiosis of material and structural mechanics. The adjective ‘‘computational’’ refers to the algorithmic component of Mechanics of Materials and Structures, which is frequently underrated. It was the advent of the digital computer that opened the door to computational mechanics, which has become a scientific discipline with a tremendous influence on our lives. This survey paper contains a report about a selection of recent research projects carried out at the Institute for Mechanics of Materials and Structures of Vienna University of Technology. Its aim is to demonstrate that the trinity of Computational Mechanics – Materials – Structures has a strong impact on modern life. ©2009
Materials; Structures
Understanding molecular structure from molecular mechanics.
Journal of computer-aided molecular design
25
4
295-316
2011
10.1007/s10822-011-9422-4
Molecular mechanics gives us a well known model of molecular structure. It is less widely recognized that valence bond theory gives us structures which offer a direct interpretation of molecular mechanics formulations and parameters. The electronic effects well-known in physical organic chemistry can be directly interpreted in terms of valence bond structures, and hence quantitatively calculated and understood. The basic theory is outlined in this paper, and examples of the effects, and their interpretation in illustrative examples is presented.
Algorithms; Computer Simulation; Mechanics; Models, Molecular; Molecular Dynamics Simulation; Molecular Structure; Quantum Theory; Software; Thermodynamics
Mechanics of the indentation test and its use to assess the adhesion of polymeric coatings
Journal of Adhesion Science and Technology
7
8 pt 1
813-836
1993
10.1163/156856193X00457
The indentation test provides a simple means by which the adhesion of coatings can be qualitatively assessed. On the way to establishing a quantitative measurement of the adhesion strength of coatings and films, it is important that the mechanics of this test are clearly understood. To investigate the influence of factors such as the coating thickness, the indenter radius, and friction during the test, numerical simulations of the indentation of a typical polymeric coating, polymethylmethacrylate (PMMA), bonded to a rigid substrate were conducted by using the finite element method. The stress generated during the indentation test were obtained by employing an accurate constitutive model of the elastic-viscoplastic behaviour of the polymeric coating under consideration. The results of this analysis illustrate the effects of the factors mentioned above on the deformation of the coating during indentation, its confinement, and interfacial shear, and the normal, shear, and hoop stress distributions occurring during indentation. These results provide insight into the possible failure mechanisms operative during the indentation of thin coatings and the important effects of the coating thickness during such tests
The out-of-plane compressive response of Dyneema ® composites
Journal of the Mechanics and Physics of Solids
70
1
200-226
2014
10.1016/j.jmps.2014.05.017
Out-of-plane compression tests were conducted on six grades of ultra high molecular weight polyethylene fibre composites (Dyneema®) with varying grades of fibre and matrix, ply thickness, and ply stacking sequence. The composites with a [0°/90°] lay-up had an out-of-plane compressive strength that was dictated by in-plane tensile fibre fracture. By contrast, the out-of-plane compressive strength of the uni-directional composites was significantly lower and was not associated with fibre fracture. The peak strength of the [0°/90°] composites increased with increasing in-plane specimen dimensions and was dependent on the matrix and fibre strength as well as on the ply thickness. A combination of micro X-ray tomography and local pressure measurements revealed the existence of a shear-lag zone at the periphery of the specimens. Finite element (FE) and analytical micromechanical models predict the compressive composite response and reveal that the out-of-plane compression generates tensile stresses along the fibres due to shear-lag loading between the alternating 0° and 90° plies. Moreover, the compressive strength data suggests that the shear strength of Dyneema® is pressure sensitive, and this pressure sensitivity is quantified by comparing predictions with experimental measurements of the out-of-plane compressive strength. Both the FE and analytical models accurately predict the sensitivity of the compressive response of Dyneema® to material and geometric parameters: matrix strength, fibre strength and ply thickness. © 2014 Elsevier Ltd.
Composites; Finite element modelling; Polymer; Pressure dependent shear strength; Shear lag
Buckling in Thin Walled Micro and Meso Structures of Lightweight Materials and Material Compounds
Computational Mechanics
37
6
470-478
2005
10.1007/s00466-005-0731-0
Abstract Modern materials and material compounds for application in lightweight structures exhibit, in addition to the use of constituents of high specific stiffness and strength, very special micro- and meso-structures. Typical representatives of such material compounds are sandwiches with thin homogeneous or composite face layers and structured core materials (for instance honeycombs and closed or open cell foams). The load carrying capacity of lightweight structures made of such materials and material compounds, respectively, is limited by a considerable number of rather different but interconnected instability modes occurring at length scales which are several orders of magnitude smaller than the size of the structural part. These non-global instabilities are the subject of the presented key-note paper.
dimpling; foams; instability; sandwich structures; wrinkling
Growth and in situ high-pressure reflection high energy electron diffraction monitoring of oxide thin films
Science China: Physics, Mechanics and Astronomy
56
12
2312-2326
2013
10.1007/s11433-013-5352-6
... Figure 8 (Color online) In situ monitoring of a LCMO film deposited on Nb: STO at 780◦C and 1 Hz ... full-width-at-half-magnitude (FWHM) of YSZ(002)rocking curve is only 0.59◦, revealing a high crystallinity. ... at 730◦C in vacuum after 37th s (b), 130th s (c), and 10 min (d) growth [20 ... \n
Interface; Oxide thin film; Pulsed laser deposition; RHEED
The extensional flow of a thin sheet of incompressible, transversely isotropic fluid
European Journal of Applied Mathematics
19
225-257
2008
Doi 10.1017/S0956792508007377
Motivated by the aim of modelling the mechanical behaviour of biological gels (such as collagen gels) which have a fibrous microstructure, we consider the extensional flow of a thin two-dimensional film of incompressible, transversely isotropic viscous fluid. Neglecting inertia, and the effects of gravity and surface tension, leading-order equations are derived from a perturbation expansion of the full flow problem in powers of the (small) inverse aspect ratio. The existence and uniqueness of the solution of the reduced system of equations for small times is then proven. Special cases, in which the solution may be determined explicitly, are considered and we discuss the physical interpretation of the results.
evolution; fibers; mechanics; model; morphogenesis; reinforced viscous fluids; surface-tension
Effect of fiber orientation on the stress distribution within a leaflet of a polymer composite heart valve in the closed position
Journal of Biomechanics
40
1099-1106
2007
10.1016/j.jbiomech.2006.04.015
Polymer trileaflet valves offer natural hemodynamics with the potential for better durability than commercially available tissue valves. Strength and durability of polymer-based valves may be increased through fiber reinforcement. A finite element analysis of the mechanics of a statically loaded polymer trileaflet aortic heart valve has been conducted. A parametric analysis was performed to determine the effects of fiber orientation and volume density in a single and double ply model. A maximum stress value of 1.02 MPa was obtained in the non-reinforced model for a transvalvular load (downstream-upstream) of 120 mmHg. The maximum stress on the downstream side of the leaflet was approximately twice the maximum stress on the upstream side, and always occurred on the interface with the valve stent. The single ply model reduced the stress on the polymer matrix, with the maximum reduction of at least 64% occurring when the fiber orientation was such that the fibers ran perpendicular to the stent edge. The double ply model further reduced the stress on the polymer matrix, with the maximum reduction of greater than 86% now occurring when the fibers are oriented most perpendicular to one another. ?? 2006 Elsevier Ltd. All rights reserved.
Fiber orientation; Finite element analysis; Trileaflet heart valve
Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics
Journal of Chemical Physics
125
11-14
2006
10.1063/1.2400851
In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.
Wafer-scale, three-dimensional helical porous thin films deposited at a glancing angle.
Nanoscale
6
16
9401-9
2014
10.1039/c4nr00249k
Minimization of helices opens a door to impose novel functions derived from the dimensional shrinkage of optical, mechanical and electronic devices. Glancing angle deposition (GLAD) enables one to deposit three-dimensional helical porous thin films (HPTFs) composed of separated spiral micro/nano-columns. GLAD integrates a series of advantageous features, including one-step deposition, wafer-scale production with mono-handedness of spirals, flexible engineering of spiral materials and dimensions, and the adaption to various kinds of substrates. Herein, we briefly review the fabrication of HPTFs by GLAD, specific growth mechanisms, physical properties in structures, mechanics and chiral optics, and the emerging applications in green energy. A prospective outlook is presented to illuminate some promising developments in enantioselection, bio-dynamic analyses, wirelessly-controlled drug delivery and mass production.
Geometrically Nonlinear Stress-Deflection Relations for Thin Film/Substrate Systems With a Finite Element Comparison
Journal of Applied Mechanics
61
4
872
1994
10.1115/1.2901570
A previously developed geometrically nonlinear stress-curvature relation is expanded in this paper to allow for a less restrictive approximation of the midplane strains in a thin film/substrate system. The previous analysis is based on a minimization of the total strain energy and predicts a bifurcation in shape as the magnitude of intrinsic film stress increases. It is reviewed here and three new cases are presented. Expanding the approximating polynomials for the normal midplane strains ε0x and ε0y, has a small effect on the solution. However, allowing the midplane shear strain, γ0xy, to be nonzero has a pronounced effect on the solution, particularly in the stress region near the bifurcation point.
Protein Mechanics: A New Frontier in Biomechanics.
Experimental mechanics
49
1
153-164
2009
10.1007/s11340-008-9154-0
Proteins play essential roles in all aspects of cellular processes, such as biosynthesis, division, growth, motility, metabolism, signaling, and transmission of genetic information. Proteins, however, could deform under mechanical forces, thus altering their biological functions. Here we present protein deformation as a possible molecular basis for mechanosensing and mechanotransduction, elucidate the important features of protein mechanics including protein deformation mode and dynamics, illustrate how protein deformation could alter biological function, and describe the important roles of protein deformation in force-sensing, force transducing and mechanochemical coupling in cells. The experimental and modeling challenges in protein mechanics are discussed.
biomechanics; conformational change; deformation; mechanotransduction; protein
Dynamics of thin films in a magnetic field
Journal of Applied Mechanics and Technical Physics
17
3
439-443
1977
10.1007/BF00853585
The oscillations of thin conducting films placed in a magnetic field are considered. The effect of the field in different directions on the effective elasticity of the film is described and dispersion relations are obtained for longitudinal and transverse waves. © 1977 Plenum Publishing Corporation.
Finite Fracture Mechanics at elastic interfaces
International Journal of Solids and Structures
49
7-8
1022-1032
2012
10.1016/j.ijsolstr.2012.01.002
In the present paper we provide a method to determine the load causing delamination along an interface in a composite structure. The method is based on the elastic interface model, according to which the interface is equivalent to a bed of linear elastic springs, and on Finite Fracture Mechanics, a crack propagation criterion recently proposed for homogeneous structures. The procedure outlined is general. Details are given for the pull-push shear test. For such geometry, the failure load is obtained and compared with the estimates provided by stress concentration analysis and Linear Elastic Fracture Mechanics. It is seen that Finite Fracture Mechanics provides intermediate values. Furthermore, it is shown that the predictions provided by Finite Fracture Mechanics are almost coincident with the ones provided by the Cohesive Crack Model. As far as we are concerned with the determination of the failure load, the advantage of using Finite Fracture Mechanics with respect to the Cohesive Crack Model is evident, since a troublesome analysis of the softening taking place in the fracture process zone is not necessary. A final comparison with classical fracture criteria based on critical distances, such as the average stress criterion, concludes the paper. © 2012 Elsevier Ltd. All rights reserved.
Cohesive crack model; Double lap joint; Elastic interfaces; Finite Fracture Mechanics
Science, Nature and Control: Interpreting Mechanics' Institutes
Social Studies of Science
7
31-74
1977
10.1177/030631277700700109
The purpose of this paper is to show how the founders of British mechanics Institutes thought a scientific education would aid in the social control of those artisans who were their designated target. The study of Mechanics' Institute movement of Great Britain has always been marginal to three academic communities, the history of education, the history of science and the history of technology. The history of these institutes has been no more than a peripheral concern for the history of science. Included in the designation Mechanics' Institute was a variety of early to mid-nineteenth-century foundations, all initially created to teach aspects of the sciences to sections of the British working classes. The study of the Institutes is still in its infancy there is still no modern book-length account of any individual British Institute, and many of the questions one shall raise go perhaps too far beyond what can be resolved by available empirical studies, Still, sufficient work has now been done to establish many features of the movement's history.
Comparison of the spinning of selachian egg case ply sheets and orb web spider dragline filaments
Biomacromolecules
2
323-334
2001
10.1021/bm0001446
Liquid crystal spinning appears to be widespread in the animal kingdom, utilizing protein dopes to give materials with a range of different secondary structures including beta-pleat, alpha-helix and collagen-fold. Here we seek to identify the essential design features used in natural liquid crystal spinning by comparing the spinning of two very different materials: the egg case wall of Selachians (dogfish, rays, and their allies) and the dragline silk of orb web spiders. The fish extrudes a "sea and island" composite in which the islands consist of flat ribbons of carefully orientated collagen and the sea, small quantities of an amorphous matrix. Dragline silk filaments are largely constructed from spidroin, a beta protein and have a skin and core structure together with two to three coats. The essential design features common to both systems appear to be the following: (i) intracellular co-storage of a hexagonal columnar liquid crystalline component and a peroxidase within the same secretory vesicles; (ii) luminal storage of a highly concentrated liquid crystalline dope; (iii) use of a dope containing immiscible droplets; (iv) hyperbolic extrusion dies; (v) control of pH and water content of the dope; (vi) preorientation of dope molecules before assembly into fibrils; (vii) combination of extrusion die, treatment/coating bath, and solvent recovery plant within a single microminiaturized device; (viii) slow natural spinning rates. The most important difference is that spiders produce a tough material by unfolding and hydrogen-bonding their silk dope molecules while Selachian fish do it by covalently cross-linking the molecules without unfolding them.
Quantum mechanics another way
European Journal of Physics
25
4
525-534
2004
10.1088/0143-0807/25/4/008
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space take the place of operators, but the functions are multiplied in an exotic way, using the -product. Here we attempt a brief, pedagogical discussion of deformation quantization, which is suitable for inclusion in an undergraduate course.
mecânica quântica
Statistical Mechanics: Theory and Molecular Simulation
New York
713
2010
Statistical mechanics is a theoretical framework that aims to predict the observable static and dynamic properties of a many-body system starting from its microscopic constituents and their interactions. Its scope is as broad as the set of “many-body” systems is large: as long as there exists a rule governing the behavior of the fun- damental objects that comprise the system, the machinery of statistical mechanics can be applied. Consequently, statistical mechanics has found applications outside of physics, chemistry, and engineering, including biology, social sciences, economics, and applied mathematics. Because it seeks to establish a bridge between the microscopic and macroscopic realms, statistical mechanics often provides a means of rationalizing observed properties of a system in terms of the detailed “modes of motion” of its basic constituents.
Visualizing quantum mechanics in phase space
Quantum
January
1-8
2011
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.
quantum physics
Upper airway mechanics
Respiration
78
2
121-33
2009
10.1159/000222508
This review discusses the pathophysiological aspects of sleep-disordered breathing, with focus on upper airway mechanics in obstructive and central sleep apnoea, Cheyne-Stokes respiration and obesity hypoventilation syndrome. These disorders constitute the end points of a spectrum with distinct yet interrelated mechanisms that lead to substantial pathology, i.e. increased upper airway collapsibility, control of breathing instability, increased work of breathing, disturbed ventilatory system mechanics and neurohormonal changes. Concepts are changing. Although sleep apnoea is considered more and more to be an increased loop gain disorder, the central type of apnoea is now considered as an obstructive event, because it causes pharyngeal narrowing, associated with prolonged expiration. Although a unifying concept for the pathogenesis is lacking, it seems that these patients are in a vicious circle. Knowledge of common patterns of sleep-disordered breathing may help to identify these patients and guide therapy.
Central sleep apnoea; Cheyne-Stokes breathing; Obesity hypoventilation syndrome; Obstructive sleep apnoea
Statistical Origin of Quantum Mechanics
Physica A: Statistical Mechanics and its Applications
307
1-2
172-184
2001
10.1016/S0378-4371(01)00626-4
The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an ontological support to the orthodox quantum mechanics. This approach to quantum mechanics, constitutes a deductive and direct method which, in a self-consistent scheme of a classical kinetics, allows us: i) to obtain the probabilistic nature of the quantum description and to interpret the wave function psi according to the Copenhagen school; ii) to derive the quantum potential and then the Schr"odinger equation; iii) to calculate the values of the physical observables as mean values of the associated quantum operators; iv) to obtain the Heisenberg uncertainty principle.
Mixed formulation in Koiter analysis of thin-walled beams
Computer Methods in Applied Mechanics and Engineering
190
26-27
3369-3399
2001
10.1016/S0045-7825(00)00268-1
The paper extends the asymptotic mixed formulation proposed in (G. Garcea, G. Salerno, Sanitizing of locking in Koiter perturbation analysis through mixed formulation, Fourth World Congress on Computational Mechanics, Buenos Aires, Argentina, 1988; G. Garcea, G. Salerno, R. Casciaro, Comput. Methods. Appl. Mech. Engrg. 180 (1-2) (1999) 137-167) to structures composed of an assemblage of flat slender elastic panels. The same type of structure has already been investigated in (A.D. Lanzo, G. Garcea, R. Casciaro. Int. J. Numer. Methods Engrg. 38 (1995) 2325-2345; A.D. Lanzo, G. Garcea, Int. J. Numer. Methods Engrg. 39 (1996) 3007-3031) with a compatible formulation and using the usual hypothesis of negligible precritical rotations in order to avoid the extrapolation locking (see also (G. Garcea, G.A. Trunfio, R. Casciaro, Comput. Methods. Appl. Mech. Engrg. 165 (1-4) (1998) 137-167) produced by the high axial to flexural stiffness ratio of the panels. The use of a mixed formulation provides a consistent way of eliminating the extrapolation locking without introducing ad hoc approximations. It is thus both reliable and accurate. When combined with a quadratic strain-displacement relationship, as presented here, it gives zero fourth-order energy variations, further computational simplifications and a 'natural' linearization of the eigenvalue problem required by the buckling analysis. An extensive numerical testing shows the effectiveness and robustness of the proposed approach. ?? 2001 Elsevier Science B.V. All rights reserved.
Accuracy; Asymptotic methods; Mixed finite elements; Multi-model buckling; Nonlinear elasticity; Reliability; Thin-walled beams
Size-dependent yield strength of thin films
International Journal of Plasticity
21
9
1834-1854
2005
10.1016/j.ijplas.2004.09.005
Biaxial strain and pure shear of a thin film are analysed using a strain gradient plasticity theory presented by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379-1406]. Constitutive equations are formulated based on the assumption that the free energy only depends on the elastic strain and that the dissipation is influenced by the plastic strain gradients. The three material length scale parameters controlling the gradient effects in a general case are here represented by a single one. Boundary conditions for plastic strains are formulated in terms of a surface energy that represents dislocation buildup at an elastic/plastic interface. This implies constrained plastic flow at the interface and it enables the simulation of interfaces with different constitutive properties. The surface energy is also controlled by a single length scale parameter, which together with the material length scale defines a particular material. Numerical results reveal that a boundary layer is developed in the film for both biaxial and shear loading, giving rise to size effects. The size effects are strongly connected to the buildup of surface energy at the interface. If the interface length scale is small, the size effect vanishes. For a stiffer interface, corresponding to a non-vanishing surface energy at the interface, the yield strength is found to scale with the inverse of film thickness. Numerical predictions by the theory are compared to different experimental data and to dislocation dynamics simulations. Estimates of material length scale parameters are presented. ?? 2004 Elsevier Ltd. All rights reserved.
B. Constitutive behaviour; C. Strain gradient plasticity; Viscoplastic material
Post-fire thin debris flows: Sediment transport and numerical modelling
Earth Surface Processes and Landforms
28
12
1341-1348
2003
10.1002/esp.590
The creation of a hydrophobic layer in the soil during fires in semi-arid environments inhibits the infiltration of rainfall. This leads to increased rates of runoff and associated sediment transport. When the hydrophobic layer is deposited beneath the soil surface, a perched water table develops which may cause thin (1-2 cm) hillslope failures that are distinguishable from features caused by rilling and sheetflow. Evidence for these failures was observed after a fire near Santa Barbara, California. The amount of sediment eroded from some hillslopes was substantial, with 290 kg of sediment per metre width of hillslope delivered to the valley floor. The mechanics of these failures are examined with a numerical model that incorporates a stability analysis with subsurface flow routing along a typical hillslope profile. The model correctly predicts the location of the failures as well as the rainfall amount necessary to trigger them. Copyright (C) 2003 John Wiley Sons, Ltd.
Mechanics of Low-Angle Normal Faults
Rheology and deformation of the lithosphere at continental margins
46-91
2004
CHAPTER THREE Mechanics of Low - Angle Normal Faults Gary J. Apen Introduction Since their discovery in the Basin and Range province (Longwell 1945; Anderson 1971; Armstrong 1972; Crittenden et al. 1980; Wernicke 1981) and subsequent recognition worldwide," ...
Quantum Mechanics.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
371
1989
20120523
2013
10.1098/rsta.2012.0523
-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics.
Mechanics and electrochemistry of ionic polymer metal composites
Journal of the Mechanics and Physics of Solids
71
156-178
2014
10.1016/j.jmps.2014.07.006
Ionic polymer metal composites (IPMCs) are electroactive materials composed of a hydrated ionomeric membrane that is sandwiched between noble metal electrodes. Here, we propose a modeling framework to study quasi-static large deformations and electrochemistry of IPMCs. Specifically, IPMC kinematics is described in terms of its mechanical deformation, the concentration of mobile counterions neutralizing the ionomer, and the electric potential. The chemoelectromechanical constitutive behavior is obtained from a Helmholtz free energy density, which accounts for mechanical stretching, ion mixing, and electric polarization. The three-dimensional framework is specialized to plane bending of thin IPMCs. Hence, we propose a structural model, where the moment and the charge stored along the IPMC are computed from the solution of a modified Poisson-Nernst-Planck system, in terms of the through-the-thickness coordinate. For small static deformations, we present a semianalytical solution based on the method of matched asymptotic expansions, which is ultimately used to study IPMC sensing and actuation. We demonstrate that the linearity of IPMC actuation in a broad voltage range could be attributed to the interplay of two competing nonlinear phenomena, associated with Maxwell stress and osmotic pressure. In agreement with experimental observations, our model confirms the possibility of tailoring IPMC actuation by varying the counterion size and the concentration of fixed ions. Finally, the model is successful in predicting the significantly different voltage levels displayed by IPMC sensors and actuators, which are associated with remarkable variations in the ion mixing and polarization energies. (C) 2014 Elsevier Ltd. All rights reserved.
Improved quantitative recovery of Listeria monocytogenes from stainless steel surfaces using a one-ply composite tissue.
Journal of food protection
67
10
2212-7
2004
Four sampling devices, a sterile environmental sponge (ES), a sterile cotton-tipped swab (CS), a sterile calcium alginate fiber-tipped swab (CAS), and a one-ply composite tissue (CT), were evaluated for quantitative recovery of Listeria monocytogenes from a food-grade stainless steel surface. Sterile 304-grade stainless steel plates (6 by 6 cm) were inoculated with approximately 106 CFU/cm2 L. monocytogenes strain Scott A and dried for 1 h. The ES and CT sampling devices were rehydrated in phosphate buffer solution. After plate swabbing, ES and CT were placed in 40 ml of phosphate buffer solution, stomached for 1 min and hand massaged for 30 s. Each CS and CAS device was rehydrated in 0.1% peptone before swabbing. After swabbing, CS and CAS were vortexed in 0.1% peptone for 1 min. Samples were spiral plated on modified Oxford agar with modified Oxford agar Rodac Contact plates used to recover any remaining cells from the stainless steel surface. Potential inhibition from CT was examined in both phosphate buffer solution and in a modified disc-diffusion assay. Recovery was 2.70, 1.34, and 0.62 log greater using CT compared with ES, CS, and CAS, respectively, with these differences statistically significant (P < 0.001) for ES and CT and for CAS, CS, and CT (P < 0.05). Rodac plates were typically overgrown following ES, positive after CS and CAS, and negative after CT sampling. CT was noninhibitory in both phosphate buffer solution and the modified disc-diffusion assay. Using scanning electron microscopy, Listeria cells were observed on stainless steel plates sampled with each sampling device except CT. The CT device, which is inexpensive and easy to use, represents a major improvement over other methods in quantifying L. monocytogenes on stainless steel surfaces and is likely applicable to enrichment of environmental samples.
Bacterial Adhesion; Colony Count; Electron; Equipment Contamination; Food Contamination; Food Contamination: analysis; Food Microbiology; Listeria monocytogenes; Listeria monocytogenes: isolation & purification; Listeria monocytogenes: physiology; Listeria monocytogenes: ultrastructure; Microbial; Microscopy; Scanning; Stainless Steel
Thin minimum-drag airfoils
Fluid Mechanics - Soviet Research
9
2
14-19
1980
The problem of 'recovery' of the suction force on a thin wing by wing-shaping is analyzed. The variational problem is carried through to final solution for a class of infinitely thin airfoils of arbitrary configuration at small angles of attack in a nonlinear gas flow. It is shown that a necessary condition for full 'recovery' of the suction force is that the leading edge of the airfoil be shock-free. It is further shown that the optimum distribution of wing curvature for subsonic and transonic flight velocities can be attained in an infinite number of ways (4 Refs.)
A4725 (Turbulent flows, convection, and heat trans; A4740 (Compressible flows; aerodynamics; drag reduction; recovery; shock and detonation phenomena); subsonic flight velocities; suction force; thin minimum drag airfoils; thin wing; transonic flight velocities; T Theoretical or Mathematical; variational problem; wing curvature; wing-shaping
Taiwan orogeny: thin-skinned or lithospheric collision?
Tectonophysics
274
191-220
1997
10.1016/S0040-1951(96)00304-6
The Taiwan orogeny is young and presently very active. It provides an excellent environment for studying ongoing orogenic processes, especially since the region is monitored intensively with dense seismological and geodetic networks, and new studies aiming at deciphering shallow and deep structures in and around Taiwan have been recently conducted or are being planned. The available data can be used continually to test critically hypotheses of the Taiwan orogeny. Hypotheses dealing with the mechanics of mountain building are basic to the understanding of Taiwan orogeny and are particularly amenable to testing. The widely cited ‘thin-skinned tectonics’ hypothesis was formulated to explain mainly the geologic and relatively shallow (<10 km) seismic data. In various forms of this hypothesis, the mountain building involves the deformation of ready-to-fail (Tertiary) sediments in a thin (<20 km at the deepest point) wedge deformed by the advancing Philippine Sea plate; the Eurasian plate is assumed to subduct the Philippine Sea plate with the Taiwan orogenic belt on top as an accretionary wedge. We tested this hypothesis against newly acquired seismological and geophysical data and found it to be largely inadequate as a model for Taiwan orogeny, because the evidence for the participation of the lower crust and even the upper mantle in the orogeny is very strong. Rather than the result of deforming a thin wedge, the formation of the Central Range is shown to include the thickening of crust as well as the extrusion of mid- to lower crustal high-velocity materials to shallow depth. Seismicity and focal mechanisms demonstrate that significant deformation is taking place at depths far below what the think-skinned tectonics hypothesis predicts. As an alternative, the lithospheric collision hypothesis is proposed. In this model the Eurasian and the Philippine Sea plates are colliding at least down to a depth of 60 km. This hypothesis involves not only greater depth but also greater lateral extent. It accounts for the formation of the deep-rooted Central Range on the Eurasian side, as well as the shortening and thickening of the margin of the Philippine Sea plate near Taiwan. It also asserts that the Central Range was built mainly under ductile conditions, while in the Western Foothills area, the deformation involves the whole brittle-ductile-brittle-ductile sandwiched crust and upper mantle. Furthermore, it is asserted that the collision effect is transmitted to the Taiwan Strait resulting in normal faulting striking perpendicular to the trend of Taiwan. Among the implications of this hypothesis some can be readily subjected to falsification. By critically evaluating the components and accepting or rejecting them, our understanding of the Taiwan orogeny in particular and mountain building in general can be improved.
00; 0 0 3 0; 004; 17; 1997 elsevier science b; 4 0 - 1; 4 - 6; 9 5 1; 9 6; 97; all rights reserved; binghamton; collision; corresponding author; crustal theology; edu; e-mail; geol; i- 1951; lithospheric structures; orogeny; pii s 0 0; sunquakes; taiwan; tectonic model; v; wu
Elastic anisotropy effect on indentation-induced thin film interfacial delamination
Engineering Fracture Mechanics
75
10
3121-3130
2008
10.1016/j.engfracmech.2007.12.008
Effect of elastic anisotropy on indentation-induced thin film interfacial delamination, especially, at the initiation and early growth stage, is examined. The indentation load is modeled as a constant pressure over an expanding semi-spherical cavity. The delamination process is approached by a cohesive zone model. The rest of the problem is formulated within the general anisotropic elasticity theory, and solved numerically by the boundary element method employing a special Green's function for multilayers. The material system of a Cu(0 0 1) film on a Si(0 0 1) substrate is studied as an example. The interfacial damage initiation and crack development under indentation are captured in the simulation. By comparing the predictions with the materials being modeled as isotropic and as anisotropic (of the cubic symmetry as they are), it is shown that the elastic anisotropy of the copper film plays a significant role in determining the delamination pattern. In the isotropic model, the delamination crack fronts are circular reflecting the problem axisymmetry. In contrast, crack fronts are square with rounded corners in the anisotropic case. This significant difference necessitates a three-dimensional anisotropic stress analysis of the indentation-induced delamination of strongly anisotropic films. © 2007 Elsevier Ltd. All rights reserved.
Anisotropy; Boundary element method; Copper; Crack initiation; Delamination; Elasticity; Green's function; Indentation; Metallic films; Stress analysis
Microscopic Aspects of Failure and Fracture in Cross-Ply Fibre Reinforced Composite Laminates
Journal of Composite Materials
23
12
1216-1231
1989
10.1177/002199838902301202
This paper examines the microscopic deformation processes in composite laminates and seeks to explain (a) the superior tensile fracture toughness of a commercial laminate of the new composite system carbon/bismaleimide over a commercial laminate of the conventional material carbon/epoxy, and (b) the dependence of interlaminar failure in glass and carbon fibre/epoxy laminates on the fracture energy of the matrix resin.
A two-ply artificial blood vessel of polyurethane and poly(L-lactide)
Colloid & Polymer Science
268
1
2-11
1990
10.1007/BF01410416
A biodegradable microporous small-caliber vascular prosthesis has been developed that consists of two layers. The inner layer has been made highly antithrombogenic by cross-linking of a mixture of linoleic acid and an aliphatic polyetherurethane with dicumylperoxide. Microporosity was introduced by adding sodiumfluoride crystals of about 5 µm in diameter prior to cross-linking and leaching them out afterwards.
Rough contacts between actual engineering surfaces. Part II. Contact mechanics
Wear
264
11-12
1116-1128
2008
10.1016/j.wear.2007.08.027
The models of roughness description by using simple parabolic functions described in Part I are here tested with different contact mechanics models. The approximation with parabolas allows the calculation of each asperity curvature radius, a fundamental quantity for contact mechanics studies. After a review of the main contact mechanics models, some of them has been selected: two different elastic models and two elastic-plastic ones, one with a discontinuity at the boundary between the elastic and the plastic region, and one with an additional elastoplastic transition region. The amplitudes of the contact zone and the load are calculated as a function of the interference of each profile with a rigid smooth flat surface for single parabolic asperities and for whole profiles extracted from five engineering surfaces with different roughness conditions. Big differences in the size of the deformed zone and in the load supported by single parabolas using the different roughness description approaches and contact mechanics models were found. However, these differences are mitigated when the whole profiles are considered. As expected, the elastic models tend to overestimate the load when profiles with a certain degree of plasticity are under investigation. The roughness description approach based on the minimization of the least square error between the measured profile and the parabolic approximation (LMS c1 c2) gives the best simulation of the profile and does not show any drawback from a contact mechanics or numerical point of view. The combination of this approach with the contact mechanics model including the elastoplastic transition developed by Zhao, Maietta and Chang (ZMC) seems to guarantee the best results. ?? 2007 Elsevier B.V. All rights reserved.
Contact mechanics; Elastic contact; Elastoplastic contact; Mathematical models; Plastic contact; Surface roughness
Laws and Statistical Mechanics
Philosophy of Science
71
707-718
2004
10.1086/425234
This paper explores some connections between competing conceptions of scientific laws on the one hand, and a problem in the foundations of statistical mechanics on the other. I examine two proposals for understanding the time asymmetry of thermodynamic phenomenal: David Albert's recent proposal and a proposal that I outline based on Hans Reichenbach's "branch systems". I sketch an argument against the former, and mount a defense of the latter by showing how to accommodate statistical mechanics to recent developments in the philosophy of scientific laws.
Laws; Thermodynamics; Temporal Asymmetry
The concept of probability in quantum mechanics
Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability
533-541
1951
The concept of probability is discussed in relation to quantum theory and the thesis of determinism. it is argued that an indeterministic probability interpretation of quantum mechanics encounters difficulties in connection with the problem of measurement. this interpretation is also criticized for not being able to give a consistent account for both stationary and transition probabilities. as an alternative, an objective concept of probability which is compatible with both determinism and quantum mechanics is proposed.
Solved problems in Lagrangian and Hamiltonian mechanics
Solved Problems in Lagrangian and Hamiltonian Mechanics
1-464
2009
10.1007/978-90-481-2393-3
Mechanics is an old science, but it acquired its great reputation at the end of the 17th century, due to Newton’s works. A century later, Euler and, above all, Lagrange renewed it and led it towards a formulation not only aesthetically elegant but also capable of applications to other fields of physics. Fifty years later, Hamilton and Jacobi gave their names to very important further contributions. Lastly, at the end of the xixth century, Poincaré took a new step with the introduction of geometry in the analysis of physical problems. During the xxth century, physicists produced new developments from the works of their famous predecessors.
Cell Mechanics Meets MEMS
CSME Bulletin SCGM
15-18
2006
... D. Magnetic Bead Measurement In this technique, a 4-5_m diameter paramagnetic bead is bound to ... underlying substrate by altering the organization of its cytoskeleton and possibly through strain-stiffening ... Leveraging the concept of vision - based cellular force sensing, Sun et al ...
Biomaterial surface modifications can dominate cell–substrate mechanics: the impact of PDMS plasma treatment on a quantitative assay of cell stiffness
Soft Matter
8
3
673
2012
10.1039/c1sm06250f
Polydimethylsiloxane (PDMS) is a bioinert synthetic polymer with tunable elastic properties that is commonly used as a cell culture substrate. Although plasma treatments are widely used to bio-functionalize otherwise hydrophobic PDMS surfaces, plasma altered surface mechanical properties and implications for cell-substrate mechanical interactions are poorly understood. We performed a multi-scale mechanical characterization of PDMS following plasma treatment: spherical indentation tests were performed with a universal testing machine (indenter diameter, d = 4.75 mm) and atomic force microscopy (AFM) with round tips of 2 different diameters (d = 2 mm, d = 20 mu m). Results indicated substantial surface stiffening at indentation depths up to 1 micron, with exponentially decreasing effects to depths of 1 mm. AFM indentation results were analyzed using a finite element (FE) based optimization to determine the substrate material properties, and thus separate the confounding influence of the underlying substrate on surface indentation experiments. We found that a two-layer material model composed of a thin, stiff plasma-oxidized layer (296 nm and 3.66 MPa, respectively) superimposed on a thick layer of bulk polymer (elastic modulus of 10.5 kPa) was able to robustly fit the experimental data. We then investigated the repercussions of the biopolymer surface modifications on cell mechanics, using an inverse finite element model to interpret cell-matrix force exchange. Estimates of cell elastic modulus neglecting the mechanical effects of plasma treatment were more than an order of magnitude lower than estimates accounting for the surface layer (9.6 +/- 4.2 kPa vs. 124 +/- 55 kPa, respectively). This study thus highlights the need to accurately consider biomaterial surface modifications and how they may influence cell-biomaterial interaction. It further provides a novel approach to characterizing cell-relevant mechanical properties of a polymer substrate. These advances may lead to an improved quantitative assessment of actin cytoskeleton function, with potential relevance to biomaterial based therapies.
Forming of UD fibre reinforced thermoplastics
University of Twente, Enschede
2013
Composite materials are a serious competitor for lightweight metals used in the aerospace and automotive industry. Uni-directional (UD) carbon fibre reinforced thermoplastics are favoured due to their high specific strength and stiffness, but also their good toughness, impact and chemical resistance properties. By heating UD reinforced thermoplastic laminates sufficiently above the melting point of the polymer, these can be stamp-formed to relatively complex geometries. The product is released after a relatively short cooling time. Hence, high production rates can be achieved, whichmakes this process very appropriate for the large volume production of high performance thin-walled products of complex shapes. Nevertheless, process-induced defects such as wrinkling are frequently encountered, which disqualify the final product. A thorough understanding of the deformation behaviour of UD laminates is required to anticipate those defects, which is therefore one of the objectives in this research. Forming simulation tools can be employed in the product design phases to anticipate the defects observed, ultimately leading to a reduction in product development costs. The predictive capability of forming simulations was therefore carefully analysed. Forming an initially flat laminate to a doubly curved surface invokes in-plane and out-of-plane deformations, such as intra-ply shear, inter-ply slippage, and bending. These are described with constitutive models, which require material data input. The sensitivity of composite forming predictions to this input was firstly investigated for a dome-shaped geometry. The resulting product shape was found to be determined by a delicate balance between the mechanisms considered, which highlights the importance of a thorough material characterisation. Wrinkle-free forming of UD laminates to doubly curved surfaces requires in-plane deformations of the plies, in particular by shear. The work therefore focuses on the intra-ply shearing mechanism, where fibres slide parallel to each other. A new shear characterisation test for UD fibre reinforced thermoplastics was proposed. Torsion bar specimens from polyetheretherketone (PEEK) with a UD carbon fibre reinforcement (UD-C/PEEK)were subjected to oscillating loads in order to determine the dynamic shear moduli from the linear visco-elasticity theory. The composite system shows a predominantly elastic behaviour for small strains, which is attributed to multiple fibre-fibre interactions. A low temperature and frequency dependency was found as well. The latter indicates the presence of yield behaviour at larger strains.Forming experimentswere conducted with quasi-isotropic UD-C/PEEK laminates on a representative product geometry used in the aerospace industry: a wing stiffening rib. These laminates are sensitive to wrinkling near areas with double curvature. Limited intra-ply shear strains develop in the final stage of forming, where further bending and wrinkling are prohibited by the tooling. The formability issues of the UD-C/PEEK material are explained by the relatively high resistance to intra-ply shear. The wing stiffening rib was used to study the predictive capabilities of finite element based forming simulations. The laminate was modelled by incorporating the characterised behaviour of intra-ply shear and inter-ply friction. The predicted intra-ply shear strain fields and the large wrinkles match well with those observed in the experiments. However, the results were dependent on the unknown bending parameters, for which an extensive characterisation programme is necessary. The small wrinkles observed in practice cannot be predicted with the element size used, however, predicted waviness at the corresponding locations may indicate potential critical spots. The simulations conducted have proven to be instrumental in obtaining a better understanding of the laminate deformations during the stamp forming process. They can be employed for design optimisation, as well as to derive design guidelines in a more general sense.
Mechanics of the burnishing process
Precision Engineering
37
1
129-134
2013
10.1016/j.precisioneng.2012.07.008
Burnishing is a low-cost surface treatment process. However, scientific studies on this process have so far failed to describe how the process leads to surface hardening and improvement in the geometric quality of the material. Indeed, in spite of its apparent simplicity the process is rather complicated to reproduce by numerical simulation. This paper proposes a finite element modelling of the ball burnishing process. Thanks to this model, the effect of the burnishing process on the material is analysed. A ridge phenomenon that affects the mechanics of the process is demonstrated, allowing for improved modelling of the burnishing process. © 2012 Published by Elsevier Inc. All rights reserved.
Contact mechanics; Deep rolling; Finite element method; Roller burnishing
Estimation of 3D shape, internal density and mechanics of proximal femur by combining bone mineral density images with shape and density templates
Biomechanics and Modeling in Mechanobiology
11
6
791-800
2012
10.1007/s10237-011-0352-9
Measurement of bone mineral density (BMD) by dual-energy X-ray absorptiometry (DXA) alone is only a moderate predictor of fracture risk. Finite element analysis (FEA) of bone mechanics, based on DXA images, may improve the prediction of fracture risk. We developed a method to estimate the 3D shape and density distribution of the proximal femur, using a 2D BMD image and a femur shape template. Proximal femurs of eighteen human cadavers were imaged using computed tomography and divided into two sets (N = 9 + 9). The template was created from the samples in first set by using 3D generalized Procrustes analysis and thin-plate splines. Subsequently, the template and 2D BMD image were utilized to estimate the shape and internal density distribution of the femurs in the second set. Finally, FEA was conducted based on the original and the estimated bone models to evaluate the effect of geometrical and density distributional errors on the mechanical strength. The volumetric errors induced by the estimation itself were low (<1.4%). In the estimation of bones in the second set, the mean distance difference between the estimated and the original bone surfaces was 0.80 ± 0.19mm, suggesting feasible estimation of the femoral shape. The mean absolute error in voxel-by-voxelBMDwas 120±8mg cm-3. InFEA, thestiffness of the proximal femur differed by-7±16% between the original and estimated bones. The present method, in comparison with methods used in previous studies, improved the prediction of the geometry, the BMD distribution and the mechanical characteristics of the proximal femur. Potentially, the proposed method could ultimately improve the determination of bone fracture risk. © Springer-Verlag 2011.
Bone mineral density; Bone strength; Finite element; Proximal femur; Shape estimation
Modeling and simulation of buckling of polymeric membrane thin film gel
Computational Materials Science
49
1 SUPPL.
S60-S64
2010
10.1016/j.commatsci.2009.12.036
The swelling- and deswelling-induced instabilities of various membrane structures are simulated using the inhomogeneous field theory of a polymeric network in equilibrium with a solvent and mechanical load/constraint and the Finite Element subroutine developed in ABAQUS. The simulating results of these membrane gels are compared with available experimental results, and a reliable prediction in deformation pattern and critical conditions has been achieved. The study has been made in attempt to mimic the shape of a plant leaves from the swelling/deswelling patterns of a gel. Furthermore, this study provides a possibility to explore the origin of intriguing natural phenomena of plants. ?? 2010 Elsevier B.V. All rights reserved.
Buckling; Deswelling; Finite element method; Gel; Swelling
Thin liquid films on chemically heterogeneous substrates: Self-organization, dynamics and patterns in systems displaying a secondary minimum
Physica A: Statistical Mechanics and its Applications
318
1-2
262-278
2003
10.1016/S0378-4371(02)01429-2
Surface instability in a thin liquid film engendered by a micro-scale wettability contrast, resulting from the spatial gradients in the intermolecular interactions, is investigated based on 3D simulations for a system displaying both the primary and secondary minima in its force vs. distance curve. Characteristic dynamical and morphological features of the evolution on a chemically heterogeneous substrate are identified for two different cases: (a) a single patch or step of heterogeneity (b) multiple periodically arranged stripes of heterogeneity. The presence of heterogeneity can cause true rupture at the primary minimum by surmounting the energy barrier between the two minima. The breakup time on heterogeneous surfaces varies inversely with the gradient in the potential induced by the heterogeneity and can be several orders of magnitude smaller than the spinodal dewetting time on homogeneous surfaces. Heterogeneity can also cause rupture in spinodally stable films and produce complex and locally ordered morphological features (e.g., ripples) absent in the spinodal dewetting. On a chemically patterned surface composed of alternating more and less wettable stripes, film breakup is suppressed on some potentially destabilizing nonwettable sites when their spacing is below a characteristic lengthscale of instability, ??h which is close to the spinodal lengthscale. Thin film pattern ideally replicates the surface energy pattern only when, (a) the periodicity of substrate pattern is greater than ??h, (b) width of the less wettable stripe is lower than a transition length above which complex morphological features are formed. ?? 2002 Elsevier Science B.V. All rights reserved.
Chemical heterogeneity; Pattern formation; Pseudo dewetting; Templating; Thin films; True dewetting
Shear-dominated plastic behavior of a cross-ply Dyneema® composite
Composites Part A: Applied Science and Manufacturing
67
316-323
2014
10.1016/j.compositesa.2014.09.012
Dyneema® composites derive some of their performance attributes from their elastic and plastic anisotropy. The principal objective of the present study is to develop a finite element framework for predicting the large-strain deformation response of these composites in a [0°/90°] configuration. We employ a binary model comprising a series of line elements to represent the axial fiber properties and a 3D effective medium to represent all off-axis properties. The model is assessed through comparisons with the results of two types of tests: (i) quasi-static punch tests and (ii) dynamic tests performed by firing (crushable) foam projectiles at high velocities. The measured load–displacement response in the punch tests and the evolution of the back-face deflection in the dynamic tests as well as the final shapes of the test specimens are represented well by the numerical simulations. Discrepancies occur only at the highest levels of displacements, wherein material damage becomes a significant factor.
A. Laminates; B. Impact behavior; B. Plastic deformation; C. Finite element analysis (FEA)
Bohmian Trajectories as the Foundation of Quantum Mechanics
arXiv preprint arXiv:0912.2666
14
2009
Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a theory known as Bohmian mechanics, to which this article is an introduction.
Mechanical properties of thin films
Metall. Trans. A
20
11
2217-2245
1989
10.1007/BF02666659
The mechanical properties of thin films on substrates are described\nand studied. It is shown that very large stresses may be present\nin the thin films that comprise integrated circuits and magnetic\ndisks and that these stresses can cause deformation and fracture\nto occur. It is argued that the approaches that have proven useful\nin the study of bulk structural materials can be used to understand\nthe mechanical behavior of thin film materials. Understanding the\nmechanical properties of thin films on substrates requires an understanding\nof the stresses in thin film structures as well as a knowledge of\nthe mechanisms by which thin films deform. The fundamentals of these\nprocesses are reviewed. For a crystalline film on a nondeformable\nsubstrate, a key problem involves the movement of dislocations in\nthe film. An analysis of this problem provides insight into both\nthe formation of misfit dislocations in epitaxial thin films and\nthe high strengths of thin metal films on substrates. It is demonstrated\nthat the kinetics of dislocation motion at high temperatures are\nexpecially important to the understanding of the formation of misfit\ndislocations in heteroepitaxial structures. The experimental study\nof mechanical properties of thin films requires the development and\nuse of nontraditional mechanical testing techniques. Some of the\ntechniques that have been developed recently are described. The measurement\nof substrate curvature by laser scanning is shown to be an effective\nway of measuring the biaxial stresses in thin films and studying\nthe biaxial deformation properties at elevated temperatures. Submicron\nindentation testing techniques, which make use of the Nanoindenter,\nare also reviewed. The mechanical properties that can be studied\nusing this instrument are described, including hardness, elastic\nmodulus, and time-dependent deformation properties. Finally, a new\ntesting technique involving the deflection of microbeam samples of\nthin film materials made by integrated circuit manufacturing methods\nis described. It is shown that both elastic and plastic properties\nof thin film materials can be measured using this technique. © 1989\nThe Minerals, Metals & Materials Society and ASM International.
Dislocation Motion Kinetics; Films; Integrated Circuits; Magnetic Devices; Materials Testing--Hardness; Metallography--Lattice Defects; Misfit Dislocations; Nanoindenter; Stresses--Measurements; Substrate Curvature; Thin Film; Thin Films
Representation of forming limits for negative incremental forming of thin sheet metals
IDDRG 04 Conference Proceedings
198-207
2004
In negative incremental forming, a punch moves on a sheet metal, plastically\ndeforming it according to a programmed path, while the sheet is clamped\nat the periphery onto a support frame. It is well recognized that\nsever strain can occur before fracture, thanks to the local and incremental\nshear deformations mechanics induced by the process. Thinning and\nfracture largely depend on the part slope. Decreasing the feed rate\nhas a positive effect on formability. Knowledge about the forming\nlimits, especially in relation to the feed rate, is essential to\nset the feed rate at the maximum possible values, thus increasing\nthe productivity of the process. The purpose of the study is to describe\nthe effect of various process parameters on the formability. Experiments\nare presented, aimed at investigating the effect of the feed rate,\nthe part slope, the part curvature in a plane perpendicular to the\nvertical z-axis, the spherical punch radius, etc. Several thin aluminum\ncups have been formed with a robotic incremental forming cell. The\ninvestigation is used for proposing new spaces for representation\nof forming limits, alternative to the frequently used forming limit\ndiagrams.
Fluid mechanics, Volume 10
Academic Press 4th ed
872
2008
Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situationswhether in the liquid or gaseous state or ...
technology & engineering
Dynamic Modulus Testing of Thin Pavement Cores
Journal of ASTM International
3
12258
2006
10.1520/JAI12258
A novel method of testing thin surface cores using the dynamic (complex) modulus test is proposed that utilizes composite mechanics theory. Rectangular specimens are sawed from the round surface layer cores, and the sawed blocks are simply stacked horizontally without bonding. Two hydrostone caps are made to provide flat and smooth loading ends, as well as to restrain the blocks from moving during loading. Two Linear Vertical Differential Transformers are attached 180 degrees apart to the flat uniform side of the horizontally stacked cores to obtain the strain response without measuring over the joint of the cores. The advantage of this approach over the diametral loading mode, used for resilient modulus testing, is that it provides homogenous testing conditions, which gives direct access to stress and strain and, therefore, constitutive equations.
Soil Mechanics for Unsaturated Soils
Stress The International Journal on the Biology of Stress
517
1993
10.1016/0267-7261(93)90011-F
"A Wiley-Interscience publication.". Includes bibliographical references (p. 490-507) and index.
Information Theory and Statistical Mechanics
The Physical Review
106
4
620-630
1957
Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncomittal with regard to the missing information. If one considers the statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argumentm and in particular independently of experimental verification; whether or not the results agree with experiment, they still present the best estimates that could have been made on the basis of the information available. It is concluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.
Mechanics of rubberlike solids
Mechanics of the 21st Century
263-274
2004
In this paper we discuss: (i) the large deformation stress-strain response of rubberlike solids based on experimental observations, including both elastic and inelastic behaviour of particle-filled and unfilled rubber, (ii) the mathematical modelling of this behaviour through its phenomeno- logical treatment using elasticity theory and extensions of the theory to account for inelastic responses such as the Mullins effect, stress soft- ening and hysteretic stress-strain cycling, (iii) an introduction to the analysis of the coupling of mechanical and magnetic effects in so-called magneto-sensitive elastomers, which are being used as ’active’ compo- nents in various applications where the mechanical properties of the material are changed rapidly when a suitable magnetic field is applied.
large deformations; magnetoelasticity; magneto-sensitive elastomers; mullins effect; rubber elasticity; rubber inelasticity; stress softening
Skeletal muscle mechanics and movement
Current Issues in Biomechanics
171-211
1993
Gregor RJ. Skeletal muscle mechanics and movement. In: Grabiner M, ed. Current Issues in Biomechanics. Champaign, IL: Human Kinetics; 1993:171–211.
figure--electromechanical delay; figure--force-length; figure--force-velocity; mechanics; Movement; muscle; muscle mechanics; review--muscle mechanics
A damage-mechanics-based approach for modelling decohesion in adhesively bonded assemblies
Engineering Fracture Mechanics
73
2774-2801
2006
10.1016/j.engfracmech.2006.04.029
A cohesive interface model formulated within the framework of damage mechanics is presented for the simulation of decohesion in adhesively bonded assemblies. Characteristic features of the model are: the introduction of a single energy-based damage variable for describing the damage state of the interface; use of a decohesion propagation condition relying upon the linear elastic fracture mechanics (LEFM) energy balance; a treatment for the mixed-mode situation based on the definition of an equivalent energy release rate whose expression is consistently derived from the formulation. The comparisons between numerical and experimental responses obtained for typical test problems illustrate the capabilities of the proposed approach. ?? 2006 Elsevier Ltd. All rights reserved.
Adhesive assemblies; Cohesive-zone models; Damage mechanics; Decohesion; Interfaces
Adaptive finite element methods in computational mechanics
Computer Methods in Applied Mechanics and Engineering
101
143-181
1992
10.1016/0045-7825(92)90020-K
We present a general approach to adaptivity for finite element methods and give applications to linear elasticity, non-linear elasto-plasticity and nonlinear conservation laws, including numerical results.
New Insights on Time-Symmetry in Quantum Mechanics
Arxiv preprint arXiv07061232
quant-ph
1-58
2007
A review of new aspects concerning time-symmetry in Quantum Mechanics.
Probing Quantum Mechanics towards the Everyday World
Progress of Theoretical Physics Supplement
170
170
100-118
2007
10.1143/PTPS.170.100
I briefly examine the motivation for experiments designed to test\nquaqntum mechanics against an alternative, "common-sense" view of\nthe everyday world which I denote "macrorealism", and review how\nfar existing experiments go towards settling the issue.
Continuum Damage Mechanics: Part I—General Concepts
Journal of Applied Mechanics
55
1
59
1988
10.1115/1.3173661
ContinuumDamage Mechanics (C.D.M.) has developed continuously since the early worksof Kachanov and Rabotnov. It constitutes a practical tool totake into account the various damaging processes in materials andstructures at a macroscopic continuum level. The main basic featuresof C.D.M. are considered in the first part together withits present capabilities, including damage definitions and measures, and itsincorporation into a thermodynamic general framework. Practical damage growth equationswill be reviewed in the second part of the paper. \n\t\t\n\t\t\t ©1988 ASME
THE TENSEGRITY-TRUSS AS A MODEL FOR SPINE MECHANICS: BIOTENSEGRITY
Journal of Mechanics in Medicine and Biology
02
03n04
375-388
2002
10.1142/S0219519402000472
This paper was first presented at the 12th International Conference on Mechanics in Medicine and Biology, Lemnos, Greece, September 2002. It was subsequently published in the Journal of Mechanics in Medicine and Biology, vol. 2, #3&4, 375-388. The copyright is held by World Scientific Publishing Co.
biomechanics; biotensegrity; models; spine; tensegrity
Consistent histories and the interpretation of quantum mechanics
Journal of Statistical Physics
36
1-2
219-272
1984
10.1007/BF01015734
The usual formula for transition probabilities in nonrelativistic quantum me- chanics is generalized to yield conditional probabilities for selected sequences of events at several different times, called "consistent histories," through a criterion which ensures that, within limits which are explicitly defined within the formal- ism, classical rules for probabilities are satisfied. The interpretive scheme which results is applicable to closed (isolated) quantum systems, is explicitly indepen- dent of the sense of time (i.e., past and future can be interchanged), has no need for wave function "collapse," makes no reference to processes of measurement (though it can be used to analyze such processes), and can be applied to sequences of microscopic or macroscopic events, or both, as long as the mathematical condition of consistency is satisfied. When applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics, though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus.
joint probabilities; measurements; quantum mechanics; time reversal; wave function collapse
Exact three-dimensional piezothermoelasticity solution for dynamics of rectangular cross-ply hybrid plates featuring interlaminar bonding imperfections
Composites Science and Technology
70
5
752-762
2010
10.1016/j.compscitech.2010.01.006
An exact three-dimensional (3D) piezothermoelasticity solution is presented for static, free vibration and steady state harmonic response of simply supported cross-ply piezoelectric (hybrid) laminated rectangular plates with interlaminar bonding imperfections. The bonding imperfection is modeled by considering the jump in the displacements, electric potential and temperature across the non-rigid interface proportional, respectively, to the associated tractions, transverse electric displacement and heat flux. The solution includes the case when electric potentials are prescribed at the interfaces for effective actuation. Numerical results are presented for hybrid composite and sandwich plates with varying imperfection compliance. The effect of location of imperfect bonding on the response is investigated for mechanical, electric potential and thermal load cases. The effect of weak bonding at elastic-piezoelectric interface on the actuation authority of the piezoelectric layer is also investigated. These results would serve as benchmark for assessing 2D plate theories incorporating interlaminar bonding imperfections. ?? 2010 Elsevier Ltd.
A. Hybrid composites; A. Smart Materials; B. Debonding; C. Laminate theory
Investigating the effect of velocity, inflation pressure, and vertical load on rolling resistance of a radial ply tire
Journal of Terramechanics
50
2
99-106
2013
10.1016/j.jterra.2013.01.005
A single-wheel tester facility at Department of Agricultural Machinery of Urmia University was utilized to investigate the effect of velocity, tire inflation pressure, and vertical load on rolling resistance of wheel. A Good year 9.5L-14, 6 radial ply tire was used as the tester wheel on clay-loam soil and was installed on a carriage traversing the length of soil bin. Three inflation pressures of 100, 200, and 300kPa as well as three levels of velocity (i.e. 0.7, 1.4, and 2m/s) and five levels of vertical load applied on wheel (i.e. 1, 2, 3, 4, and 5kN) were examined. Covariance analysis (ANCOVA) of resulted data revealed that rolling resistance is less effected by applicable velocities of tractors in farmlands but is much influenced by inflation pressure and vertical load. An approximate constant relationship existed between velocity and rolling resistance indicating that rolling resistance is not a function of velocity particularly in lower ones. Moreover, it was observed that increase of inflation pressure results in decrease of rolling resistance. Additionally, increase of vertical load brings about increase of rolling resistance which was estimated to have polynomial relation with order of two. A model comprising tested variables was developed with relative high accuracy.
Inflation pressure; Rolling resistance; Soil bin; Tire; Velocity; Vertical load
Matrix cracking and delamination in laminated composites. Part II: Evolution of crack density and delamination
Mechanics of Materials
43
4
194-211
2011
10.1016/j.mechmat.2011.01.002
This paper presents a model to predict the propagation of transverse cracks in polymer matrix composite laminates. Different possibilities for the crack pattern are analyzed and the different stress–strain response are compared. Taking into account that matrix cracking promotes delamination between the plies, the propagation of delamination is also simulated. The model predictions are compared with experimental data obtained in composite laminates that accumulate transverse cracks and delaminations before failing catastrophically. The possibility and limitations of a general constitutive law applied at ply level, as a mesomodel, is analyzed and the bounds of applicability of the model are explained.
Constitutive behaviour; Energy release rate; Fiber-reinforced composite material; Fracture; Layered material
Whose Hands Ply the Strands? Survey of Eastern Michigan University Psychology Faculty Regarding Faculty and Librarian Roles in Nurturing Psychology Information Literacy
Behavioral & Social Sciences Librarian
31
2
112-127
2012
10.1080/01639269.2012.713845
The Association of College and Research Libraries developed information literacy standards and associated performance indicators for undergraduate psychology students. A survey of tenure-track faculty members and full-time lecturers in the Psychology Department at Eastern Michigan University was conducted to discover how those professors viewed the importance of these indicators, and how those professors perceived their role, as well as the role of librarians, in supporting instruction that develops those skills. The psychology faculty acknowledged the curricular value of the information literacy performance indicators and perceived librarians as having a supportive role relative to their own more primary role in developing the skills.
Fracture mechanics criteria and applications
Meccanica
27
2
144-144
1992
10.1007/BF00420594
The book is recommended for engineers and research workers interested in modern mechanics of materialsIn addition, there is a very rich and up-to-date collection of references that is very useful for readers wishing to improve their knowledge of any specific topic in fracture mechanics.' Meccanica 27:143-145 1992
The flow and stability of thin liquid films on a rotating disk
Journal of Fluid Mechanics
53
2
227-255
1972
10.1017/S0022112072000138
Measurements of the thickness and the stability of thin films of liquid (1150 ?mthick) formed on a rotating horizontal disk are presented and correlated in terms of an asymptotic-expansion solution of the thin-film equations. Water, various alcohols and water with wetting activities were used to cover a range of viscosity (1-2.5cP) and surface tension (20-72 dynes/cm). Smooth flow was found to occur in a region defined by the flow rate, rotational speed and physical properties of the liquid. Outside this region various wave patterns were observed (concentric, spiral and irregular waves). A linear theory of the stability of the film based on an extension of classical stability theories for plane films on inclined planes is given and contrasted with the experimental results. Surface phenomena associated with the use of wetting agents were found to have a strong effect on the stability of the film.
Instability of long-wavelength disturbances on gravity-modulated surfactant-covered thin liquid layers
Journal of Fluid Mechanics
466
249-258
2002
10.1017/S0022112002001325
The effect of gravity modulation on long-wavelength disturbances at the free surface of a surfactant-covered thin liquid layer is analysed. The surfactants are assumed to be insoluble so that variations in their concentration along the free surface produce Marangoni flows in the underlying liquid. Lubrication theory is applied to obtain nonlinear partial differential equations that describe the behaviour of the free surface height and surfactant concentration, and the stability of these equations to small-amplitude disturbances is examined by applying Floquet theory. It is found that long-wavelength disturbances are destabilized by gravity modulation when surfactants are present, whereas such disturbances are stable when surfactants are absent. Results from additional calculations indicate that the instability becomes more difficult to excite as the Marangoni forces, body forces, capillary forces and surfactant diffusivity increase, and becomes easier to excite as the van der Waals forces increase.
Alternative Method for Determining Surface Energy by Utilizing Polymer Thin Film Dewetting
Langmuir
10
1419-1428
2003
10.1021/la026489m
Contact angle and contact mechanics, the most common estimating methods for surface energy, exhibit intrinsic drawbacks when determining surface energy or surface energy variation of micron-scaled areas. In this study, the dewetting of a polymer thin film was explored as a means for surface energy determination. In particular, two empirical plots were generated through modification of silicon wafers with various organosilanes and organosilane mixtures. One plot correlated dewetting velocity of a polystyrene thin film as a function of surface energy for both polar and nonpolar surfaces; the other plot consisted of variation of dewetting hole diameters with surface energy for strictly nonpolar surfaces. The empirical plots were then applied to deduce surface energies of micron-scaled areas of gradient and heterogeneous-patterned surfaces. This approach resulted in reasonable values with less than 1% difference as compared to those expected for perfluorodecyl- 1H, 1H,2H,2H-trichlorosilane/n-decyltrichlorosilane surfaces. But the difference was slightly higher (35%) for the n-octadecyltrichlorosilane (OTS) contact-printed surfaces, which might be a result of better contact with the surface and higher OTS concentration on the stamps when smaller stamps were used.
Spatio-temporal instability in free ultra-thin films
European Journal of Mechanics, B/Fluids
17
3
371-384
1998
DOI:%2010.1016/S0997-7546(98)80264-1
The linear evolution of an initially localized disturbance is investigated for a free ultra-thin film of viscous liquid, which is subjected to capillary and long range intermolecular forces. The analysis is based on the long-wave model proposed by Erneux and Davis (1993, Phys. Fluids A, 5, 1117), which is reformulated in an equivalent form by means of the disjoining pressure approach. A negative disjoining pressure due to the van der Waals attraction strongly promotes instability. Both the growth rate along rays x = Ut and speed of the disturbance edges increase as the thickness of the undisturbed film decreases. The estimated film rupture time is larger than that found from linear temporal stability analysis. © Elsevier, Paris.
Disjoining pressure; Spatio-temporal instability; Thin film
On (Non)Linear Quantum Mechanics
Symmetry in Nonlinear Mathematical Physics
270-278
1997
We review a possible framework for (non)linear quantum theories, into which linear quantum mechanics fits as well, and discuss the notion of “equivalence” in this setting. Finally, we draw the attention to persisting severe problems of nonlinear quantum theories.
Influence of the interface ply orientation on the fatigue behaviour of bonded joints in composite materials
International Journal of Fatigue
32
1
82-93
2010
10.1016/j.ijfatigue.2009.02.008
The paper deals with the study of the fatigue behaviour of bonded joints in composite materials. The influence of the orientation of the composite layer at the adhesive–adherend interface is investigated on single lap joints prepared by carbon fabric/epoxy laminates bonded together with a two-part epoxy adhesive. Different laminate lay-ups ([45/02]s and [452/0]s), overlap lengths (20 and 40mm) and corner geometry of bonded area (square edge and fillet, respectively) were investigated under tension–tension fatigue. Particular attention was devoted to the analysis of the fatigue damage evolution to identify initiation and subsequent growth of cracks. A previous model developed by the authors, for the prediction of the fatigue life of bonded joints as the sum of an initiation and propagation phase, was successfully applied to summarise the new data.
Composite bonded joints; Crack initiation; Crack propagation; Interface orientation; Life prediction
Characterization of the interface adhesion of elastic-plastic thin film/rigid substrate systems using a pressurized blister test numerical model
Mechanics of Materials
42
10
908-915
2010
10.1016/j.mechmat.2010.07.009
The quality of interface adhesion of an elastic-plastic thin film/rigid substrate system can be characterized by its interface adhesion energy. To estimate the interface adhesion energy, a numerical model for the pressurized blister test has been proposed, which includes three steps: dimensional, forward and reverse analyses. The dimensional analysis is applied to derive a preliminary nondimensional relationship of the interface adhesion energy, and then the forward and reverse analyses are carried out to establish its explicit form and to extract the interface adhesion energy, respectively. The results are in good agreement with experimental measurements, which confirms the effectiveness of the model. (C) 2010 Elsevier Ltd. All rights reserved.
Blister test; coatings; composites; crack-growth; Dimensional analysis; Elastic-plastic thin film; equilibrium craze; films; fracture; Interface adhesion energy; nonlinear-analysis; parameters; sharp indentation; toughness
Testing and life prediction for composite rotor hub flexbeams
International Journal of Fatigue
28
1124-1135
2006
10.1016/j.ijfatigue.2006.02.029
A summary of several studies of delamination in tapered composite laminates with internal ply-drops is presented. Initial studies used 2D FE models to calculate interlaminar stresses at the ply-ending locations in linear tapered laminates under tension loading. Strain energy release rates for delamination in these laminates indicated that delamination would likely start at the juncture of the tapered and thin regions and grow unstably in both directions. Tests of glass/epoxy and graphite/epoxy linear tapered laminates under axial tension delaminated as predicted. Nonlinear tapered specimens were cut from a full-size helicopter rotor hub and were tested under combined constant axial tension and cyclic transverse bending loading to simulate the loading experienced by a rotor hub flexbeam in flight. For all the tested specimens, delamination began at the tip of the outermost dropped-ply group and grew first toward the tapered region. A 2D FE model was created that duplicated the test flexbeam layup, geometry, and loading. Surface strains calculated by the model agreed very closely with the measured surface strains in the specimens. The delamination patterns observed in the tests were simulated in the model by releasing pairs of multi-point constraints (MPCs) along those interfaces. Strain energy release rates associated with the delamination growth were calculated for several configurations and using two different FE analysis codes. Calculations from the codes agreed very closely. The strain energy release rate results were used with material characterization data to predict fatigue delamination onset lives for nonlinear tapered flexbeams with two different ply-dropping schemes. The predicted curves agreed well with the test data for each case studied. ?? 2006 Elsevier Ltd. All rights reserved.
Delamination; Flexbeam; Ply-drop; Rotor hub; Strain energy release rate
Anomalous scaling behavior in polymer thin film growth by vapor deposition
Journal of Statistical Mechanics: Theory and Experiment
2009
02
P02031
2009
10.1088/1742-5468/2009/02/P02031
As a first step towards understanding the anomalous kinetic roughening with multifractality found in recent experiments on vapor deposition polymerization (VDP) growth, we study a simple toy model of the VDP growth in a (1+1)-dimensional lattice, along with monomer diffusion, polymer nucleation, limited active end bonding, and shadowing effects. Using extensive numerical simulations, we observe that the global roughness exponent is different from the local one. It is argued that such anomalies in VDP growth are attributable to the instability induced by the non-local shadowing effects on active ends of polymers. Varying the ratio of the diffusion coefficient to the deposition rate by means of a cosine flux, we also consider the role of diffusion in kinetic roughening of polymer thin film growth, which is quite different from that for metal or semiconductor film growth. Finally, we suggest a (2+1)-dimensional version, which can be directly compared with experimental results.
chemical vapor deposition (theory); kinetic roughening (theory); self-affine roughness (theory); thin film deposition (theory)
Quantum mechanics without wavefunctions
Journal of chemical physics
136
3
031102
2012
10.1063/1.3680558
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications-theoretical, computational, and interpretational-are discussed.
Quantum Theory
An Analysis and Evaluation of the Damage and Durability Performance of Steel Belted Radial Ply Passenger Tires That Have Experienced Severe Impacts
SAE Technical Papers
2012
10.4271/2012-01-0795
It is widely known and well understood that a pneumatic tire can be vulnerable to irreparable damage as a result of severe road hazard impacts while in service. A wide variety of vehicle and laboratory test procedures exist to evaluate the effect on tire/wheel assemblies from impacting a road hazard such as a pothole. An example of a standardized procedure is SAE J1981, the primary purpose of which is to evaluate wheel performance. However derivations of this procedure have been used to evaluate tire performance, and to specifically characterize failure modes in tires. This Paper discloses a series of frontal impact tests on tire/wheel assemblies, combined with a series of nondestructive tests, culminating with controlled, fatigue endurance tests, to identify the damage and ultimately confirm the failure modes in steel belted radial ply tires. Copyright © 2012 SAE International.
Mechanics and pathomechanics in the overhead athlete
Clinics in Sports Medicine
32
4
637-651
2013
10.1016/j.csm.2013.07.003
The overhead throwing or serving motion requires the coordinated activation of all of the bony segments in a kinetic and kinematic chain to generate and regulate the forces and motions to accomplish the task. Proper mechanics create the optimum forces and motions. Pathomechanics are frequently associated with alterations in performance and injury risk or injury. Knowledge of normal mechanics and possible pathomechanics can help in the evaluation of athletes with shoulder pain. The evaluation should be comprehensive, including the presence of pathomechanics, the anatomic and physiologic reasons for the pathomechanics, and evaluation of all elements in the kinetic chain. © 2013 Elsevier Inc.
Kinetic chain; Mechanics of throwing; Pathomechanics of throwing; Shoulder injury
An introduction to continuum mechanics with applications
International Journal
2008
10.1017/CBO9781107415324.004
This textbook on continuum mechanics reflects the modern view that scientists and engineers should be trained to think and work in multidisciplinary environments. A course on continuum mechanics introduces the basic principles of mechanics and prepares students for advanced courses in traditional and emerging fields such as biomechanics and nanomechanics. This text introduces the main concepts of continuum mechanics simply with rich supporting examples but does not compromise mathematically in providing the invariant form as well as component form of the basic equations and their applications to problems in elasticity, fluid mechanics, and heat transfer. The book is ideal for advanced undergraduate and beginning graduate students. The book features: derivations of the basic equations of mechanics in invariant (vector and tensor) form and specializations of the governing equations to various coordinate systems; numerous illustrative examples; chapter-end summaries; and exercise problems to test and extend the understanding of concepts presented.
Quantum mechanics from self-interaction
Foundations of Physics
15
1
63-87
1985
10.1007/BF00738738
We explore the possibility thatzitterbewegung is the key to a complete understanding of the Dirac theory of electrons. We note that a literal interpretation of thezitterbewegung implies that the electron is the seat of an oscillating bound electromagnetic field similar to de Broglie's pilot wave. This opens up new possibilities for explaining two major features of quantum mechanics as consequences of an underlying physical mechanism. On this basis, qualitative explanations are given for electron diffraction, the existence of quantized radiationless states, the Pauli principle, and other features of quantum mechanics.
GBT-based elastic–plastic post-buckling analysis of stainless steel thin-walled members
Thin-Walled Structures
83
85-102
2014
10.1016/j.tws.2014.01.004
When compared with carbon steel, stainless steel exhibits a more pronounced non-linearity and no well-defined yield plateau, as well as appealing features such as aesthetics, higher corrosion resistance and lower life cycle cost. Due to its considerably high ductility/strength and cost, stainless steel structural solutions tend to be adopted mostly for slender/light structures, thus rendering the assessment of their structural behaviour rather complex, chiefly because of the high susceptibility to instability phenomena. The first objective of this paper is to present the main concepts and procedures involved in the development of a geometrically and materially non-linear Generalised Beam Theory (GBT) formulation and numerical implementation (code), intended to analyse the behaviour and collapse of thin-walled members made of materials with a highly non-linear stress–strain curve (e.g., stainless steel or aluminium). The second objective is to validate and illustrate the application of the proposed GBT formulation, by comparing its results (equilibrium paths, ultimate loads, deformed configurations, displacement profiles and stress distributions) with those provided by shell finite element analyses of two lean duplex square hollow section (SHS) columns previously investigated, both experimentally and numerically, by Theofanous and Gardner (Eng Struct 2009; 31(12): 3047–3058.). The stainless steel material behaviour is modelled as non-linear isotropic and the GBT analysis includes initial geometrical imperfections, but neglects corner strength enhancements and membrane residual stresses. It is shown that the GBT unique modal nature makes it possible to acquire in-depth knowledge concerning the mechanics of the column behaviour, by providing “structural x-rays” of the (elastic or elastic–plastic) equilibrium configurations: modal participation diagrams showing the quantitative contributions of the global, local, warping shear and transverse extension deformation modes - moreover, this feature makes it possible to exclude, from future similar GBT analyses, those deformation modes found to play a negligible role in the mechanics of the behaviour under scrutiny, thus further reducing the number of degrees of freedom involved in a GBT analysis, i.e., increasing its computational efficiency.
Elastic–plastic behaviour; Generalised beam theory (GBT); Post-buckling behaviour; Stainless steel; Thin-walled members; Tubular columns
Quantum mechanics needs no interpretation
Arxiv Preprints
1-10
2004
10.1135/cccc20050621
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule, probability density current, commutation relations, momentum operator, uncertainty relations, rules for including the scalar and vector potentials and existence of antiparticles can be derived from the definition of the mean values of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schroedinger equation and Dirac equation are obtained from requirement of the relativistic invariance of the theory. Limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems are also discussed.
classical mechanics; probability theory; quantum mechanics
Physical chemistry: quantum mechanics for plants.
Nature
431
7006
256-257
2004
10.1038/431256a
To what extent do photosynthetic organisms use quantum mechanics to optimize the capture and distribution of light? Answers are emerging from the examination of energy transfer at the submolecular scale.
dynamics; energy-transfer
Stable and unstable fracture of thin brittle disks under a ball-on-3-balls loading
Engineering Fracture Mechanics
76
16
2486-2494
2009
10.1016/j.engfracmech.2009.08.008
Ball-on-3-balls tests carried out on a coarse-grained alumina exhibited typical features of stable crack extension well-known for macroscopic cracks in materials with an increasing crack growth resistance. In order to interpret this effect unexpected for small natural cracks, stress intensity factors of semi-elliptical surface cracks were computed by applica- tion of the procedure proposed by Cruse and Besuner. For these computations an analytical description for the stress distribution in the disk under ball-on-3-balls loading was applied. The stresses strongly decrease with increasing distance from the disk centre. It can be con- cluded from the results that natural small cracks can propagate stably due to this decrease.
ball-on-3-balls loading
New methods of celestial mechanics
books.google.com
2007
10.2174/97816080518781100101
Page 1. History of Modem Physics and Astronomy Volum e New Methods of Celestial 1. Periodic and Asymptotic Solutions HENRI Edited and Introduced by DANIEL L. GOROFF Originally published as Les M6thodes ncuvefles de !a MGcanique celeste AIP American
Thin-cap fibroatheroma rupture is associated with a fine interplay of shear and wall stress.
Arteriosclerosis, thrombosis, and vascular biology
34
10
2224-31
2014
10.1161/ATVBAHA.114.303426
In this review, we summarized the effect of mechanical factors (shear and wall stress) on thin-cap fibroatheroma formation and rupture. To make this review understandable for a biology-oriented audience, we start with detailed definitions of relevant mechanical metrics. We then describe how biomechanics has supported histopathologic efforts to understand the basis of plaque rupture. In addition to plaque rupture, biomechanics also contributes toward the progression of thin-cap fibroatheroma through a multitude of reported mechanobiological mechanisms. We thus propose a new mechanism whereby both shear stress and wall stress interact to create thin-cap fibroatheromas. Specifically, when regions of certain blood flow and wall mechanical stimuli coincide, they synergistically create inflammation within the cellular environment that can lead to thin-cap fibroatheroma rupture. A consequence of this postulate is that local shear stress is not sufficient to cause rupture, but it must coincide with regions of local tissue stiffening and stress concentrations that can occur during plaque progression. Because such changes to the wall mechanics occur over a micrometer scale, high spatial resolution imaging techniques will be necessary to evaluate this hypothesis and ultimately predict plaque rupture in a clinical environment.
Animals; Arteries; Arteries: metabolism; Arteries: pathology; Arteries: physiopathology; Atherosclerosis; Atherosclerosis: complications; Atherosclerosis: metabolism; Atherosclerosis: pathology; Atherosclerosis: physiopathology; Atherosclerotic; Biomechanical Phenomena; Cellular; Disease Progression; Fibrosis; Humans; Mechanical; Mechanotransduction, Cellular; Plaque, Atherosclerotic; Regional Blood Flow; Risk Factors; Rupture, Spontaneous; Spontaneous; Stress, Mechanical
Crystal structures of TiO2 thin coatings prepared from the alkoxide solution via the dip-coating technique affecting the photocatalytic decomposition of aqueous acetic acid
Journal of Materials Science
29
22
5911-5915
1994
10.1007/BF00366875
TiO2 coatings with different crystal structures were prepared from alkoxide solutions via the dip-coating technique. The physical properties, except the crystal struture, were adjusted to distinguish the effect of crystal structure on their photocatalytic property. The results of photocatalytic measurements using TiO2 coatings with different crystal structures showed that the decomposition of aqueous acetic acid was enhanced by the content of anatase phase
Analysis of cracked laminates: a variational approach
Mechanics of Materials
4
2
121-136
1985
10.1016/0167-6636(85)90011-0
Cross-ply ([0°m, 90°n]s) laminates which contain distributions of intralaminar cracks within the 90° ply are analyzed by variational methods for tensile and for shear membrane loading. Admissible stress systems which satisfy equilibrium and all boundary and interface conditions are constructed and the principle of minimum complementary energy is employed to find an optimal approximation. This yields approximate stress fields and rigorous lower bounds for stiffnesses. The analysis allows for crack interaction and statistical distribution of cracks. Results for Young's modulus are in perfect agreement with experimental data. Young's modulus and shear modulus results approach definite limits for large crack density. Typical stress variations are presented for glass/epoxy and for graphite/epoxy laminates and their implications for the progressive damage and failure process of laminates are discussed.
Geometrical aspects of a generalized statistical mechanics
Physica A: Statistical Mechanics and its Applications
373
273-282
2007
10.1016/j.physa.2006.05.024
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics models. The thermodynamics of the system is the focus of attention in this geometric context. ?? 2006 Elsevier B.V. All rights reserved.
Generalized q-divergence; Information geometry; Nonextensive statistical mechanics
Boundary-layer separation control on a thin airfoil using local suction
Journal of Fluid Mechanics
535
March 2004
415-443
2005
10.1017/S002211200500501X
High-speed incompressible flow past a thin airfoil in a uniform stream is considered. When the angle of attack for a solid airfoil exceeds a certain critical value, the boundary layer in the leading-edge region separates in a process known to lead to dynamic stall. Here suction near the leading edge is studied as a means of controlling separation and thereby inhibiting dynamic stall. First, steady boundary-layer solutions are obtained to determine the nature of suction distributions required to suppress separation on an airfoil at an angle of attack beyond the critical value (for a solid wall). Unsteady boundary-layer solutions are then obtained, using a combination of Eulerian and Lagrangian techniques, for an airfoil at an angle of attack exceeding the critical value; the effects of various parameters associated with the finite-length suction slot, its location and the suction strength are considered. Major modifications of the Lagrangian numerical method are required to account for suction at the wall. It is determined that substantial delays in separation can be achieved even when the suction is weak, provided that the suction is initiated at an early stage.
Hamiltonian time-dependent mechanics
Journal of Mathematical Physics
39
5
2714
1998
10.1063/1.532416
The usual formulation of time-dependent mechanics implies a given splitting Y=RxM of an event space Y. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The goal is the frame-covariant formulation of time-dependent mechanics on a bundle Y >R, whose fibration Y >M is not fixed. Its phase space is the vertical cotangent bundle VY, provided with the canonical 3-form and the corresponding canonical Poisson structure. An event space of relativistic mechanics is a manifold Z whose fibration Z >R is not fixed.
Quantum mechanics for nanostructures
MRS Bulletin
37
05
531
2012
10.1557/mrs.2012.113
The properties of new nanoscale materials, their fabrication and applica- tions, as well as the operational principles of nanodevices and systems, are solely determined by quantum-mechanical laws and principles. This textbook introduces engineers to quantum mechanics and the world of nanostructures, enabling them to apply the theories to numerous nanostructure problems. The book covers the fundamentals of quantum mechanics, including uncer- tainty relations, the Schr¨ odinger equation, perturbation theory, and tunneling. These are then applied to a quantum dot, the smallest artificial atom, and com- pared with the case of hydrogen, the smallest atom in nature. Nanoscale objects with higher dimensionality, such as quantum wires and quantum wells, are introduced, as well as nanoscale materials and nanodevices. Numerous exam- ples throughout the text help students to understand the material. VLADIMIR V.MITIN is SUNY Distinguished Professor at the Department of Electrical Engineering and Adjunct Professor of Physics at the University at Buffalo, The State University of New York. He is the author of eight text- books and monographs and more than 490 professional publications and presentations.
Damage Detection in Thin Composite Laminates Using Piezoelectric Phased Sensor Arrays and Guided Lamb Wavew Interrogation
Journal of Intelligent Material Systems and Structures
21
994-1010
2010
10.1177/1045389X10372003
Damage detection in composite laminated panels using Lamb waves is demon- strated with an innovative use of a sensor array and processing algorithm. Two models were developed to characterize the Lamb wave propagation properties of orthotropic panels. Predictions of the dispersion relations were made for a fiber-reinforced composite laminate. Experiments were conducted to empirically characterize the wave propagation behavior in a manufactured laminate. Piezoelectric patches were used as sensors and actuators in the exper- iments. Comparisons were made between analytical predictions and experimental results, which demonstrate that the higher order model captured essential wave propagation behavior at frequencies of interest. Sensor arrays and associated processing were used for wavenumber decomposition and filtering of the Lamb wave modes. Composite laminates were manufac- tured with an embedded defect to simulate inter-ply delamination. Experiments were con- ducted to detect the presence of delamination damage in a composite laminate.
piezoelectric; sensor; structural health monitoring
Adhesion of a Rigid Punch to a Thin Elastic Layer
The Journal of Adhesion
48
1-4
75-84
1995
10.1080/00218469508028155
Adhesion between a rigid flat cylindrical punch and an elastic layer has been investigated. FE analysis was employed to determine the layer stiffness. Linear elastic fracture mechanics was then used to determine the energy release rate, G(a), per unit of bonded area for a circular debond propagating inwards from the edge of the punch. The calculations showed a strong effect of Poisson's ratio for thin layers, small departures from complete incompressibility causing large reductions in stiffness and hence in detachment force. Experiments were performed with an aluminum punch adhered to a rubber layer using a rubber-based adhesive. The ratio of punch radius to layer thickness was varied over the range 0.07 to 3.3. Detachment forces were measured and compared with calculated values. Reasonable agreement was obtained for thick layers but not for thin ones, possibly because of a change in the mode of failure.
Modelling Fabric Mechanics
Journal of the Textile Institute
92
3
53-69
2001
10.1080/00405000108659614
Mechanics of textile fabrics by modelling of equilibrium of forces is difficult to apply broadly in practical applications. An alternative, which offers more promise for industrial utility in computer-aided design, is the energy-based approach described by Hearle and Shanahan (1978 a,b). The paper reviews the basic principles and considers the ways of introducing appropriate energy terms to cover yarn extension, yarn bending, yarn flattening, and friction at crossovers. The main discussion is given for the elastic response of simple, plain-weave fabrics, based on several different geometric models, but the ways to deal with other fabrics and conditions are also suggested. The paper provides a protocol for advancing the subject from academic research to commercial use. © Textile Institute.
Nonequilibrium statistical mechanics
Book
54
viii+222
2001
This is a presentation of the main ideas and methods of modern nonequilibrium statistical mechanics. It is the perfect introduction for anyone in chemistry or physics who needs an update or background in this time-dependent field. Topics covered include fluctuation-dissipation theorem; linear response theory; time correlation functions, and projection operators. Theoretical models are illustrated by real-world examples and numerous applications such as chemical reaction rates and spectral line shapes are covered. The mathematical treatments are detailed and easily understandable and the appendices include useful mathematical methods like the Laplace transforms, Gaussian random variables and phenomenological transport equations.
A mechanistic model for fatigue damage evolution in composite laminates
Mechanics of Materials
29
2
123-140
1998
10.1016/S0167-6636(98)00007-6
We propose a mechanistic model which is capable of describing the evolution of transverse cracking in cross ply laminates subjected to cyclic tension in the longitudinal direction. The key feature of the model is that it incorporates delamination associated with transverse cracks in a manner that induces further formation of transverse cracks as delamination grows in fatigue. A variational approach is taken to estimate the stresses in the region between transverse cracks, and these are found to be accurate away from the crack planes when comparison is made with finite element computations. The evolution of transverse crack density and the associated overall elastic moduli changes predicted by the model are in agreement with experimental results. (C) 1998 Elsevier Science Ltd. All rights reserved.
cross ply laminates; delamination; TRANSVERSE CRACKING; transverse cracks; VARIATIONAL APPROACH
Boundary-Layer Effects in Composite Laminates : Part 1- Free-Edge Stress Singularities
Journal of Applied Mechanics
49
September
541-548
1982
10.1115/1.3162514
A study of boundary-layer stress singularities in multilayered fiber-reinforced composite laminates is presented. Based on Lekhnitskii's stress potentials and the theory of anisotropic elasticity, formulation of the problem leads to a pair of coupled governing partial differential equations (P.D.E.'s). An eigenfunction expansion method is developed to obtain the homogeneous solution for the governing P.D.E. 's. The order or strength of boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution for the problem. Numerical examples of the singular strength (or singular eigenvalues) of boundary-layer stresses are given for angle-ply and cross-ply composites as well as the cases of more general composite lamination
Shape Recovery after Nanoindentation of NiTi Thin Films
2003 SEM Annual Conference & Exposition on Experimental and Applied Mechanics
1-6
2003
The shape memory effect is a visually striking phenomenon, whereby a material is able to recover its initial shape after significant deformation by heating past the material’s transformation temperature. In the case of shape memory alloys, the effect arises from a thermally-induced atomic-level structural change. This solid-state phase change is known as a martensitic transformation and occurs in a wide variety of metal alloys, including NiTi. In our research, a series of nanoindentations were made on NiTi shape memory alloy thin films at mN load levels with a Berkovich indenter. Mapping of the indentation topography using Atomic Force Microscopy (AFM) revealed direct evidence that the thermally-induced martensitic transformation of these films allows for partial indent recovery on the nanoscale. Indeed, recovery is nearly complete at indentation depths of less than 100 nm.
The Concepts of Quantum Mechanics
Most
10
1914
1-6
1985
10.1021/cr60035a006
This books presents a competent and interesting pedagogic account of certain topics in functional analysis and their applications to a selection of problems in quantum mechanics, quantum field theory and quantum statistical mechanics. The typography and page layouts are, as one expects in a Springer publication, superb. However, one must add that the title is misleading. Quantum mechanics uses practically every branch of mathematics and has significantly influenced the development of each branch used. Such branches which deserve special mention include group theory, ring theory, lattice theory, topology, topological dynamics, manifold theory, tensor analysis and probability theory and they are all more or less ignored in this book as are certain concepts in functional analysis such as rigged Hilbert space, distribution theory and the Dirac formalism. These lists are by no means exhaustive.
S HEAR LAG OF THIN WALLED CURVED BOX GIRDER BRIDGES
Journal of Engineering Mechanics
126
October
1111-1114
2000
This note investigates the influence of shear lag for thin-walled curved box girders, including longitudinal warping. The longitudinal warping displacement functions of the flange slabs are approximated by a cubic parabolic curve instead of a quadratic curve of Reissner’s method. On the basis of the thin-walled curved bar theory and the potential variational principle, the equations of equilibrium considering the shear lag, bending, and torsion (St. Venant and warping) for a thin-walled curved box girder are established. The closed-form solutions of the equations are derived, and Vlasov’s equation is further developed. The obtained formulas are applied to calculate the shear lag effects for curved box girder bridges. Numerical examples are presented to verify the accuracy and applicability of the present method.
11.5: Electron transport and emission from thin film semiconductors
2010 IEEE International Vacuum Electronics Conference (IVEC)
209-210
2010
10.1109/IVELEC.2010.5503530
Electron transport through thin film semiconductors is common to both the development of semiconductor photocathodes and to secondary emission electron sources. We discuss the modeling and numerical simulation of such transport in the presence of scattering and loss mechanisms, to enable predictive estimations of energy distributions, time response, and the nature of the distribution of the emitted electrons.
Cathodes; Diamond Amplifier; Electron beams; Electron emission; electron transport; electron transport theory; energy distributions; Free Electron Laser; Free electron lasers; Monte Carlo methods; numerical analysis; numerical simulation; Particle scattering; photoemission; Photonic band gap; Physics; Quantum mechanics; secondary electron emission; secondary emission; secondary emission electron sources; Semiconductor thin films; Surface emitting lasers; thin film semiconductors
Mathematical model I. Electron and quantum mechanics
AIP Advances
1
12105
2011
10.1063/1.3559460
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we havemade an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Classical mechanics; Electrodynamics; Quantum mechanics
Thin film fine line work of adhesion by microwedge indentation
Materials Research Society Symposium - Proceedings
356
Pittsburgh, PA, United States
693-698
1995
The mechanics for plane strain geometry are presented for thin film fine lines by considering the case of microwedge indentation of a fine line subject to no residual stress. The analysis is separated into three parts depending on the absence or presence of buckling. During indentation, unbuckled or double-buckled configurations may exist, while single-buckling may occur when the indenter tip is removed. A microwedge tip was employed in the indentation testing of unstressed rf-sputtered tungsten fine lines to demonstrate some of the analysis.
Adhesion; Buckling; Cracks; Interfaces (materials); Mechanics; Microwedge indentation; Residual stresses; Sputtering; Strain; Thin film fine line; Thin films; Tungsten
Compression and post-buckling damage growth and collapse analysis of flat composite stiffened panels
Composites Science and Technology
68
15-16
3150-3160
2008
10.1016/j.compscitech.2008.07.017
Experimental and numerical investigations were conducted into the damage growth and collapse behaviour of composite blade-stiffened structures. Four panel types were tested, consisting of two secondary-bonded skin-stiffener designs in both undamaged and pre-damaged configurations. The pre-damaged configurations were manufactured by replacing the skin-stiffener adhesive with a centrally located, full-width Teflon strip. All panels were loaded in compression to collapse, which was characterised by complex post-buckling deformation patterns and ply damage, particularly in the stiffener. For the pre-damaged panels, significant crack growth was seen in the skin-stiffener interface prior to collapse, which caused a reduction in load-carrying capacity. In the numerical analysis of the undamaged panels, collapse was predicted using a ply failure degradation model, and a global-local approach that monitored a strength-based criterion in the skin-stiffener interface. The pre-damaged models were analysed with ply degradation and a method for capturing interlaminar crack growth based on multi-point constraints controlled using the Virtual Crack Closure Technique. The numerical approach gave close correlation with experimental results, and allowed for an in-depth analysis of the damage growth and failure mechanisms contributing to panel collapse. The successful prediction of collapse under the combination of deep post-buckling deformations and several composite damage mechanisms has application for the next generation of composite aircraft designs. © 2008 Elsevier Ltd. All rights reserved.
B. Debonding; C. Buckling; C. Damage mechanics; C. Delamination; C. Finite element analysis
Bohmian Mechanics Revisited
Foundations of Physics
28
34
1998
10.1007/978-3-540-89344-8
We consider the problem of whether there are deterministic theories describing the evolution of an individual physical system in terms of the definite trajectories of its constituent particles and which stay in the same relation to Quantum Mechanics as Bohmian Mechanics but which differ from the latter for what concerns the trajectories followed by the particles. Obviously, one has to impose on the hypothetical alternative theory precise physical requirements. We analyse various such constraints and we show step by step how to meet them. This way of attacking the problem allows to recall and focus on some relevant features of Bohm's theory. One of the central requirements we impose on the models we are going to analyse has to do with their transformation properties under the transformations of the extended Galilei group. In a context like the one we are interested in one can put forward various requests that we refer to as physical and genuine covariance and invariance. Other fundamental requests are that the theory allows the description of isolated physical systems as well as that it leads to a solution (in the same sense as Bohmian Mechanics) of the measurement problem. We show that there are infinitely many inequivalent (from the point of view of the trajectories) bohmian-like theories reproducing the predictions of Quantum Mechanics.
Generalized constrained finite strip method for thin-walled members with arbitrary cross-section: Primary modes
Thin-Walled Structures
84
150-169
2014
10.1016/j.tws.2014.06.001
In this paper the generalization of the constrained finite strip method (cFSM) is discussed. cFSM is a special version of the semi-analytical finite strip method (FSM), where carefully defined constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanics, e.g., to allow buckling only in flexural, lateral–torsional, or a distortional mode. In the original cFSM only open cross-section members are handled, here the method is extended to cover any flat-walled member, including those with closed cross-sections or cross-sections with open and closed parts. Moreover, in the original cFSM only 4 deformation classes are defined, here the deformation field is decomposed into additional, mechanically meaningful, sub-fields. Formal mechanical criteria are given for the deformation classes, and implementation of the criteria regardless of cross-section topology is illustrated. In this paper, the primary deformation classes are presented in detail. Primary deformations are associated with minimal cross-section discretization, i.e. nodal lines located at folds and ends only. This paper is accompanied by a companion, where secondary modes and additional practical aspects in the selection of base vectors for the deformation classes are discussed. With the proposed modifications the powerful cFSM capabilities of buckling mode decomposition and identification are extended to essentially arbitrary thin-walled cross-sections.
Arbitrary cross-section; Constrained finite strip method
Secret and joy of configurational mechanics: From foundations in continuum mechanics to applications in computational mechanics
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
89
8
614-630
2009
10.1002/zamm.200800132
Over the recent years configurational mechanics has developed into a very active and successful topic both in continuum mechanics as well as in computational mechanics. On the continuum mechanics side the basic idea is to consider energy variations that go along with changes of the material configuration. Configurational forces are then energetically dual to these configurational changes. Configurational forces take the interpretation as being the driving forces in the kinetics of defects; like e.g., cracks, inclusions, phase boundaries, dislocations and the like. On the computational side it turns out that a discretisation scheme brings in artificial, discrete configurational forces that indicate in a certain sense the quality, e.g., of a finite-element mesh. This information can then be used to optimize the nodal material positions. Surprisingly, even driven by energetical arguments, it turns out that a finite element mesh optimized with respect to discrete configurational forces also renders superior results in terms of classical error measures. The manuscript will span the field from the underlying theoretical foundations over the algorithmic challenges to various computational applications.
Computational mechanics; Configurational mechanics
"Material" mechanics of materials
Theoretical and Applied Mechanics
27
1-12
2002
10.2298/TAM0227001G
The paper outlines recent developments and prospects in the application of the continuum mechanics expressed intrinsically on the material manifold itself. This includes applications to materially inhomogeneous materials, physical effects which, in this vision, manifest themselves as quasi-inhomogeneities, and the notion of thermodynamical driving force of the dissipative progress of sin- gular point sets on the material manifold with special emphasis on fracture, shock waves and phase-transition fronts.
Lattice Boltzmann equation for quantum mechanics
Physica D: Nonlinear Phenomena
69
3-4
327-332
1993
10.1016/0167-2789(93)90096-J
It is shown that the lattice Boltzmnn equation for hydrodynamics can be extended in such a way as to describe non-relativistic quantum mechanics.
Experimental study of electroosmotic flow in thin slit channels
Journal of Applied Mechanics and Technical Physics
50
5
805-808
2009
10.1007/s10808-009-0109-8
This paper gives the results of experimental studies of flow of two immiscible liquids in a thin slit channel under the action of an external electric field. A comparison is made of numerical calculation results and experimental data on the time dependence of the position of the interface. The employed model is shown to provide an adequate qualitative description of electroosmotic flow in thin slit channels of width not less than 20 μm. © MAIK/Nauka 2009.
Electric double layer; Electric fields; Electrochemistry; Electroosmosis; Electroosmotic flow; Experimental data; Experimental studies; External electric field; Immiscible liquids; Numerical calculation; Thin slit channels; Time dependence
Fracture Mechanics Tests for Measuring the Adhesion of Magnetron Sputtered TiN Coatings
Interface
14
207-211
1996
10.1163/156856193X00466
Experiments for determining the adhesion strength between TiN coatings and high-speed steel substrates have been performed using the three-point bend test and a modified shear test. Sample preparation is easier for the modified shear test; however, the interpretation of the results is more complicated. The three-point bend test yields fracture mechanics data such as the interface fracture energy Gc and the fracture toughness Kc. The most critical problem is to prepare a sample with a notch which initiates crack propagation at the coating/substrate interface. Various sublayers with weak adhesion have been tested as a notch, such as carbon, oxides, and metals, as well as thin mechanical slits. The results obtained so far demonstrate that the adhesion strength depends on the substrate cleaning treatment and on the contamination of the sputter gas with oxygen. Typical values of the fracture toughness Kc for non-sputter-cleaned substrates are in the range of 1-3 MN m 3/2. The advantages and disadvantages of the various methods used are analysed and critically discussed with respect to sample preparation, reproducibility, and data evaluation.
Viscoelastic modelling of regular cross-ply polymer-matrix laminates
High Performance Structures and Materials Iv
97
13-22
2008
Recent rheological experiments performed on cross-ply laminates have pointed out that polymer-matrix laminates may exhibit valuable creep shear strains. So far, a problem of viscoelastic modelling has been developed only for UD xFRP composites, i.e. thermosets reinforced with long fibres aligned unidirectionally. In the modelling, the most advanced rheological model of thermosets, denoted with the symbol HWKK/H, has been employed. This model is capable of modelling short-, moderate- and long-term rheological processes. In this study, the analytical approach developed for UD xFRP composites has been extended on a regular cross-ply polymer-matrix laminate, denoted with the symbol CP xFRP, of the [0/90](ns), n >= 4 plies' configuration. The plies, made of a specified woven fabric, are repeatable with respect to their thickness and microstructure. On the micromechanics level, each ply is modelled as a linearly viscoelastic monotropic continuum with the monotropy axis coinciding the direction of fibres' alignment. A regular CP xFRP laminate is modelled as a homogeneous orthotropic continuum. Standard and inverse viscoelasticity equations of an orthotropic solid body modelling a homogenized CP xFRP laminate are formulated and analytic algorithms for determination of elasticity and viscoelasticity constants are developed. The calculation algorithms have been computerized and used to calculate the viscoelasticity coefficients of the specified CP CFRP laminate.
cross-ply polymer-matrix laminates; elastic-viscoelastic analogy principle; inverse constitutive equations; linear viscoelasticity; long-term creep coefficients; long-term relaxation coefficients; standard constitutive equations
Application of an automatic hp adaptive Finite Element Method for thin-walled structures
Computer Methods in Applied Mechanics and Engineering
198
21-26
1967-1984
2009
10.1016/j.cma.2008.12.041
The paper investigates the possibility of solving beam and thin-walled structures with an automatic hp-adaptive Finite Element Method for three-dimensional linear elasticity. This technique generates sequences of meshes with nonuniform distribution of element sizes h and their spectral orders p to minimize the interpolation error for the hypothetical exact solution with constant number of degrees-of-freedom. The intent of using hp method for beam and thin-walled structures is that it should automatically create FE meshes with adequate distribution of the approximation orders to prevent the numerical locking phenomenon and to provide accurate solutions. The method also reduces the human work spent on building the numerical model to generation of the description of the geometry. We discuss energy based and goal-oriented versions of hp-adaptivity. The paper presents a broad spectrum of examples of engineering applications.
finite element method; goal-oriented; hp adaptive; shells; thin-walled
Single ply roofing: Introduction to a new sustainability standard for the roofing industry
Journal of ASTM International
1538 STP
9
42-49
2011
10.1520/JAI103741
This standard development began with a partnership between members of the roofing industry and NSF International to facilitate the thorough communication of information that is verifiable and accurate about the environmental and social impacts associated with the production and use of single ply roofing membranes. This industry among other product manufacturing industries is responding to the global pressures of sustainable practices. Attributes in this standard were developed to address this growing need. Key elements of the standard include product design, life cycle assessment considerations, minimization of chemicals of concern, product manufacturing, energy, water, waste, durability, corporate governance (social responsibility), and innovation. Sustainability related information may influence a manufacturer's decisions about supply chain modifications, product content changes, manufacturing adjustments, performance improvements, end-of-life options, and corporate governance with the goal of producing more sustainable products. NSF International is an accredited standards developer with American National Standards Institute (ANSI). The consensus body for this standard, called a joint committee, is balanced among the following interest categories: industry, public health/regulatory, and user. Work has been ongoing since the first stakeholder meeting in May 2009. Various task groups and experts have been participating in meetings on a monthly basis. This paper will introduce the Single Ply Roofing Membrane Sustainability Standard (NSF 347) along with background on its development. Additionally, other standards that may be applicable to single ply roofing membranes, certification, and conformance will be reviewed including third party certification versus conformity assessment. The anticipated voluntary consensus based standard should be available late 2011. Copyright © 1996-2011 ASTM.
American National Standards Institute; Chemicals of concern; Conformity assessment; Construction industry; Corporate governance; Economic and social effects; End-of-life options; Energy conversion; Industrial management; Key elements; Life cycle; Life-cycle assessments; Manufacture; Nsf internationals; Performance improvements; Product design; Product manufacturing; Public health; Roofing; Roofing membranes; Roofs; Single ply; Single-ply roofing membrane; Social impact; Social responsibilities; Standard development; Standardization; Standards; Supply chains; Sustainability; Sustainable development; Sustainable practices; Sustainable products; Task groups; Third party certification
Cavity opto-mechanics
2008 Conference on Quantum Electronics and Laser Science Conference on Lasers and Electro-Optics, CLEO/QELS
1
10-11
2008
10.1109/CLEO.2008.4551967
Cavity enhancement of optical fields is providing a new way to couple light and mechanical motion. Its application to mechanical cooling and amplification, example implementations, and prospects for new science and technology are reviewed.
Tensile Properties of Manila Hemp Fabric Reinforced Cross-Ply "Green" Composites
Zairyo/Journal of the Society of Materials Science, Japan
52
8
916-921
2003
This paper deals with the tensile properties of Manila hemp fabric reinforced cross-ply "green" composites. The composites were made from woven Manila hemp fibers as the reinforcement and starch-based emulsion-type biodegradable polymer as the matrix. Experimental results showed that their flexural strength increased with increasing the fiber content. However, the tensile strength increased with the fiber content until nearly 50mass% and leveled off thereafter. We found from the result of tensile tests that maximum tensile force of 0° ply sheets decreased with increasing the fiber content. This dependence on the fiber content is due to the decrease in the fiber strength caused by fiber's damages introduced during hot-pressing. In order to avoid the damage of fibers aligned in loading direction, fiber sheets were produced by using hemp fibers for warp and cotton threads for weft. As a result of using the cotton weft, the tensile strength of cross-ply "green" composites increased from 153MPa to 188MPa.
Bending strength; Biodegradable composite material; Biodegradable plastics; Biodegradation; Cotton; Cotton thread; Cross-ply; Fiber reinforced materials; Manila hemp fiber; Plastics; Reinforcement; Tensile testing
POLOXAMER-COATED 3-PLY-WALLED MICROCAPSULES FOR CONTROLLED DELIVERY OF DICLOFENAC SODIUM
JOURNAL OF MICROENCAPSULATION
12
1
13-22
1995
10.3109/02652049509051123
The three-ply-walled-based system for controlled delivery of diclofenac\nwas developed. The preparation of three-ply-walled microcapsules is\nessentially based on the technique of multiple-emulsion formation\npolymer at the interface followed by rigidization of the wall on\nevaporation of solvent. The protective colloids with surface-active\nproperties were selected for the present study, viz. acacia gelatin,\npolyvinyl alcohol and sodium alginate. Ethyl cellulose was taken as\nhydrophobic polymer. The acacia/ethylcellulose/acacia-based\nthree-ply-walled microcapsule system was selected for further studies.\nThe three-ply-walled microcapsule were subsequently coated with\npoloxamer 188. The non-ionic hydrophilic surfactant coating retards\nuptake into the reticuloendothelial system. The coated and uncoated\nmicrocapsules were characterized for in vitro and in vivo performance.\nThe microcapsules were noted to provide sustained release of the\ncontained diclofenac. The plasma level observed indicated that poloxamer\ncoating results in prolonged release of the drug. Organ distribution\ndemonstrated a different distribution pattern when compared with\nuncoated microcapsules.
POLOXAMER; DICLOFENAC; MICROCAPSULE; ACACIA; ETHYL
Superconformal mechanics
Journal of Physics A: Mathematical and Theoretical
45
17
173001
2012
10.1088/1751-8113/45/17/173001
We survey the salient features and problems of conformal and superconformal mechanics and portray some of its developments over the past decade. Both classical and quantum issues of single- and multiparticle systems are covered.
Modelling cochlear mechanics.
BioMed research international
2014
150637
2014
10.1155/2014/150637
The cochlea plays a crucial role in mammal hearing. The basic function of the cochlea is to map sounds of different frequencies onto corresponding characteristic positions on the basilar membrane (BM). Sounds enter the fluid-filled cochlea and cause deflection of the BM due to pressure differences between the cochlear fluid chambers. These deflections travel along the cochlea, increasing in amplitude, until a frequency-dependent characteristic position and then decay away rapidly. The hair cells can detect these deflections and encode them as neural signals. Modelling the mechanics of the cochlea is of help in interpreting experimental observations and also can provide predictions of the results of experiments that cannot currently be performed due to technical limitations. This paper focuses on reviewing the numerical modelling of the mechanical and electrical processes in the cochlea, which include fluid coupling, micromechanics, the cochlear amplifier, nonlinearity, and electrical coupling.
Auditory; Auditory: physiology; Basilar Membrane; Basilar Membrane: physiology; Biological; Biomechanical Phenomena; Biomechanical Phenomena: physiology; Hair Cells, Auditory; Hair Cells, Auditory: physiology; Hearing; Hearing: physiology; Humans; Models, Biological
A solid mechanics approach to surface relief formation in photosensitive hybrid sol-gel materials
Applied Physics a-Materials Science & Processing
78
3
407-409
2004
DOI 10.1007/s00339-002-1953-z
Surface corrugation has been photo-induced in a single-step process in hybrid sol-gel thin films. A model based on elastic deformation under photo-induced stress is developed to explain relief formation in this material. Computation is carried out with finite-element software. Theoretical and experimental values of relief amplitude variation with film thickness and grating period agree for small deformations. Mass transfer from illuminated to non-illuminated areas has to be associated with the elastic model to account for surface corrugation in the case of large photo-induced deformation. A comparison with a fluid mechanics model is presented.
films; gratings
Self-organization of rotaxane thin films into spatially correlated nanostructures: morphological and structural aspects
Journal of the American Chemical Society
128
2
526-32
2006
10.1021/ja054886o
The self-organization of rotaxane thin films into spatially correlated nanostructures is shown to occur upon a thermal stimulus. The mechanism of formation of nanostructures and their organization has been investigated using atomic force microscopy, bright field transmission electron microscopy, selected area electron diffraction, and molecular mechanics simulations. The evolution of the nanostructures follows a complex pathway, where a rotaxane thin film first dewets from the substrate to form nanosized droplets. Droplets coalesce by ripening, generating spatially correlated motifs. In a later stage, the larger droplets change shape, nucleate, and coalesce to yield crystallites that grow into larger crystals by incorporating the surrounding droplets. The results show the following: (i) the nanostructures represent a metastable state of a crystallization process; (ii) spatial correlations emerge during ripening, but they are destroyed as stable nuclei are formed and crystallization proceeds to completion; iii) crystallization, either on graphite or amorphous carbon films, leads to a precise basal plane, viz. (010), which has minimum surface energy. The inherent degrees of freedom permitted in the rotaxane architecture favors the re-organization and nucleation of the film in the solid state. Low-energy trajectories leading to crystallites with stable surfaces and minimum energy contact plane are found to occur via concerted, small amplitude, internal motions without disruption of packing and intermolecular contacts.
Ordered growth of substituted phthalocyanine thin films: Hexadecafluorophthalocyaninatozinc on alkali halide (100) and microstructured Si surfaces
Chemistry of Materials
12
4
989-995
2000
10.1021/cm9905388
Physical vapor deposition of hexadecafluorophthalocyaninatozinc (F16PcZn) is performed under UHV conditions from monolayer coverages to an average thickness of about 20 nm on the (100) surfaces of NaCl, KCl, and KBr and on quartz glass as well as on microstructured interdigitated electrode arrays on amorphous SiO2. UV?vis absorption spectroscopy indicates stacks of cofacial parallel molecules for thin films on SiO2 and NaCl, whereas a component typical for a head-to-tail arrangement of molecules is detected on KCl and KBr. Atomic force microscopy shows well-defined crystals oriented in a defined azimuth angle relative to the substrate lattice on KCl and KBr, indicating a growth in molecular square lattices parallel to the substrate surface which is confirmed by molecular mechanics and periodic surface potential calculations. Plateaus of molecules predominantly standing upright on the surface are seen for the films on NaCl and SiO2 which is confirmed by the relative intensity of optical absorptions and by the electrical conductivity changes observed during growth on SiO2. The temperature dependence of the electrical conductivity of films on SiO2 yields an increase of the thermal activation energy around 200 °C corresponding to a loss in spectral fine structure as reported earlier [J. Phys. Chem. B 1999, 103, 3078]. A clear correlation is seen between film structure and electrical as well as optical properties of molecular semiconductor thin films.
Pseudotachylytes and earthquake source mechanics
International Geophysics
94
C
87-133
2009
10.1016/S0074-6142(08)00005-3
Destructive earthquakes nucleate at depth (10 to 15 km), therefore monitoring active faults at the Earth's surface, or interpreting seismic waves, yields only limited information on earthquake mechanics. Tectonic pseudotachylytes (solidified friction-induced melts) decorate some exhumed ancient faults and remain, up to now, the only fault rocks recognized as the unambiguous signature of seismic slip. It follows that pseudotachylyte-bearing fault networks might retain a wealth of information on seismic faulting and earthquake mechanics. In this chapter, we will show that in the case of large exposures of pseudotachylyte-bearing faults, as the glacier-polished outcrops in the Adamello massif (Southern Alps, Italy), we might constrain several earthquake source parameters by linking field studies with microstructural observations, high-velocity rock friction experiments, modeling of the shear heating and melt flow, and dynamic rupture models. In particular, it is possible to estimate the rupture directivity and the fault dynamic shear resistance. We conclude that the structural analysis of exhumed pseudotachylyte-bearing faults is a powerful tool for the reconstruction of the earthquake source mechanics, complementary to seismological investigations. ?? 2009 by Academic Press, Inc.
Quantum mechanics as an approximation to classical mechanics in Hilbert space
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
36
23
L329
2003
10.1088/0305-4470/36/23/101
Classical mechanics is formulated in complex Hilbert space with the\nintroduction of a commutative product of operators, an antisymmetric\nbracket and a quasidensity operator that is not positive definite.\nThese are analogues of the star product, the Moyal bracket, and the\nWigner function in the phase space formulation of quantum mechanics.\nQuantum mechanics is then viewed as a limiting form of classical\nmechanics, as Planck's constant approaches zero, rather than the\nother way around. The forms of semiquantum approximations to classical\nmechanics, analogous to semiclassical approximations to quantum mechanics,\nare indicated.
Asynchronous variational contact mechanics
Computer Methods in Applied Mechanics and Engineering
200
March
2181-2194
2011
10.1016/j.cma.2011.03.010
An asynchronous, variational method for simulating elastica in complex contact and impact scenarios is developed. Asynchronous variational integrators [1] (AVIs) are extended to handle contact forces by associating different time steps to forces instead of to spatial elements. By discretizing a barrier potential by an infinite sum of nested quadratic potentials, these extended AVIs are used to resolve contact while obeying momentum- and energy-conservation laws. A series of two- and three-dimensional examples illustrate the robustness and good energy behavior of the method. ?? 2011 Elsevier B.V.
Contact; Impact; Variational integrators
Finite element analysis of transverse cracking behaviour in hybrid angle-ply composite laminates
Journal of Reinforced Plastics and Composites
18
15
1428-1448
1999
The authors previously presented a 3D finite element method for calculating strain energy release rate and stiffness reduction in transversely cracked cross-ply hybrid laminates. The procedure is based on the computation of strain energy in the laminates with simulated crack and their incremental extensions for applied strains. In the present paper 3D FE method is further extended to study the crack behaviour in hybrid angle-ply laminates under constant applied strain. Variations of strain energy release rate and stiffness reduction with fibre orientation angle θ of outer GR/E layers for different GR/E-GL/E hybrid angle-ply laminates have been calculated. The effects of different geometrical parameters on the crack extension behaviour in width direction have been studied. Variation of strain energy release rate and stiffness reduction in cracked hybrid angle-ply laminates depend not only on the fibre orientation angle θ of the outer GE/E layers but also on the material properties and number of cracked and uncracked layers in the laminate.
Studies of Nail Connectors Used in Wood Frame Shear Walls with Ply-Bamboo Sheathing Panels
Journal of Materials in Civil Engineering
04014216
2014
10.1061/(ASCE)MT.1943-5533.0001167
AbstractBased on Johansen yield theory (European yield model) and experimental observations, mechanical models and capacity equations for nail connectors used in wood-frame shear walls with cross-prefabricated ply-bamboo sheathing panels were studied. Embedment strength of ply-bamboo panel was obtained in accordance with a British Standards Institution (BSI) standard. Monotonic and cyclic tests of nails applied in timber-bamboo shear walls were performed to validate the capacity equations. The adopted capacity equation based on European yield model meets the test results well, in the average and with a reduced scatter. The theoretical and experimental results obtained from the research suggested a capacity model and equations to predict the bearing capacity of timber-bamboo nail connections, indicating that ply-bamboo panels can be used as sheathings for light-weight timber structures, as well as included in existing timber design code.
Capacity equation; Nail connector; Ply-bamboo sheathing panel; Shear wall
Interlaminar stresses around a hole in symmetric cross-ply laminates under bending/torsion
AIAA journal
31
6
1118-1124
1993
An efficient approximate solution for calculating the complete state of stress around a circular hole in symmetric cross-ply laminates under a set of far-field bending and torsion is presented. This approach is based on the boundary-layer theory in conjunction with Lekhnitskii's solutions for anisotropic plates and the principle of minimum complementary energy. All of the boundary conditions around the hole edge of each ply and traction continuity at the ply interface are exactly satisfied. Numerical examples are compared with the NASTRAN finite element solutions to demonstrate the efficiency and accuracy of the current method.
Bending (deformation); Boundary layer flow; Boundary layers; Elasticity; Finite element method; Free edge effect; Interfaces (materials); Laminar flow; Laminated composites; Laminates; Lekhnitskii's solutions; NASTRAN finite element solutions; Plates (structural components); Software package NASTRAN; Stress analysis; Stresses; Symmetric cross ply laminates; Torsional stress
A coupled theory of damage mechanics and finite strain elasto-plasticity I. Damage and elastic deformations
International Journal of Engineering Science
28
5
421-435
1990
10.1016/0020-7225(90)90007-6
A coupled theory of elasticity and continuum damage mechanics is formulated here. It is assumed that the material undergoes damage with small elastic strains. The hypothesis of elastic energy equivalence is used in order to produce the proposed coupling. The damage variable used represents average material degradation which reflects the various types of damage at the microscale level like nucleation and growth of voids, cavities, micro-cracks and other microscopic defects. The proposed model is numerically implemented using finite elements with an Updated Lagrangian description. It is also shown how the model can be applied to problems of ductile frActare. The problem of crack initiation in a thin plate with a center crack that is subjected to uniaxial tension is analyzed using the proposed model. The theory is extended to coupling of damage and finite strain plasticity in the companion paper. It is shown there how the model can be used to solve problems in elasto-plastic ductile fracture.
Mechanics of crack propagation in delamination wear
Wear
44
1
39-56
1977
10.1016/0043-1648(77)90083-7
Abstract A mathematical model of subsurface crack propagation in sliding contact is developed. It is shown that linear elastic fracture mechanics may be applied to such problems, even for elastoplastic solids. An equation to predict wear rates is derived, which ... \n
Wigner Method in Quantum Statistical Mechanics
Journal of Mathematical Physics
8
5
1097
1967
10.1063/1.1705323
The Wigner method of transforming quantum‐mechanical operators into their phase‐space analogs is reviewed with applications to scattering theory, as well as to descriptions of the equilibrium and dynamical states of many‐particle systems. Inclusion of exchange effects is discussed.
Extension of Stoney's formula to non-uniform temperature distributions in thin film/substrate systems. the case of radial symmetry
Journal of the Mechanics and Physics of Solids
53
11
2483-2500
2005
10.1016/j.jmps.2005.06.003
Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to non-uniform, but axisymmetric temperature distributions, we derive relations between the film stresses and temperature, and between the plate system's curvatures and the temperature. These relations featured a "local" part which involves a direct dependence of the stress or curvature components on the temperature at the same point, and a "non-local" part which reflects the effect of temperature of other points on the location of scrutiny. Most notably, we also derive relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary radial non-uniformities. These relations also feature a "non-local" dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. Finally, it is shown that the interfacial shear tractions between the film and the substrate are proportional to the radial gradients of the first curvature invariant and can also be inferred experimentally. © 2005 Elsevier Ltd. All rights reserved.
Interfacial shears; Non-local effects; Non-uniform film temperatures and stresses; Non-uniform substrate curvatures; Stress-curvature relations
Computational applications of nonextensive statistical mechanics
Journal of Computational and Applied Mathematics
227
1
51-58
2009
10.1016/j.cam.2008.07.030
Computational applications of the nonextensive entropy Sq and nonextensive statistical mechanics, a current generalization of the Boltzmann-Gibbs (BG) theory, are briefly reviewed. The corresponding bibliography is provided as well. ?? 2008 Elsevier B.V. All rights reserved.
Entropy; Nonextensive statistical mechanics; Nonlinear dynamical systems; Numerical applications
Interpretations of Quantum Mechanics and the measurement problem
Arxiv Preprints
24
2010
10.1166/asl.2010.1133
We present a panoramic view on various attempts to "solve" the problems of quantum measurement and macro-objectivation, i.e. of the transition from a probabilistic quantum mechanic microscopic world to a deterministic classical macroscopic world.
foundations of quantum mechanics; macro-objectivation; quantum coherence
Molecular mechanics: Illustrations of its application
Journal of Chemical Education
59
4
275
1982
10.1021/ed059p275
Applying molecular mechanics to n-butane and cyclohexane.\nApplying molecular mechanics to n-butane and cyclohexane.
Fluid mechanics for sailing vessel design
Annual Review of Fluid Mechanics
30
613-653
1998
10.1146/annurev.fluid.30.1.613
The design of sailing vessels is an ancient art that places an ever-increasing reliance on modem engineering sciences. Fluid mechanics shares the forefront of this reliance along with structural mechanics. This review focuses on the application of fluid mechanics in modem sailing vessel design. It is now common practice to predict sailing performance with what are called velocity prediction computer programs. The validity of the predictions is crucially dependent an accurate modeling of the air and water forces on the vessel. This article reviews existing methods of force modeling that include theory, experimentation, and numerical fluid mechanics and aerodynamics. The accuracy and reliability of the numerical methods are considered on the basis of experimental results and full-scale performance in areas for which the information is available.
hull design; model testing; numerical hydrodynamics; numerical simulation; sailing vessels; ships; velocity prediction
Fracture mechanics and damage mechanics based fatigue lifetime prediction of adhesively bonded joints subjected to variable amplitude fatigue
Engineering Fracture Mechanics
77
7
1073-1090
2010
10.1016/j.engfracmech.2010.03.008
The first part of the paper describes an investigation into the behaviour of adhesively bonded single lap joints (SLJs) subjected to various types of variable amplitude fatigue (VAF) loading. It was seen that a small proportion of fatigue cycles at higher fatigue loads could result in a significant reduction in the fatigue life. Palmgren-Miner's damage sum tended to be less than 1, indicating damage accelerative load interaction effects. In the second part of the paper, fracture mechanics (FM) and damage mechanics (DM) approaches are used to predict the fatigue lifetime for these joints. Two FM based approaches were investigated, which differed with respect to the cycle counting procedure, however, both approaches were found to under-predict the fatigue lifetime for all the types of spectra used. This was attributed to the inability of the FM based models to simulate the crack initiation phase. A DM based approach was then used with a power law relationship between equivalent plastic strain and the damage rate. Good predictions were found for most of the spectra, with a tendency to over-predict the fatigue life. © 2010 Elsevier Ltd.
Bonded joints; Damage mechanics; Fracture mechanics; Variable amplitude fatigue
An energy based damage mechanics approach to modelling impact onto woven composite materials - Part I: Numerical models
Composites Part A: Applied Science and Manufacturing
37
2041-2056
2006
10.1016/j.compositesa.2006.02.023 10.1016/j.compositesa.2005.12.013
The increased use of composite materials in a wide spectrum of industries has led to the development of improved predictive techniques, which can aid in the detailed understanding of the behaviour of a composite component or structure to a range of potentially damaging threats. This paper presents an energy based damage mechanics model for woven carbon composites under high strain loading. This damage mechanics approach introduces five damage variables for in plane damage per ply layer. The damage variables are associated with warp and weft fibre damage in both tensile and compressive failure modes, with an additional damage variable to determine the deterioration of the fibre-matrix interface. The damage variables are directly related to the stiffness degradation within the composite laminae and ultimately within the laminate. The evolution of damage in each mode is controlled via a series of damage-strain equations, thus allowing the total energy dissipated for each damage mode to be set as a material parameter, which is mesh size independent. The damage mechanics approach has been implemented into both the LLNL and LS versions of DYNA3D for plane stress (shell) elements. This encompasses both the standard shell element and the solid-shell formulations available within these codes. In the present paper, validation examples are presented for this damage model. The tensile and the tensile-shear responses are modelled at a coupon level, including relevant strain rate effects and tabs, with the proposed damage model. The results show very good agreement with the available experimental data. Suggestions are also presented for additional non-standard experimental tests to derive all material model parameters directly, rather than an inverse modelling approach in which uniqueness may not be guarantee. This paper also presents an interface modelling technique for explicit FE codes. The formulation is again based on damage mechanics and uses only two constants for each delamination mode; firstly, a stress threshold for damage to commence, and secondly, a critical energy release rate for the particular delamination mode. The model has also been implemented into the LLNL DYNA3D Finite Element (FE) code and the LS-DYNA3D commercial FE code. The interface element modelling technique is applied to a series of common fracture toughness based delamination problems, typically the Double Cantilever Beam (DCB) test, and validated for the dynamic case via a simple analytical plate impact simulation. A subsequent part 11 paper describes the results of simulations using the proposed damage mechanics based models on a series of experimental CRAG plate impact tests. (c) 2006 Elsevier Ltd. All rights reserved.
IMPACT
Quantum mechanics on curved 2D systems with electric and magnetic fields.
Quantum
1-10
2008
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the well-known geometric potential. The electric and magnetic fields are included via the four-potential. We find that there is no coupling between the fields and the surface curvature and that, with a proper choice of the gauge, the surface and transverse dynamics are exactly separable. Finally, the Hamiltonian for the cylinder, sphere and torus are analytically derived.
Quantum mechanics needs no consciousness
Annalen der Physik
523
11
931-938
2011
10.1002/andp.201100078
It has been suggested that consciousness plays an important role in quantum mechanics as it is necessary for the collapse of wave function during the measurement. Furthermore, this idea has spawned a symmetrical proposal: a possibility that quantum mechanics explains the emergence of consciousness in the brain. Here we formulated several predictions that follow from this hypothetical relationship and that can be empirically tested. Some of the experimental results that are already available suggest falsification of the first hypothesis. Thus, the suggested link between human consciousness and collapse of wave function does not seem viable. We discuss the constraints implied by the existing evidence on the role that the human observer may play for quantum mechanics and the role that quantum mechanics may play in the observer's consciousness.
double-slit experiment; measurement problem; observer; wave function collapse
Classical mechanics and quantum mechanics: an elementary approach to the comparison of the two viewpoints
European Journal of Science Education
4
3
241-251
2007
10.1080/0140528820040303
Summaries English The relationship between classical mechanics and quantum mechanics is illustrated by considering how we form the images of moving objects. Brownian motion is an helpful example because it can be analyzed in two related, but different frames which show how the images we construct depend on the conditions of our observation and on some intrinsic characters of the observed objects.
Nonequilibrium statistical mechanics of self-propelled hard rods
Journal of Statistical Mechanics: Theory and Experiment
cond-mat.s
P04019
2010
10.1088/1742-5468/2010/04/P04019
... is a purely dynamical derivation of the familiar Onsager excluded-volume potential for equilibrium hard rods , given in section 4.1. doi:10.1088/1742-5468/2010/04/P04019 4 Page 6. J.Stat.M ech. (2010) P04019 Nonequilibrium statistical mechanics of self - propelled hard rods ...
Mechanical Testing of Thin-Films
International Materials Reviews
39
1
24-45
1994
The extensive use of thin films in the manufacture of microelectronic devices and for protection against wear and corrosion has stimulated considerable interest in their mechanical properties. In this review the most widely used testing methods of free standing films and of films adherent to their substrates are described. Particular attention is given to problems and difficulties experienced with each of the techniques. Results obtained by these methods are discussed and critically examined.
aluminum films; bulge test; deformation-behavior; enhanced elastic-modulus; experiments; films; hardness indentations; hertzian stress-field; indentation; properties microprobe; vacuum-deposited; wear-resistant coatings
Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography
Journal of Fluid Mechanics
509
253-280
2004
10.1017/S0022112004009425
A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver. Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full NavierStokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The NavierStokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography. Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decré & Baret (2003) for the motion of thin water films over finite trenches. The spread of the bow wave, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function. An explanation, in terms of local flow rate, is given for the presence of the downstream surge following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two equal-but-opposite topographies. Results confirm the findings of Decré & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion.
VIBRATIONS OF IMPERFECT LAMINATED PANELS UNDER COMPLEX PRELOADS
International Journal of Non-Linear Mechanics
27
1
51-62
1992
The objective of this paper is to analyze the effect of complex, arbitrary in-plane and out-of-plane loads on the transverse vibrations of thin arbitrarily laminated panels with or without geometric imperfections. The finite-element method is used. A 48 degree-of-freedom thin shell element previously formulated by the senior author is employed. The formulation is general with respect to the boundary conditions, types of imperfections, and number, orientation, and stacking sequence of the lamina. A large radius to thickness ratio is assumed so as to ignore the shear and rotary inertia effects. The results are presented for angle-ply rectangular plates and cross-ply cylindrical panels, with both of these having simply supported edge conditions along all the four edges, and isotropic square plates involving free edges under non-uniform combined loads. The panels are subjected to both axial and shear in-plane stresses. The effects of geometric parameters (aspect ratio, panel curvature, and geometric imperfections) and material properties (varying the number of layers but the same thickness) are examined. The results are presented in the form of frequency-load interaction curves for various geometric parameters. Whenever possible, the present results are compared with those available in the existing literature. A good agreement is observed.
Mechanics of tectonic faulting
Developments in Structural Geology
1
407
1988
This series, under the editorship of Professor H.J. Zwart, will deal with all topics within this field, such as: micro structures, large scale tectonics, experimental structural geology, fabrics, rock mechanics, and modelling in structural geology. The aim is to publish advanced level reference books to provide state-of-the-art reviews of these and other aspects of structural geology. This series will be of value to researchers and professionals in structural geology, rock mechanics, petroleum geology and tectonophysics.This first volume in the series deals with the mechanics of tectonic faulting and its central theme is the formation of faults in the tectonic stress field and the interaction between faults and stresses. The author, Dr. G. Mandl, was one of the top research people with Shell International Research. Part I of the book deals with the mechanical genesis of general fault features, such as fault shape and antithetic, precursory and secondary faulting and elaborates on these more general aspects within the context of specific tectono-mechanical models for extensional faulting and thrusting. Besides critical reviews, Part I contains a number of new or hitherto unpublished results, in particular on model experiments and numerical analyses. The central chapter of Part II presents a full introduction into mechanical theory and rock plasticity - the theory most adequate to tectonic faulting and therefore forming the backbone of the book. Besides presentations of basic concepts of stress and strain, special chapters are devoted to poro-elasticity and fluid flow through porous rocks. This branch of geomechanics requires a multidisciplinary approach that combines continuum mechanics, rock mechanics and structural geology, and applies theoretical, numerical and experimental methods, together with the study of field cases. The book has evolved from such multidisciplinary research and is written for structural geologists, petroleum geologists, engineering geologists, rock engineers and geophysicists whose work demands a similar approach. In addition, the book is intended to encourage mechanical engineers and even mathematicians to enter the fascinating and in parts still untilled fields of tectono-mechanical processes in the Earth's crust. The book is richly illustrated by drawings, photographs and reproductions of seismic records.
Stability problems in fracture mechanics
Journal of Applied Mechanics
64
1
188
1996
10.1115/1.2787290
A leading authority's important new approach to fracture-related mechanic A significant contribution to our understanding of structural stability, Stability Problems in Fracture Mechanics bridges the gap between fracture mechanics and analytical (rational) mechanics, and provides a new perspective on classical problems of fracture mechanics. The author uses his extensive knowledge of stability theory to foster a deeper understanding of fracture, fatigue, and related phenomena within the context of stability, dynamic response, structural safety, and reliability. This unique "unified" approach allows for a new generalization of current concepts of fracture mechanics, including versions developed for various material properties, loading, and environmental conditions. Within the context of these generalizations, the author offers his own mechanical theory of fatigue and related phenomena, based on the synthesis of micro- and macromechanics of fracture Important topics covered include: A brief introduction to elementary fracture mechanics, both linear and nonlinear A generalized approach to fracture mechanics within a framework of analytical mechanics Fracture problems involving bodies with single- and multiple-parameter cracks A theory of fatigue cracks as they relate to problems of stability A theory of dynamic crack propagation, focusing on the instability of steady states and dynamic processesp>Fracture of structures or their load-carrying components is one of the primary causes of potentially dangerous failures in such vital engineering systems as aircraft, ships, bridges, pipelines, and offshore platforms. These failures are, in fact, caused by a loss of stability, or a sudden unexpected transfer from one state to another Stability Problems in Fracture Mechanics seeks to provide a new and more complete understanding of fractures and related phenomena by discussing these occurrences from the standpoint of stability. The author, a world-renowned authority in the field, maintains that this stability-based approach will foster more effective methods of evaluating structural safety and reliability parameters, especially in the presence of cracks and crack-like defects that are often unavoidable in exceptionally large structures The text follows a logical structure built on general principles of fracture mechanics, making it easily accessible for anyone with a basic understanding of calculus and the mechanics of solids. New ideas are clearly illustrated with elementary "beam" examples, and the text is richly illustrated with figures and graphs for easy reference and visual clarity Well-organized and lucidly written, Stability Problems in Fracture Mechanics serves as a valuable resource for structural engineers and analysts responsible for project evaluation and decision making. Within the framework of basic analytical mechanics, Dr. Bolotin presents his own extensively researched mechanical theory of fatigue and related phenomena, presenting both a new approach to classic problems as well as a number of new problems that allow for further development
Nonlinear mechanics of the organ of Corti caused by Deiters cells
IEEE Trans Biomed Eng
45
10
1227-1233
1998
10.1109/10.720200
Though the organ of Corti (OC) has been an object of experimental and theoretical hearing research, open questions remain concerning the processing of acoustic signals by the cochlea where the OC is located. Today there is extensive knowledge about single parts of the organ but a lack of understanding as to how these elements act together. One of the reasons for this is the missing analysis of the mechanics of the OC in three dimensions. In order to fill this gap, we have analyzed a short section (0.06 mm) of the basilar membrane including the OC and evaluated its nonlinear finite element model numerically. The Deiters cells are idealized as thin elastic beams with a comparably low modulus of elasticity of actin. Therefore, they show nonlinear mechanical behavior generating additional frequency components with two-tone stimulation.
Basilar Membrane/cytology/physiology; Biomechanics; Elasticity; Hair Cells, Outer/cytology/*physiology; Human; *Models, Biological; *Nonlinear Dynamics; Stress, Mechanical; Support, Non-U.S. Gov't
The need for delivery room intubation of thin meconium in the low-risk newborn: a clinical trial.
American journal of perinatology
15
12
675-82
1998
10.1055/s-2007-999301
The delivery room management of meconium-stained amniotic fluid remains controversial. We attempted to determine if intubation of the low-risk newborn with thin meconium affects the incidence of respiratory symptoms. Exclusion criterion included moderate or thick meconium, fetal distress, neonatal depression, or prematurity. Eligible infants were randomized to either an intubation (group I) or to a nonintubation group (group II). The outcome was the presence of respiratory symptoms. Patients were studied from May 1994 to June 1997. There were 8967 births during this period: 7.9% (708/8967) were delivered through meconium. Thin meconium was noted in 50.3% (356/708) of all births. 24/356 infants with thin meconium were excluded for medical criterion. One hundred sixty-three infants were medically eligible but could not be randomized due to lack of consent, late arrival of the team, or obstetrician request. These were placed into intubation (group I B) and nonintubation (group II B) groups. Seventy-seven infants were randomized into group I and 92 infants into group II. From the intubation groups I and I B, one required supplemental oxygen and was weaned to room air in 7 hr. From the nonintubation groups II and II B, two infants required oxygen, weaning to room air in 11 and 46 hr. Comparing birth weight, gestational age, sex, mode of delivery and 5-min Apgar, there were no significant differences. However, the intubation groups had significantly lower 1-min Apgar scores. There was no airway morbidity reported in the intubation groups. In the infant with thin meconium and an otherwise low-risk pregnancy, we were unable to demonstrate a difference in respiratory symptoms with intubation and intratracheal suctioning.
Airway Obstruction; Airway Obstruction: physiopathology; Apgar Score; Chi-Square Distribution; Delivery Rooms; Female; Follow-Up Studies; Humans; Infant, Newborn; Intubation, Intratracheal; Meconium Aspiration Syndrome; Meconium Aspiration Syndrome: diagnosis; Meconium Aspiration Syndrome: physiopathology; Meconium Aspiration Syndrome: therapy; Pregnancy; Prospective Studies; Respiratory Mechanics; Respiratory Mechanics: physiology; Severity of Illness Index; Suction; Treatment Outcome
The effect of square cut-outs on the natural frequencies and mode shapes of GRP cross-ply laminates
Composites Science and Technology
47
1
91-101
1993
10.1016/0266-3538(93)90100-U
In this work, effects of square cut-outs on the natural frequencies and mode shapes of cross-ply laminates made of S-glass/epoxy, unidirectional pre-preg tape (Fiberite, Hy-E 9134B) are reported. The first three natural frequencies and mode shapes of cantilever plates (with or without cut-out defects) are investigated both experimentally and numerically. Holographic interferometry and piezo-electric sensing techniques are applied in the tests to record vibration mode shapes and natural frequencies, respectively. A finite element code based on the shear deformation theory of plates is developed to analyze the problem numerically. The test findings and calculated results for the first three natural frequencies agree well. The computed mode shapes and laser holograms resemble each other closely for all cases studied. Effects of the size of cut-outs, the location of defects, and the number of layers removed on the vibration frequencies are reported.
cantilever plates; cut-outs; GRP; holography; piezo-electric sensor; vibration, cross-ply laminates
Higher-order theory based boundary-discontinuous Fourier analysis of simply supported thick cross-ply doubly curved panels
Composite Structures
89
3
448-458
2009
10.1016/j.compstruct.2008.09.007
A boundary-discontinuous double Fourier series based solution methodology is employed to solve the problem of a HSDT-based thick cross-ply doubly curved panel, characterized by a system of five highly coupled linear partial differential equations, with the SS1-type simply supported boundary condition prescribed at all four edges. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. Such discontinuities form a set of measure zero. The present solution methodology is based on the fact that the complementary boundary constraints, which are inequalities, play as important a role as the prescribed (admissible) boundary conditions, which are equalities. The effects of curvature, lamination, material property, thickness as well as their interactions are investigated in detail. Numerical results presented herein illustrate the severity of the effects of those parameters. © 2008 Elsevier Ltd. All rights reserved.
Boundary constraints; Boundary-discontinuous double Fourier series; Cross-ply; Doubly curved panel; Higher-order shear deformation theory (HSDT); Thick composite laminate
Spin Glass: A Bridge between quantum computation and statistical mechanics
Arxiv:1204.2865
1-62
2012
We show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Second, we show another interesting technique to employ quantum nature, quantum annealing. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.
Is Quantum Mechanics Pointless?
Philosophy of Science
70
1447-1457
2003
10.1086/377421
There exist well‐known conundrums, such as measure‐theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space‐time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space‐time.
Fluid mechanics. Jets from a singular surface
Nature
403
6768
377-378
2000
10.1038/35000330
All theories of continuous systems begin with the assumption that there is a separation of scales between the macroscopic variables needed by the theory and the microscopic motions that are ignored. So, the bulk motion of fluid in a teacup stirred by a spoon occurs on a scale that is orders of magnitude larger than the distance between the molecules. When this basic assumption is violated for an instant in time, the consequences can be important and dramatic. On page 401 of this issue, Zeff et al. describe such a violation that occurs when a tub of viscous liquid is shaken up and down. When done just right, a relatively modest shaking can produce extremely thin and violent jets, which spout upwards at velocities of more than 50 metres per second. The fact that violent jets can be produced in this fashion was first observed by Longuet-Higgins, who invented this experiment during a study of bubble cavitation. It has long been known that negative pressure in a liquid can create bubbles whose subsequent collapse can severely damage solid surfaces. The damage is believed to result from the impact of high-speed jets that form as the bubble collapses. Longuet-Higgins's experiment suggested that the creation of such jets from an oscillating free surface is a general phenomenon and that there may be a unique underlying mechanism. Over the years, there has been an emerging consensus in the theoretical community that jet formation in many different situations is coupled to a singular event on a free surface, such as that shown in Fig. 1.
Elastic wave damping in thin-layered saturated porous media
Journal of Applied Mathematics and Mechanics
53
6
721-727
1989
10.1016/0021-8928(89)90076-2
Monochromatic wave propagation in thin-layered saturated porous media is examined by averaging differential equations with rapidly oscillating coefficients. Particular attention is given to the transformation mechanism for the damping of such waves. Existing results in this area /l/ are extended and refined.
An improvement on Donnell's approximation for thin-walled circular cylinders
The Quarterly Journal of Mechanics and Applied Mathematics
12
1
89-99
1959
10.1093/qjmam/12.1.89
Donnell's equation for thin-walled circular cylinders is replaced by where w is a non-dimensional form of the radial displacement and q is the distributed radial loading. This equation retains the essential simplicity of the original but, unlike Donnell's equation, the accuracy does not decrease as the wavelength of circumferential distortion increases.
Criticism of the image analysis of discontinuous thin films
Physica A: Statistical Mechanics and its Applications
157
1
64-67
1989
The requirements for reliability of the parameters deduced from the statistical analysis of the cluster morphology of thin inhomogeneous films near the percolation threshold are first pointed out. Two experimental examples of non-relevance in the treatment of films very close to the percolation threshold are discussed.
Buckling of a thin-layer Couette flow
Journal of Fluid Mechanics
694
5-28
2012
10.1017/jfm.2011.437
We analyse the buckling stability of a thin, viscous sheet when subject to simple shear, providing conditions for the onset of the dominant out-of-plane modes using two models: (i) an asymptotic theory for the dynamics of a viscous plate, and (ii) the full Stokes equations. In either case, the plate is stabilized by a combination of viscous resistance, surface tension and buoyancy relative to an underlying denser fluid. In the limit of vanishing thickness, plates buckle at a shear rate $\gamma / (\ensuremath{\mu} d)$ independent of buoyancy, where $2d$ is the plate thickness, $\gamma $ is the average surface tension between the upper and lower surfaces, and $\ensuremath{\mu} $ is the fluid viscosity. For thicker plates stabilized by an equal surface tension at the upper and lower surfaces, at and above onset, the most unstable mode has moderate wavelength, is stationary in the frame of the centreline, spans the width of the plate with crests and troughs aligned at approximately $4{5}^{\ensuremath{\circ} } $ to the walls, and closely resembles elastic shear modes. The thickest plates that can buckle have an aspect ratio (thickness/width) of approximately 0.6 and are stabilized only by internal viscous resistance. We show that the viscous plate model can only accurately describe the onset of buckling for vanishingly thin plates but provides an excellent description of the most unstable mode above onset. Finally, we show that, by modifying the plate model to incorporate advection and make the model material-frame-invariant, it is possible to extend its predictive power to describe relatively short, travelling waves.
Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture
Journal of Fluid Mechanics
240
259
1992
10.1017/S0022112092000090
Lubrication theory and similarity methods are used to determine the spreading rate of a localized monolayer of insoluble surfactant on the surface of a thin viscous film, in the limit of weak capillarity and weak surface diffusion. If the total mass of surfactant increases as tα, then at early times, when spreading is driven predominantly by Marangoni forces, a planar (axisymmetric) region of surfactant is shown to spread as t(1 + α)/3 (t(1 + α)/4). A shock exists at the leading edge of the monolayer; asymptotic methods are used to show that a wavetrain due to capillary forces exists ahead of the shock at small times, but that after a finite time it is swamped by diffusive effects. For α< 1/2 (α< 1), the diffusive lengthscale at the shock grows faster than the length of the monolayer, ultimately destroying the shock; subsequently, spreading is driven by diffusion, and proceeds as t^1/2. The asymptotic results are shown to be good approximations of numerical solutions of the governing partial differential equations in the appropriate limits. Additional forces are also considered: weak vertical gravity can also destroy the shock in finite time, while effects usually neglected from lubrication theory are important only early in spreading. Experiments have shown that the severe thinning of the film behind the shock can cause it to rupture: the dryout process is modelled by introducing van der Waals forces.
On boundary potential energies in deformational and configurational mechanics
Journal of the Mechanics and Physics of Solids
56
3
772-800
2008
10.1016/j.jmps.2007.07.001
This contribution deals with the implications of boundary potential energies, i.e. in short surface, curve and point potentials, on deformational and configurational mechanics. Within the realm of deformational mechanics the surface/curve potentials are allowed in the most general case to depend on the deformation, the surface/curve deformation gradient and the spatial surface normal/curve tangent and are parametrised in the material placement and the material surface normal/curve tangent. The point potentials depend on the deformation and are parametrised in the material placement. From the configurational mechanics perspective the roles of fields and parametrisations are reversed. By considering variational arguments based on the kinematics of deforming surfaces/curves, in particular the relevant surface/curve stresses and distributed forces contributing to (localized) deformational and configurational force balances at surfaces/curves/points, which extend the common traction boundary conditions, are derived. Thereby, dissipative distributed configurational forces that are energetically conjugate to configurational changes are introduced as definitions. The (localized) force balances at surfaces/curves/points together with the contributing stresses and distributed forces within deformational and configurational mechanics display an intriguing duality. The resulting dissipative configurational tractions at the boundary are exemplified for some illustrative cases of boundary potentials. ?? 2007 Elsevier Ltd. All rights reserved.
Boundary energies; Configurational mechanics; Surface/curve tension and stress
Assessment of peripheral lung mechanics.
Respiratory physiology & neurobiology
163
1-3
54-63
2008
10.1016/j.resp.2008.03.012
The mechanical properties of the lung periphery are major determinants of overall lung function, and can change dramatically in disease. In this review we examine the various experimental techniques that have provided data pertaining to the mechanical properties of the lung periphery, together with the mathematical models that have been used to interpret these data. These models seek to make a clear distinction between the central and peripheral compartments of the lung by encapsulating functional differences between the conducing airways, the terminal airways and the parenchyma. Such a distinction becomes problematic in disease, however, because of the inevitable onset of regional variations in mechanical behavior throughout the lung. Accordingly, lung models are used both in the inverse sense as vehicles for extracting physiological insight from experimental data, and in the forward sense as virtual laboratories for the testing of specific hypothesis about mechanisms such as the effects of regional heterogeneities. Pathologies such as asthma, acute lung injury and emphysema can alter the mechanical properties of the lung periphery through the direct alteration of intrinsic tissue mechanics, the development of regional heterogeneities in mechanical function, and the complete derecruitment of airspaces due to airway closure and alveolar collapse. We are now beginning to decipher the relative contributions of these various factors to pathological alterations in peripheral lung mechanics, which may eventually lead to the development and assessment of novel therapies.
Compression failure of angle-ply laminates
Ninth DoD(NASA)FAA Conference on Fibrous Composites in Structural Design1
185-196
1992
The present work deals with modes and mechanisms of failure in compression of angle-ply laminates. Experimental results were obtained from 42 angle-ply IM7/8551-7a specimens with a lay-up of ((plus or minus theta)/(plus or minus theta)) sub 6s where theta, the off-axis angle, ranged from 0 degrees to 90 degrees. The results showed four failure modes, these modes being a function of off-axis angle. Failure modes include fiber compression, inplane transverse tension, inplane shear, and inplane transverse compression. Excessive interlaminar shear strain was also considered as an important mode of failure. At low off-axis angles, experimentally observed values were considerably lower than published strengths. It was determined that laminate imperfections in the form of layer waviness could be a major factor in reducing compression strength. Previously developed linear buckling and geometrically nonlinear theories were used, with modifications and enhancements, to examine the influence of layer waviness on compression response. The wavy layer is described by a wave amplitude and a wave length. Linear elastic stress-strain response is assumed. The geometrically nonlinear theory, in conjunction with the maximum stress failure criterion, was used to predict compression failure and failure modes for the angle-ply laminates. A range of wave length and amplitudes were used. It was found that for 0 less than or equal to theta less than or equal to 15 degrees failure was most likely due to fiber compression. For 15 degrees less than theta less than or equal to 35 degrees, failure was most likely due to inplane transverse tension. For 35 degrees less than theta less than or equal to 70 degrees, failure was most likely due to inplane shear. For theta less than 70 degrees, failure was most likely due to inplane transverse compression. The fiber compression and transverse tension failure modes depended more heavily on wave length than on wave amplitude. Thus using a single parameter, such as a ratio of wave amplitude to wave length, to describe waviness in a laminate would be inaccurate. Throughout, results for AS4/3502, studied previously, are included for comparison. At low off-axis angles, the AS4/3502 material system was found to be less sensitive to layer waviness than IM7/8551-7a. Analytical predictions were also obtained for laminates with waviness in only some of the layers. For this type of waviness, laminate compression strength could also be considered a function of which layers in the laminate were wavy, and where those wavy layers were. Overall, the geometrically nonlinear model correlates well with experimental results.
Woven ply thermoplastic laminates under severe conditions: Notched laminates and bolted joints
Composites Part B: Engineering
42
3
341-349
2011
10.1016/j.compositesb.2010.12.025
This work is aimed at investigating the influence of environmental conditions on the mechanical behavior of carbon fiber fabric reinforced PPS laminates. Changes in the strength and in the failure mechanisms of notched laminates and bolted joints were investigated for different environmental conditions: room temperature/dry - 120 °C/hygrothermally aged. These conditions help enhance the ductile behavior of the PPS matrix but degrade the fiber/matrix interface. However, the degree of retention of mechanical properties is quite high for a quasi-isotropic lay-up and hole sensitivity is slightly decreased by environmental conditions. For bolted joint tests, severe conditions increase the strength of double-lap joints (+11%) but are detrimental to the strength of single-lap joints (-26%). © 2010 Elsevier Ltd. All rights reserved.
A. Thermoplastic resin; B. Environmental degradation; D. Mechanical testing; E. Joints
Quantum Mechanics, Gravity, and the Multiverse
arXiv:1205.2675
7
5
18
2012
The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.
gravity; multiverse; quantum mechanics; spacetime; string theory
Channel cracks in atomic-layer and molecular-layer deposited multilayer thin film coatings
Journal of Applied Physics
115
23
2-7
2014
10.1063/1.4884438
Metal oxide thin film coatings produced by atomic layer deposition have been shown to be an effective permeation barrier. The primary failure mode of such coatings under tensile loads is the propagation of channel cracks that penetrate vertically into the coating films. Recently, multi-layer structures that combine the metal oxide material with relatively soft polymeric layers produced by molecular layer deposition have been proposed to create composite thin films with desired properties, including potentially enhanced resistance to fracture. In this paper, we study the effects of layer geometry and material properties on the critical strain for channel crack propagation in the multi-layer composite films. Using finite element simulations and a thin-film fracture mechanics formalism, we show that if the fracture energy of the polymeric layer is lower than that of the metal oxide layer, the channel crack tends to penetrate through the entire composite film, and dividing the metal oxide and polymeric materials into thinner layers leads to a smaller critical strain. However, if the fracture energy of the polymeric material is high so that cracks only run through the metal oxide layers, more layers can result in a larger critical strain. For intermediate fracture energy of the polymer material, we developed a design map that identifies the optimal structure for given fracture energies and thicknesses of the metal oxide and polymeric layers. These results can facilitate the design of mechanically robust permeation barriers, an important component for the development of flexible electronics.
Polymer Statistical Mechanics
Annual Review of Physical Chemistry
25
1
179-200
1974
10.1146/annurev.pc.25.100174.001143
These subjects have recently been reviewed, with many references cited, by Fixman & Stockmayer (I), (2, 3), and Casassa (4 the statistics of real (discrete- modcl or rotational-isomeric model), random flight , and stiff ( model).
Stress Intensity Factor of Mode III Cracks in Thin Sheets
Physical Review E - Statistical, Nonlinear and Soft Matter Physics
83
2 Pt 2
026106
2010
The stress field at the tip of a crack of a thin plate of elastic material that is broken due to a mode III shear tearing has a universal form with a non-universal amplitude, known as the stress intensity factor, which depends on the crack length and the boundary conditions. We present in this paper exact analytic results for this stress intensity factor, thus enriching the small number of exact results that can be obtained within Linear Elastic Fracture Mechanics (LEFM).
The MM2QM tool for combining docking, molecular dynamics, molecular mechanics, and quantum mechanics ???
Journal of Computational Chemistry
34
9
750-756
2013
10.1002/jcc.23192
The use of the MM2QM tool in a combined docking + molecular dynamics (MD) + molecular mechanics (MM) + quantum mechanical (QM) binding affinity prediction study is presented, and the tool itself is discussed. The system of interest is Mycobacterium tuberculosis (MTB) pantothenate synthetase in complexes with three highly similar sulfonamide inhibitors, for which crystal structures are available. Starting from the structure of MTB pantothenate synthetase in the "open" conformation and following the combined docking + MD + MM + QM procedure, we were able to capture the closing of the enzyme binding pocket and to reproduce the position of the ligands with an average root mean square deviation of 1.6 Å. Protein-ligand interaction energies were reproduced with an average error lower than 10%. The discussion on the MD part and a protein flexibility importance is carried out. The presented approach may be useful especially for finding analog inhibitors or improving drug candidates.
docking; drug design; molecular mechanics; quantum mechanics; tuberculosis
Mechanics of Polymers: Viscoelasticity
Springer Handbook of Experimental Solid Mechanics
49-96
2008
10.1007/978-0-387-30877-7
With the heavy influx of polymers into engineering designs their special, deformation-rate-sensitive properties require particular attention. Although we often refer to them as time-dependent materials, their properties really do not depend on time, but time histories factor prominently in the responses of polymeric components or structures. Structural responses involving time-dependent materials cannot be assessed by simply substituting time-dependent modulus functions for their elastic counterparts. The outline provided here is intended to provide guidance to the experimentally inclined researcher who is not thoroughly familiar with how these materials behave, but needs to be aware of these materials because laboratory life and applications today invariably involve their use.
Thermomechanics of thin films and interfaces
Journal of Electronic Materials
19
9
895-901
1990
10.1007/BF02652914
Several mechanics and thermomechanics problems associated with the\ndeposition of thin films on substrates are reviewed. They include:\n(1) Stress concentrations in interfacial cracks, and the corresponding\ncalculation of the energy release rate for crack growth along the\nfilm-substrate interface. (2) The effect of microstructure and of\nstress relaxation by diffusional creep during the growth of a thin\nfilm on the residual stresses present in the film; and (3) the thermal\nconductivity in film-substrate assemblies, and the issue of extracting\nfilm thermal properties from composite measurements. The relation\nbetween bulk and thin film values of the thermal conductivity is\ndiscussed. The issue of interfacial thermal resistance, which may\nlead to interfacial temperature drops of the order of 0.6 K is also\naddressed, and discussed in view of the inhomogeneous interface in\nfilms deposited by electron beam evaporation or ion beam sputtering.
interfaces; Thermomechanics; thin films
Contact mechanics
International Journal of Solids and Structures
37
1-2
29-43
2000
10.1016/S0020-7683(99)00075-X
Contact problems are central to Solid Mechanics, because contact is the principal method of applying loads to a deformable body and the resulting stress concentration is often the most critical point in the body. Contact is characterized by unilateral inequalities, describing the physical impossibility of tensile contact tractions (except under special circumstances) and of material interpenetration. Additional inequalities and/or non-linearities are introduced when friction laws are taken into account. These complex boundary conditions can lead to problems with existence and uniqueness of quasi-static solution and to lack of convergence of numerical algorithms. In frictional problems, there can also be lack of stability, leading to stick slip motion and frictional vibrations. If the material is non-linear, the solution of contact problems is greatly complicated, but recent work has shown that indentation of a power-law material by a power law punch is self-similar, even in the presence of friction, so that the complete history of loading in such cases can be described by the (usually numerical) solution of a single problem. Real contacting surfaces are rough, leading to the concentration of contact in a cluster of microscopic actual contact areas. This affects the conduction of heat and electricity across the interface as well as the mechanical contact process. Adequate description of such systems requires a random process or statistical treatment and recent results suggest that surfaces possess fractal properties that can be used to obtain a more efficient mathematical characterization. Contact problems are very sensitive to minor profile changes in the contacting bodies and hence are also affected by thermoelastic distortion. Important applications include cases where non-uniform temperatures are associated with frictional heating or the conduction of heat across a non-uniform interface. The resulting coupled thermomechanical problem can be unstable, leading to a rich range of physical phenomena. Other recent developments are also briefly surveyed, including examples of anisotropic materials, elastodynamic problems and fretting fatigue. © 1999 Published by Elsevier Science Ltd. All rights reserved.
Principles of Fractional Quantum Mechanics
Arxiv preprint arXiv:1009.5533
2
31
2010
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity of the Hamilton operator, parity conservation law and the current density. Applications of fractional quantum mechanics cover dynamics of a free particle, new representation for a free particle quantum mechanical kernel, infinite potential well, bound state in {\delta}-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the L\'evy path integral approach to fractional statistical mechanics.
Mathematical Physics; Quantum Physics
Thin Film Phenomena
Journal of The Electrochemical Society
117
5
180C
1970
10.1149/1.2407581
depostion technologies thickness measurement techniques nucleation,growth,\nand structure of films mechanical effects in thin films electron-transport\nphenomena in metal films, insulator, SC, superconducting thin films ferromagnetism\nin thin films optical properties
Modelling and Analysis of the Muskat Problem for Thin Fluid Layers
Journal of Mathematical Fluid Mechanics
1-11
2011
10.1007/s00021-011-0053-2
We consider the evolution of two thin fluid films in a porous medium. Starting from the classical equations modelling the Muskat problem we pass to the limit of small layer thickness and obtain a system of two coupled and degenerate parabolic equations for the films height. In the absence of surface tension forces we prove local well-posedness of the problem and show that the steady-states are exponentially stable.
Physics and Astronomy
Natural Frequencies of Thin-Walled Bars of Open Cross Section
Journal of Engineering Mechanics
113
l0
1584-1593
1987
http://dx.doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1584)
The natural vibration frequencies of thin-walled bars of open cross\nsection are studied, with particular emphasis on the influence of\nasymmetry and destabilizing forces on the interaction between various\nmodes. It is concluded that interactive vibrations are induced by\nboth asymmetry and destabilizing forces. The validity of the solutions\nobtained is confirmed by the fact that the lowest natural frequencies\nreduce to zero when the applied forces are equal to the static critical\nforces for instability in the corresponding modes.
Mechanics of merging events for a series of layers in a stratified turbulent fluid
Journal of Fluid Mechanics
577
251
2007
10.1017/S0022112007004703
This study attempts to explain the evolutionary pattern of a series of well-mixed layers separated by thin high-gradient interfaces frequently observed in stratified fluids. Such layered structures form as a result of the instability of the equilibrium with uniform stratification, and their subsequent evolution is characterized by a sequence of merging events which systematically increase the average layer thickness. The coarsening of layers can take one of two forms, depending on the realized vertical buoyancy flux law. Layers merge either when the high-gradient interfaces drift and collide, or when some interfaces gradually erode without moving vertically. The selection of a preferred pattern of coarsening is rationalized by the analytical theory-the merging theorem-which is based on linear stability analysis for a series of identical layers and strongly stratified interfaces. The merging theorem suggests that the merger by erosion of weak interfaces occurs when the vertical buoyancy flux decreases with the buoyancy variation across the step. If the buoyancy flux increases with step height, then coarsening of a staircase may result from drift and collision of the adjacent interfaces. Our model also quantifies the time scale of merging events and makes it possible to predict whether the layer merging continues indefinitely or whether the coarsening is ultimately arrested. The merging theorem is applied to extant one-dimensional models of turbulent mixing and successfully tested against the corresponding fully nonlinear numerical simulations. It is hypothesized that the upscale cascade of buoyancy variance associated with merging events may be one of the significant sources of the fine-scale (similar to 10 m) variability in the ocean.
Spinning thin-walled beams made of functionally graded materials: modeling, vibration and instability
European Journal of Mechanics - A/Solids
23
3
499-515
2004
http://dx.doi.org/10.1016/j.euromechsol.2003.12.003
The thermoelastic modeling, vibration and instability of spinning thin-walled beams made of functionally graded ceramic-metal based materials are addressed. In this context, the case of pretwisted beams of non-uniform cross-section along their longitudinal axis and subjected to a temperature field of a prescribed gradient through the blade wall thickness, is considered. A continuously graded variation in composition of the ceramic and metal phases across the beam wall thickness in terms of a simple power law distribution is implemented. Results highlighting the effects of the volume fraction, temperature gradient, cross-section aspect ratio, pretwist, compressive axial load on vibration and instability of spinning beams are presented and pertinent conclusions are outlined.
Divergence and flutter instabilities; Functionally graded materials; Pretwist; Spinning beams
The electro-mechanical response of elastomer membranes coated with ultra-thin metal electrodes
Journal of the Mechanics and Physics of Solids
53
11
2557-2578
2005
DOI 10.1016/j.jmps.2005.05.002
This paper presents experimental and theoretical analyses of the electro-mechanical response of metal/elastomer multilayers. A novel test has been devised to determine the relationship between the mechanical response of clamped elastomer membranes, coated on both sides with metal electrodes, and an applied electric field. The load-deflection response of the multilayers subjected to different voltages was measured using an instrumented spherical indenter having dimensions comparable to the freestanding span. The measurements are used with closed-form solutions for membrane deflection to determine the effective plane-strain modulus of cracked multilayers and electrically induced in-plane strains. The experiments demonstrate that: (i) electrically induced strains vary with the square of the electric field, as expected from electrostatic models of parallel plate capacitors, (ii) the transverse stiffness of membranes can be controlled using applied electric fields, (iii) analytical models accurately predict the relationship between electrode crack spacing, layer properties and effective moduli. Finally, we estimate the toughness of the sub-micron metal electrodes, using cracking models that relate crack spacing, imposed strain and the energy release rate governing channel crack formation. (c) 2005 Published by Elsevier Ltd.
cracking; elastomer; electro-mechanical; films; indentation; membrane; pump; thin film toughness
The mechanics of brain injuries
British Medical Bulletin
3
147-149
1945
10.1016/S0140-6736(01)87815-6
725 THE OF BRAIN Rotation causes the so<alled contrecoup , and presumably (as the It follows that if the can only rotate slowly
Statistical mechanics of chain molecules
Biopolymers
8
5
699-700
1969
10.1002/bip.1969.360080514
... Book Review. Statistical mechanics of chain molecules . Paul. J. Flory,; M. Volkenstein. Article first published online: 1 FEB 2004. ... Additional Information. How to Cite. Flory, Paul. J. and Volkenstein, M. (1969), Statistical mechanics of chain molecules . Biopolymers, 8: 699–700. ... \n
Fatigue performance of tungsten inert gas (TIG) and plasma welds in thin sections
International Journal of Fatigue
21
6
587-601
1999
10.1016/S0142-1123(98)00084-X
The greatest potential for the use of TIG and plasma welding is in the joining of thin sections, less than 10 mm thickness. This may introduce an additional benefit from the fatigue viewpoint, since fatigue strength is expected to increase with a decrease in plate thickness. Superior fatigue performance was confirmed for TIG and plasma transverse butt, cruciform and non-load carrying fillet welds of a carbon-manganese steel, all failing from the weld toe, justifying a one class increase in Eurocode 3. Weld details, which failed by fatigue cracking in the weld throat, showed no influence of welding process. Extensive measurements of the weld toe geometries confirmed that TIG and plasma welds had more favourable profiles than MMA welds, with lower weld toe angles and larger weld toe radii. Fracture mechanics modelling confirmed that the differences in weld toe geometry were consistent with the differences in fatigue life actually observed. Weld toe radius appeared to be more significant than weld toe angle.
fatigue; modelling; plasma and pulsed tig; thin sections; welded joints
High order thin-walled solid finite elements applied to elastic spring-back computations
Computer Methods in Applied Mechanics and Engineering
195
5377-5389
2006
10.1016/j.cma.2005.08.019
In this paper we present a new approach for computing elastic spring-back based on a strictly three-dimensional, high order, solid, finite element formulation for curved, thin-walled structures allowing for an anisotropic discretization. In combination with appropriate mesh design, the p-version yields an exponential rate of convergence in the error in energy norm in contrast to low-order elements, which yield only an algebraic rate of convergence. Anisotropic Ansatz spaces based on high order elements lead to very efficient discretizations. The structural behavior of three-dimensional thin-walled continua can be predicted with a similar number of degrees of freedom as in the two-dimensional case, yet significantly more accurately because of the three-dimensional model. We also introduce an approach for the efficient computation of the relevant geometrically nonlinear problem. Furthermore the paper describes the necessary model conversion from a low-order deep drawing simulation to a spring-back computation based on the p-version of the FEM. © 2005 Elsevier B.V. All rights reserved.
Geometric modeling; p-FEM; Spring-back
The deformation mechanism of thin-walled non-circular composite tubes subjected to bending
Composite Structures
30
2
131-146
1995
10.1016/0263-8223(94)00049-2
The present work is dealing with the experimental investigation of the bending of thin-walled composite tubes of non-circular cross-section, designed for the construction of various parts of the car body. Simultaneously much effort is given to explore the fracture mechanism governing the phenomenon examining as well as the influence of many of the factors associated with the energy absorbing efficiency and crashworthiness characteristics of the structures tested. Moreover, a theoretical analysis for the prediction of the ultimate bending strength for tubes of various composite materials and cross-sections subjected to bending, is presented. Theoretical results are compared with experimetal measurements and are found to be in good agreement.
A computational design methodology for assembly and actuation of thin-film structures via patterning of eigenstrains
Journal of Microelectromechanical Systems
18
5
1137-1148
2009
10.1109/JMEMS.2009.2025562
We develop a computational approach to design 3-D structures that can be fabricated and then assembled and/or actuated by spatially tailoring the layout of multilayer films with eigenstrains. Eigenstrains are stress-free strains when they occur in an unconstrained solid. They are almost an inevitable companion, albeit often unwanted, of thin-film processes. When they vary through the thickness, the constraint of the layers leads to internal stresses and bending and buckling deformations can occur; when they additionally vary in the plane of the film, more complex deformations can result. To advantageously use this phenomenon, we build on relatively simple mechanics ideas in a continuum formulation and combine geometrically nonlinear finite-element analysis of arbitrary-shaped multilayer films with a topology optimization methodology to determine the material layout in each layer so the film deforms into a prescribed shape. We expand our previous experimentally validated approach to include initially curved films and anisotropic eigenstrains. Using an extended system formulation for directly computing instability points allows us to tailor postbuckling response while explicitly controlling the design at limit and bifurcation points. We demonstrate the potential and versatility of our approach by applying it to a series of problems of contemporary and emerging interest.
Design methodology; Microelectromechanical devices; Patterning; Thin film
What is a state in quantum mechanics?
American Journal of Physics
72
3
348
2004
10.1119/1.1636164
In quantum mechanics, states are supposed to be specified by vectors in Hilbert space. However, students become confused about the representation of states and the meaning of “state” itself. We discuss consequences of the fact that quantum mechanics is intrinsically a probabilistic theory, and the ubiquitous confusion over whether quantum states, when specified as well as nature permits, are described by state vectors or rays.
Fluid mechanics.
Applied Mechanics and Engineering
61
11
xiii, 736 p.
1995
This is the most comprehensive introductory graduate or advanced undergraduate text in fluid mechanics available. It builds up from the fundamentals, often in a general way, to widespread applications, to technology and geophysics. New to this second edition are discussions on the universal dimensions similarity scaling for the laminar boundary layer equations and on the generalized vector field derivatives. In addition, new material on the generalized streamfunction treatment shows how streamfunction may be used in three-dimensional flows. Finally, a new Computational Fluid Dynamics chapter enables compulations of some simple flows and provides entry to more advanced literature. Basic introduction to the subject of fluid mechanics, intended for undergraduate and beginning graduate students of science and engineering. Includes topics of special interest for geophysicists and to engineers. New and generalized treatment of similar laminar boundary layers, streamfunctions for three-dimensional flows, vector field derivatives, and gas dynamics. Also a new generalized treatment of boundary conditions in fluid mechanics, and expanded treatment of viscous flows.
ta engineering (general). civil engineering (gener
A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates
International Journal of Solids and Structures
47
9
1297-1305
2010
10.1016/j.ijsolstr.2010.01.018
Free edge delamination in composite structures results from very localised stress fields which induce a stress concentration promoting the nucleation of an interfacial crack. To predict such a delamination onset at the free edge of a (±θ)s laminate in traction, use is made of a strength and toughness criterion which combines a stress condition with an energy analysis. A generalised plane strain model allows to determine the stress distribution near the free edge and the energy released by the nucleation of an interfacial crack. The results show that this approach can predict the delamination onset for ((±10)s,(±20)s) laminates provided the interfacial fracture energy and interlaminar shear strength are known. These characteristic values can be identified with the help of traction tests performed on samples with different thicknesses.
Composite materials; Delamination; Energy methods; Interlaminar
Liquid-to-solid transitions in thin liquid films induced by confinement
Physica A: Statistical Mechanics and its Applications
249
1-4
206-215
1998
10.1016/S0378-4371(97)00467-6
The mechanical properties of confined thin films of simple liquids were measured via a surface force balance as a function of the film thickness. We find an abrupt transition from liquid-like to a solid-like behaviour at a confinement corresponding to ca. six molecular layers of the liquid. The effect is due to confinement alone and does not require external applied pressure. At the transition the effective viscosity increases by at least seven orders of magnitude. It is proposed that this is a cooperative effect, reminiscent of a Lindemann-like mechanism originating in the suppression of the freedom of the confined molecules to move, (C) 1998 Elsevier Science B.V. All rights reserved.
Structure and magnetic properties of Mn4NMn4N thin films synthesized by plasma-based ion implantation
Physica A: Statistical Mechanics and its Applications
358
1
136-141
2005
10.1016/j.physa.2005.06.014
Plasma-based ion implantation was used to synthesize the manganese nitride Mn4Nby implanting nitrogen in manganese layers first deposited by sputtering assisted by multi-dipolar microwave plasma. The structural characterization of the layer has been performed using X- ray diffraction at grazing incidence and XPS. The magnetic properties have been measured using a SQUID susceptometer. In parallel, a FLAPW method has been used to calculate the theoretical magnetic state of Mn4N. The modeling results are compared with neutron diffraction and magnetization saturation measurements.
magnetic; manganese; nitride; thin film
Classical and quantum Nambu mechanics
Physical Review D
68
8
085001
2003
10.1103/PhysRevD.68.085001
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation and illustrated with detailed specific cases. Quantization is carried out with standard Hilbert space methods. With the proper physical interpretation, obtained by allowing for different time scales on different invariant sectors of a theory, the resulting non-Abelian approach to quantum Nambu mechanics is shown to be fully consistent.
Soil mechanics in engineering practice
Engineering Geology
48
149-150
1996
10.1016/S0013-7952(97)81919-9
One of the best-known and most respected books on geotechnical engineering, this updated version features expanded coverage of vibration problems, mechanics of drainage, passive earth pressure and consolidation. In the years since publication of the past editions there has been a proliferation of soil mechanics research, much of it irrelevant to engineering practice. It is the aim of the authors to bring order out of this confusion.
Developments in stochastic structural mechanics
Archive of Applied Mechanics
75
10-12
755-773
2006
10.1007/s00419-006-0067-z
Uncertainties are a central element in structural analysis and design. But even today they are frequently dealt with in an intuitive or qualitative way only. However, as already suggested 80 years ago, these uncertainties may be quantified by statistical and stochastic procedures. This contribution attempts to shed light on some of the recent advances in the now established field of stochastic structural mechanics and also solicit ideas on possible future developments.
On Noncommutative Classical Mechanics
Quantum
43
00
14
2003
10.1023/B:IJTP.0000028864.02161.a3
In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, cite1. I treat some classical systems with various potentials and some Physical interpretations are given concerning the presence of noncommutativity at large scales (Celeste Mechanics) directly tied to the one present at small scales (Quantum Mechanics) and its possible relation with UV/IR mixing.
Mechanics of fluid-activated, clustered satellite bellows
International Journal of Solids and Structures
45
4173-4183
2008
10.1016/j.ijsolstr.2008.02.027
A bellows, or a closed thin-walled elastic tube with corrugated walls, undergoes longitudinal extension when subjected to internal fluid pressure. Investigated herein is the mechanical behavior of several pressurized bellows in clusters, which are designed to bend and twist as well as to extend and compress longitudinally. Bellows in clusters can be employed as robotic limbs, such as manipulator arms and legs for walking machines. For limb bending, analysis shows that there is an optimal geometry for satellite bellows, or a set of identical bellows clustered longitudinally about a central core. For limb torsion, the bellows are clustered in a cylindrical helix whose angle is chosen to produce the desired load-displacement relationships, for instance the highest rotation for a given torque. For both bending and torsional limbs, experimental results are included that exhibit the predicted mechanical behavior. ?? 2008 Elsevier Ltd. All rights reserved.
Actuators; Bellows; Corrugated tubes; Helical springs; Robotics
A novel cylindrical punch method to characterize interfacial adhesion and residual stress of a thin polymer film
Engineering Fracture Mechanics
74
7
1101-1106
2007
10.1016/j.engfracmech.2006.12.010
Adhesion of a pre-stressed silicone rubber film to a planar graphite surface was investigated by a new cylindrical punch method. A homemade apparatus was constructed to meet force and displacement resolutions of 0.1 [mu]N and 10 nm. When the punch approached the intersurface force range across the punch-film gap, the film jumped into contact at "pull-in". Upon unloading, once the tensile load reached a threshold, a spontaneous delamination occurred at "pull-off" with a non-zero contact circle. A theoretical model was constructed based a simple energy balance. The new method can be used to characterize an adhesion interface between a pre-stressed free-hanging film and a rigid substrate.
Free vibration analysis of rotating thin-walled composite beams
Proceedings of 5th International Conference on Recent Advances in Space Technologies - RAST2011
38-42
2011
10.1109/RAST.2011.5966860
In this paper, both analytical and finite element formulations of a rotating thin-walled composite beam are derived for the flapwise bending, chordwise bending and torsional displacements. In the analytical part, derivation of both strain and kinetic energy expressions are made and the equations of motion are obtained by applying the Hamilton's principle. The equations of motion are solved by applying the Differential Transform Method (DTM). In the finite element part, structural matrices are obtained by using the derived energy expressions and a finite element code is written to calculate the natural frequencies. The analysis is carried out for anti-symmetric lay-up configuration also referred as Circumferentially Uniform Stiffness (CUS). Effect of the ply orientation on the natural frequencies is investigated. The natural frequencies are validated by making comparisons with the results in literature. Consequently, it is observed that there is a good agreement between the results.
differential transform method; Finite element method; Rotating composite box-beams
Dynamic stiffness matrix of continuous element for vibration of thick cross-ply laminated composite cylindrical shells
Composite Structures
98
93-102
2013
10.1016/j.compstruct.2012.11.014
This paper investigates the vibration analysis of thick laminated composite cylindrical shells by a continuous element constructed from the dynamic stiffness matrix. Based on the analytical solutions of the differential equations of thick composite cylindrical shell taking into account the shear deflection effects, the dynamic stiffness matrix has been built from which natural frequencies are easily calculated. A computer program is developed for performing the numerical calculations and results from specific case studies are presented. Results on natural frequencies and harmonic responses of this work are compared to published analytical and Finite Element Method (FEM) results. Numerical examples demonstrate that the proposed model can be used to solve efficiently the vibration analysis of thick cross-ply composite cylindrical shell with many advantages: size of model reduced, time of computing saved, higher precision, direct acquisition of harmonic response and suitable for the analysis of medium and high frequency range.
Continuous element method; Dynamic stiffness matrix; Dynamic transfer matrix; Free vibration; Thick laminated composite cylindrical shell
Cylindrical bending responses of angle-ply piezoelectric laminates with viscoelastic interfaces
Applied Mathematical Modelling
38
24
6018-6030
2014
http://dx.doi.org/10.1016/j.apm.2014.05.025
Abstract The time-dependent behavior of a simply supported, angle-ply piezoelectric laminate in cylindrical bending with viscoelastic interfaces is investigated. The interfacial bonding in piezoelectric laminates is considered to be dielectrically weakly (or highly) conducting, and mechanically compliant characterized by the Kelvin–Voigt viscoelastic law. The state-space approach, which is directly based on the piezoelectricity equations and very effective in analyzing laminated structures, is employed. For exact analysis, a state equation of the relative sliding displacements with respect to the time variable is further presented. Comparison study shows that the numerical results by the present analysis agree well with those reported before. Numerical results also indicate that the electromechanical response of the piezoelectric laminates with viscoelastic interfaces changes remarkably with time elapsing. Thus, the bonding imperfection should be considered carefully in the practical design of piezoelectric laminates.
Exact solution; Kelvin–Voigt viscoelastic model; Piezoelectric laminates; State-space approach
Thin spray-on liner adhesive strength test method and effect of liner thickness on adhesion
International Journal of Rock Mechanics and Mining Sciences
47
5
808-815
2010
10.1016/j.ijrmms.2010.05.004
The adhesive strength between a thin spray-on liner (TSL) and rock is an important property controlling the design and performance of TSL rock support systems. The advantages and disadvantages of various adhesion test methods used by the coatings, microelectronics and concrete industries with respect to TSLs are discussed. A suggested test method for TSL materials is presented, which is based on direct pull-off of an elevator bolt that is attached to a liner with strong epoxy. To interpret the test results correctly, the effect of the liner thickness on adhesive strength must be assessed. This was shown experimentally and was supported by an analytical solution. The adhesive strength is inversely proportional to the square root of the liner thickness. Tests were performed using Tekflex as a liner material, which was applied to concrete or granite substrates.
Adhesion test; Adhesive strength; Liner thickness; Rock support; Substrate; Thin spray-on liner
Element free method for static and free vibration analysis of spatial thin shell structures
Computer Methods in Applied Mechanics and Engineering
191
51-52
5923-5942
2002
10.1016/S0045-7825(02)00504-2
The implementation of the element free Galerkin method (EFG) for spatial thin shell structures is presented in this paper. Both static deformation and free vibration analyses are considered. The formulation of the discrete system equations starts from the governing equations of stress resultant geometrically exact theory of shear flexible shells. Moving least squares approximation is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometry. Discrete system equations are obtained by incorporating these interpolations into the Galerkin weak form. The formulation is verified through numerical examples of static stress analysis and frequency analysis of spatial thin shell structures. For static load analysis, essential boundary conditions are enforced through penalty method and Lagrange multipliers while boundary conditions for frequency analysis are imposed through a weak form using orthogonal transformation techniques. The EFG results compare favorably with closed-form solutions and that of finite element analyses.
21; 49; 67; 80; Element free Galerkin method; Free vibration; Mesh free method; Numerical analysis; Shell structures
Non-linear buckling and postbuckling behavior of thin-walled beams considering shear deformation
International Journal of Non-Linear Mechanics
43
5
345-365
2008
10.1016/j.ijnonlinmec.2007.12.019
The static stability of thin-walled composite beams, considering shear deformation and geometrical non-linear coupling, subjected to transverse external force has been investigated in this paper. The theory is formulated in the context of large displacements and rotations, through the adoption of a shear deformable displacement field (accounting for bending and warping shear) considering moderate bending rotations and large twist. This non-linear formulation is used for analyzing the prebuckling and postbuckling behavior of simply supported, cantilever and fixed-end beams subjected to different load condition. Ritz's method is applied in order to discretize the non-linear differential system and the resultant algebraic equations are solved by means of an incremental NewtonRapshon method. The numerical results show that the beam loses its stability through a stable symmetric bifurcation point and the postbuckling strength is in relation with the buckling load value. Classical predictions of lateral buckling are conservative when the prebuckling displacements are not negligible and the non-linear buckling analysis is required for reliable solutions. The analysis is supplemented by investigating the effects of the variation of load height parameter. In addition, the critical load values and postbuckling response obtained with the present beam model are compared with the results obtained with a shell finite element model (Abaqus).
postbuckling; prebuckling; ritz method; shear flexibility; thin-walled beams
Quantum mechanics without measurements
Quantum
December
22
2006
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic probabilities in quantum theory requires setting up appropriate sample spaces taking proper account of quantum incompatibility. When this is done the Schrodinger equation can be used to calculate probabilities independent of whether a system is or is not being measured, and the results usually ascribed to wave function collapse are obtained in a less misleading way through conditional probabilities. Toy models that include measurement apparatus as part of the total quantum system make this approach accessible to students. Some comments are made about teaching this material.
Meshfree particle methods for thin plates
Computer Methods in Applied Mechanics and Engineering
209-212
156-171
2012
10.1016/j.cma.2011.10.011
In this paper, we are concerned with meshfree particle methods for the solutions of the classical plate model. The vertical displacement of a thin plate is governed by a fourth order elliptic equation and thus the approximation functions for numerical solutions are required to have continuous partial derivatives. Hence, the conventional finite element method has difficulties to solve the fourth order problems. Meshfree methods have the advantage of constructing smooth approximation functions, however, most of the earlier works on meshfree methods for plate problems used either moving least squares method with penalty method or coupling FEM with meshfree method to deal with essential boundary conditions. In this paper, by using generalized product partition of unity, introduced by Oh et al., we introduce meshfree particle methods in which approximation functions have high order polynomial reproducing property and the Kronecker delta property. We also prove error estimates for the proposed meshfree methods. Moreover, to demonstrate the effectiveness of our method, results of the proposed method are compared with existing results for various shapes of plates with variety of boundary conditions and loads. © 2011 Elsevier B.V.
Generalized product partition of unity; Kirchhoff plate model; Meshfree methods; Partition of unity function with flat-top; Reproducing polynomial particle shape functions
Substrate-Induced Order and Multilayer Epitaxial Growth of Substituted Phthalocyanine Thin Films
Langmuir
16
6
2872-2881
2000
10.1021/la991111i
Thin films of hexadecafluorophthalocyaninatooxovanadium (F16PcVO) are vapor-deposited under organic molecular beam epitaxy (OMBE) conditions on the (100) surfaces of NaCl, KCl, and KBr and on quartz glass. Beginning at submonolayer coverages and extending to a film thickness of several tens of nanometers the film structure is determined in situ by reflection high energy electron diffraction (RHEED). Following deposition the film morphology is characterized by tapping mode atomic force microscopy (AFM) and chromophore coupling of the molecules within the films is studied by optical absorption spectroscopy. Highly ordered growth of crystalline domains of F16PcVO with dimensions in the micrometer range leading to films of quite uniform thickness is observed. On KBr a commensurate √10 ? √10, R = 18.4° square lattice is seen in RHEED of the first monolayers with the molecules parallel to the substrate surface which is also preserved at higher film thickness. On KCl a surface lattice of the same size is formed which is, however, understood as a result of point-on-line coincidence. Diffraction of transmitted electrons yield a constant three-dimensional crystal structure of the films on KBr and KCl with a tetragonal unit cell of a = b = 1.47 nm and c = 0.62 nm. On NaCl with its smaller lattice constant no ordered relative orientation is possible and hence an increased part of the film appears amorphous. On quartz glass on the other hand, ordered films are formed with the molecular plane predominantly oriented cofacially parallel to each other and vertical to the surface. Calculations of molecular mechanics as well as of periodic surface potentials are performed to support the proposed structures and to discuss the crystallization in thin films of phthalocyanines and related materials. Implications of the present results for the electrical properties to be expected from such layers and their potential use in molecular semiconductor thin films are discussed.
Hydrogen effect on fracture toughness of thin film/substrate interfaces
Engineering Fracture Mechanics
77
5
803-818
2010
http://dx.doi.org/10.1016/j.engfracmech.2009.11.011
The effect of hydrogen on the interface fracture toughness of two nano-film/substrate structures, Ni/Si and Cu/Si, were evaluated using four-point bend specimens with and without hydrogen charging. Hydrogen typically decreases the fracture toughness of materials. However, we found in this study that the interfacial toughness between the Ni film and the Si substrate increased due to the presence of hydrogen, while that of Cu/Si decreased. Nanoindentation experiments for the Ni and Cu films revealed that local plasticity in the Ni and Cu films is promoted by the charged hydrogen. The critical stress intensity at the Ni/Si interface crack considering the plasticity of Ni, namely the true fracture toughness, is scarcely influenced by the existence of hydrogen. The apparent increase in fracture toughness of the Ni/Si interface is due to the large stress relaxation near the crack tip caused by softening due to the presence of hydrogen. Although the promotion of plastic deformation of Cu relaxes the stress intensity at the Cu/Si interface crack, the apparent interfacial toughness still decreases because of the significant decrease in the true toughness due to the presence of hydrogen.
Adhesion; Cu; Fracture toughness; Hydrogen; Interfaces; Ni; Plasticity; Thin films
Structural damage identification for thin plates using smart piezoelectric transducers
Computer Methods in Applied Mechanics and Engineering
194
3192-3209
2005
10.1016/j.cma.2004.08.007
An impedance-based structural damage identification method for thin plates is presented in this paper using piezoelectric ceramic (PZT) transducers. The local damages are characterized by introducing a damage parameter in each finite element. A two-dimensional electromechanical impedance model is proposed to predict the electric admittance of the PZT transducer bonded to the plates. The general equations for generating structural dynamic stiffness from normal modes are formulated based on finite element analysis. The first-order perturbation method is introduced to obtain the electric admittance change on PZT transducers due to damage. A damage identification scheme for solving nonlinear optimization problem is proposed to locate and quantify the damage by matching the numerical and experimental electric admittance change on PZT transducers. The proposed technique is verified through numerically simulated damage identification tests. ?? 2004 Elsevier B.V. All rights reserved.
Damage identification; Finite element analysis; Impedance; Piezoelectricity; Structural dynamics
A top-down analytic approach for the analysis of edge effects of angle-ply symmetric laminates
Composite Structures
104
60-70
2013
10.1016/j.compstruct.2013.04.016
A top-down approach has been proposed to achieve the free-edge stresses in a [??/-??]s rectangular laminate under a longitudinal tensile load. At the first stage, the laminate is subdivided into two antisymmetric parts and the upper one is analyzed by including an unknown twisting moment. This problem has been solved by extending an analytical solution for torsion of orthotropic laminates to antisymmetric laminates. At the second stage, the upper lamina was analyzed alone by including the shear force induced by the lower lamina. In this way, closed-form solutions for in-plane and out-of-plane stresses were obtained. The results for the case of a [45/-45]s strip have been compared to other analytical and numerical results. [??/-??]s laminates of different widths have been analyzed and analytical results have been compared with results obtained by the FEM, after applying the submodeling technique. ?? 2013 Elsevier Ltd.
Analytic approach; Finite elements; Free-edge stresses; Symmetric angle-ply laminates; Tensile load
Fatigue behavior of a cross-ply titanium matrix composite under tension-tension and tension-compression cycling
Materials Science and Engineering: A
200
1-2
1-11
1995
10.1016/0921-5093(95)07006-0
The fatigue behavior of a titanium-based metal-matrix composite reinforced with silicon carbide fibers, SCS-6/Ti-15-3, with the cross-ply lay-up of [090]2S, was investigated at room temperature for two conditions; tension-tension and tension-compression. On the maximum applied stress basis, the tension-tension condition had longer fatigue lives than the tension-compression condition. On the stress-range basis, however, the tension-tension condition had shorter fatigue lives than the tension-compression condition. For both conditions, three distinct regimes of fatigue behavior were present. These were fiber-dominated, matrix-dominated, and mixed fiber/matrix-dominated regions. In these regimes, fatigue damage mechanisms and the stress-strain response during cycling were, in general, similar for both fatigue conditions. However, additional damage mechanisms and plasticity sites were present in tension-compression cycling which resulted in different fatigue lives in comparison with tension-tension cycling.
Fatigue; Tension compression; Tension-tension; Titanium matrix composite
The Context of Professional Learning for Inclusion: A 4-Ply Model
International Journal of Whole Schooling
6
1
39-52
2010
EJ872440
This paper outlines the findings from one dimension of a large-scale research project which addressed the PL requirements of specialist inclusion/SEN teachers in Ireland. Two aspects relating to the context of professional learning are explored here: the professional learning opportunities preferred by teachers and the professional learning opportunities which, in principals' and teachers' estimations have been found to be most beneficial in enhancing teachers' expertise. In the light of the research findings and current literature pertaining to the area, opportunities for PL for inclusion are reviewed and a "4-ply" model proposed which draws on four complementary layers: system supports, tertiary level input, school development and teacher self-enhancement. (Contains 2 tables.
Bending of thin crystalline strips: Comparison of continuum dislocation-based models
Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing
400
439-442
2005
10.1016/j.msea.2005.01.059
It is suggested that the size effect in plastic bending of thin crystalline strips is due to bowing of dislocations that nucleate at the free surface and glide towards the neutral plane. The approach is an application of the continuum dislocation-based model, which considers fields of curved dislocations endowed with line tension and which is embedded in a rigorous continuum mechanics framework. The model equations are evaluated and the results are compared with the previous version of the model where pre-existing straight dislocations were assumed in the strip. (c) 2005 Elsevier B.V. All rights reserved.
Buckling of Anisotropic Composite Plates under Stress Gradient
Journal of Engineering Mechanics-Asce
117
2
260-275
1991
10.1061/(ASCE)0733-9399(1991)117:2(260)
In composite structures characterized by lightweight, thin-walled members, the linear buckling load is one of the most important design considerations. Plate structures (bridge decks and ship hulls) are often subjected to differential compression due to nonuniform bending during their service life. This paper presents a general formulation for the buckling of rectangular, anisotropic, symmetric, angle-ply composite laminates under linearly varying, uniaxial compressive force using the energy method in conjunction with orthogonal polynomial sequences, generated by a Gram-Schmidt process. Orthogonal polynomials provide a simpler and efficient tool for handling complex combinations of simple and clamped boundaries. The present study highlights the unusual insensitivity of the buckling load of anisotropic laminates to fiber orientation under in-plane tension-compression-type loading. Such behavior is not known to exist under idealized loading of constant, uniaxial compression, and orthotropic material behavior. The paper introduces an effective approximation technique of differential quadrature as an alternative to energy methods and discusses its credibility for solving complex plate stability problems against benchmark solutions provided by the Ritz method.
characteristic orthogonal polynomials; differential quadrature; natural frequencies; rayleigh-ritz method; rectangular-plates
Stability of thin, radially moving liquid sheets
Journal of Fluid Mechanics
87
02
289-298
1978
10.1017/S0022112078001597
An analysis of the stability of thin viscous liquid sheets, such as those emitted from industrial spraying nozzles, is presented. These sheets are in the form of a circular sector whose thickness reduces as the distance from the nozzle increases. The Kelvin-Helmholtz type of instability usually observed causes the breakup and atomization of the sheet, as required in most industrial spraying processes. Waviness, like that of a flapping flag, is produced and increasing amplitudes finally cause breakup. An analytical solution in the form of hypergeometric functions for the shape of the sheet and the waves is obtained. This solution includes, as special cases, analyses existing in the literature, in addition to establishing the possibility of a new type of instability dependent on the distance from the nozzle. Also, the classical type of instability, in which the waves increase with time, is examined and relations for unstable waves as a function of parameters such as the fluid viscosity, surface tension and sheet velocity are obtained. It is shown that there is no single wave that has a maximum growth rate, but that the wavenumber for maximum instability increases with the distance from the nozzle orifice.
AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS
International Journal of Geometric Methods in Modern Physics
09
05
1250048
2012
10.1142/S021988781250048X
We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e. an effective description of some underlying degrees of freedom.
Elastic field of a thin-film/substrate system under an axisymmetric loading
International Journal of Solids and Structures
34
35-36
4463-4478
1997
10.1016/S0020-7683(97)00053-X
This paper presents the elastic solution of a layered half space with perfect interfacial bonding under an axisymmetrical compressive loading on the plane surface. The analysis is intended to model the nano-indentation of thin-film coating/substrate systems. Unlike most of the existing work of which the substrate is assumed as rigid and the numerical results are obtained by finite element analysis, the present paper presents theoretical solutions for the elastic coating/substrate systems. The surface displacement profiles and the stress fields are shown to be sensitive to the thickness of the coating layer and the ratio of the elastic modulus of the coating material to that of the substrate. When the film thickness is comparable to the loading contact radius, the film elastic property cannot be accurately determined by using Sneddon's half-space indentation solution. Furthermore, there are pronounced differences in the stress fields of the hard-coating and the soft-coating systems. When an indentation load is applied to a soft-thin-film/hard-substrate system, most the stress components are compressive. But for a hard-thin-film/soft-substrate system, the radial and hoop stresses in the film near the film/substrate interface change from tension to compression as the film thickness decreases. The normal and shear stress results are compared with those obtained from finite element analysis (Jayachandran, R., Boyce, M. C. and Argon, A. S. (1995) Mechanics of the indentation test and its use to assess the adhesion of polymeric coatings. In Adhesion Measurement of Films and Coatings, ed. K. L. Mittal. VSP, pp. 189-215) for the rigid substrate system. Also, the load-indentation depth results are compared with the experimental data of Oliver and Pharr (Oliver, W. C. and Pharr, G. M. (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Material Research7(6), 1564-1583) for tungsten subjected to elastic indentation. The agreement is quite satisfactory. Implications of the elastic field on the failure mechanisms of coating/substrate systems are also discussed.
Generating and Adapting Game Mechanics
Proceedings of the 2014 Foundations of Digital Games Workshop on Procedural Content Generation in Games
2014
Game designs often center on the game mechanics—rules governing the logical evolution of the game. We seek to de- velop an intelligent system that generates computer games and assists humans in designing games. As first steps to- wards this goal we present a composable and cross-domain representation for game mechanics that draws from AI plan- ning action representations. We use a constraint solver to generate mechanics subject to design requirements on the form of those mechanics—what they do in the game. A planner takes a set of generated mechanics and tests whether those mechanics meet playability requirements—controlling how mechanics function in a game to affect player behav- ior. We demonstrate our system by modeling and generat- ing mechanics in a role-playing game, platformer game, and combined role-playing-platformer game.
game design; game mechanics; procedural content generation
Mathematical Analysis of a Bonded Joint with a Soft Thin Adhesive
Mathematics and Mechanics of Solids
4
2
201-225
1999
10.1177/108128659900400204
This paper considers the problem of two adherents joined by a soft thin adhesive along their common surface. Using the asymptotic expansion method, the authors obtain a simplified model in which the adhesive is treated as a material surface and is replaced by returning springs. The authors show weak and strong convergence of the exact solution toward the solution of the limit problem. The singularities of the limit problem are analyzed, and it is shown that typically they are logarithmic. Furthermore, the authors investigate the phenomenon of boundary layer by studying the correctors, the extra terms, which must be added to the classical asymptotic expansion to verify the boundary conditions. The correctors show that, contrary to the adherents, in the adhesive there are power-type singularities, which are at the base of the failure of the assemblage.
Thin viscous middle-crust and evolving fault distribution during continental rifting: Insights from analog modeling experiments
Tectonophysics
608
161-175
2013
10.1016/j.tecto.2013.10.001
Analog modeling of continental rifting, assuming a crustal scale "jelly sandwich"-like rheology, was carried out to test the mechanical effect of varying the absolute thickness of a weak (viscous) middle crust (silicone layer), interbedded between a brittle upper crust (sand layer) and a strong lower crust.Results consistently show a delocalization of the brittle deformation (i.e. a uniform scattering of the faults) throughout the upper brittle layer. This effect is interpreted to be associated with pressure driven flow in the viscous layer, caused by the tectonic collapse of upper brittle fault blocks into the viscous substratum. A reduction of the overall viscous layer thickness increases its resistance to accommodate internal thickness variations, which promotes delocalization of the fault pattern in the upper brittle layer.Our results contribute to the understanding of the mechanics of the so-called "upper plate paradox", a large-scale structure often recognized at non-volcanic rifted margins. A thin viscous middle crust provides means of decoupling the deformation affecting upper and lower crust during rifting. On one hand this promotes a uniform scattering of faults throughout the upper brittle crust, on the other hand it allows for a strong localization of the deformation in lower crust and upper mantle expressed by the lithospheric necking in the rift center. ?? 2013 Elsevier B.V.
Analog modeling; Continental rifting; Localized vs. delocalized fault pattern; Non-volcanic rifted margins; Soft thin middle crust; Upper-plate paradox
Room Temperature Recrystalization of Electroplated Copper Thin Films: Methods and Mechanics
Mat. Res. Soc. Symp. Proc.
62
D10.1.1--10
2000
We report a comparison of the room temperature recrystallization of\nelectroplated (EP) copper in blanket films as a function of thickness\nmeasured by focused ion beam (FIB) microscope images and sheet resistance\nmeasurements. Both sets of data show an increase in rate with film\nthickness from 0.75 μm up to 5 μm, while little recrystallization\nis observed in films thinner than 0.75 μm. Interestingly, the recrystallization\nrates from FIB analysis are consistently faster than those from the\nsheet resistance measurements. These data suggest that the recrystallization\nis initiated close to the top surface of the EP Cu film, but that\nin thinner films a high surface-to-volume ratio allows surface inhibition\nor pinning to retard the transformation. A Johnson-Mehl-Avrami- Kolmogorov\n(JMAK) analysis of the two data sets yields unusually high values\nfor the Avrami exponent α of up to 7 for the FIB data, while lower\nvalues of around 4 are obtained for the sheet resistance data. X-ray\ndiffraction pole figures of the films have also been collected and\ncorrelations between the crystallographic texture, film thickness\nand recrystallization are discussed.
Computational Mechanics
Annual Review of Materials Research
32
1
437-465
2002
10.1146/annurev.matsci.32.103101.153157
Computational mechanics comprises all types of computer modeling of the mechanical behavior of materials. In this contribution we concentrate on new developments in modeling based on the finite element method (FEM), especially deformation analyses based on numerical homogenization techniques (self-consistent embedding procedure, matricity model), simulations of real microstructural cut-outs, damage analyses of artificial and real microstructures, and multiscale modeling aspects. The limit flow stresses for transverse loading of metal matrix composites reinforced with continuous fibers and for uniaxial loading of spherical particle reinforced metal matrix composites are investigated by recently developed embedded cell models in conjunction with the finite element method. A fiber of circular cross section or a spherical particle is surrounded by a metal matrix, which is again embedded in the composite material, with the mechanical behavior to be determined iteratively in a self-consistent manner. Stress-strain curves have been calculated for a number of metal matrix composites with the embedded cell method and verified with literature data of a particle reinforced Ag/58vol.%Ni composite and for a transversely loaded uniaxially fiber reinforced Al/46vol.%B composite. Good agreement has been obtained between experiment and calculation, and the embedded cell model is thus found to well represent metal matrix composites with randomly arranged inclusions. Systematic studies of the mechanical behavior of fiber- and particle-reinforced composites with plane strain and axisymmetric embedded cell models are carried out to determine the influence of fiber or particle volume fraction and matrix strain-hardening ability on composite strengthening levels. Results for random inclusion arrangements obtained with self-consistent embedded cell models are compared with strengthening levels for regular inclusion arrangements from conventional unit cell models. It is found that with increasing inclusion volume fractions pronounced differences in composite strengthening exist between all models. Finally, closed-form expressions are derived to predict composite strengthening for regular fiber arrangements and for realistic random fiber or particle arrangements as a function of matrix hardening and particle volume fraction. The impact of the results on effectively designing technically relevant metal matrix composites reinforced by randomly arranged strong inclusions is emphasized. Atomistic modeling such as Monte Carlo (MC) simulations and molecular dynamics (MD) methods, dislocation theoretical modeling, and continuum mechanical methods are applied in order to provide insight into the mechanical behavior of materials. Simulations are presented graphically in a systematic manner for different material systems and are compared with experimental results. Finally, it will be shown that the results can be used to predict the future behavior of materials presently in service and even to design new materials.
composites; comprises all types of; computer modeling; concentrate on new; deformation analyses; finite element method; in this contribution we; micromechanical modeling; multiscale modeling; of materials; of the mechanical behavior; s abstract computational mechanics
Riemann-Cartan Geometry of Nonlinear Dislocation Mechanics
Archive for Rational Mechanics and Analysis
205
59-118
2012
10.1007/s00205-012-0500-0
We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold – where the body is stress free – is a Weitzenbock manifold, i.e. a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan’s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance.
Fractal mechanics
Physica D: Nonlinear Phenomena
220
1
54-68
2006
10.1016/j.physd.2006.06.008
A mechanical theory of fractals and of non-smooth objects in general is developed on the basis of the theory of differential spaces of Sikorski. Once the (generally infinite dimensional) configuration space is identified, an extended form of the principle of virtual work is used to define the concept of generalized force and stress. For the case of self-similar fractals, an appropriate integration based on the Hausdorff measure is introduced and applied to the numerical formulation of stiffness matrices of some common fractals, which can be used in a finite element implementation. © 2006 Elsevier Ltd. All rights reserved.
Differential geometry; Differential spaces; Finite elements; Fractals; Solid mechanics
Fracture mechanics principles.
Dental materials : official publication of the Academy of Dental Materials
11
2
111-2
1995
10.1016/0109-5641(95)80044-1
The principles of linear elastic fracture mechanics (LEFM) were developed in the 1950s by George Irwin (1957). This work was based on previous investigations of Griffith (1920) and Orowan (1944). Irwin (1957) demonstrated that a crack shape in a particular location with respect to the loading geometry had a stress intensity associated with it. He also demonstrated the equivalence between the stress intensity concept and the familiar Griffith criterion of failure. More importantly, he described the systematic and controlled evaluation of the toughness of a material. Toughness is defined as the resistance of a material to rapid crack propagation and can be characterized by one parameter, Kic. In contrast, the strength of a material is dependent on the size of the initiating crack present in that particular sample or component. The fracture toughness of a material is generally independent of the size of the initiating crack. The strength of any product is limited by the size of the cracks or defects during processing, production and handling. Thus, the application of fracture mechanics principles to dental biomaterials is invaluable in new material development, production control and failure analysis. This paper describes the most useful equations of fracture mechanics to be used in the failure analysis of dental biomaterials.
Ceramics; Ceramics: chemistry; Dental Materials; Dental Materials: chemistry; Dental Porcelain; Dental Porcelain: chemistry; Dental Stress Analysis; Elasticity; Glass; Glass: chemistry; Materials Testing; Materials Testing: methods; Mechanical; Models; Pliability; Probability; Stress; Survival Analysis; Theoretical
Flow along a long thin cylinder
Journal of Fluid Mechanics
602
1-37
2008
10.1017/S0022112008000542
Two different approaches have been used to calculate turblent flow along a long thin culinder where the flow is aligned with the cylinder. A boundary-layer code is used to predict the mean flow for very long cylinders (length to ratio of up to O(106)), with the effects of the turbulence estimated through a turbulence model. Detailed comparison with experimental results shows that the mean properties of the flow are predicted within experimental accuracy. The boundary-layer model predicts that, sufficiently far downstream, the surface shear stress will be (almost) constant. This is consistent with experimental results from long cylinders in the form of sonar arrays. A periodic Navier-Stokes problem is formulated, and solutions generated for the boundary-layer model and experiments. Strongly turbulent flow occurs only near the surface of the cylinder, with relatively weak turbulence over most of the boundary layer. For a thick boundary layer with the boundary-layer thickness much larger than the cylinder radius, the mean flow is effectively constant near the surface, in both temporal and spatial frameworks, while the outer flow continues to develop in time or space. Calculations of the circumferentially averaged surface pressure spectrum sho that, in physical terms, as the radius of the cylinder decreases, the surface noise from the turbulence increases, with the maximum noise at a Reynolds number of O(103). An increase in noise with a decrease in radius (Reynolds number) is consistent with experimental results.
ta engineering (general). civil engineering (gener
Statistical Mechanics of Hamiltonian Adaptive Resolution Simulations
arXiv preprint arXiv: …
Mmd
1-36
2014
10.1063/1.4907006
The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows one to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory.
Quantum approach to classical statistical mechanics
Physical Review Letters
99
3
1-4
2007
10.1103/PhysRevLett.99.030603
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Fluid mechanics revisited
Physica A: Statistical Mechanics and its Applications
370
2
190-224
2006
10.1016/j.physa.2006.03.066
Öttinger's recent nontraditional incorporation of fluctuations into the formulation of the friction matrix appearing in the phenomenological GENERIC theory of nonequilibrium irreversible processes is shown to furnish transport equations for single-component gases and liquids undergoing heat transfer which support the view that revisions to the Navier–Stokes–Fourier (N–S–F) momentum/energy equation set are necessary, as empirically proposed by the author on the basis of an experimentally supported theory of diffuse volume transport. The hypothesis that the conventional N–S–F equations prevail without modification only in the case of “incompressible” fluids, where the density ρ of the fluid is uniform throughout, serves to determine the new phenomenological parameter α ′ appearing in the GENERIC friction matrix. In the case of ideal gases the consequences of this constitutive hypothesis are shown to yield results identical to those derived theoretically by Öttinger on the basis of a “proper” coarse-graining of Boltzmann's kinetic equation. A major consequence of the present work is that the fluid's specific momentum density v is equal to its volume velocity v v , rather than to its mass velocity v m , contrary to current views dating back 250 years to Euler. In the case of rarefied gases the proposed modifications are also observed to agree with those resulting from Klimontovich's molecularly based, albeit ad hoc, self-diffusion addendum to Boltzmann's collision integral. Despite the differences in their respective physical models—molecular vs. phenomenological—the role played by Klimontovich's collisional addition to Boltzmann's equation in modifying the N–S–F equations is noted to constitute a molecular counterpart of Öttinger's phenomenological fluctuation addition to the GENERIC friction matrix. Together, these two theories collectively recognize the need to address multiple- rather than single-encounter collisions between a test molecule and its neighbors when formulating physically satisfactory statistical–mechanical theories of irreversible transport processes in gases. Overall, the results of the present work implicitly support the unorthodox view, implicit in the GENERIC scheme, that the translation of Newton's discrete mass-point molecular mechanics into continuum mechanics, the latter as embodied in the Cauchy linear momentum equation of fluid mechanics, cannot be correctly effected independently of the laws of thermodynamics. While Öttinger's modification of GENERIC necessitates fundamental changes in the foundations of fluid mechanics in regard to momentum transport, no basic changes are required in the foundations of linear irreversible thermodynamics (LIT) beyond recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in single-species fluid continua, namely mass, momentum and energy. An alternative, nonGENERICally based approach to LIT, derived from our findings, is outlined at the conclusion of the paper. Finally, our proposed modifications of both Cauchy's linear momentum equation and Newton's rheological constitutive law for fluid-phase continua are noted to be mirrored by counterparts in the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffuse volume transport.
Two-photon wave mechanics
Physical Review A - Atomic, Molecular, and Optical Physics
74
6
1-4
2006
10.1103/PhysRevA.74.062104
The position-representation wave function for multi-photon states and its equation of motion are introduced. A major strength of the theory is that it describes the complete evolution (including polarization and entanglement) of multi-photon states propagating through inhomogeneous media. As a demonstration of the two-photon wave function's use, we show how two photons in an orbital-angular-momentum entangled state decohere upon propagation through a turbulent atmosphere.
Cell membrane mechanics.
Methods in cell biology
55
157-171
1998
10.1016/S0091-679X(08)60407-0
Volume 55 in Methods in Cell Biology is a concise laboratory book that emphasizes the methods and technologies needed to use single polarized laser light source that functions simultaneously as an optical trap and a dual-beam interferometer.* * Provides a practical laboratory guide for methods and technologies used with laser tweezers* Includes comprehensive and easy-to-follow protocols
Calculation of Residual Stresses of Cross-Ply Laminates
Journal of Composite Materials
37
11
945-966
2003
10.1177/0021998303037011001
Residual stresses in composite laminates are primarily caused by the difference between the volume change in the polymer matrix and the reinforcing fibres. In resins, volume changes are produced by the chemical shrinkage during the cure and by thermal expansion through the whole manufacturing process. In the laminate plane the resin volume change is restricted, which causes quite large dimension change in thickness direction. In addition, global and local structures of the laminate are engaged such that they together determine the laminate temperature, degree of cure and dimension change histories. Unlike most existing work, which model the laminates either in global or in local level only, a calculation procedure of the residual stresses is developed using both the global and the local model. A perfect coupling between the models has not been reached, but the residual stresses in the local structure are obtained by using the results of the global structure as boundary conditions. The computations address that the local stresses in the resin and fibres differ remarkably from the macro scale stresses in the laminate layers. Also, it is necessary to model the laminate in three dimensions, because the residual stresses in the resin are closely related to the changes in the laminate thickness.
cte
Scattering in -symmetric quantum mechanics
Annals of Physics
322
2
397-433
2007
10.1016/j.aop.2006.05.011
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance.
03.65.Ca; 03.65.Nk; Non-hermitian quantum mechanics; Non-relativistic scattering theory
A hygroelastic self-consistent model for fiber-reinforced composites
Journal of Reinforced Plastics and Composites
24
5
485-502
2005
10.1177/0731684405045014
Stress analyses are performed in unidirectional fiber-reinforced composites, exposed to ambient fluid, by extending a classical self-consistent model to hygroelastic solicitations. Constitutive laws are given for the macroscopic elastic properties and Coefficients of Moisture Expansion (CME) by considering a jump in moisture content between the fiber and the matrix. Inverse forms for the unknown CME of the constituent matrix are proposed. The macroscopic (ply) and local (fiber and matrix) internal stress states are evaluated for various moisture content ratios between the matrix and the ply. The macroscopic stresses are calculated by using continuum mechanics formalisms and the local stresses are deduced from the scale transition model.
hygroelastic stresses; internal-stresses; moisture expansion coefficients; polycrystals; self-consistent model
Operator formulation of classical mechanics
American Journal of Physics
48
5
379
1980
10.1119/1.12109
An operator formulation of classical mechanics is given. Rather than being concerned with Lie algebraic or abstract Hilbert spaceproperties of classical mechanics, the present formulation is directly concerned with wave packets in configuration space and is thus more similar to that of conventional quantum theory than other extant operator formulations of classical mechanics. Among other things, the following items are discussed for classical systems: Ehrenfest’s theorem, the uncertainty principle, dissipative systems, and field theory.
Mechanics of the surf skimmer revisited
American Journal of Physics
71
September 2002
144
2003
10.1119/1.1523073
The mechanics of the surf skimmer, fun sport at the beach, is re-examined\nby using fundamental fluid mechanics. Comparison of the existing\ntheories and consideration of the effects previously neglected lead\nto the conclusion: Edge's model is physically incorrect; Tuck and\nDixon's theory provides physical insights into the surf skimming;\nthere are several trade-offs in the mechanics of the surf skimmer\nand these make this sport fun and challenging. �2003 American Association\nof Physics Teachers.
Crystallization waves in thin amorphous layers on heat conducting substrates
Proceedings in Applied Mathematics and Mechanics
10
1
493-494
2010
10.1002/pamm.201010239
A crystallization process in thin films is considered, where, driven by the release of the latent heat of fusion, the transformation from an amorphous state to the crystalline state takes place in a progressing wave of invariant shape. The crystallization rate is determined by a rate equation. The influence of the heat loss due to heat conduction into the substrate is taken into account. The resulting system of an ordinary differential equation and an integro-differential equation is solved numerically using a collocation method. The propagation speed of the wave in dependence on a non-dimensional heat loss parameter is determined. It turns out that the existence of a self-sustaining crystallization wave requires the heat loss parameter to be smaller than a certain critical value.
Extensional thin layer flows
New England Journal of Medicine
322
408
1994
In this thesis we derive and solve equations governing the flow of slender threads and sheets of viscous fluid. Our method is to solve the Navier-Stokes equations and free surface conditions in the form of asymptotic expansions in powers of the inverse aspect ratio of the fluid, i.e. the ratio of a typical thickness to a typical length. In the first chapter we describe some of the many industrial processes in which such flows are important, and summarise some of the related work which has been carried out by other authors. We introduce the basic asymptotic methods which are employed throughout this thesis in the second chapter, while deriving models for two-dimensional viscous sheets and axisymmetric viscous fibres. In chapter 3 we show that when these equations govern the straightening or buckling of a curved viscous sheet, simplification may be made via the use of a suitable short timescale. In the following four chapters, we derive models for nonaxisymmetric viscous fibres and fully three-dimensional viscous sheets; for each we consider separately the cases where the dimensionless curvature is small and where the dimensionless curvature is of order one. We find that the models which result bear a marked similarity to the theories of elastic rods, plates and shells. In chapter 8 we explain in some detail why the Trouton ratio - the ratio between the extensional viscosity and the shear viscosity - is 3 for a slender viscous fibre and 4 for a slender viscous sheet. We draw our conclusions and suggest further work in the final chapter.
fluid mechanics; partial differential equations
Game design mechanics
The Art of Game Design A book of lenses
Masters
129-168
2008
53-609 (Carnegie-Mellon) - a lecture and project based course that teaches the mechanics and processes of good game design. The principles learned in this class apply equally well to card games, board games, party games, any types of games, and design many games. Anyone interested in interactive entertainment or in creating compelling experiences should benefit from this course.
Towards a Nominalization of Quantum Mechanics
Mind
105
418
209-226
1996
10.1093/mind/105.418.209
This paper contains the most important part of a nominalization of quantum mechanics, namely, a nominalistic recovery of the algebraic structure of Hilbert space; thus, it contains a response to David Malament's objection that Hartry Field's nominalization program cannot be extended to quantum mechanics. My basic strategy of nominalization is to take the closed subspaces of the Hilbert spaces appearing in quantum mechanics as representing physically real (and nominalistically kosher) propensities of quantum systems. (This does not commit me to any definite interpretation of quantum mechanics is irreducibly indeterministic.)
Preparation of thin films
Solar Energy Materials
16
471-475
1987
10.1016/0165-1633(87)90048-7
"Preparation of Thin Films provides a comprehensive account of various deposition techniques for the preparation of thin films of elements, compounds, alloys, ceramics, and semiconductors - emphasizing inorganic compound thin films and discussing high vacuum and chemical deposition methods used for preparing high temperature superconducting oxide thin films. "
Econophysics, Statistical Mechanics Approach to
Distribution
24
2007
This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.
Applications; Data Analysis, Statistics and Probability; Physics and Society; Statistical Finance; Statistical Mechanics
Modified Wöhler Curve Method and multiaxial fatigue assessment of thin welded joints
International Journal of Fatigue
43
30-42
2012
10.1016/j.ijfatigue.2012.01.026
The present paper is concerned with the use of the Modified W??hler Curve Method to estimate fatigue lifetime of thin welded joints of both steel and aluminium subjected to in-phase and out-of-phase multiaxial fatigue loading. The Modified W??hler Curve Method postulates that, in welded connections subjected to in-service complex time-variable loading, fatigue damage reaches its maximum value on that material plane experiencing the maximum range of the shear stress amplitude, such a stress quantity being calculated according to the Maximum Variance concept. The most important peculiarity of the above multiaxial fatigue criterion is that it can be applied by performing the stress analysis in terms of both nominal and local quantities, where in the latter case the relevant stress state at the assumed critical locations can be estimated according to either the reference radius concept or the Theory of Critical Distances. The accuracy and reliability of our multiaxial fatigue criterion was systematically checked through several experimental results taken from the literature and generated by testing, under in-phase and out-of-phase biaxial loading, welded joints of both steel and aluminium having thickness of the main tube lower than 5 mm. Such a systematic validation exercise allowed us to prove that the Modified W??hler Curve Method is a powerful tool suitable for performing the fatigue assessment of thin welded joints, this holding true independently of the strategy adopted to perform the stress analysis. Finally, a microstructural motivation of the length scales included in the Theory of Critical Distances can be established by linking this technique to gradient mechanics, as we will argue. ?? 2012 Elsevier Ltd. All rights reserved.
Gradient mechanics; Multiaxial fatigue; Notch stress; Theory of Critical Distances; Thin welded joints
On the optimum design of thin-walled compression members
Journal of the Mechanics and Physics of Solids
20
2
101-109
1972
10.1016/0022-5096(72)90034-8
Current discussions concerning the validity of simultaneous buckling as a criterion of optimization are quantified by the formulation of a simple design problem for a thin-walled strut. Here, simultaneity of overall and local buckling leads to a well-defined optimum for a perfect column, and recent calculations by A. van der Neut are used to examine the extent to which this optimum can be eroded away by imperfection-sensitivity associated with coupled-branching behaviour. The optimum is seen to shift quite significantly for small imperfections, and for larger ones it can be entirely eliminated.
The reinterpretation of wave mechanics
Foundations of Physics
1
1
5-15
1970
10.1007/BF00708650
... It is therefore tempting to establish a relation between the two fundamental relativistic invariants, action and entropy. ... This concludes the account of my present ideas on the reinterpretation of wave mechanics with the help of images which had guided me in my early work. ...
Experimental and Computational Modeling of Joint and Ligament Mechanics
Journal of applied biomechanics
20
450-474
2004
... JAB Volume 20, Issue 4, November. Original Research Experimental and Computational Modeling of Joint and Ligament Mechanics . Quantitative data on the mechanics of diarthrodial joints and the function of ligaments are needed ...
Fracture mechanics and its relevance to botanical structures
American Journal of Botany
93
10
1449-1454
2006
10.3732/ajb.93.10.1449
In the field of fracture mechanics, an analytical framework has been established for understanding the mechanical failure of any structure made of inherently flawed materials. In the context of botany, this includes an extraordinarily wide variety of turgid and/or woody structures made of cellulose-based tissues, the diverse soils penetrated by their roots, and a multitude of plant-based commodities and foodstuffs. The goal of this article is to provide an overview of the theory of engineering fracture mechanics and to identify some special characteristics of wood and other plant-based materials that require further development in this area.
Crack; Fracture mechanics; Fracture toughness; Stress intensity factor
TORQUE GENERATED IN SINGLE AND MULTI-PLY YARNS AS A FUNCTION OF CHANGES IN YARN TENSION.
Textile Research Journal
49
9
499-506
1979
This paper presents a theoretical and experimental investigation of the torque generated in a yarn as a result of a change in applied tensile stress. Single and plied yarn structures are analyzed, and it is shown that small elastic extensions of a yarn, the change in yarn torque is linearly related to the applied tensile force P and also to the yarn twist. For plied yarns, a ratio of ply twist to single-yarn exists, for which the structure is torsionally insensitive to changes in applied tension. An expression is derived, relating this twist ratio to the yarn geometry, and values of 0. 33, 0. 20, and 0. 11 are experimentally verified for 2-, 4-, and 7-ply yarns, respectively.
On the linear and nonlinear analysis of cross-ply laminated composite plates
Composite Structures
29
1
89-98
1994
http://dx.doi.org/10.1016/0263-8223(94)90038-8
The cylindrical bending of a cross-ply laminated plate subjected to a uniform transverse load is evaluated via classical laminated plate theory and Von Karman's large deflection theory, respectively. It is shown that for the analysis of several cross-ply composite laminates, the common concept which expects that the linear analysis will provide a more accurate result for the plate with smaller deflection is not always correct, and the classical laminated plate theory may be inadequate even in the range of small deflection. Finally, the influence of the amplitude of deflection, temperature variation, boundary conditions, span-to-thickness ratio and stacking sequence on the accuracy of the linear and nonlinear analysis is evaluated.
Probabilities in Statistical Mechanics
Oxford Handbook of Probability and Philosophy
1-41
2014
This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended ... \n
Quantum dressed classical mechanics
The Journal of Chemical Physics
114
15
6641
2001
10.1063/1.1357787
We have formulated a new way of making quantum corrections to classical mechanics. The method is based on a time-dependent discrete variable representation (DVR) of the wave function with grid points defined by the Hermite part of a basis set, the Gauss–Hermite basis set. The formulation introduces a set of grid points which follow the classical trajectory in space. With enough trajectories (DVR-points) the method approaches the exact quantum formulation. With just a single grid point in each dimension, we recover classical mechanics.
Stability of free-surface thin-film flows over topography
Journal of Fluid Mechanics
2001
10.1017/S0022112001006231
We consider the stability of the steady free-surface\nthin-film flows over topography examined in detail by Kalliadasis\net al. (2000). For flow over a step-down, their computations\nrevealed that the free surface develops a ridge just before the\nentrance to the step. Such capillary ridges have also been observed\nin the contact line motion over a planar substrate, and are a key\nelement of the instability of the driven contact line. In this\npaper we analyse the linear stability of the ridge with respect to\ndisturbances in the spanwise direction. It is shown that the\noperator of the linearized system has a continuous spectrum for\ndisturbances with wavenumber less than a critical value above which\nthe spectrum is discrete. Unlike the driven contact line problem\nwhere an instability grows into well-defined rivulets, our analysis\ndemonstrates that the ridge is surprisingly stable for a wide range\nof the pertinent parameters. An energy analysis indicates that the\nstrong stability of the capillary ridge is governed by\nrearrangement of fluid in the flow direction owing to the net\npressure gradient induced by the topography at small wavenumbers\nand by surface tension at high wavenumbers.\n
A numerical approach for the stability analysis of open thin-walled beams
Mechanics Research Communications
48
76-86
2013
10.1016/j.mechrescom.2012.12.008
A finite differences procedure is used to study the buckling of non-trivial equilibrium solutions for open thin-walled beams in a dynamic setting. A direct one-dimensional model with a coarse descriptor of warping is adopted. The algorithm describes non-trivial equilibrium paths by integrating discretized field equations, suitably written in terms of velocities. Some benchmark cases under conservative loading are discussed. Known results for the first critical loads are found to validate the procedure. New results are found accounting for non-trivial equilibrium paths, thus providing an estimate for the error made by linearizing around trivial equilibrium paths. The effect of warping on the critical loads is also investigated.
Buckling; Finite differences; Thin-walled beams
Modelization and numerical approximation of piezoelectric thin shells Part III: From the patches to the active structures
Computer Methods in Applied Mechanics and Engineering
192
4075-4107
2003
10.1016/S0045-7825(03)00363-3
A two-dimensional modelization of piezoelectric thin shells is studied in the first part of this work. The associated approximation by finite element method is analyzed and numerically illustrated in the second part of this work. Practically, these piezoelectric structures are generally used as patches or thin films bonded on, or inserted into, classical structures in order to detect or to generate some deformations, i.e., as sensors or actuators. The objective of this third part is to modelize such a type of assemblage, to analyze its associate approximation and to illustrate the relevance of this method by considering significant numerical experiments. ?? 2003 Elsevier B.V. All rights reserved.
From Lagrangian mechanics fractal in space to space fractal Schr??dinger's equation via fractional Taylor's series
Chaos, Solitons and Fractals
41
4
1590-1604
2009
10.1016/j.chaos.2008.06.027
By considering a coarse-grained space as a space in which the point is not infinitely thin, but rather has a thickness, one can arrive at an equivalence, on the modeling standpoint, between coarse-grained space and fractal space. Then, using fractional analysis (slightly different from the standard formal fractional calculus), one obtains a velocity conversion formula which converts problems in fractal space to problems in fractal time, therefore one can apply the corresponding fractional Lagrangian theory (previously proposed by the author). The corresponding fractal Schr??dinger's equation then appears as a direct consequence of the usual correspondence rules. In this framework, the fractal generalization of the Minkowskian pseudo-geodesic is straightforward. ?? 2008 Elsevier Ltd. All rights reserved.
A comparison of ply-level and sublaminate-level scaling of fibre-metal laminates with in-plane dimensions
Advanced Composites Letters
16
6
233-236
2007
The work presented in this paper investigates size effects in 2D-scaled (in-plane dimensions) FMLs based on a self-reinforcing polypropylene composite and aluminum. Two different scaling approaches are adopted in this study, these being ply-level scaling using laminates with a stacking sequence of [Al-n, 0 degrees/90 degrees(n)](s) and sublaminate-level scaling involving a stacking sequence of [Al, 0 degrees/90 degrees](ns) where n =1/4, 1/2, 3/4 and 1, representing the increase of in-plane dimensions. An apparent increase in strength for ply-level specimens was observed with scale size while sublaminate-level scaling did not present scaling effects.
The three-ply analytic approaches of cycle working chart in design of automatic packaging machine
Proceedings of 15th IAPRI World Conference on Packaging
242-246
2006
Movement of each executive mechanism of the automatic packaging machines are complicated. The packaging machine standard executive mechanism requests coordination between the movements each other, and a strict machine operating cycle period is required. The paper assimilates conventional design knowledge about periodic diagram of the automaton and gives a very comprehensive analysis of the internal relation among periodic motions of executive mechanisms of automatic packaging machines, Summarizes three period: movement-period > coordination-period > integration-period. A new way began to form in the paper, called as three-ply analytics, of which principle is conciseness, it easy to be popularized.
Automatic packaging machine; Movement design; Three-ply analytic approaches; Working cycle chart
POSTBUCKLING RESPONSE OF ANTISYMMETRIC ANGLE-PLY LAMINATES TO UNIFORRM TEMPERATURE LOADING
Acta Mechanica
72
Compendex
173-183
1988
The postbuckling behavior of antisymmetric angle-ply plates, resting on sumple supports and subjected to a gradually increasing uniform temperature field is investigated. Stable equilibrium configurations are determined through a direct application of the principle of minimum potential energy. Since nonunique equilibrium states may exist, a method of incremental loading is employed to identify the particular state associated with a given thermal loading path. Numerical results of fiber-reinforced laminates illustrate the effects of ply orientation, number of layers and aspect ratio on the postbuckling behavior. The phenomena of secondary buckling is examined in detail.
COMPOSITE STRUCTURES; LAMINATED PRODUCTS - Performance; PLATES - Buckling
An energy criterion to predict delayed failure of multi-directional polymer matrix composites based on a non-linear viscoelastic model
Composites Part A: Applied Science and Manufacturing
35
559-571
2004
10.1016/j.compositesa.2003.12.002
The life-time prediction of multi-directional polymer composite under creep loading is proposed and assessed. Energy failure criterion, based on the theoretical developments of Reiner and Weissenberg, is modified and incorporated into a computer program called LAMFLU. This algorithm was developed to predict the long-term behavior of viscoelastic polymer matrix composite laminates. In the present theoretical model, failure is part of the complete constitutive description of the material. The laminate failure prediction is based on the last ply failure; each ply failure promotes a stiffness degradation related with the failure mode. The quality of theoretical predictions is good compared with published experimental results. ?? 2004 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Creep; B. Strength; C. Laminate mechanics
Recycling of waste RFL (Resorcinol-Formaldehyde Latex) dip solid in natural rubber-based ply skim compound
Progress in Rubber, Plastics and Recycling Technology
23
3
181-193
2007
Waste resorcinol - formaldehyde - latex (RFL) dip solid was collected from the suction chamber of a typical tyre industry dip unit. The cure acceleration effect of the waste material was studied in a natural rubber (NR) based filled compound. The effect of the waste material was examined in a natural rubber (NR) based ply skim compound of a bias tyre with cure package modification. Rheological, tack index, stress-strain properties, swell index, dynamic mechanical properties, H-adhesion before and after anaerobic aging was also studied. © Rapra Technology, 2007.
Nonlinear free and forced vibrations of anti-symmetric angle-ply hybrid laminated rectangular plates
Journal of Composite Materials
48
9
1091-1111
2014
10.1177/0021998313482156
In this article, the nonlinear equations of motion for anti-symmetric angle-ply composite rectangular plates have been derived using the first-order shear deformation theory, including shear deformation and rotary inertia. By using the Galerkin method, five coupled nonlinear partial differential equations of motion are reduced to a nonlinear ordinary differential equation. Then, the multiple time scales method is used to solve the obtained equation and to derive an analytical relation for the nonlinear frequency. Results are compared with the literature and good agreement is achieved. After proving the validity of this study, nonlinear free and forced vibration of a fiber metal laminated rectangular plate have been studied and the effects of some system parameters on the nonlinear behavior of the FML rectangular plate have been investigated.
Effect of Off – Axis Matrix Cracking on Stiffness of Symmetric Angle-Ply Composite Laminates
International Journal of Fracture
139
3-4
529-536
2006
10.1007/s10704-006-0100-9
Matrix cracking models developed for cross-ply composite laminates\ncannot easily be applied to more complicated geometries. In this paper\na detailed analysis of the effect of matrix cracking on the\nlongitudinal Young's Modulus of a {[}0/45](s) plate under uniaxial\ntension is attempted. The theoretical approach, based on a\nsemi-analytical generalized plane strain model, is compared to\nexperimental data obtained by microscopic strain, measurements on a\nfiber sensor using the technique of laser Raman Spectroscopy. The\nexperimental results are in a good agreement with theoretical stiffness\ndegradation predictions obtained using the semi-analytical model.
Non-homogeneous response of cross-ply laminated elastic plates using a higher-order theory
Composite Structures
44
4
297-305
1999
10.1016/s0263-8223(99)00006-9
A consistent formulation for the bending of cross-ply laminated composite plates that possess non-homogeneous elastic properties is presented. Based on a third-order shear deformation plate theory, the governing equations are obtained using the principle of virtual work. With the help of the small parameter method, a wide variety of results are presented for the symmetric and antisymmetric analysis of non-homogeneous rectangular laminated plates. The influence of non-homogeneity, lamination schemes, aspect ratio and material anisotropy on the deflections and stresses is investigated. The new results for non-homogeneous response of composite plates should serve as bench marks for future comparisons. (C) 1999 Elsevier Science Ltd. All rights reserved.
Low Velocity Transverse Impact Behavior of 8-ply, Graphite-Epoxy Laminates
Journal of Reinforced Plastics and Composites
2
4
216-225
1983
10.1177/073168448300200401
This work discusses the behavior of 8-ply, quasi-isotropic, graphite epoxy laminates subjected to low velocity transverse impact loading. Large deflection theory of plates was used to predict the load-deflection characteristics during the impact event. The im pact model considered that the indentation, flexural and shear stiffnesses could be represented by 3-equivalent springs in series.The analysis of static and dynamic impact loading test-data concluded that the mem brane parameter, β, used in flexural stiffness relation was proportional to the square of the coefficient of restitution, e, of the impactor. Use of β = 0.443 e2 was made in load- deflection relations to consider the drop in plate stiffness due to delamination.The results of impact tests up to impact velocity 5.3 m/sec. were found in close agreement of the predictions.
Statistical Mechanics of Jammed Matter
Science
cond-mat.s
0503081v1
51
2005
10.1002/352760362X.ch3
A thermodynamic formulation of jammed matter is reviewed. Experiments and simulations of compressed emulsions and granular materials are then used to provide a foundation for the thermodynamics.
Microstructure and magnetic properties of CoFe2O4 thin films deposited on Si substrates with an Fe3O4 under-layer
Science China Physics, Mechanics and Astronomy
54
7
1235-1238
2011
10.1007/s11433-011-4366-1
The microstructure and magnetic properties of cobalt ferrite thin films deposited by the sputtering method on an Fe(3)O(4) under-layer were investigated at different post-annealing temperatures. Results show that the Fe(3)O(4) under-layer can accelerate the grain growth of cobalt ferrite films due to the phase transformation of the Fe(3)O(4) under-layer at about 400A degrees C-500A degrees C. By introducing the Fe(3)O(4) under-layer, cobalt ferrite nanocrystalline thin films with high coercivity can be obtained at lower post-annealing temperatures.
A modified Shkadov's model for thin film flow of a power law fluid over an inclined surface
Comptes Rendus - Mecanique
2009
10.1016/j.crme.2009.01.002
A new evolution equation coherent up to order one in the long wave parameter is derived to describe the non-linear behavior of a thin film flow down an inclined plane of a power law fluid for small to moderate Reynolds numbers. The method we have used combines the lubrication theory and the weighted residual approach, with a suitable weighting function. That approach was first developed by Ruyer-Quil and Manneville (2000) for Newtonian fluids. The model has the advantages of both the Shkadov type approach far from criticality and that of Benney close to criticality. To cite this article: M. Amaouche et al., C. R. Mecanique 337 (2009). ?? 2009 Acad??mie des sciences.
Fluid mechanics; Shkadov's model; Thin film flow
Controllable crystallization of Ge2Sb2Te5 phase-change memory thin films driven by multiple femtosecond laser pulses
Materials Science and Engineering: B
193
189-197
2015
10.1016/j.mseb.2014.12.017
In this study, controllable crystallization processes of as-deposited amorphous Ge2Sb2Te5 phase-change memory thin films driven by multiple femtosecond laser pulses were investigated in detail. The threshold effects of pulse fluence and the number of pulses were analyzed comprehensively using real-time reflectivity measurements and two-temperature model calculations. The different optical transients indicated three kinds of crystallization processes at low, medium, and high fluences. These results may provide further insights into the ultrafast phase-transition mechanics and are useful in the design of programmable multi-level logic devices based on phase change memory materials.
Crystallization dynamics; Femtosecond laser pulse; Ge2Sb2Te5 thin film; Phase change memory material
Quantum mechanics, randomness, and deterministic reality
Physics Letters A
172
1-2
6-12
1992
10.1016/0375-9601(92)90181-K
We describe and analyze a new formulation of Bohmian mechanics — the deterministic theory of particles in motion that emerges from Schrödinger's equation for a system of particles when we merely insist that “particles” means particles. This mechanics resolves all paradoxes associated with the measurement problem in nonrelativistic quantum mechanics. It accounts for quantum randomness, absolute uncertainty, the meaning of the wave function of a system, collapse of the wave function, and familiar (macroscopic) reality.
Bistable shape memory thin film actuators
Smart Structure and Materials 2003: Active Materials: Behavior and Mechanics
5053
101-109
2003
Doi 10.1117/12.484696
Shape memory alloys (SMA) are able to provide high work output when they undergo the martensitic transformation. Therefore, they present a favorable actuation mechanism for microsystems, e.g. for microvalves, switches or microgrippers. Sputter deposited thin SMA films are already in use as free-standing films or as composites in combination with a substrate. In the case of a composite, the substrate works as a bias spring and enables the SMA actuator to show a two way behavior. To enlarge the potentialities of shape memory based actuators a bistable principle is presented. This is realized by the combination with a polymer exhibiting a glass transition temperature (T-g) between the hysteresis loop of the shape memory composite. The fabrication of this composite is described with a special emphasis on the development of suitable polymer samples.
actuators; polymer blends; random copolymer; shape memory; thermoplastic elastomer; thin films
Delamination of compressed thin layers at corners
International Journal of Solids and Structures
45
5867-5878
2008
10.1016/j.ijsolstr.2008.07.004
An analysis of delamination for a thin elastic layer under compression, attached to a substrate at a corner is carried out. The analysis is performed by combining results from interface fracture mechanics and the theory of thin shells. In contrast with earlier results for delamination on a flat substrate, the present problem is not a bifurcation problem. Crack closure at sufficiently high stress levels are shown to occur. Results show a very strong dependency on fracture mechanical parameters of the angle of the corner including the range of parameters where crack closure occurs. Analytical results for the fracture mechanical properties have been obtained, and these are applied in a study of the effect of contacting crack faces. Special attention has been given to analyse conditions under which steady state propagation of buckling driven delamination takes place. © 2008 Elsevier Ltd. All rights reserved.
Crack closure; Delamination; Fracture mechanics; Steady state crack propagation; Thin layers
Exact two-dimensional piezoelasticity solution for buckling of hybrid beams and cross-ply panels using transfer matrices
Composite Structures
64
1
1-11
2004
10.1016/S0263-8223(03)00140-5
Two-dimensional exact piezoelasticity solution is presented for buckling of simply supported symmetrically laminated hybrid beam and cross-ply panel with elastic substrate and piezoelectric layers. Buckling is considered under axial strain and actuation potentials for movable inplane end conditions and under actuation potential alone for immovable inplane end conditions. The governing equations for buckling mode are formulated in terms of six variables: displacements u, w, potential ??, stresses ??z, ??zx and electric displacement Dz. These entities are expanded in Fourier series that satisfy the end conditions. The governing equations reduce to differential equations in z with coefficients dependent on the axial load and actuation potentials. The solution has six constants for each layer. The transfer matrix is derived relating the six primary variables at the top and bottom of a layer. The six conditions ??z=??zx=0, ??=0 at the top and bottom of the beam are used to set up three homogeneous equations for u, w, Dz at the bottom. The determinant of their coefficient matrix is set to zero to obtain the buckling axial strain/potential. The present benchmark solution would help assess one-dimensional theories for buckling of hybrid beams. ?? 2003 Elsevier Ltd. All rights reserved.
Actuator; Buckling; Column; Exact solution; Hybrid beam; Piezoelasticity; Transfer matrix
Imprints of the Quantum World in Classical Mechanics
Foundations of Physics
41
9
1415-1436
2011
10.1007/s10701-011-9544-5
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless particles is a classical equation which is equivalent to Hamilton's equations.
Hamiltonian flows; Quantization; Schr??dinger's equation; Stone's theorem; Symplectic covariance of Weyl calculus
Fatigue behaviour of cross-ply Nicalon/CAS-II glass-ceramic matrix composite at room and elevated temperatures
Composites Part A: Applied Science and Manufacturing
35
83-94
2004
10.1016/j.compositesa.2003.08.009
An experimental study was carried out on cross-ply Nicalon/CAS-II glass-ceramic matrix composite under monotonic, static, cyclic and a combination of static and cyclic loadings. Tests were carried out at room temperature (20 °C) and 800 °C in air with varying levels of peak stress, stress ratio and loading history. At room temperature and 800 °C, the composite exhibited fatigue limit (106 cycles) at 40 and 20% of the room temperature flexural strength, respectively. Therefore, the fatigue limit of the composite at 800 °C reduced to half of its room temperature value. The composite also exhibited a shorter lifetime under cyclic loading than under static loading at 800 °C. Although the residual strength of the specimens those survived 106 cycles at 20 °C was ̃15% lower than the original flexural strength, the residual strength of the specimens those survived 106 cycles at 800 °C was ̃20% higher than the corresponding flexural strength. It indicates that the fatigue damage mechanisms at 20 °C is different from that at 800 °C. Parameters such as peak stress, stress ratio and loading history were also found to play strong role on the fatigue damage mechanisms of this composite. © 2004 Published by Elsevier Ltd.
A. Ceramic-matrix composites (CMCs); B. Fatigue; D. Fractography; D. Mechanical testing
In-situ SEM study of transverse cracking and delamination in laminated composite materials
Composites Science and Technology
105
118-126
2014
http://dx.doi.org/10.1016/j.compscitech.2014.10.012
Abstract Transverse microcrack growth and delamination are two key damage mechanisms in laminated composite materials, and while often treated separately in damage prediction studies, they are, in fact, highly coupled. Essentially, transverse cracks initiate around fibres, coalesce and grow until they extend to ply boundaries, at which point they initiate micro-delaminations. Under increasing load these micro-delaminations eventually coalesce to form macroscopic delaminations, which severely reduce material stiffness and lead to catastrophic failure of the composite structure. This paper presents an investigation into how altering transverse crack densities can influence the growth of delaminations. Novel in-situ SEM micromechanical testing and acoustic damage detection techniques were coupled and used to determine transverse crack initiation loads, transverse crack density, and local micro-delamination lengths for a number of cross-ply laminates. The laminates were loaded in a four-point bending mode to induce crack opening direct stresses on the tension side. To examine the effect of combined direct and shear stresses, the laminates were also loaded in a three-point bending mode, and suitable comparisons between both bending modes allowed for the influence of the shear stress to be isolated. The main variable under investigation is the thickness of the transverse ply block, and it is shown that increasing the number of transverse plies (i.e. thickness) can significantly increase the load carrying capacity of the laminate by reducing the transverse crack density. It was found that the lower transverse crack densities meant that the micro-delaminations which initiated at the ply boundary required significantly greater stress to fully coalesce as the distance between transverse cracks was greater. Once micro-delamination had initiated, its length was found to be linearly related to the load applied. For all layups investigated, the average micro-delamination length seen immediately prior to catastrophic failure was approximately 1.2 times the thickness of the tensile 90° ply portion of the laminate.
B. Delamination; C. Damage mechanics; C. Transverse cracking; D. Scanning electron microscopy (SEM)
An improved prediction of stability lobes using nonlinear thin wall dynamics
Journal of Materials Processing Technology
210
6-7
969-979
2010
10.1016/j.jmatprotec.2010.02.009
With manufactured sections getting much thinner due to weight requirements, there is the vital need for more accurate prediction of stable cutting conditions in machining. The tools used in machining vary in shapes and design hence a more robust model is required to include these varieties. This paper first presents improvements to the well known stability model, by considering the nonlinearity of the cutting force coefficients, and axial immersion angle and their dependency on the axial depth of cut. Secondly, a finite element (FE) and Fourier transform approach to including the nonlinearity of the workpiece dynamics in thin wall machining when predicting stable region is presented. The model and approach are validated extensively using experimental results and a very good agreement has been achieved. ?? 2010 Elsevier B.V. All rights reserved.
Axial immersion; Cutting force; Cutting force coefficients; Discrete Fourier transform; FEA; Finite element modal analysis; High speed milling; Transfer function
Measuring elastic-plastic properties of thin films on elastic-plastic substrates by sharp indentation
Mechanics of Materials
41
3
308-318
2009
10.1016/j.mechmat.2008.10.008
A new technique has been proposed to measure the elastic-plastic properties of thin film materials on elastic-plastic substrates from the force-displacement curve of the sharp indentation. With the assistance of the substrate effect, explicit relationships between the indentation parameters and the elastic-plastic properties of film-substrate materials are established through extensive finite element analysis. The forward analysis predicts an indentation response from a given set of elastic-plastic properties of film/substrate systems considering the substrate effect, whereas the reverse analysis seeks to extract film elastic-plastic properties from depth-sensing indentation response with a moderate penetration depth. Numerical indentation tests are carried out to examine the effectiveness of the proposed method. Both nanoindentation and uniaxial tensile tests are also carried out on Ni films coated on mild steel substrates and the good agreement shows that the proposed film indentation technique can be applied in practice. Crown Copyright ?? 2008.
Elastic-plastic; Finite element analysis; Force-displacement; Indentation parameter; Nanoindentation
Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry
Journal of the Mechanics and Physics of Solids
51
2191-2211
2003
10.1016/j.jmps.2003.09.031
Large deformation behavior prior to and after bifurcation of thin W films on much thicker Si substrates is investigated by recourse to coherent gradient sensing (CGS), which is an optical, full-field and vibration-insensitive technique. Since fringes obtained by CGS represent the contours of gradient in out-of-plane displacement through appropriate optics, curvature of the wafer can be obtained directly from the fringe number density. The measured curvatures in two orthogonal principal directions, whose values agree reasonably with both analytical and numerical predictions based on large deformation theory, clearly show that the equilibrium shape of the wafer changes from a sphere to an ellipsoid when bifurcation occurs. In contrast to the one-dimensional scanning method, which provides only a single normal (or direct) curvature component, twist (or shear) as well as normal components of curvatures can be obtained as the wafer is rotated with respect to its flat zone. A classical Mohr's circle representation is also used to rationalize evolution of the twist curvatures. Finally, local curvature variations due to non-uniform film stresses can be captured by full-field curvature maps using image processing analysis. © 2003 Elsevier Ltd. All rights reserved.
Bifurcation; Coherent gradient sensing; Full-field curvature map; Large deformation; Twist curvature
4 . Some statistical mechanics
Lattice Boltzmann models- An Introduction
1946
2007
139-158
2000
Contents. 4.1 The Boltzmann equation 4.1.1 Five collision invariants and Maxwells distribution 4.1.2 Boltzmanns H-theorem 4.1.3 The BGK approximation 4.2 Chapman-Enskog: From Boltzmann to Navier-Stokes 4.2.1 The conservation laws 4.2.2 The Euler equation 4.2.3 Chapman-Enskog expansion 4.3 The maximum entropy principle
Mechanical behavior and health monitoring by Acoustic Emission of unidirectional and cross-ply laminates integrated by piezoelectric implant
Applied Acoustics
86
118-125
2014
10.1016/j.apacoust.2014.04.011
Recent progress in sensor technologies, signal processing and electronics has made it possible to fulfill the need for the development of in-service structural health monitoring (SHM) systems. This study presents a health monitoring of composite materials integrated by piezoelectric sensor using Acoustic Emission (AE) technique. A series of specimens of composite laminates with and without piezoelectric implant were subject to three-point bending in static and creep tests while continuously monitoring the response by the AE technique. The analysis and observation of AE signals lead to the identification of the acoustic signatures of damage mechanisms in composite laminates. The mechanical behavior of composites with and without integrated sensor shows no difference in the form. The incorporation of piezoelectric sensor influences specially the fracture load and causes low degradation of mechanical properties of materials. One of the major differences between the two types of materials (with and without embedded sensor) is the intense acoustic activity in the integrated material. © 2014 Elsevier Ltd. All rights reserved.
Acoustic Emission; Creep; Damage; Laminates; Piezoelectric implant; Static; Three-point bending
Experimental and numerical analysis of delamination growth in double cantilever laminated beams
Engineering Fracture Mechanics
69
6
687-699
2002
10.1016/S0013-7944(01)00106-0
Delamination crack growth in laminated composites is investigated using experiments and finite element (FE) models. Tests are performed on cross-ply graphite/epoxy specimens under static conditions. The load-displacement response is monitored in the tested coupons along with crack length. The FE models employ a cohesive layer that is used to simulate the debonding and crack propagation. The cohesive parameters are calibrated from the experimental load-displacement curves. Crack growth and strain measurements are compared with those from the FE models. The predicted results from the FE models are in good agreement with the test results. The same modeling approach is also used to simulate crack propagation in the transverse direction of a notched laminate. The proposed FE analysis with cohesive layers can simplify fracture toughness assessment in multilayered specimens. ?? 2002 Elsevier Science Ltd. All rights reserved.
Cohesive; Composite; Crack; Cross-ply; Double cantilever beam; Experiment; Finite element; Graphite/epoxy; Growth; Laminate
Mechanics of plasma exposed spin-on-glass (SOG) and polydimethyl siloxane (PDMS) surfaces and their impact on bond strength
Applied Surface Science
253
9
4220-4225
2007
10.1016/j.apsusc.2006.09.028
Silicone polymer (PDMS), widely used for micro-fluidic and biosensor applications, possesses an extremely dynamic surface after it is subjected to an oxygen plasma treatment process. The surface becomes extremely hydrophilic immediately after oxygen plasma exposure by developing silanol bond (SiOH), which promotes its adhesion to some other surfaces like, silicon, silicon dioxide, glass, etc. Such a surface, if left in ambient dry air, shows a gradual recovery of hydrophobicity. We have found an identical behavior to occur to surfaces coated with a thin continuous film of SOG (methyl silsesquioxane). The chemistry induced by oxygen plasma treatment of a spin-on-glass (SOG) coated surface provides a much higher density of surface silanol groups in comparison to precleaned glass, silicon or silicon dioxide substrates thus providing a higher bond strength with polydimethyl siloxane (PDMS). The bonding protocol developed by using the spin coated and cured SOG intermediate layer provides an universal regime of multi level wafer bonding of PDMS to a variety of substrates. The paper describes a contact angle based estimation of bond strength for SOG and PDMS surfaces exposed to various combinations of plasma parameters. We have found that the highest bond strength condition is achieved if the contact angle on the SOG surface is less than 10°.
47.54.Jk; 47.55.D−; 47.55.dr; 47.57.Ng; ATR-FTIR; Bond strength; Contact angle; PDMS; Plasma; SOG
Fundamentals of the Phenomenological Theory of Nonlinear Fracture Mechanics
Journal of Applied Mechanics
50
4b
1042-1051
1983
10.1115/1.3167187
An introduction to the theoretical foundations of the phenomenological theory of nonlinear fracture mechanics is given. Following an outline of the full range of objectives of nonlinear fracture mechanics, the paper focuses on the phenomenological, or semiempirical, approach to the initiation of crack growth and the subsequent quasi-static crack growth and loss of stability under monotonic load histories.
Quantum Mechanics, Group Theory, and C60
Journal of Chemical Education
71
6
464
1994
10.1021/ed071p464
A model for the electronic structure of C60 based on the principles of quantum mechanics and group theory.
Short-term plyometric training improves running economy in highly trained middle and long distance runners
J.Strength.Cond.Res.
20
1064-8011 (Print)
947-954
2006
Fifteen highly trained distance runners VO(2)max 71.1 +/- 6.0 ml.min(-1).kg(-1), mean +/- SD) were randomly assigned to a plyometric training (PLY; n = 7) or control (CON; n = 8) group. In addition to their normal training, the PLY group undertook 3 x 30 minutes PLY sessions per week for 9 weeks. Running economy (RE) was assessed during 3 x 4 minute treadmill runs (14, 16, and 18 km.h(-1)), followed by an incremental test to measure VO(2)max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km.h(-1) (4.1%, p = 0.02), but not at 14 or 16 km.h(-1). This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p = 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p = 0.09), and a lower VO(2)-speed slope (14%, p = 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or VO(2)max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics
Adult; Analysis of Variance; Australia; blood; Humans; Lactates; Male; methods; Muscle Strength; Oxygen Consumption; Physical Education and Training; Physical Endurance; physiology; Research; Running; Running economy; Time; trends
Electrohydrodynamic instabilities in thin viscoelastic films - AC and DC fields
Journal of Non-Newtonian Fluid Mechanics
196
102-111
2013
10.1016/j.jnnfm.2012.12.013
Electrohydrodynamic instabilities in thin liquid films are a promising route for the self-assembly of well-defined topographical features on the surfaces of materials. Here, we study the effect of viscoelasticity on these instabilities under the influence of AC and DC electric fields. Viscoelasticity is incorporated via a Jeffreys model, and both perfect and leaky dielectric materials are considered. In the case of DC fields, asymptotic methods are employed to shed light on the nature of a singularity that arises when solvent viscosity is neglected (i.e., the Maxwell-fluid limit). In the case of AC fields, we apply a numerical procedure based on Floquet theory to determine the maximum growth rate and corresponding wave number as a function of the oscillation amplitude and frequency. Elasticity is found to increase both the maximum growth rate and corresponding wave number, with the effects being most pronounced when the oscillation period is comparable to the fluid relaxation time. © 2013 Elsevier B.V..
Electrohydrodynamics; Instability; Thin films; Viscoelasticity
Frequency-dependent vibration analysis of symmetric cross-ply laminated plate of Levy-type by spectral element and finite strip procedures
Applied Mathematical Modelling
37
12-13
7193-7205
2013
10.1016/j.apm.2013.01.046
This research describes spectral finite element formulation for vibration analysis of rectangular symmetric cross-ply laminated composite plates of Levy-type based on classical lamination plate theory (CLPT). Formulation based on SFEM includes partial differential equations of motion, spectral displacement field, dynamic shape functions, and spectral element stiffness matrix (SESM). In this paper, vibration analysis of composite plate is investigated in two sections: free vibrations and forced vibrations. In free vibrations, natural frequencies are calculated for different Young’s moduli ratios and boundary conditions. In forced vibrations, plate vibrations are investigated under high-frequency concentrated impulsive loads. The resulting responses due to spectral element formulation are compared with those of (time-domain) finite element and analytical formulations, whenever available. The results demonstrate the superiority of SFEM with respect to FEM, in reducing computational burden, simultaneously increasing numerical accuracy, specifically for excitations of high-frequency content. By reducing the time duration of impulsive loads, and consequently increasing the modal contribution of higher modes in the transient response of plate, the accuracy of FEM responses decreases substantially accompanied with a high volume of computations, while the accuracy of the SFEM response results is very high and simultaneously, with a low computational burden. Practically, SFEM follows very closely exact analytical solutions.
Finite element method (FEM); Finite strip method (FSM); Spectral element stiffness matrix (SESM); Spectral finite element method (SFEM); Structural dynamics; Symmetric cross-ply laminated plate
An Experimental Investigation into the Strength of Angle Ply GRP Tubes under High Rate of Loading
Journal of Composite Materials
23
3 PG - 288
-305
1989
Static and dynamic burst tests were carried out on filament wound glass reinforced plas tic (GRP) tubes. The tubes were loaded under internal pressure with minimum end con straints.
Physically based damage models for laminated composites
Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications
217
163-199
2003
10.1177/146442070321700301
The computing power that is available for engineering calculation continues to grow at a dramatic pace. Engineers in industry want to have seamless models that can be used to design across the scale range from atoms to structures, including simulation of the manufacturing process. A limited aspect of this wish is the requirement to deal effectively with the progressive growth of microstructural damage in composites and its effect on both property degradation and the catastrophic failure event. This paper reviews progress that is being made at the National Physical Laboratory (NPL) with the development and validation of physically based damage growth models for laminated composites. The review includes: (a) prediction of undamaged ply properties determined from the properties of the fibre and the matrix, with emphasis on comparison of analytical models with each other, and with finite and boundary element solutions; (b) discussion of various stress transfer models, and their validation, that have been developed for application to the prediction of the properties of composite laminates having ply crack damage; (c) prediction of ply cracking in multiple-ply cross-ply laminates subject to triaxial loading (without shear) and bending; (d) prediction of ply cracking in general symmetric laminates subject to combined triaxial loading and in-plane shear loading; (e) consideration in a damage mechanics context of progressive ply crack formation in general symmetric laminates subject to thermal residual stresses and general in-plane loading, where an important new methodology is described that results from attempting to develop a continuum damage model from a physically based discrete ply cracking model based on energy concepts; (f) discussion of how the models might be integrated into finite element analysis (FEA) systems to enable strain softening in structures to be adequately modelled. The paper also includes statements concerning the status of the various models in relation to alternative approaches, and to model validation.
bending; damage mechanics; in-plane biaxial loading; laminates; loading; ply cracking; polymer composites; thermal residual stress; through-thickness
Effects of cooking using multi-ply cookware on absorption of potassium and vitamins: a randomized double-blind placebo control study.
International journal of food sciences and nutrition
63
5
530-6
2012
10.3109/09637486.2011.642342
This 2-week interventional study involved a randomized allocation of subjects into three groups: Group A (daily ingestion of 350 g vegetables cooked without water using multi-ply [multilayer-structured] cookware), Group B (daily ingestion of 350 g vegetables; ordinary cookware) and Group C (routine living). Before and after intervention, each subject underwent health examination with 24-h urine sampling. Blood vitamin C significantly increased after intervention from the baseline in Group A (P < 0.01) and Group B (P < 0.05). β-Carotene levels also increased significantly after intervention in Group A (P < 0.01) and Group B (P < 0.01). Oxidized low-density lipoprotein decreased significantly after intervention in Group A (P < 0.01). In Group A, 24-h urinary potassium excretion increased significantly (P < 0.01) and 24-h urinary sodium (Na)/K ratio improved significantly (P < 0.05) after intervention. In conclusion, a cooking method modification with multi-ply cookware improved absorption of nutrients from vegetables and enhanced effective utilization of the antioxidant potentials of vegetable nutrients.
Adolescent; Adult; Antioxidants; Antioxidants: metabolism; Ascorbic Acid; Ascorbic Acid: blood; beta Carotene; beta Carotene: blood; Cooking; Cooking: methods; Diet; Double-Blind Method; Energy Intake; Female; Humans; Intestinal Absorption; Lipoproteins, LDL; Lipoproteins, LDL: blood; Male; Micronutrients; Micronutrients: metabolism; Potassium; Potassium: urine; Sodium; Sodium: urine; Vegetables; Vegetables: chemistry; Young Adult
Petroleum Rock Mechanics
Petroleum Rock Mechanics
297-318
2011
10.1016/B978-0-12-385546-6.00014-0
The two most costly drilling problems are stuck pipes and circulation losses. This chapter addresses circulation loss. This can occur at any time during a drilling operation, is very common in depleted reservoirs, and must be cured before drilling can resume. If water-based drilling fluids are in use, the problem can often be reduced by pumping Lost Circulation Materials (LCM) into the wellbore. Mud companies have many techniques to stop mud losses, which basically all use particles in various combinations as bridging materials. This chapter provides a detailed insight into the interpretation of leak-off tests at the onset of the fracture initiation. Research indicates that two main characteristics of a filter cake can give a high fracture pressure. The model presented here applies to a typical drilling operation, using particle laden drilling muds with filtrate control, performing leak-off tests with a large annular volume, and relative small fractures opening during the tests. It suggests that increased intra-particle friction may help reduce circulation losses with oil-based drilling fluids. One way to do this is to increase angularity of the mud particles.
The influence of fault geometry on small strike-slip fault mechanics
Journal of Structural Geology
73
49-63
2015
10.1016/j.jsg.2014.12.007
Meter-scale subvertical strike-slip fault traces in the central Californian Sierra Nevada exhibit geometric complexities that significantly contribute to their mechanical behavior. Sections of faults that opened at depth channelized fluid flow, as evidenced by hydrothermal mineral infillings and alteration haloes. Thin sections show a variation in the style of ductile deformation of infill along the fault, with greater intensities of deformation along restraining bends. Orthorectified photomosaics of outcrops provide model geometries and parameter constraints used in a two-dimensional displacement discontinuity model incorporating a complementarity algorithm. Model results show that fault shape influences the distribution of opening, and consequently the spatial distribution of fluid conduits. Geometric irregularities are present at many scales, and sections of opening occur along both releasing and restraining bends. Model sensitivity tests focus on boundary conditions along the fault: frictional properties on closed sections and fluid pressure within sections of opening. The influence of the remote stress state varies along a non-planar fault, complicating the relationships between remote stresses, frictional properties, slip, and opening. Discontinuous sections of opening along model faults are similar in spatial distribution and aperture to the epidote infill assemblages observed in the field.
Fault mechanics; Fault shape; Frictional properties; Hydrothermal alteration; Opening
Mechanics of verbal ability.
Psychological Review
85
2
109-130
1978
10.1037/0033-295X.85.2.109
Hunt, Earl ; Psychological Review, Vol 85(2), Mar, 1978. pp. 109-130. Publisher: American Psychological Association [Journal Article]
Effects of End Mill Helix Angle on Accuracy for Machining Thin-Rib Aerospace Component
Applied Mechanics and Materials
315
773-777
2013
10.4028/www.scientific.net/AMM.315.773
Accuracy of machined component is one of the challenging tasks for manufacturer. In the aerospace industry, machining process is widely used for fabrication of unitized-monolithic component that contains a thin-walled structure. During machining, the cutting forces cause deflection to the thin-wall section, leading to dimensional form errors that cause the finished part to be out of specification or failure. Most of the existing research for machining thin-wall component only concentrated on the process planning and the effects of cutter geometric feature is often neglected. Tool geometric feature has a direct influence on the cutting performance and should not be neglected in the machining consideration. This paper reports on the effect of helix angle on the magnitude of wall deflection. The established effects will be used for the development of high performance cutting tool for specifically machining thin-wall component. © (2013) Trans Tech Publications, Switzerland.
abstract; accuracy of machined component; aerospace industry; challenging tasks for manufacturer; component that contains a; during machining; end mill; helix angle; in the; is one of the; machining; machining process is widely; surface error; the cutting forces cause; thin-walled structure; unitized-monolithic; used for fabrication of
Head-disk interface contact mechanics for ultrahigh density magnetic recording
Wear
238
1
1-11
2000
10.1016/S0043-1648(99)00333-6
Extremely smooth surfaces, high relative speeds, and remarkably low flying heights are required in ultrahigh density magnetic recording. As a consequence, higher contact stresses and shear strains can be encountered at the head-disk interface (HDI) due to the enhancement of asperity interactions. Detailed knowledge of the damage due to inelastic deformation at asperity microcontacts is therefore of paramount importance to the durability of high-performance disk drives. A comprehensive elastic-plastic contact analysis for the HDI that is based on a realistic surface topography description and a finite element model is presented in this publication. Magnetic head and smooth and textured rigid disk surfaces were scanned with an atomic force microscope (AFM) at various scales in order to determine the corresponding fractal parameters. Surface topographies equivalent to those of a slider in contact with smooth and textured disks were determined from a fractal analysis of the obtained AFM surface images. The equivalent surface corresponding to smooth disk surfaces was incorporated into a finite element model of the thin-film disk medium to provide a more realistic approximation of the actual surface topographies. Simulation results for the contact pressure at asperity microcontacts and subsurface von Mises equivalent stress, maximum tensile stress, and equivalent plastic strain are interpreted in terms of the carbon overcoat thickness and maximum surface interference distance. The evolution of plasticity and likelihood of cracking in the carbon and magnetic layers of smooth rigid disks are discussed. It is shown that AFM measurements, fractal surface characterization, and finite element modeling can be combined in contact analyses of layered media possessing realistic surface topographies and mechanical properties typical of engineering components. (C) 2000 Elsevier Science S.A. All rights reserved.
Asperity microcontacts; Elastic-plastic deformation; Finite element method; Fractal geometry; Head-disk interface mechanics; Magnetic recording; Surface topography
Cast filling simulations of thin-walled cavities
Computer Methods in Applied Mechanics and Engineering
128
199-230
1995
10.1016/0045-7825(95)00882-9
Computer simulation models of casting processes which couple the velocity potential approach with a transient Bernoulli equation are developed. Instead of employing three primitive variables, displacement, velocity and pressure, only one variable-velocity potential is needed. When the thickness integrated equation is also employed, the method can provide practical results with very reasonable computing time and storage for the 3-D casting of an arbitrary shape thin-walled cavity. In this study, the flexibility of the finite element method in dealing with complex geometries and the efficient algorithm of volume of fluid (VOF) approach for tracking moving free surfaces are combined for solving casting filling problems. Multiple free surface contacts are developed when the stream finally turns back and impacts the original free surface. A double-node scheme is developed to treat these multiple free surface contacts. The movement of the interface is small and an inflexible wall across the separating surface is assumed. Because the casting process involves phase change, and the interface between the solid and liquid is generally an unknown curve, the enthalpy model with fixed mesh is used to determine the temperature distribution and the thickness of the filling. Numerical examples for prediction of filling patterns, effects of solidification on patterns and parametric studies are presented. Fairly good agreement between this method and experimental results and other numerical simulations have also been obtained. The computational techniques developed in this study can provide a powerful and flexible tool for analyzing the fluid flow and heat transfer in metal casting of thin-walled cavities and can help design engineers reduce the costly and time-consuming process of designing complex molds for the manufacture of casted parts.
Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates
European Journal of Mechanics - A/Solids
29
5
844-850
2010
10.1016/j.euromechsol.2010.02.012
A meshless method based on thin plate spline radial basis functions and higher-order shear deformation theory are presented to analyze the free vibration of clamped laminated composite plates. The singularity of thin plate spline radial basis functions is eliminated by adding infinitesimal to the zero distance. Convergence characteristics of the present thin plate spline radial basis functions for the vibration analysis of the clamped laminated plates are investigated. The frequencies computed by the present method agree well with the available published results.
GPU-accelerated molecular mechanics computations
Journal of Computational Chemistry
34
26
2249-2260
2013
10.1002/jcc.23384
In this article, we describe an improved cell-list approach designed to match the Kepler architecture of General-purpose graphics processing units (GPGPU). We explain how our approach improves load balancing for the above algorithm and how warp intrinsics are used to implement Newton's third law for the nonbonded force calculations. We also talk through our approach to exclusions handling together with a method to calculate bonded forces and 1-4 electrostatic scaling using a single Cuda kernel. Performance benchmarks are included in the last sections to show the linear scaling of our implementation using a step minimization method. In addition, multiple performance benchmarks demonstrate the contribution of various optimizations we used for our implementations. © 2013 Wiley Periodicals, Inc.
cell lists; Cuda; GPU; MMFF94; molecular mechanics
Dynamic analysis of membrane systems undergoing overall motions, large deformations and wrinkles via thin shell elements of ANCF
Computer Methods in Applied Mechanics and Engineering
258
81-95
2013
10.1016/j.cma.2013.02.006
A computational approach is proposed for the dynamic analysis of complicated membrane systems, such as parachutes and solar sails, which undergo overall motions, large deformations, as well as wrinkles owing to the small membrane resistance to the compressive stress therein. Based on previous studies, a thin shell element of gradient deficient Absolute Nodal Coordinate Formulation (ANCF) is proposed first. Then, the strain energy of the above shell element is derived by using the definition of the Green–Lagrange strain tensor in continuum mechanics. The computationally efficient formulations of elastic forces and their Jacobian for the above shell element are also derived via the skills of tensor analysis. Afterwards, a membrane element of ANCF is proposed by integrating the criterion of wrinkle/slack into the above shell element. To deal with the small compressive stiffness for the membrane element, the Stiffness Reduction Model (SRM) is introduced to the membrane elements. Finally, four case studies including both statics and dynamics of different membrane systems are given to validate the proposed approach. The final example of the spinning deployment of a solar sail shows the efficacy of the proposed approach in the dynamic analysis of complicated membrane system undergoing an overall motion, large deformations and wrinkles.
Quantum Mechanics and Determinism
Quantum
43
170
13
2001
10.2307/2219939
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied to free Maxwell fields. Lorentz invariance is demonstrated.
The fracture mechanics of delamination tests
The Journal of Strain Analysis for Engineering Design
24
4
207-214
1989
10.1243/03093247V244207
Fracture mechanics has, quite reasonably, been developed for simple fractures in homogeneous, isotropic materials, but the physics inherent in its methods are equally applicable to failures in inhomogeneous, anisotropic materials such as composites. Much effort has been expended on developing new, tough matrix materials to give high performance structures. It is the function of fracture mechanics to provide a rigorous basis for characterizing, and thus comparing, these materials. The experience and methods of analysis used has produced some very precise tests, and these will form the basis of design methods. This paper will now describe how fracture mechanics has been used to define toughness in laminates and indicate how it has been applied.
Application of statistical mechanics to the wetting of complex liquids
Physica A
274
1-2
19-29
1999
Doi 10.1016/S0378-4371(99)00323-4
We study the wetting laws for binary mixtures with antagonist components: the solvent wets but the solute does not. Naively, we would expect a wetting transition at a composition phi=phi(w) We measure the contact angle theta(phi) which decreases from theta(1) up to a plateau value theta(L) for phi less than or equal to phi(L) In the plateau regime, the solution droplet is in equilibrium with a precursor film of pure solvent. At phi(L), We have a "leak out transition", which results from the frustration of the solvent attracted by both the polymer and the solid. Because the contact angle is finite at all composition, films of solution dewet below a critical thickness e(c)(phi). We observe two regimes of dewetting (i) dry dewetting at composition phi > phi(L). The final state after dewetting are multitude of droplets on a dry solid, (ii) "wet" dewetting for phi < phi(L), where the final droplets coexist with a film of pure solvent. All these results can be extended to other complex systems, where wetting processes and phase separation are coupled. (C) 1999 Elsevier Science B.V. All rights reserved.
drops; dynamics; thin polymer-films
Mechanics of damage initiation and growth in a TBC/superalloy system
International Journal of Solids and Structures
38
19
3329-3340
2001
10.1016/S0020-7683(00)00261-4
Creep analysis was used to estimate stresses in different layers especially in bond coat and the thermally grown oxide (TGO) layer to determine the role of creep on damage initiation in the TBC system. Microcracks were observed to initiate near the bond coat/TGO interface after only a few thermal cycles. The origin of these microcracks can be attributed to the buildup of thermal stresses that may magnify due to asperity of the TGO layer and the bond coat. The TGO/bond coat interface was modeled as a rough periodic surface. Finite element calculations were conducted to determine the magnitude of stresses at the bond coat/oxide interface (modeled as a sine wave). It was found that large normal interface stresses arise at the peaks, while large shear stresses arise at the mean line of the rough interface. These residual stresses can exceed the interfacial tensile or shear strength of TGO. Effect of oxide layer growth between bond coat and Thermal barrier coating (TBC) was modeled as volume increase and subsequently as an induced pressure across the interface inside the crack. Mixed-mode fracture analysis of a thin circular delamination in an axisymmetric multi-layer circular plate was developed to assess growth. © 2001 Elsevier Science Ltd. All rights reserved.
Damage initiation; Superalloy system; TBC
Short-Term Plyometric Training Improves Running Economy In Highly Trained Middle And Long Distance Runners
Journal of Strength & Conditioning Research (Allen Press Publishing Services Inc.)
20
947-954
2006
Fifteen highly trained distance runners (Vo<sub>2</sub>max 71.1 ± 6.0 ml · min<sup>-1</sup> · kg<sup>-1</sup>, mean ± SD) were randomly assigned to a plyometric training (PLY; n = 7) or control (CON; n = 8) group. In addition to their normal training, the PLY group undertook 3 x 30 minutes PLY sessions per week for 9 weeks. Running economy (RE/was assessed during 3 x 4 minute treadmill runs (14, 16, and 18 km · h<sup>-1</sup>), followed by an incremental test to measure Vo<sub>2</sub>max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km · h<sup>-1</sup> (4.1%, p = 0.02), but not at 14 or 16 km · h<sup>-1</sup> This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p = 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p = 0.09), and a lower Vo<sub>2</sub>speed slope (14%, p = 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or Vo<sub>2</sub>max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics. ABSTRACT FROM AUTHOR
*AEROBIC capacity; elite runners; *LONG-distance running; oxygen consumption; *PHYSICAL fitness testing; *PLYOMETRICS; *RUNNERS (Sports); strength training; *WEIGHT training
Applied Bohmian mechanics
The European Physical Journal D
68
10
286
2014
10.1140/epjd/e2014-50222-4
Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics. Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectory-based explanation of complicated quantum phenomena. Here we present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for this kind of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this work also emphasizes that the Bohmian formalism can be a useful tool in other types of (non-unitary and nonlinear) quantum problems where the influence of the environment or the global wave function are unknown. This review contains also examples on the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory among the scientific community will be greatly influenced by its potential success in these type of problems that present non-unitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism and some of its extensions are presented in the last part of this review.
Telescoping composite mechanics for composite behavior simulation
Computer Methods in Applied Mechanics and Engineering
185
2-4
399-411
2000
10.1016/S0045-7825(99)00268-6
Telescoping composite mechanics are described and implemented in terms of recursive laminate theory. The initial elemental scale is defined where simple equations are derived. Subsequently these mechanics are applied to homogeneous composites, hybrid composites, smart composites and composite enhanced reinforced concrete structures. Results from those applications are presented in terms of tables/figures to illustrate the versatility and generality of telescoping composite mechanics. Comparisons with methods such as approximate, single cell, and 2D and 3D finite element demonstrate the predictive accuracy and computational effectiveness of composite telescoping mechanics.
Aging infrastructures; Computational simulation; Elemental scale; Fiber composites; Finite element; Hybrid composite; Infrastructure enhancement; Laminate theory; Micromechanics; Minimechanics; Progressive fracture; Reinforced concrete; Scale definition; Scale substructuring; Scale telescoping; Smart composites; Structural analysis; Unit cell
Statistical mechanics of a one-dimensional lattice gas
Communications in Mathematical Physics
9
4
267-278
1968
10.1007/BF01654281
We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result ofvan Hove we show that, for a large class of interactions, such a system has no phase transition. The equilibrium state of the system is represented by a measure which is invariant under the effect of lattice translations. The dynamical system defined by this invariant measure is shown to be a K -system.
Mechanics of film formation during the spray pyrolysis of tin oxide
Thin Solid Films
165
1
265-277
1988
http://dx.doi.org/10.1016/0040-6090(88)90698-0
The trajectories of aerosol droplets are examined in an attempt to model tin oxide film growth in the spray pyrolysis and the corona spray pyrolysis of aqueous tin tetrachloride. It is found that, during the distillation of tin tetrachloride solutions, the boiling point will increase to 152 °C at which point hydrolysis occurs and tin oxide powder is formed. From this and other measurements, it is concluded that tin oxide films are grown from the distilled vapour of droplets passing very close to a hot glass surface in a kind of chemical vapour deposition. Droplets which strike the surface form a powdery deposition whether or not hydrolysis occurs before or after impact. Thermophoretic forces keep most of the aerosol from the surface in non-electrostatic spraying but the use of corona charging often causes extensive powder formation. By the use of a laminar flow geometry and moderate electric field deflection of charged aerosol, we hope to improve the efficiency of film growth. This can be accomplished by forcing the droplets closer to the hot glass while avoiding actual contact.
Ductile tearing in thin aluminum panels : experiments and analyses using large-displacement , 3-D surface cohesive elements
Engineering Fracture Mechanics
69
983-1002
2002
10.1016/S0013-7944(01)00113-8
This paper describes a large-displacement formulation for a 3-D, interface-cohesive finite element model and its application to predict ductile tearing in thin aluminum panels. A nonlinear traction–separation relationship defines the constitutive response of the initially zero thickness interface elements. Applications of the model simulate crack ex- tension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Tests of the M(T) specimens without guide plates exhibit significant out-of-plane (buckling) dis- placements during crack growth which necessitates the large-displacement, cohesive formulation. The measured load vs. outside surface crack extension behavior of high constraint (T-stress > 0) C(T) specimen drives the calibration process of the cohesive fracture model. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a=W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and measured outside surface crack extensions. The models capture accurately the strong 3-D effects leading to out-of-plane buckling and various degrees of crack front tunneling in the C(T) and M(T) specimens. Previous analyses of these specimens using a crack tip opening angle (CTOA) criterion for growth show good agreement with measured peak loads. However, without the ability of the interface-cohesive model to predict tunneling behavior, the CTOA approach overestimates crack extensions early in the loading when tunneling behavior dominates the response. ? 2002 Elsevier Science Ltd. All rights reserved.
2024-t3 aluminum; 3-d finite; ctoa; ductile tearing; finite deformation cohesive elements; quasi-static crack growth
Analytical investigation of laminated arches with extension and shear piezoelectric actuators
European Journal of Mechanics a-Solids
37
185-192
2013
Doi 10.1016/J.Euromechsol.2012.06.009
Static deformations in symmetric and antisymmetric cross-ply laminated arches with extension and shear piezoelectric actuators are investigated. The state space approach is used to generate exact solutions for the static response of cross-ply smart arches for arbitrary boundary conditions. A rigorous first order shear deformation arch theory is used in the analysis. Deflections are computed for thirty layer arches with various lamination schemes and boundary conditions incorporating piezoelectric actuators. The feasibility of using extension and shear mode actuators in smart arches is investigated. It is observed that an antisymmetric cross ply cantilever arch with a shear piezoelectric actuator provides twice tip deflection more than that with extension piezoelectric actuators. (C) 2012 Elsevier Masson SAS. All rights reserved.
arbitrary boundary conditions; cross ply smart arches; curved beams; cylindrical-shell; design; exact solutions; extension and shear piezoelectric actuators; finite-element; model; plates; static response
Fracture of Composite Compact Tension Specimens
Fracture Mechanics of Composites
143-162
1975
Fracture experiments were carried out on compact tension specimens of unidirectional and cross-ply S-glass/epoxy and graphite/epoxy. Fracture toughness values were determined by the compliance calibration techuique and by measuring the area under the load-displacement curve. In unidirectional specimens, crack extension was always parallel to the fibers and was dependent on crack length. Toughness did not vary significantly with fiber orientation relative to the load direction in unidirectional S-glass/cpoxy. Tests on cross-ply S-glass specimens were not valid because crack propagntion did not occur; instead, a zone containing a system of superficial parallel cracks and other damage developed which extended with increasing load. Cross-ply graphite specimens, on the other hand did appear to give valid test results although the cracks propagated were not always straight and other damage mechanisms were also present. Toughness values for cross-ply graphite were approximatcly two orders of magnitude higher than for unidirectional specimens due chiefly to the fracture resistans or fibers transverse to the crack . Toughness values determined by the compliance calibrtion method were consistent with reported values obtained by other methods.
composite materials; crack propagation; evaluation; fiber composites; fracture ( materials); fracture properties; mechanical properties; tests
Quantum Mechanics and Path Integrals
Rays
13
1-39
1965
10.1049/sqj.1966.0063
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to instantons and lead to time/energy uncertainty. In practice, 'classical' particle trajectories with additional degrees of freedom have arisen in several different formulations of quantum mechanics. In this talk we compare the extended phase space of the closed time-path formalism with that of complex classical mechanics, to suggest that hbar has a role in our understanding of the latter. However, differences in the way that trajectories are used make a deeper comparison problematical. We conclude with some thoughts on quantisation as dimensional reduction.
High-fidelity simulations of multiple fracture processes in a laminated composite in tension
Journal of the Mechanics and Physics of Solids
59
7
1355-1373
2011
10.1016/j.jmps.2011.04.007
The augmented finite element method (A-FEM) is used to study the fundamental composite failure problem of delamination and associated damage events spreading from a stress concentrator during tensile loading. The solution exploits the ability of A-FEM to account for coupled multiple crack types that are not predetermined in shape or number. The nonlinear processes of each fracture mode are represented by a cohesive model, which provides a unified description of crack initiation and propagation and can also describe crack coalescence and bifurcation. The study problem is an orthogonal double-notched tension specimen, in which delaminations interact with transverse ply cracks, intra-ply splitting cracks, non-localized fine-scale matrix shear deformation, and fiber breaks. Cohesive laws and constitutive laws for matrix shear deformation are calibrated using literature data from independent tests. The calibrated simulations are mesh independent and correctly reproduce all qualitative aspects of the coupled damage evolution processes. They also correctly predict delamination sizes and shapes, the density of transverse ply cracks, the growth rate of splitting cracks, softening of the global stressstrain curve, and the ultimate strength. A sensitivity analysis relates variability in cohesive law parameters to predicted deviance in engineering properties. Given the known variability in cohesive law parameters, the predicted deviance in ultimate strength agrees with that in experimental data. The importance of including the interactions between different crack systems and non-localized shear deformation is demonstrated by suppressing the presence of separate mechanisms; the predicted delamination shapes, splitting crack growth rate, and the stressdisplacement relationship fall into significant error. ?? 2011 Elsevier Ltd. All rights reserved.
Fiber-reinforced composite material; Finite elements; Fracture
A physically nonlinear plate in tension, with a hole reinforced by a thin strip
International Applied Mechanics
1966
The problem of the biaxial homogeneous stress state of an in- finite plate with a hole is solved for a case where the boundary of the hole is reinforced by a thin elastic strip. The nonlinear law of elasticity [1] is used in solving
Viscoelastic analysis of processing-induced residual stresses in thick composite laminates
Mechanics of Composite Materials and Structures
4
September 2012
361-387
2007
10.1080/10759419708945889
Residual stresses induced during the processing of thick composite laminates are analyzed. A two-dimensional thermochemical analysis is used to obtain temperature and degree of cure distributions during cure. A two-dimensional finite-element model is developed to predict the residual stress history in rectangular laminated plates. A cure-dependent viscoelastic material model is used in the analysis. Both unidirectional and cross ply laminates are investigated. Unidirectional laminates are studied because residual stresses in this class of laminates is driven purely by thickness effects. Regardless of the layup, for moderately thick (2.54-cm) laminates the nonuniformities in temperature and degree of cure are mild As a result, the development of residual stress is very similar to the analysis of thin laminates. For laminates of large thickness (7.5 cm) stronger variations in temperature and degree of cure develop during the cure cycle, The development of residual stress in this case is more complex. The transverse stress distribution in unidirectional laminates is tensile at the center and compressive on the edge at the end of cool-down. The profile is inverted twice during the cure cycle as competing mechanisms of thermal expansion, chemical shrinkage, and chemical hardening interact. The transverse residual stress for 7.5-cm-thick unidirectional laminates was shown to reach a value of 3.5 MPa after cure, compared to a value of only 0.65 MPa for 2.54-cm-thick laminates. In all of the cases analyzed the laminates exhibited a center-to-surface cure behavior. Thicker laminates and laminates constructed of materials with different cure kinetics could show a surface-to-center cure behavior, In such cases the residual stress development will be significantly changed from the results presented in this article.
Analytical method for the construction of solutions to the F??ppl-von K??rm??n equations governing deflections of a thin flat plate
International Journal of Non-Linear Mechanics
47
3
1-6
2012
10.1016/j.ijnonlinmec.2012.01.004
We discuss the method of linearization and construction of perturbation solutions for the F??ppl-von K??rm??n equations, a set of non-linear partial differential equations describing the large deflections of thin flat plates. In particular, we present a linearization method for the F??ppl-von K??rm??n equations which preserves much of the structure of the original equations, which in turn enables us to construct qualitatively meaningful perturbation solutions in relatively few terms. Interestingly, the perturbation solutions do not rely on any small parameters, as an auxiliary parameter is introduced and later taken to unity. The obtained solutions are given recursively, and a method of error analysis is provided to ensure convergence of the solutions. Hence, with appropriate general boundary data, we show that one may construct solutions to a desired accuracy over the finite bounded domain. We show that our solutions agree with the exact solutions in the limit as the thickness of the plate is made arbitrarily small. ?? 2012 Elsevier Ltd. All rights reserved.
Deflections of thin flat plates; Discrete residual error analysis; F??ppl-von K??rm??n equations; Homotopy analysis; Non-linear PDEs; Perturbation methods
Wrinkle-Based Measurement of Elastic Modulus of Nano-Scale Thin Pt Film Deposited on Polymeric Substrate: Verification and Uncertainty Analysis
Experimental Mechanics
50
5
635-641
2010
10.1007/s11340-009-9243-8
Wrinkle-based measurement of elastic modulus for a nano-scale thin film was analyzed. As a demonstrative example, the wrinkles of Pt films on a Polydimethylsiloxane (PDMS) substrate under compressive loading were formed with a well-defined wavelength, corresponding to the difference of elastic moduli between the films and substrates. The elastic modulus of the Pt nano-scale thin film measured with the wrinkle-based measurement was found to be consistent with that independently measured with micro-tensile test. Uncertainty of the wrinkle-based measurement was analyzed to figure out the main uncertainty components for the evaluation of elastic modulus measurement, and guidelines for the reliable wrinkle-based measurement were suggested.
Engineering
Thermocapillary flow in thin liquid films
Fluid Mechanics - Soviet Research
15
1
95-106
1986
citeulike-article-id:7882142
The authors derive the equation of three-dimensional thermocapillary\nmotion in a thin film. A quasilinear equation of the first order\nwith respect to time and fourth order with respect to spatial variables\nis obtained. Under certain conditions this equation may be converted\ninto a second-order equation, which in some cases may become identical\nto the principal equation of the filtration theory of a polytropic\ngas. The authors analyse formulations of the initial- and boundary-value\nproblem for the complete and truncated equations of the thin film,\ndefine the qualitative properties of their solutions, describe the\nsteady-state and self-similar solutions of these equations, and analyse\ntheir stability.
bifurcation; equation; evolution; theory
Modeling of multiple cracking and decohesion of a thin film on a polymer substrate
Engineering Fracture Mechanics
73
17
2614-2626
2006
10.1016/j.engfracmech.2006.04.013
Thin brittle films on polymer substrates are finding increasing use as gas barriers for example in the medical and food packaging industries and also for the next generation of ultra-light displays based on flexible polymer substrates. In order to determine the durability of the barrier under thermal and mechanical loads, test procedures and corresponding data reduction methods are needed to feed the analysis models. One of the tests frequently employed for this kind of multi-layer material systems is the fragmentation test, whose designation comes from the progressively denser pattern of parallel cracks developing when the specimen is loaded under uniaxial tension. From the crack-density versus strain data obtained, a critical strain for crack growth and an assessment of the adhesion of the coating to substrate can be obtained. However, no accepted data reduction methods exist to extract material properties from the test or inversely, successfully predict the crack density as a function of a set of material properties without fitting parameters. In an earlier paper, the authors presented a finite element based analysis methodology to determine the fracture toughness of both the coating and the interface from the fragmentation data. In the simulations, the plastic constitutive behavior of the substrate and the debonding of the coating from the substrate were explicitly included, the latter by use of a cohesive zone model. In this paper an extension of this methodology is presented that enables crack-density evolution with strain to be predicted. The results presented comprise comparisons with experiments to validate the methodology and the influence of (i) coating toughness, (ii) interface toughness and (iii) coating thickness on crack density versus strain. © 2006 Elsevier Ltd. All rights reserved.
Adhesion; Cohesive zone; Finite element method; Polymer substrate; Thin film
Predicting the first-ply failure of multilayered composite cylinders under hygrothermal loading
Journal of Reinforced Plastics and Composites
24
17
1781-1789
2005
The present study deals with the effects of combined internal pressures, temperatures, and moistures on filament-wound multilayered composite cylinders for the plane-strain case. The analysis accounts for the failure pressure for various orientation angles under hygrothermal conditions. The Tsai-Wu criterion is used for checking the first-ply failure of layers. The chosen orientation angles are 15, 30, 45, 60, and 75°. © 2005 SAGE Publications.
Composite cylinders; Composite structures; Cylinders (shapes); Failure analysis; Failure pressure; Filament-wound; Hydrothermal synthesis; Moisture; Multilayered pipes; Pipe
Nonlinear flexural vibrations of initially deflected cross-ply laminated plates with elastically restrained edges
Fibre Science and Technology
17
3
157-168
1982
Based on dynamic Marguerre equations for initially deflected rectangular plates, a series solution is given for large amplitude, free, flexural vibration of a cross-ply laminated plate with elastically restrained edges. By virtue of orthogonal functions the governing equations are reduced to two nonlinear second-order differential equations. Convergent solutions can be determined to any desired degree of accuracy. Using Galerkin procedure and perturbation technique the effects of initial deflections on the nonlinear frequency of the plate is studied.
Stability of workface using long-wall mining method in extremely thin and gently inclined iron mine
Safety Science
50
4
624-628
2012
10.1016/j.ssci.2011.09.001
Long-wall mining method has its own advantages, such as small mining-cutting ratio, the simple technique of recovery and high level of mechanization, which is the optimal method used to mine gently inclined and extremely thin iron mine. How to ensure the safety of workers and equipment during mining is the key technical process. Based on elastic–plastic mechanics theory, the mechanic model of long-wall method mining gently inclined and extremely thin iron mine is established and the critical safety distance of workface is obtained. With the FLAC-2D simulation software, the rule of stress change, the deformation of workface and surrounding rock in different control-roof width are also summarized. The final results accord with the ones of theory test. We confirm the support-frame resistance of workface by analogy-statistic method. The results prove that hydraulic support-frame have the ability to provide enough pressure to assure the stability of working face within the 5-m of control-roof width.
Extremely thin; Iron mine; Long-wall method; Stability; Surrounding rock
Statistical mechanics of anyons
Nuc. Phys. B
251
117-126
1985
http://dx.doi.org/10.1016/0550-3213(85)90252-4
We study the statistical mechanics of a two-dimensional gas of free anyons-particles which interpolate between Bose-Einstein and Fermi-Dirac character. Thermodynamic quantities are discussed in the low-density regime. In particular, the second virial coefficient is evaluated by two different methods and is found to exhibit a simple, periodic, but nonanalytic behavior as a function of the statistics determining parameter.
Three-dimensional Elasticity Solution for Uniformly Loaded Cross-ply Laminates and Sandwich Plates
Journal of Sandwich Structures and Materials
9
3
213-238
2007
10.1177/1099636207065675
This article establishes the bending problem of cross-ply laminated plates using the three-dimensional elasticity equations as well as the technique based on the state space concept. It presents a wide variety of results for the symmetric and antisymmetric analyses of rectangular multilayer plates subjected to a sinusoidally/uniformly distributed load (SDL/UDL). In addition, this study provides a strong mathematical tool allowing one to determine, in an exact and unified manner, the state of stress and displacement of cross-ply laminated composites and sandwich plates. The well-known results (given in Pagano ((1970), Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates, Journal of Composite Materials, 4(1): 20—24.) and Pagano and Hatfield ((1972), Elastic Behaviour of Multilayered Bidirectional Composites, AIAA Journal, 10(12): 931—933.) due to the exact three-dimensional elasticity solution are in fact special cases of the present technique.
Application of the boundary shape perturbation method to stress analysis of laminated composites with ply waviness
Composites Part A: Applied Science and Manufacturing
36
137-143
2005
10.1016/j.compositesa.2004.06.006
Ply waviness is a manufacturing defect that occurs in thick fibre-reinforced composite laminates during the curing process. It is known to cause significant degradation of mechanical properties and fatigue life, particularly under compressive loading. To predict failure in the vicinity of the wavy layer, accurate information about stresses at the undulating interfaces is needed. In this paper, an analytical approach to determination of stresses in laminated composites with ply waviness subjected to compressive or flexural loading is presented. Using the boundary shape perturbation method, 3D elasticity problem for a laminate with undulating interfaces is transformed into a sequence of 3D elasticity problems for a reference laminate with perfectly flat layers. The application of the presented analytical approach to a particular problem is illustrated with the example of a transversally loaded laminated plate with a wavy layer. ?? 2004 Elsevier Ltd. All rights reserved.
A. Laminates; B. Elasticity; B. Stress concentration; C. Analytical modelling
Numerical simulation of the influence of stacking sequence on transverse ply cracking in composite laminates
Composite Structures
17
1
23-35
1991
10.1016/0263-8223(91)90058-7
This study concerns a numerical simulation of the transverse damage state of cross ply laminates which present a periodic stacking sequence. The variation, with crack density, of the longitudinal stiffness and energy release rate of any periodic stacking sequence laminate is deduced from basic finite element results of a repeating unit cell by using similitude considerations. Two particular laminates which have similar stacking sequences, the same total ply number but different layer thicknesses are then studied. It is established that the relationship between their respective stiffnesses and energy release rates only involves their similarity ratio. It is shown that the transverse crack phenomenon is accentuated by increased cross layer thicknesses. A comparison with experimental data confirms this result and seems to prove that, in the characteristic damage state, the stiffness reduction does not depend on the 90° layer thickness.
Wind safety of single-ply roofs under time varying wind load
Journal of Wind Engineering and Industrial Aerodynamics
41
44
1513-1524
1992
Wind damage on lightweight roofs of industrial and commercial buildings appears to be more common in North America than in Europe. One of the primary reasons for this fact is inadequate design against wind uplift due to inadequate testing procedures in North America. This paper describes the load mechanism and the UEAtc-testing methodolody (to be used in Europe) of mechanically-attached, single-ply roof membranes and presents a newly designed fastener system incorporating the consequences of the load mechanism.
Three-dimensional microscopic analysis of inter-laminar area in cross-ply laminate using a homogenization theory
Micro-Nanomechatronics and Human Science, and The Fourth Symposium Micro-Nanomechatronics for Information-Based Society
1-6
2004
10.1109/MHS.2004.1421281
In this study, the microscopic interaction between 0° and 90°-plies at the inter-laminar area of a CFRP cross-ply laminate is investigated by performing the three-dimensional microscopic analysis based on a homogenization theory. To this end, the point-symmetry of internal structure in the laminate is utilized to reduce the domain of analysis by half. Moreover, the substructure method is combined with the homogenization theory in order to decrease computational loads. We then analyze stress distributions at the inter-laminar area of a carbon fiber/epoxy cross-ply laminate subjected to in-plane off-axial tensile load. It is thus shown that inter-laminar shear stress occurs significantly at the interface between 0°- and 90°-plies. It is also shown that the microscopic interaction between two plies markedly appears only in the vicinity of the interface.
The Prediction of Cracking in Biaxially Loaded Cross-Ply Laminates Having Brittle Matrices
Composites
24
2
84-92
1993
For a cross-ply laminate, assuming biaxial loading and conditions of perfect bonding, it is shown how the dependence of the relevant thermoelastic constants on transverse crack density may be determined. Using energy balance concepts, it is shown how the effect of biaxial loading on transverse cracking may be determined, and how account can be taken of the thermal residual stresses. The formation of multiple transverse cracks is considered which are formed simultaneously or progressively, either at regular or random locations. It is shown how to construct non-linear stress/strain curves for axial and transverse loading assuming that the 0-degrees plies remain undamaged. The combined effect of axial and transverse applied stresses on the initiation and growth of damage in the 90-degrees plies is analysed. It is shown that the occurrence of transverse cracking can be characterized by the energy absorbed per unit volume during microcracking, a quantity which can be estimated from experimental stress/strain curves.
biaxial loading; composite materials; cracking; cross-ply laminates; residual stresses; thermoelastic constants; transverse
Sensitivity of the post-localization response of a thick cross-ply imperfect ring to transverse Young’s modulus nonlinearity
Composite Structures
84
1
44-55
2008
10.1016/j.compstruct.2007.06.006
A fully nonlinear finite elements analysis for prediction of localization (onset of deformation softening) and post-localization response of a thick cross-ply [90/0/90] imperfect plane strain ring (infinitely long cylindrical shell) under applied hydrostatic pressure is presented. The present investigation is concerned with the prediction of post-“yield” and post-localization equilibrium paths for moderately thick and thick cross-ply rings, which are often unstable in the presence of modal imperfections and material nonlinearity, and which are considered to “bifurcate” from the primary equilibrium paths, representing periodic buckling patterns pertaining to global or structural level stability. The present nonlinear finite element solution methodology, based on the total Lagrangian formulation, employs a quasi-three-dimensional hypothesis, known as layer-wise linear displacement distribution theory (LLDT) to capture the three-dimensional interlaminar (especially, shear) deformation behavior, associated with the localized interlaminar shear-crippling failure. The combined effects of modal imperfections, interlaminar shear/normal deformation and nonlinear (hypoelastic) material property for the transverse Young’s modulus, ETT, on the localization phenomenon are thoroughly investigated, and physically meaningful conclusions are drawn from these numerical results.
Compression failure; Deformation softening; Delocalization; Localization; Nonlinear transverse Young’s modulus; Post-buckling
A damage mechanics tool for laminate delamination
Composite Structures
25
547-555
1993
10.1016/0263-8223(93)90203-3
A simplified method based upon damage mechanics for the delamination analysis of carbon-resin composites is presented. In the neighbourhood of a laminate structure quasi-straight edge, damage is taken concentrated on the interface between layers. The finite element code EDA, acting as a post-processor of an elastic laminate shell computation, allows the onset and propagation forecast of delamination. First numerical simulations of delamination are given and compared with experimental results from literature.
Bohmian Mechanics and Quantum Theory: An Appraisal
British Journal for the Philosophy of Science
49
2
1998
This is not a Festschrift in honor of David Bohm or a collection of papers simply stating uncritically a particular interpretation of quantum mechanics. Rather, it is a contribution to the serious and ongoing critical analysis, extension and application of the central ideas of David Bohm's version of quantum mechanics to test them for consistency, empirical adequacy and fruitfulness in generating new avenues of research. The papers in this volume are grouped around four main topics: the essentials of Bohmian mechanics; detailed applications and extensions of these basics; historical and conceptual analyses of the program; comparisons and contrasts with other formulations of quantum mechanics. This book will be of interest to physicists and to philosophers and historians of science - really to anyone concerned with foundational issues in quantum mechanics.
Adsorption of meso-tetraphenylporphines on thin films of C60 fullerene
Applied Surface Science
275
374-383
2013
10.1016/j.apsusc.2012.07.161
Noncovalent porphyrin-fullerene hybrids represent promising materials for organic photovoltaic applications and the construction of novel platforms for the immobilization of diverse molecules. In such hybrids, a structural aspect of particular interest is self-assembled monolayers (SAMs) of porphyrins on fullerene films supported on solid substrates. In the present work, we performed combined theoretical-experimental analysis of the behavior of meso-tetraphenylporphine (or 5,10,15,20-tetraphenyl-21H,23H-porphine, H 2TPP) and its complexes with Ni(II) and Co(II) (NiTPP and CoTPP, respectively) when adsorbed from gas phase in vacuum (by means of physical vapor deposition, PVD) onto HOPG-supported fullerene C60 films. The general film morphology was characterized by atomic force microscopy, whereas more detailed molecular structure as well as the adsorption of porphyrins was studied by scanning tunneling microscopy (STM). The results of STM imaging were compared with theoretical models, consisting of graphene sheets covered with a dense monolayer of fullerene cages and accommodating H2TPP molecules in different ways; their geometry was optimized by using MM+ force field. The results showed that NiTPP and CoTPP molecules are able to form ordered surface structures on the C60 thin films. The geometries observed included such basic structural elements as equilateral triangles or parallel rows formed by porphyrin molecules. Nevertheless, the areas of the assemblies on C 60 turned out to be very limited, owing to the fact that the C 60 thin films are composed of overlapping 20-70 nm-sized clusters, whereas each individual cluster exhibits additional imperfections; altogether resulting in a highly irregular surface, inconvenient for the formation of extended porphyrin arrays. © 2012 Elsevier B.V.
Adsorption; Atomic force microscopy; Fullerene C60 thin films; Molecular mechanics; Porphyrins; Scanning tunneling microscopy
Continuum damage mechanics for the lithosphere
Journal of Geophysical Research
116
B4
B04205
2011
10.1029/2010JB007501
... Abstract. Cited By (0). Abstract. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, B04205, 14 PP., 2011 doi: 10.1029 / 2010JB007501 . Continuum damage mechanics for the lithosphere. ... Res., 116, B04205, doi: 10.1029 / 2010JB007501 . Cited By. Please wait one moment ... ...
http://dx.doi.org/10.1029/2010JB007501, doi:10.102
Postbuckling analysis of axially-loaded laminated cylindrical shells with piezoelectric actuators
European Journal of Mechanics, A/Solids
20
1007-1022
2001
10.1016/S0997-7538(01)01176-7
A compressive postbuckling analysis is presented for a laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness, and the electric field is assumed to be the transverse component EZ only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with von K??rm??n-Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.
Boundary layer theory of shell buckling; Cylindrical shell; Hybrid laminated; Postbuckling; Singular perturbation technique; Thermo-piezoelectric effect
Metallic thin film composites with shape memory alloys for microswitches and tactile graphical displays
International Journal of Applied Electromagnetics and Mechanics
23
1-2
113-118
2006
A new mechanism to switch thin film actuators between two stable states has been developed. Bistable membrane switches can be realized by snap-dome shaped metallic foils which are coated on opposite surfaces with Ti(Ni,Cu) and (Ti,Hf)Ni respectively whereby the narrow hysteresis of Ti(Ni,Cu) is within the broad one of (Ti,Hf)Ni. If both SMAs are martensitic or both are austenitic, they apply similar forces on the intermediate foil and the shape of the membrane remains constant. However, if one of them is austenitic and the other one martensitic, the austenitic one determines the curvature of the membrane. Switching is possible by two different heat pulses. Therefore, energy is only required to change the state of the membrane. The new mechanism is described and first successful processing steps are presented. The mechanism allows the fabrication of microswitches and tactile displays. © 2006 - IOS Press and the authors. All rights reserved.
Austenite; Haptic interfaces; Heat pulses; Hysteresis; Martensitic transformations; Metallic compounds; Microswitches; Shape memory effect; Thin film actuators; Thin films
Determination of elastic and plastic material properties using indentation: Development of method and application to a thin surface coating
Nature materials
399
1-2
254-266
2003
10.1038/nmat855
The role of surface roughness in contact mechanics is relevant to processes ranging from adhesion to friction, wear and lubrication. It also promises to have a deep impact on applied science, including coatings technology and design of microelectromechanical systems. Despite the considerable results achieved by indentation experiments, particularly in the measurement of bulk hardness on nanometre scales, the contact behaviour of realistic surfaces, showing random multiscale roughness, remains largely unknown. Here we report experimental results concerning the mechanical response of self-affine thin films indented by a micrometric flat probe. The specimens, made of cluster-assembled carbon or of sexithienyl, an organic molecular material, were chosen as prototype systems for the broad class of self-affine fractal interfaces, today including surfaces grown under non-equilibrium conditions, fractures, manufactured metal surfaces and solidified liquid fronts. We observe that a regime exists in which roughness drives the contact mechanics: in this range surface stiffness varies by a few orders of magnitude on small but significant changes of fractal parameters. As a consequence, we demonstrate that soft solid interfaces can be appreciably strengthened by reducing both fractal dimension and surface roughness. This indicates a general route for tailoring the mechanical properties of solid bodies.
alkyd; Atomic Force; Atomic Force: methods; binder; Carbon; Carbon: chemistry; Chemical; elastic; Elasticity; emulsifier; Equipment Design; finite element method; Fractals; Hardness; Hardness Tests; Hardness Tests: instrumentation; Hardness Tests: methods; latex paints; material property determination; Materials Testing; Materials Testing: instrumentation; Materials Testing: methods; Mechanics; Microscopy; Models; nano-indentation; Nanotechnology; Nanotechnology: instrumentation; Nanotechnology: methods; paint properties; paints; plasticizers; plastic material; polymerizable; polymers; Polymethacrylic Acids; Polymethacrylic Acids: chemistry; pyrolysis; Sensitivity and Specificity; Solubility; Surface-Active Agents; Surface-Active Agents: pharmacology; surface coatings; Surface Properties; surfactant; surfactants; Theoretical; Transducers; water-borne
Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures
Computer Methods in Applied Mechanics and Engineering
284
881-905
2015
10.1016/j.cma.2014.11.014
Thin shell structures are widely used in the aerospace, automotive and mechanical engineering industries. They are ideal candidates for the isogeometric analysis paradigm profiting from the smoothness of the geometry model, and the higher order approximation and higher continuity properties of NURBS. To model complex shell structures which need to be assembled from multiple patches, the bending stiffness should be maintained across the patch interfaces. We propose a variationally consistent weak coupling method for thin-walled shell patches. The method overcomes the need for C1-continuity along the patch interface to ensure a corresponding geometric continuity in the deformed configuration and a correct transfer of bending moments across the interface. Importantly, it allows a blended coupling of shells based on different mathematical models, e.g. Kirchhoff–Love and solid-like shell models. The proposed approach retains the high level of accuracy of single patch solutions and reveals its potential for authentic multi-patch NURBS modeling. We illustrate the good performance of the method for pure Kirchhoff–Love shell models and blended shell models with various examples. The presented approach supports local model refinements where e.g. full 3D stress states are of interest, and further opens the door for the coupling of laminated composites belonging to different lamina theories.
Isogeometric analysis; Kirchhoff–Love shells; Mixed-dimensional coupling; Nitsche; Solid-like shells; Weak coupling
Surface Enhanced Second Harmonic Generation from Macrocycle, Catenane, and Rotaxane Thin Films: Experiments and Theory
The Journal of Physical Chemistry B
110
15
7648-7652
2006
10.1021/jp0561468
Surface enhanced second harmonic generation (SE SHG) experiments on molecular structures, macrocycles, catenanes, and rotaxanes, deposited as monolayers and multilayers by vacuum sublimation on silver, are reported. The measurements show that the molecules form ordered thin films, where the highest degree of order is observed in the case of macrocycle monolayers and the lowest in the case of rotaxane multilayers. The second harmonic generation activity is interpreted in terms of electric field induced second harmonic (EFISH) generation where the electric field is created by the substrate silver atoms. The measured second order nonlinear optical susceptibility for a rotaxane thin film is compared with that obtained by considering only EFISH contribution to SHG intensity. The electric field on the surface of a silver layer is calculated by using the Delphi4 program for structures obtained with TINKER molecular mechanics/dynamics simulations. An excellent agreement is observed between the calculated and the measured SHG susceptibilities.
Mechanics of fibroblast locomotion: quantitative analysis of forces and motions at the leading lamellas of fibroblasts.
The Journal of cell biology
111
6 Pt 1
2513-26
1990
10.1083/jcb.111.6.2513
Shapes, motions, and forces developed in lamellipodia and ruffles at the leading edges of primary chick embryo heart fibroblasts were characterized by differential interference contrast microscopy and digital video enhancement techniques. The initial extension of the cell edge to form a thin, planar lamellipodium parallel to the substrate surface was analyzed in two dimensions with temporal and spatial resolution of 3 s and 0.2 micron, respectively. An extension begins and ends with brief, rapid acceleration and deceleration separated by a long period of nearly constant velocity in the range of 4-7 microns/min. Extensions and retractions were initiated randomly over time. As demonstrated by optical sectioning microscopy, the extended lamellipodia formed ruffles by sharply bending upward at hinge points 2-4 microns behind their tips. Surprisingly, ruffles continued to grow in length at the same average rate after bending upward. They maintained a straight shape in vertical cross section, suggesting the ruffles were mechanically stiff. The forces required to bend ruffles of these cells and of BC3H1 cells were measured by pushing a thin quartz fishpole probe against the tip of a ruffle 7-10 microns from its base either toward or away from the center of the cell. Force was determined by measuring the bending of the probe monitored by video microscopy. Typically the probe forced the ruffle to swing rigidly in an arc about an apparent hinge at is base, and ruffles rapidly, and almost completely, recovered their shape when the probe was removed. Hence, ruffles appeared to be relatively stiff and to resist bending with forces more elastic than viscous, unlike the cell body. Ruffles on both types of cells resisted bending with forces of 15-30 mudyn/microns of displacement at their tips when pushed toward or away from the cell center. The significance of the observations for mechanisms of cell locomotion is discussed.
Animals; Cell Membrane; Cell Membrane: physiology; Cell Membrane: ultrastructure; Cell Movement; Cells, Cultured; Chick Embryo; Fibroblasts; Fibroblasts: physiology; Heart; Heart: physiology; Mathematics; Models, Biological; Video Recording
Refined geometrically nonlinear formulation of a thin-shell triangular finite element
Journal of Applied Mechanics and Technical Physics
48
5
755-765
2007
10.1007/s10808-007-0098-4
A refined geometrically nonlinear formulation of a thin-shell finite element based on the Kirchhoff-Love hypotheses is considered. Strain relations, which adequately describe the deformation of the element with finite bending of its middle surface, are obtained by integrating the differential equation of a planar curve. For a triangular element with 15 degrees of freedom, a cost-effective algorithm is developed for calculating the coefficients of the first and second variations of the strain energy, which are used to formulate the conditions of equilibrium and stability of the discrete model of the shell. Accuracy and convergence of the finite-element solutions are studied using test problems of nonlinear deformation of elastic plates and shells. © Springer Science+Business Media, Inc. 2007.
Bending (deformation); Computational geometry; Convergence of numerical methods; Degrees of freedom (mechanics); Differential equations; Finite element method; Finite-element method; Invariants; Kinematic group; Kirchoff-Love hypotheses; Nonlinear deformation; Planar curve; Shells (structures); Strain energy; Strain rate; Thin shell
Validation of low velocity impact modelling on different stacking sequences of CFRP laminates and influence of fibre failure
Composite Structures
106
549-559
2013
10.1016/j.compstruct.2013.07.008
This paper presents a validation of low-velocity impact Finite Element (FE) modelling. Based on switching ply location of reference layup [02,452,902,-452]s T700GC/M21 laminated plates from Bouvet et al. (2012) [1], twelve possible layups under a constraint of double-ply, mirror-symmetric, balanced, and quasi- isotropic are allowed. However only seven layups are chosen for the study and one of them reveals the importance of longitudinal fibre compressive failure during impact events. Therefore, the second aspect of this work is the introduction of a fibre compressive failure law associated with fracture damage development. This makes it possible to improve the simulation for all seven different layups. Good correspondence is achieved between simulation and experiment for aspects such as delamination areas/shapes and force-displacement responses. The influence of the addition of fibre compressive failure according to fracture toughness in mode I is discussed. ?? 2013 Elsevier Ltd.
Damage mechanics; Damage tolerance; Fibre failure; Finite element analysis (FEA); Impact behaviour
Mechanical properties of ultrananocrystalline diamond thin films relevant to MEMS/NEMS devices
Experimental Mechanics
43
3
256-268
2003
10.1007/BF02410524
The mechanical properties of ultrananocrystalline diamond (UNCD) thin films were measured using microcantilever deflection and membrane deflection techniques. Bending tests on several free-standing UNCD cantilevers, 0.5 μm thick, 20 μm wide and 80 μm long, yielded elastic modulus values of 916-959 GPa. The tests showed good reproducibility by repeated testing on the same cantilever and by testing several cantilevers of different lengths. The largest source of error in the method was accurate measurement of film thickness. Elastic modulus measurements performed with the novel membrane deflection experiment (MDE), developed by Espinosa and co-workers, gave results similar to those from the microcantilever-based tests. Tests were performed on UNCD specimens grown by both micro and nano wafer-seeding techniques. The elastic modulus was measured to be between 930-970 GPa for the microseeding and between 945-963 GPa for the nanoseeding technique. The MDE test also provided the fracture strength, which for UNCD was found to vary from 0.89 to 2.42 GPa for the microseeded samples and from 3.95 to 5.03 for the nanoseeded samples. The narrowing of the elastic modulus variation and major increase in fracture strength is believed to result from a reduction in surface roughness, less stress concentration, when employing the nanoseeding technique. Although both methods yielded reliable values of elastic modulus, the MDE was found to be more versatile since it yielded additional information about the structure and material properties, such as strength and initial stress state.
Elastic moduli; Microelectromechanical devices; Nanostructured materials; Stresses; Ultrathin films
Effects of fibre inter-ply distance on the transverse tensile behaviour of titanium matrix composites
Scripta Materialia
44
3
443-448
2001
10.1016/S1359-6462(00)00622-9
Titanium matrix composites unidirectionally reinforced with continuous SiC fibers show improved mechanical properties over monolithic titanium alloys. A parameter that combines both fiber spacing and volume fraction was developed for use in predicting the transverse strength of these composites. In spite of the substantial differences, very similar stress-strain curves were obtained from the finite element analyses for the composite models.
Bond strength (materials); Fiber reinforced metals; Metallic matrix composites; Titanium matrix composites
A Framework for Cooperative Communication Game Mechanics from Grounded Theory
Proceedings of CHIPlay '14
257-266
2014
10.1145/2658537.2658681
A rich element of cooperative games are mechanics that communicate. Unlike automated awareness cues and synchronous verbal communication, cooperative communication mechanics enable players to share information and direct action by engaging with game systems. These include both explicitly communicative mechanics, such as built-in pings that direct teammates’ attention to specific locations, and emergent communicative mechanics, where players develop their own conventions about the meaning of in-game activities, like jumping to get attention. We use a grounded theory approach with 40 digital games to identify and classify the types of cooperative communication mechanics game designers might use to enable cooperative play. We provide details on the classification scheme and offer a discussion on the implications of cooperative communication mechanics.
analysis; communication; cooperation; Game design; teams
Polar continuum mechanics
Arxiv preprint arXiv:1009.3252
1-40
2010
The existing polar continuum theory contains unresolved indeterminacies in the spherical part of the couple-stress tensor. This severely restricts its applicability in the study of micro and nano-scale solid and fluid mechanics and, perhaps more importantly, in the investigation of fluid turbulence phenomena, which involve a broad range of scales. In this paper, we rely on the energy equation, along with some kinematical considerations, to establish a consistent couple-stress theory for polar continua that resolves all indeterminacies. After presenting the general formulation and obtaining conservation laws, we concentrate exclusively on couple stress theory for polar fluid mechanics. We specialize the theory for linear viscous flow and consider several boundary value problems in couple-stress fluid mechanics. More generally, the resulting theory presented here may provide a basis for fundamental continuum-level studies at the finest scales.
GBT-based local and global vibration analysis of loaded composite open-section thin-walled members
Int J Struct Stab Dy
6
1
1-29
2006
http://dx.doi.org/10.1142/S0219455406001800
This paper begins by presenting a Generalized Beam Theory (GBT) formulation\nfor analyzing the vibration behavior of loaded composite thin-walled\nmembers, which accounts for the effects of (i) cross-section in-plane\ndeformation, (ii) shear deformation, (iii) geometric and material\ncoupling, (iv) primary, secondary and non-linear warping, and (v)\nrotary inertia. This formulation is then used to investigate the\nlocal and global vibration behavior of lipped channel columns and\nbeams displaying cross-ply orthotropy, focusing on issues dealing\nwith the variation of the fundamental frequency and vibration mode\nnature with the member length and applied stress level. For validation\npurposes, some GBT-based results are also compared with values obtained\nby means of 4-node shell finite element analyses using ABAQUS. Some\nrelevant conclusions are drawn concerning the dependence of the member\nvibration mode shape (wave number) on the compression/bending level\n(applied-to-critical ratio).
A geometrically nonlinear discontinuous solid-like shell element (DSLS) for thin shell structures
Computer Methods in Applied Mechanics and Engineering
201-204
191-207
2012
10.1016/j.cma.2011.10.008
In this contribution a new geometrically nonlinear, discontinuous solid-like shell finite element is presented for the simulation of cracking phenomena in thin shell structures. The discontinuous shell element is based on the solid-like shell element, having a layout similar to brick elements but better performance in bending. The phantom node method is employed to achieve a fully discontinuous shell finite element, which incorporates a discontinuity in the shell mid-surface, director and in thickness stretching field. This allows the element to model arbitrary propagating cracks in thin shell structures in combination with geometrical non-linearities. The kinematics of the discontinuous shell element as well as the detailed finite element formulation and implementation are described. Several numerical examples are presented to demonstrate the performance of the element. ?? 2011 Elsevier B.V.
Cohesive cracking; Discontinuous solid-like shell element; Geometrical instabilities
Common ground in engineering geology, soil mechanics and rock mechanics: Past, present and future
Bulletin of Engineering Geology and the Environment
65
2
209-216
2006
10.1007/s10064-005-0020-3
Engineering geology, to- gether with soil mechanics and rock mechanics, is commonly considered to be one of the three fundamental scientific disciplines in ground engi- neering. Historically, the interrela- tion between these three disciplines has never been free of ambiguity. This, for instance, is highlighted by the fact that both Karl von Terzaghi, the founder of soil mechanics, and LeopoldMu ller, the founder of rock mechanics, considered themselves foremost as engineering geologists without, however, succeeding in establishing engineering geology as a free-standing discipline with auton- omous intellectual merits, methods and procedures. This situation has changed recently as evidenced in Knills fundamental publication (2002) on Core Values in Engineer- ing Geology and by the fact that the relevant three International Societies are currently in the process of mov- ing together towards a Federation of Geo-Engineering Societies.
Engineering geology; Rock mechanics; Soil mechanics
Gap-junction quantification in biological tissues: freeze-fracture replicas versus thin sections
J Microsc
163
Pt 1
65-78
1991
The relative efficiency of freeze-fracture replicas versus thin sections for the visualization and quantification of gap junctions in biological tissues has been evaluated. Both methods may underestimate gap-junction number--thin sections for reasons of tissue resolution and freeze-fracture replicas due to the mechanics of the fracturing process. Freeze-fracture misses gap junctions in regions of plasma membrane which are highly contoured, such as the overlapping basal cell processes of Drosophila imaginal wing discs and the interdigitating lateral membrane plications of intercalated discs in cardiac tissue. If the missed gap junctions are relatively large, as they are in both of these examples, freeze-fracture significantly underestimates the total gap-junctional area. Thin sections may miss small gap junctions, but in tissues which contain a range of gap-junction sizes the lost junctions constitute a relatively small fraction of the total junctional area. In neoplastic imaginal wing discs, thin sections were as efficient as freeze-fracture replicas in identifying even the smallest gap junctions. Although freeze-fracture may be the better technique for the qualitative and quantitative documentation of small gap junctions in tissues with relatively flat to gently contoured plasma membranes and thin sections may be the superior method for gap-junction quantification in tissues containing a range of gap-junctional sizes and highly contoured cellular processes, the data suggest that a combination of the two approaches should be utilized whenever possible.
Animals; Drosophila melanogaster; *Freeze Fracturing; Intercellular Junctions/*ultrastructure; Microscopy, Electron; *Microtomy
Inclusion problems associated with thin fcc films: Linkage between eigenstrain and inter-atomic potential
Mechanics of Materials
39
8
803-818
2007
10.1016/j.mechmat.2007.02.002
Often, during fabrication of thin films on substrates, different types of defects may be introduced into the films. Recently, the determination of the elastic fields due to the self-assembly of quantum dots or strained islands in thin films has been of major concern. In the micromechanical studies, such strained islands are modeled by inclusions. This paper aims to develop a theory pertaining to the presence of nano-inclusions of various geometries within thin films having face centered cubic (fcc) structure. To this end, the notion of eigenstrain is combined with a many body inter-atomic potential suitable for fcc crystals. The interaction between atoms is modeled via Sutton-Chen (SC) potential. The displacements of the atoms are computed by employing the integral transform to the discretized equilibrium equation. Incorporation of the interaction between the inclusion and the free surface makes it feasible to investigate the effect of distance of the inclusion from the free surface. For the sake of comparison with the result from the continuum theory of elasticity, the problem of dislocation loop in an infinite domain is considered. Moreover, the behavior of the thin film in the presence of inclusion is studied using three-dimensional (3D) molecular dynamics (MD) simulation, and the result is compared with that obtained from the proposed theory. During the initial processes of introducing the inclusion into the film, the temperature is held at 0�K using a simple temperature scaling method. Afterwards, for the situations where thermal loading is of interest, the temperature is increased, and the pertinent thermo-mechanical fields are examined.
eigenstrain; inclusion; inter-atomic potential; md simulation; thin film
Fracture mechanics analysis of a fire tube boiler
Engineering Fracture Mechanics
17
4
335-348
1983
This paper is involved with the fracture mechanics study of the fire tube and the outer shell of a boiler. A simplistic approach for determining the stress-intensity to load relations is presented. The results of this approach agreed well with those obtained from a special fracture mechanics finite element program. This approach may well be used in any thin walled cracked problem. The fire tube has been treated as one of the following problems: 1. (1) A straight elliptical externally pressurized tube with a longitudinal crack. 2. (2) A corrugated elliptical externally pressurized tube with longitudinal crack. 3. (3) A perfectly round externally pressurized corrugated tube with a circumferential crack. The allowable working pressure has been obtained for different crack to thickness ratios and different out of roundness. The external shell of the boiler has been checked using the leak before burst criterion. © 1983.
FRACTURE MECHANICS
Quantum-Opto-Mechanics in the Strong Coupling Regime
Quantum optics
1176
2008
30405-30405
2010
We have recently demonstrated strong coupling between light and a micromechanical system. This provides a new level of quantum optical control over mechanics by accessing interactions beyond the rotating wave approximation.
Mechanics, slip behavior, and seismic potential of corrugated dip-slip faults
Journal of Geophysical Research: Solid Earth
117
November 2011
1-19
2012
10.1029/2011JB008642
0545 Computational Geophysics: Modeling (1952, 4255, 4316); 8004 Structural Geology: Dynamics and mechanics of faulting (8118); 8010 Structural Geology: Fractures and faults; 8108 Tectonophysics: Continental tectonics: compressional; 8118 Tectonophysics: Dynamics and mechanics of faulting (8004)
corrugation; mechanics; nonplanar fault; seismic moment; slip distribution; three dimensional
Mixed mode modeling of a thin adhesive layer using a meso-mechanical model
Mechanics of Materials
40
8
665-672
2008
10.1016/j.mechmat.2008.02.006
A representative volume element is modeled using the finite element method. It is used to analyze mixed mode behavior of a thin adhesive layer. Two sources of dissipation is modeled; plasticity and decohesion. Macroscopic traction–separation laws are extracted from the simulations. The results indicate that a boundary of mode mix exists between a region where major plastic dissipation is present and a region where it is not. Without major plastic dissipation, the fracture energy is low and essentially governed by the cohesive properties. This is the case in peel dominated loading cases. In shear dominated loading cases plastic dissipation gives a substantial contribution to the fracture energy. The results show that pure shear loading gives the largest fracture energy.
Adhesive; Cohesive laws; Fracture energy; Mixed mode; Representative volume element; Traction–separation laws
read with quantum mechanics
Nature Nanotech
5
4
246-247
2010
10.1038/nnano.2010.72
Electron tunnelling can be used to selectively identify the basic constituents of DNA, indicating that the approach could be used to efficiently read a DNA sequence.
Molecular mechanics: theoretical basis, rules, scope and limits
Coordination Chemistry Reviews
212
1
3-10
2001
http://dx.doi.org/10.1016/S0010-8545(00)00353-2
Molecular mechanics is a simple model, and it is based on a classical parameterization of non-classical effects for the computation of molecular structure. The basic concept of force field calculations is discussed and, based on the theoretical frame, the emerging scope and limits of the approach, and rules for the application, interpretation of the results and their communication are presented.
Force field; Molecular mechanics; Molecular modeling; Strain energy; Structure
New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using integrated force method
Structural Engineering and Mechanics
33
4
485-502
2009
A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.
Green quasifunction method for free vibration of clamped thin plates
Acta Mechanica Solida Sinica
25
1
37-45
2012
10.1016/S0894-9166(12)60004-4
The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula. Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation. Two examples demonstrate the validity of the present method. Comparison with both the series solution and ANSYS finite-element solution shows fine agreement. The present method is a novel and effective mathematical one. ?? 2012 The Chinese Society of Theoretical and Applied Mechanics.
clamped thin plates; free vibration; Green function; integral equation; R-function
What happened to the mechanics in rock mechanics and the geology in engineering geology
Journal of the Southern African Institute of Mining and Metallurgy
108
6
309-323
2008
A good thing is becoming a bad thing. Rock mass classification systems, that are so excellent for communications between engineers and geologists, and that can be valuable in categorizing project experience, are emasculating engineering geology and rock mechanics. Some engineering geologists have been sucked into thinking that Q and RMR values are all that is needed for engineering purposes, and seem to have put aside what can be learned from structural geology and geomorphology. Many rock mechanics engineers seem to have forgotten the scientific method. This paper attempts to redress the situation by showing how mechanics can be used in rock engineering to design with a similar rigour to that used in the fields of structural engineering, hydraulics and soil mechanics. It also attempts to remind practitioners of what can be achieved by skilled engineering geology.
Earth sciences; Engineering; Engineering geology; Rock mass; Rock mechanics
QUANTUM MECHANICS EXPLAINED
International Journal of Quantum Information
07
01
435
2009
10.1142/S0219749909004487
The physical motivation for the mathematical formalism of quantum mechanics is made clear and compelling by starting from an obvious fact - essentially, the stability of matter - and inquiring into its preconditions: what does it take to make this fact possible?
Quantum Physics
Optical and microwave properties of metal-insulator thin films: possibility of light localization
Physica A: Statistical Mechanics and its Applications
207
1-3
372-378
1994
10.1016/0378-4371(94)90398-0
High frequency response (optical, infrared and microwave) of thin metal-dielectric inhomogeneous films is studied. We propose a new approach based on a direct solution of Maxwell's equations without having to invoke the quasi-static approximation. Our theory reproduces most of the known experimental results including the anomalous absorption near a percolation threshold. For the strong skin effect case or for superconducting-dielectric films we predict an electromagnetic wave localisation at the percolation threshold. © 1994.
An accurate model of thin 2d fluid flows with inertia on curved surfaces
ADVANCES IN FLUID MECHANICS
16
69–88
1998
Consider the 2d flow of a viscous Newtonian fluid upon a curved substrate when the fluid layer is thin as occurs in many draining, coating and biological flows. I derive a model of the dynamics of the fluid layer based upon the layer thickness h, and the mean lateral velocity u. The model accurately includes the effects of fluid inertia, the curvature of the substrate, and a gravitational body force, and may be used to describe wave-like phenomena in the dynamics of viscous fluid flows
Treatment of industrial landfill leachate by means of evaporation and reverse osmosis
Waste Management
22
8
951-955
2002
10.1016/S0956-053X(02)00079-X
In this paper a process for the treatment of landfill leachate involving evaporation and reverse osmosis was proposed. Experimental tests were performed on an industrial landfill leachate. The leachate was subjected to evaporation so as to obtain a distillate containing a small amount of organic material and a substantial amount of inorganic substances (consisting primarily of metals and ammonium salts). The distillate of the evaporation treatment was then subjected to reverse osmosis. The reverse osmosis tests were performed using two different membranes: the AD membrane (thin two-ply film of polyamide) and the SC membrane (thin three-ply film of polyamide). Tests carried out at different values of pH showed a reduction of organic content of about 88% when AD membranes were used and about 80% with SC membranes independently of pH. As regards ammonium, comparable reductions of over 97% were registered for both types of membrane in the optimal conditions of pH = 6.4 (97.1% for AD membranes and 97.7% for SC). ?? 2002 Elsevier Science Ltd. All rights reserved.
Problems of soil Mechanics and construction on soft clays
8th International conference on soil mechanics and foundation engineering
3
111-159
1973
Publication View. 18700540. and Structurally Unstable Soils (Collapsible, Expansive and Others) (9999).
Information Theory and Statistical Mechanics
Physical Review
106
4
620-630
1957
10.1103/PhysRev.106.620
Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncom- mittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available. It is conCluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists only of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.
bayesianism; Information Theory; probability
The compression of a thin strip of material in a superplasticity state
Journal of Applied Mathematics and Mechanics
73
6
722-726
2009
10.1016/j.jappmathmech.2010.01.012
The viscoplastic flow of a thin strip of material in a superplasticity state between rigid, converging parallel planes (an analogue of Prandtl's problem) is investigated. An analytical quadrature solution of the problem is constructed, asymptotically precise in the same sense as Prandtl's solution. Special cases are considered where the solution (including an approximate solution) is written out fully. The effects of superplasticity are determined. © 2010 Elsevier Ltd. All rights reserved.
Approximate solution; Parallel flow; Parallel planes; Strip metal; Superplasticity; Thin strips; Viscoplastic flows
Stress concentration/intensity around elliptical/circular cylinder shaped surface flaws in cross-ply plates and validity of St. Venant's principle in the presence of interacting singularities
Applied Mathematical Modelling
37
3
1362-1377
2013
10.1016/j.apm.2012.04.001
Effects of localized elliptical (circular being a special case) cylindrical surface flaws in laminated composite plates are investigated by using C??-type triangular composite plate elements, formulated on the assumptions of transverse inextensibility and layer-wise constant shear-angle theory (LCST). Numerical results for a cross-ply laminate compromised by the presence of an external part-through elliptical/circular cylindrical slot indicate the existence of severe cross-sectional warping in the vicinity of the surface flaw and plate boundaries. Furthermore, three-dimensional nature of the stress concentration factor in the neighborhood of the elliptical or circular cylinder shaped surface flaw boundary is clearly exhibited. Besides, very high stress concentration factors are found in the layer weakened by the surface flaw. Most importantly, the effects of stress singularity in the neighborhood of the circumferential re-entrant corner lines of the elliptical/circular cylindrical surface flaws, weakening laminated composite plates, are numerically assessed, because of their role in crack initiation. Finally, the interaction of this singularity with free edge stress singularity at the plate boundary, and the implication of such interactions (i.e., violation of St. Venant's principle) in regards to testing of laminated composite specimens are thoroughly investigated. ?? 2012 Elsevier Inc.
Cross-ply laminate; Elliptical or circular cylindrical surface hole; Free-edge stress singularity; Interaction of singularities; Stress concentration factor (SCF); St. Venant's principle
Mechanics of bellows: A critical survey
International Journal of Mechanical Sciences
26
11-12
593-605
1984
10.1016/0020-7403(84)90013-4
Bellows are thin-walled corrugated tubes designed for high flexibility when subjected to longitudinal loads, internal pressure or bending moments. Theoretical and experimental studies on bellows published since the first analysis in 1932 are reviewed herein. The key results dealing primarily with load-deflection behavior are summarized. Results for a variety of corrugation geometries are cast in common sets of nondimensional geometric and material parameters for comparison and evaluation. New experimental results for the mechanical behavior of polyethylene bellows are compared to those predicted by classical beam, plate, and shell theories. Future use of bellows as robotic manipulators is envisioned. That is, bellows will be designed to execute a desired motion in response to internal pressure, controlled through a computer coupled to touch and vision sensors.
Fractional Quantum Mechanics
Physical Review E Statistical Physics Plasmas Fluids And Related Interdisciplinary Topics
62
3 Pt A
27
2008
10.1103/PhysRevE.62.3135
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the L'evy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the L'evy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schr"odinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.
Influences of artificial pre-stressing on ply stresses and tensile properties of Vinylon fibre-reinforced aluminium laminates (VIRALL)
Journal of Materials Science
31
16
4415-4421
1996
A simple micromechanical model based primarily upon the rule-of-mixtures is developed which allows prediction of the effects of fibre preload on the ply stresses (i.e., the initial residual stresses of fibre, adhesive and matrix) induced within VIRALL laminates, and the tensile stress-strain curves and mechanical properties of VIRALL laminates. The analysis of the ply stresses of VIRALL laminates indicates that pre-stressing will dramatically influence the ply stresses. The predicted tensile stress-strain curves of VIRALL laminates are in good agreement with the experimental curves and the results show that the stress-strain curves of VIRALL laminates move upwards when the prestress increases. The predicted tensile mechanical properties of VIRALL laminates at room temperature show good agreement with those obtained experimentally; both show that prestress can improve the tensile properties (i.e., elastic limit strength, 0.2% yield strength and failure strength) of VIRALL laminates. © 1996 Chapman & Hall.
Adhesives; Artificial pre stressing; Composite micromechanics; Cooling; Curing; Elasticity; Laminated composites; Mathematical models; Mechanical properties; Ply stresses; Residual stresses; Rule of mixtures; Solidification; Stresses; Tensile mechanical properties; Tensile properties; Tensile stress strain curves; Thermal expansion; Thermal mismatch; Vinylon fibre reinforced aluminum laminates
Quantum mechanics: interference in the matter.
Nature
448
7151
262-263
2007
10.1038/448262a
Like any particle, electrons are also waves that can interfere with each other. Remarkably, this interference can even happen between electrons from different sources that have never physically interacted.
Pervaporation dehydration of aqueous ethanol and isopropanol mixtures through alginate/chitosan two ply composite membranes supported by poly(vinylidene fluoride) porous membrane
Journal of Membrane Science
167
2
275-289
2000
10.1016/S0376-7388(99)00293-8
Composite membranes consisting of an active alginate layer and supporting chitosan layer on top of the base porous blended polyvinylidene fluoride (PVDF) membrane were prepared and tested for pervaporation dehydration applications. Efforts to enhance the surface properties of PVDF by blending with relatively hydrophilic polymethyl methacrylate (PMMA) were carried out and evaluated by contact angle measurements. Various modifications for the alginate/chitosan composite membranes such as converting to the free acid form and cross-linking with cobalt ion were investigated. They were then compared for the pervaporation dehydration of ethanol/water and isopropanol/water mixtures and the temperature effect on the permeation flux was also investigated. (C)2000 Elsevier Science B.V.
Waves on the surface of a thin layer of viscous liquid
Journal of Applied Mechanics and Technical Physics
14
2
237-241
1975
10.1007/BF01200661
Under the assumption that the boundary layer approximation for the original equations is valid, we show the possibility of the existence of progressive waves on the surface of a vertically flowing film when surface tension is neglected. From the system of equations obtained for a thin layer of viscous liquid flowing down an inclined plane, one equation for perturbations of a thin film follows. Steady solutions of this equation allow periodic discontinuous solutions of the roll-wave type. © 1975 Plenum Publishing Corporation.
Universal transmission conditions for thin reactive heat-conducting interphases
Continuum Mechanics and Thermodynamics
25
1
1-21
2013
DOI 10.1007/s00161-012-0241-1
New imperfect transmission conditions for a thin nonlinear heat-resistant reactive interphase situated between two different materials are evaluated. The transmission conditions are mathematically derived under a minimum set of assumptions, much less restrictive in comparison with those known in the literature. Numerical simulations based on the finite element method demonstrate the high efficiency of the approach by evaluating the involved error.
composite-materials; elasticity; heat transfer; interphase/imperfect interface; nonlinear transmission conditions; numerical simulation; soft; thin interphase
Size effect in plastically deformed passivated thin films
Science in China Series G-Physics Mechanics & Astronomy
52
9
1375-1381
2009
10.1007/s11433-009-0192-0
The flow theory of mechanism-based strain gradient plasticity theory (MSG) developed by Qiu et al. (2003) is extended for incompressible material. The MSG flow theory is used to predict the increase of plastic work hardening for plane strain tension of surface-passivated Cu thin film. The theoretical predictions agree well with experiments for suitably chosen material parameters.
BAUSCHINGER; CONVENTIONAL THEORY; DEFORMATION; INCOMPATIBILITY; LENGTH SCALE; MSG theory; passivation; plain; strain gradient plasticity; STRAIN GRADIENT PLASTICITY; strain tension; thin film
The Fluid Mechanics of Carbon Dioxide Sequestration
Annual Review of Fluid Mechanics
46
1
255-272
2014
10.1146/annurev-fluid-011212-140627
Humans are faced with a potentially disastrous global problem owing to the current emission of 32 gigatonnes of carbon dioxide (CO2) annually into the atmosphere. A possible way to mitigate the effects is to store CO2 in large porous reservoirs within the Earth. Fluid mechanics plays a key role in determining both the feasibility and risks involved in this geological sequestration. We review current research efforts looking at the propagation of CO2 within the subsurface, the possible rates of leakage, the mechanisms that act to stably trap CO2, and the geomechanical response of the crust to large-scale CO2 injection. We conclude with an outline for future research.
convective dissolution; gravity currents; leakage; residual trapping
From creases to conical deflections in a buckled thin sheet: stress focusing vs singularities in strong deformations of a thin elastic sheet
Journal of the Mechanics and Physics of Solids
48
3
565-579
2000
10.1016/S0022-5096(99)00047-2
The localization of deformation is a simple consequence of the fact that bending a thin sheet is energetically cheaper than stretching it. Thus, on examining a crumpled piece of paper, we find that it is made of nearly-planar or cylindrically curved regions folded along line-like stretched ridges or point-like conical singularities. Since the real crumpled paper problem is fairly difficult to deal with, we investigate two simple model experiments where one or two singularities are isolated and studied. When a cylindrical panel is axially compressed, a crease terminated by two conical type singularities appears. The length of this crease is selected by the width of the panel when the length and the thickness of the panel are kept constant. We study also a single conical singularity. This is achieved by pushing a thin sheet into a hollow cylinder similar to pushing coffee-filter paper in a funnel. We measured the singularity energy of the plate, or the work required to form a scar in the sheet. A simple model is proposed to understand the energetics of the crease formation.
Buckling; Nondestructive evaluation; Plastic collapse; Shells and membranes; Stress concentrations
Mechanics of dielectric elastomer-activated deformable transmission grating
Smart Materials and Structures
23
9
095010
2014
10.1088/0964-1726/23/9/095010
Laminating a thin layer of elastomeric grating on the surface of a prestretched dielectric elastomer (DE) membrane forms a basic design of electrically tunable transmission grating. We analyze the inhomogeneous deformation of a circular multiple-region configuration. Variation of the geometric and material parameters, as well as of the critical condition determined by loss of tension instability, is probed to aid the design of a DE-based deformable grating. The predicted changes in the grating period agree substantially with the experimental results reported by Aschwanden et al (Aschwanden et al 2007 IEEE Photon. Technol. Lett. 19 1090).
Quantum Mechanics of Spin Transfer in Ferromagnetic Multilayers
Arxiv preprint cond-mat/0407365
1
1-5
2004
We use a quantum mechanical treatment of a ballistic spin current to describe\nnovel aspects of spin transfer to a ferromagnetic multilayer. We demonstrate\nquantum phenomena from spin transmission resonance (STR) to magnetoelectric\nspin echo (MESE), depending on the coupling between the magnetic moments in the\nferromagnetic thin films. Our calculation reveals new channels through which\nthe zero spin transfer occurs in multilayers: the STR and MESE. We also\nillustrate that counter-intuitively, a negative spin torque can act initially\non the second moment in a bilayer system.
Mesoscale and Nanoscale Physics
Mechanics of tunnelling cracks in trilayer elastic materials in tension
International Journal of Fracture
148
3
233-241
2008
10.1007/s10704-008-9197-3
In this work, the crack driving force for a tunnelling crack in a thin brittle layer confined by dissimilar thick, and more compliant, elastic layers is considered at tensile loading. The steady-state energy release rate is evaluated using distributed dislocation technique and series representation of the complex potentials for an isotropic trimaterial. Evolution of the energy release rate with the crack length is studied by means of FEM. The 3D FEM simulations for tunnel cracks suggest that the ERR can represented by a universal relation (mastercurve) in suitably normalised co-ordinates. An analytical approximation of the ERR mastercurve is obtained as a function of crack length, cracking layer thickness, and a non-dimensional steady-state ERR.
laminate; tunnelling crack
Ventilation and respiratory mechanics.
Comprehensive Physiology
2
2
1093-1142
2012
10.1002/cphy.c100046
During dynamic exercise, the healthy pulmonary system faces several major challenges, including decreases in mixed venous oxygen content and increases in mixed venous carbon dioxide. As such, the ventilatory demand is increased, while the rising cardiac output means that blood will have considerably less time in the pulmonary capillaries to accomplish gas exchange. Blood gas homeostasis must be accomplished by precise regulation of alveolar ventilation via medullary neural networks and sensory reflex mechanisms. It is equally important that cardiovascular and pulmonary system responses to exercise be precisely matched to the increase in metabolic requirements, and that the substantial gas transport needs of both respiratory and locomotor muscles be considered. Our article addresses each of these topics with emphasis on the healthy, young adult exercising in normoxia. We review recent evidence concerning how exercise hyperpnea influences sympathetic vasoconstrictor outflow and the effect this might have on the ability to perform muscular work. We also review sex-based differences in lung mechanics.
Aging; Aging: physiology; Carbon Dioxide; Carbon Dioxide: blood; Dyspnea; Dyspnea: physiopathology; Exercise; Exercise: physiology; Feedback; Female; Humans; Hyperventilation; Hyperventilation: physiopathology; Male; Muscle Fatigue; Muscle Fatigue: physiology; Oxygen; Oxygen: blood; Physiological; Physiological: physiology; Regional Blood Flow; Regional Blood Flow: physiology; Respiratory Mechanics; Respiratory Mechanics: physiology; Respiratory Muscles; Respiratory Muscles: blood supply; Respiratory Muscles: physiology; Sex Characteristics; Vasoconstriction; Vasoconstriction: physiology
Contact Problem For Thin Biphasic Cartilage Layers: Perturbation Solution
Quarterly Journal of Mechanics and Applied Mathematics
64
3
297-318
2011
Doi 10.1093/Qjmam/Hbr008
A three-dimensional unilateral contact problem for articular cartilage layers is considered in the framework of the biphasic cartilage model. The articular cartilages bonded to subchondral bones are modelled as biphasic materials consisting of a solid phase and a fluid phase. It is assumed that the subchondral bones are rigid and shaped close to an elliptic paraboloid. The obtained analytical solution is valid over long time periods and can be used for increasing loading conditions.
articular-cartilage; asymptotic solution; behavior; creep; geometry; joint contact; mechanics; model; osteoarthritis; pressure
Fractal solid mechanics
Revista Mexicana de Física
40
4
506-532
1994
The purpose of present article is to review a new general approach to salid mechanics, named, fractal salid mechanics. The attention is focused on systematic account of the proposed basic concepts, as well as on the most important result of fractal salid mechanics. Special attention is paid to the thermodynamic theory of elasticity of multifractals which is effective for modeling various types of behavior patterns of deformed materials with multifractal microstructure. The fractal concepts in fracture mechanics are considered. It is shown, that the nature of fractal geometry of fracture of a salid is associated with fundamental phenomenon of transverse strains of salid (Poisson's effect). This is manifested by the self-similarity of self-affinity of heterogeneous stresses in irreversibly deformed solids. Some of the most useful analytical and computer models are discussed. The result of theoretical predictions are compared with experimental data. It is shown that the proposed approach is very effective for adequate description of various behavior patterns and some other phenomena in deformed solids.
Solution method of the Poisson equation for the electric field with a thin sheath
Computer Physics Communications
164
1-3
428-433
2004
10.1016/j.cpc.2004.06.057
In the simulation of materials processing plasmas, one has to solve the Poisson equation for electric field at each electron timestep. This is a bottleneck for the numerical simulation of processing plasmas. In this paper, a drastically efficient method for solving the Poisson equation is proposed. In obtaining the solution, the variational principle is used together with the boundary-layer theory in fluid mechanics.
boundary-layer theory; electric field; plasma simulation; poisson equation; variational principle
Forced oscillation assessment of respiratory mechanics in ventilated patients.
Critical care (London, England)
5
1
3-9
2001
10.1186/cc972
The forced oscillation technique (FOT) is a method for non-invasively assessing respiratory mechanics that is applicable both in paralysed and non-paralysed patients. As the FOT requires a minimal modification of the conventional ventilation setting and does not interfere with the ventilation protocol, the technique is potentially useful to monitor patient mechanics during invasive and noninvasive ventilation. FOT allows the assessment of the respiratory system linearity by measuring resistance and reactance at different lung volumes or end-expiratory pressures. Moreover, FOT allows the physician to track the changes in patient mechanics along the ventilation cycle. Applying FOT at different frequencies may allow the physician to interpret patient mechanics in terms of models with pathophysiological interest. The current methodological and technical experience make possible the implementation of portable and compact computerised FOT systems specifically addressed to its application in the mechanical ventilation setting.
Humans; Oscillometry; Oscillometry: instrumentation; Oscillometry: methods; Respiration, Artificial; Respiratory Function Tests; Respiratory Function Tests: instrumentation; Respiratory Function Tests: methods; Respiratory Mechanics; Respiratory Mechanics: physiology
Links between microscopic and macroscopic fluid mechanics
Molecular Physics
101
11
1559-1573
2003
Doi 10.1080/0026897021000026647
The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories {q(t)} may be time-averaged or ensemble-averaged so as to generate field quantities corresponding to macroscopic variables. On the other hand, the macroscopic continuum fields described by fluid mechanics follow irreversible partial differential equations. Smooth particle methods bridge the gap separating these two views of fluids by solving the macroscopic field equations with particle dynamics that resemble molecular dynamics. Recently, nonlinear dynamics have provided some useful tools for understanding the relationship between the microscopic and macroscopic points of view. Chaos and fractals play key roles in this new understanding. Non-equilibrium phase-space averages look very different from their equilibrium counterparts. Away from equilibrium the smooth phase-space distributions are replaced by fractional-dimensional singular distributions that exhibit time irreversibility.
canonical ensemble; continuum-mechanics; entropy; equilibrium; molecular-dynamics; particle applied mechanics; simulations; statistical-mechanics; temperature; time reversibility
The mechanics of the anal sphincter complex.
Journal of biomechanics
21
7
601-4
1988
10.1016/0021-9290(88)90223-0
The anal sphincter complex consists of circumferentially arranged muscle fibres, which surround a relatively thick anal lining. This apparatus was modelled mechanistically as two concentric homogeneous isotropic linear elastic cylinders. The inner cylinder (anal lining) was considered to be thick walled, while the outer (the circular muscle) was assumed to be thin walled. The model predicts that the anal sphincter tension varies linearly with luminal diameter. This prediction was confirmed experimentally under normal conditions as well as during external sphincter contraction and internal sphincter relaxation. Under conditions of negligible hoop stress in the anal lining the model also predicts that the intra-luminal pressure falls to zero before the luminal diameter reaches zero. Hence, an autoregulatory mechanism of anal cushion thickening, as the luminal pressure falls to zero, to produce anal closure was proposed. Deficiencies in this autoregulation mechanism may explain anal incontinence and the obstructed defaecation often found in subjects with haemorrhoids.
Adult; Aged; Anal Canal; Anal Canal: physiology; Biological; Biomechanical Phenomena; Humans; Male; Mathematical Computing; Middle Aged; Models; Pressure
Effect of residual stress on ferroelectric properties of PZT thin film deposited by pulsed laser deposition
Mechanics and Material Engineering for Science and Experiments
263-266
2003
In this paper, ferroelectric thin films Pb(Zr0.58Ti 0.42)O3(PZT) were prepared by a pulse laser deposition (PLD) method. The residual stress in thin film was tested by two methods, which were x-ray diffractometer (XRD) and indentation fracture. In the indentation fracture method, two models including GLFW model and ZCF model were adopted. The results measured by ZCF model were closer to the results measured by XRD. The relationship of properties such as microstructures, ferroelectric response with residual stress was discussed. A simple theoretical model for residual stress formation in PZT thin film preparation was proposed.
Ferroelectricity; Indentation fracture; Lead compounds; PLD; Pulsed laser deposition; PZT thin film; Residual stress; Residual stresses; Thin films; XRD
Fracture mechanics of concrete: applications of fracture mechanics to concrete, rock and other quasi-brittle materials
Engineering Structures
18
11
887-888
1996
10.1016/0141-0296(96)84816-4
FRACTURE MECHANICS OF CONCRETE AND ROCKThis book offers engineers a unique opportunity to learn, from internationally recognized leaders in their field, about the latest theoretical advances in fracture mechanics in concrete, reinforced concrete structures, and rock. At the same time, it functions as a superb, graduate-level introduction to fracture mechanics concepts and analytical techniques.Reviews, in depth, the basic theory behind fracture mechanics * Covers the application of fracture mechanics to compression failure, creep, fatigue, torsion, and other advanced topics * Extremely well researched, applies experimental evidence of damage to a wide range of design cases * Supplies all relevant formulas for stress intensity * Covers state-of-the-art linear elastic fracture mechanics (LEFM) techniques for analyzing deformations and cracking * Describes nonlinear fracture mechanics (NLFM) and the latest RILEM modeling techniques for testing nonlinear quasi-brittle materials * And much moreOver the past few years, researchers employing techniques borrowed from fracture mechanics have made many groundbreaking discoveries concerning the causes and effects of cracking, damage, and fractures of plain and reinforced concrete structures and rock. This, in turn, has resulted in the further development and refinement of fracture mechanics concepts and tools. Yet, despite the field's growth and the growing conviction that fracture mechanics is indispensable to an understanding of material and structural failure, there continues to be a surprising shortage of textbooks and professional references on the subject.Written by two of the foremost names in the field, Fracture Mechanics of Concrete fills that gap. The most comprehensive book ever written on the subject, it consolidates the latest theoretical research from around the world in a single reference that can be used by students and professionals alike.Fracture Mechanics of Concrete is divided into two sections. In the first, the authors lay the necessary groundwork with an in-depth review of fundamental principles. In the second section, the authors vividly demonstrate how fracture mechanics has been successfully applied to failures occurring in a wide array of design cases. Key topics covered in these sections include: * State-of-the-art linear elastic fracture mechanics (LEFM) techniques for analyzing deformations and cracking * Nonlinear fracture mechanics (NLFM) and the latest RILEM modeling techniques for testing nonlinear quasi-brittle materials * The use of R-Curves to describe cracking and fracture in quasi-brittle materials * The application of fracture mechanics to compression failure, creep, fatigue, torsion, and other advanced topicsThe most timely, comprehensive, and authoritative book on the subject currently available, Fracture Mechanics of Concrete is both a complete instructional tool for academics and students in structural and geotechnical engineering courses, and an indispensable working resource for practicing engineers.
Biological applications of hybrid quantum mechanics/molecular mechanics calculation.
Journal of biomedicine & biotechnology
2012
236157
2012
10.1155/2012/236157
Since in most cases biological macromolecular systems including solvent water molecules are remarkably large, the computational costs of performing ab initio calculations for the entire structures are prohibitive. Accordingly, QM calculations that are jointed with MM calculations are crucial to evaluate the long-range electrostatic interactions, which significantly affect the electronic structures of biological macromolecules. A UNIX-shell-based interface program connecting the quantum mechanics (QMs) and molecular mechanics (MMs) calculation engines, GAMESS and AMBER, was developed in our lab. The system was applied to a metalloenzyme, azurin, and PU.1-DNA complex; thereby, the significance of the environmental effects on the electronic structures of the site of interest was elucidated. Subsequently, hybrid QM/MM molecular dynamics (MD) simulation using the calculation system was employed for investigation of mechanisms of hydrolysis (editing reaction) in leucyl-tRNA synthetase complexed with the misaminoacylated tRNA(Leu), and a novel mechanism of the enzymatic reaction was revealed. Thus, our interface program can play a critical role as a powerful tool for state-of-the-art sophisticated hybrid ab initio QM/MM MD simulations of large systems, such as biological macromolecules.
Azurin; Azurin: chemistry; Azurin: metabolism; Catalytic Domain; Computational Biology; Computational Biology: methods; Hydrolysis; Leucine-tRNA Ligase; Leucine-tRNA Ligase: chemistry; Leucine-tRNA Ligase: metabolism; Models, Biological; Molecular Dynamics Simulation; Quantum Theory; Software
[Monitorization of respiratory mechanics in the ventilated patient].
Medicina intensiva / Sociedad Española de Medicina Intensiva y Unidades Coronarias
38
1
49-55
2014
10.1016/j.medin.2013.09.003
Monitoring during mechanical ventilation allows the measurement of different parameters of respiratory mechanics. Accurate interpretation of these data can be useful for characterizing the situation of the different components of the respiratory system, and for guiding ventilator settings. In this review, we describe the basic concepts of respiratory mechanics, their interpretation, and their potential use in fine-tuning mechanical ventilation.
Chest wall mechanics; Deformación pulmonar; Lung deformation; Mecánica de la pared torácica; Mecánica respiratoria; Mechanical ventilation; Respiratory mechanics; Ventilación mecánica
Econophysics, Statistical Mechanics Approach to
Physical Review Letters
24
2007
This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.
Applications; Data Analysis; Physics and Society; Statistical Finance; Statistical Mechanics; Statistics and Probability
Recurrence in quantum mechanics
International Journal of Theoretical Physics
41
1
45-61
2002
10.1023/A:1013217415677
We first compare the mathematical structure of quantum and classical mechanics when both are formulated in a C*-algebraic framework. By using finite von Neumann algebras, a quantum mechanical analogue of Liouville's theorem is then proposed. We proceed to study Poincare recurrence in C*-algebras by mimicking the measure theoretic setting. The results are interpreted as recurrence in quantum mechanics, similar to Poincare recurrence in classical mechanics.
-algebras; c; classical mechanics; liou-; quantum mechanics; recurrence; s theorem; ville; von neumann algebras
Remarks on geometric quantum mechanics
Journal of Geometry and Physics
51
2
229-243
2004
10.1016/j.geomphys.2003.10.008
Pursuing the aims of geometric quantum mechanics, it is shown in a geometrical fashion that, at least in finite dimension, Schrödinger dynamics enjoys classical complete integrability, and several consequences therefrom are deduced, including a Hannay-type reinterpretation of Berry's phase and a geometric description of some aspects of the quantum measurement problem. © 2003 Elsevier B.V. All rights reserved.
Complete integrability; Geometric phases; Geometric quantum mechanics; Quantum measurement theory
Complex-extended Bohmian mechanics.
The Journal of chemical physics
132
13
134102
2010
10.1063/1.3364870
Complex-extended Bohmian mechanics is investigated by analytically continuing the wave function in polar form into the complex plane. We derive the complex-extended version of the quantum Hamilton-Jacobi equation and the continuity equation in Bohmian mechanics. Complex-extended Bohmian mechanics recovers the standard real-valued Bohmian mechanics on the real axis. The trajectories on the real axis are in accord with the standard real-valued Bohmian trajectories. The trajectories launched away from the real axis never intersect the real axis, and they display symmetry with respect to the real axis. Trajectories display hyperbolic deflection around nodes of the wave function in the complex plane.
Robert W. Zwanzig: Formulated nonequilibrium statistical mechanics.
Proceedings of the National Academy of Sciences of the United States of America
111
32
11572-11573
2014
10.1073/pnas.1412827111
This article is a brief Retrospective on the life and work of Robert W. Zwanzig, who formulated nonequilibrium statistical mechanics and who passed away in May of this year.
Contact mechanics
getcited.org
1985
... Post a Comment. CONTRIBUTORS: Author: Johnson , KL (b. 1925, d. ----. PUBLISHER: ... VOLUME/EDITION: PAGES (INTRO/BODY): xi, 452 p. SUBJECT(S): Mechanics, Applied; Surfaces (Technology); Rolling contact; Contact mechanics . DISCIPLINE: No discipline assigned. ...
Deformation quantization in the teaching of quantum mechanics
American Journal of Physics
70
5
537
2002
10.1119/1.1450573
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between classical and quantum mechanics. We demionstrate how it can be used to solve specific problems and clarify its relation to conventional quantization and path integral techniques. We also discuss its recent applications in relativistic quantum field theory.
Classical Analytical Mechanics and Entropy Production
American Journal of Physics
75
11
993
2007
10.1119/1.2772279
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing entropy must also be considered. The notion of entropy then enters into the general classical mechanical formalism. The resulting general formulation and its physical consequences are explored.
Introduction: basic concepts and definitions in mechanics.
Injury
31 Suppl 2
S-B1-B13
2000
10.1016/S0020-1383(00)80039-X
This introduction aims to expound the basic ideas of mechanics of materials to clinicians. What happens when a bone (mechanically a beam) is submitted to standard loads: Centric axial load, bending, eccentric axial load, torque? How does the bone deform? The basic ideas of mechanical engineering are presented using an eraser under load as an illustrative object, and trying to maintain the mathematical formulae as far as possible.
2; 31; bone; injury 2000; linear bending theory; materials; mechanics; strain; stress; suppl; vol
The quantum mechanics SUSY algebra: an introductory review
arXiv preprint hep-th/0205017
01
49
2002
Starting with the Lagrangian formalism with N=2 supersymmetry in terms of two Grassmann variables in Classical Mechanics, the Dirac canonical quantization method is implemented. The N=2 supersymmetry algebra is associated to one-component and two-component eigenfunctions considered in the Schr\"odinger picture of Nonrelativistic Quantum Mechanics. Applications are contemplated.
Predicting fatigue transverse crack growth in cross-ply carbon – epoxy laminates from quasi static strength tests by using iso-damage curves
International Journal of Fatigue
32
1
166-173
2010
10.1016/j.ijfatigue.2009.02.045
Cross-ply laminates made of carbon/epoxy IM7/977-2 system are investigated. The fatigue study is confined to ambient temperature conditions and zero loading ratio. Damage is characterized by the transverse crack density @r in the central 90^o-layer. The family of experimental fatigue cracking curves (@r versus N, where N is the number of cycles, for each tensile test maximum stress amplitude) can be replaced with a set of ''iso-damage curves'', i.e. contour curves of constant @r in the @s-log(N) plane. The iso-damage curves approximately constitute a fan of straight lines that intersect at a common point (@s"e,log(N"s)), where N"s is a very large number of cycles beyond which no more crack appears, and @s"e is some fatigue limit. Our aim is to propose a simple method to predict fatigue cracking at an arbitrary maximum stress level loading by using data stemming from a constant strain rate test. This method essentially rests upon the construction of the above ''iso-damage'' curves, using very simple assumptions.
Applications of statistical mechanics in molecular biology
J. Chem. Educ.
49
7
462
1972
10.1021/ed049p462
Lists and briefly describes references in statistical mechanics,\nparticularly those applicable to molecular biology.
Distribution Functions in Classical and Quantum Mechanics
Progress of Theoretical Physics Supplement
98
98
109-156
1989
10.1143/PTPS.98.109
The correspondence between classical and quantum mechanics is an important subject for the better understandings of "quantum chaos". In particular, it is very important to investigate the correspondence between distribution functions in classical mechanics and in phase space representation of quantum mechanics. This is the review of our recent progresses in the study of distribution functions in classical and quantum mechanics, namely distribution functions in classical mechanics and in coarse-grained classical mechanics as well as the Wigner function and the Husimi function. Topics dealt with include formulations of the Wigner representation, the Husimi representation and coarse-grained classical mechanics, and their applications to the analyses of the eigenstates and time developments of the distribution functions.
Solving for three-dimensional central potentials using matrix mechanics
arXiv preprint arXiv:1211.5236
343
Mc
9
2012
10.1119/1.4793594
Matrix mechanics is an important component of an undergraduate education in quantum mechanics. In this paper we present several examples of the use of matrix mechanics to solve for a number of three dimensional problems involving central forces. These include examples with which the student is familiar, such as the Coulomb interaction. In this case we obtain excellent agreement with exact analytical methods. More importantly, other interesting `non-solvable' examples, such as the Yukawa potential, can be solved as well. Much less mathematical expertise is required for these methods, while some minimal familiarity with the usage of numerical diagonalization software is necessary.
Quantum mechanics: State secrets squeezed
Nature Physics
8
4
254-255
2012
10.1038/nphys2260
Squeezed states push the limits of quantum measurement precision, but observing them is never straightforward. In spin-1 Bose–Einstein condensates, an elegant algebra reveals squeezed states that would otherwise go unnoticed.
About the influence of temperature and matrix ductility on the behavior of carbon woven-ply PPS or epoxy laminates: Notched and unnotched laminates
Composites Science and Technology
71
7
998-1007
2011
10.1016/j.compscitech.2011.03.006
Could thermoplastic-based composites be used to replace thermosetting-based composites in high-temperature secondary aircraft structures? The purpose of this work is to establish the ability of a material system to be used in aircraft engine nacelles when subjected to static loadings, with a key upper temperature of 120??C. In order to provide answers to this question, the thermo-mechanical behaviors of carbon fiber fabric reinforced PPS or epoxy laminates have been compared specifically within the temperature change with 120??C at the upper bound. The temperature-dependent ductile behavior of laminates is more or less exacerbated, depending on polymers glass transition temperature, and laminates stacking sequence. For both materials, the degree of retention of tensile mechanical properties is quite high in notched and unnotched quasi-isotropic laminates. A Digital Image Correlation technique has been used in order to understand the influence of temperature and matrix ductility on the mechanisms of overstresses accommodation near the hole. In fabric reinforced laminates, the high-temperature results suggest a competition between the mechanisms of damage, and the mechanism of plasticization, enhanced in angle-ply lay-ups. Thus, the highly ductile behavior of TP-based laminates, at temperatures higher than their Tg, is very effective to accommodate the overstresses near the hole. ?? 2011 Elsevier Ltd.
A. Fabrics; A. PMCs; B. High-temperature properties; C. Notch
Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials
Mechanics of Composite Materials
36
2
117-130
2000
10.1007/BF02681828
The interlaminar fracture and the low-velocity impact behavior of carbon/epoxy composite materials have been studied using width-tapered double cantilever beam (WTDCB), end-notched flexure (ENF), and Boeing impact specimens. The objectives of this research are to determine the essential parameters governing interlaminar fracture and damage of realistic laminated composites and to characterize a correlation between the critical strain energy release rates measured by interlaminar fracture and by low-velocity impact tests. The geometry and the lay-up sequence of specimens are designed to probe various conditions such as the skewness parameter, beam volume, and test fixture. The effect of interfacial ply orientations and crack propagation directions on interlaminar fracture toughness and the effect of ply orientations and thickness on impact behavior are examined. The critical strain energy release rate was calculated from the respective tests: in the interlaminar fracture test, the compliance method and linear beam theory are used; the residual energy calculated from the impact test and the total delamination area estimated by ultrasonic inspection are used in the low-velocity impact test. Results show that the critical strain energy release rate is affected mainly by ply orientations. The critical strain energy release rate measured by the low-velocity impact test lies between the mode I and mode II critical strain energy release rates obtained by the interlaminar fracture test.
and boeing impact; been; cantilever beam; carbon; composites; crack propagation direction; delamination; end-notched flexure; enf; epoxy; epoxy composite materials have; impact; interfacial ply orientation; interlaminar frac-; low-veloci; o f carbon; residual energy; strain energy release rate; studied using width-tapered double; the interlaminar fracture and; the low-velocity impact behavior; ture; ultrasonic inspection; wtdcb
薄厚層を有する高靱性CFRP積層板の面外衝撃損傷挙動及びCAI特性
日本航空宇宙学会論文集
55
643
388-395
2007
by using thin-ply prepregs; cai; cfrp laminates used for; composite materials; damage behaviors and compressive; delamination; impact; impact loadings; it has been recognized; laminates can be improved; prepregs subjected to out-of-plane; strength of cfrp laminates; strength properties of cfrp; that damage resistance and; the evaluation; thin-ply prepreg; this study investigates the; using thin-ply and standard
Planck's Legacy to Statistical Mechanics
Arxiv:cond-mat
11
2001
In this talk I will describe the deep influence Planck had on the development of statistical mechanics. At this end I will first outline the theoretical situation of statistical mechanics before Planck. I will then describe his main contributions to this field and the progresses obtained as an immediate consequence of his work. I will also outline the later evolution of statistical mechanics in relation with Planck's work. I will finally report on a still unsolved problem in statistical mechanics, historically related to the properties of black-body radiation.
Quantum Mechanics in Phase Space
Reports on mathematical physics
1-14
2007
10.1142/S2251158X12000069
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
A Mechanics of Materials Model for the Creping Process
Journal of Manufacturing Science and Engineering
133
5
051011
2011
10.1115/1.4004925
The manufacture of low density paper such as tissue and towel utilizes the creping pro- cess that consists of adhesively bonding the paper in wet state, onto the sUrface of a smooth drying cylinder and scraping it off with a blade once dried. In this paper, a mechanics of materials description of the creping process is presented. Based upon previ- ous experimental observations, the mechanism of this creping process is proposed as a periodic debonding with a strength-ol-materials failure criterion applied and buckling sequence of an elastic thin film. Numerical calculations show results consistent with ex- perimental data and known industria!' observations. Crepe wavelength versus creping angle data from experiments can be satisfactorily reproduced by a reasonable set ofval- ues for input parameters to the model. Parametric study shows the adhesive shear strength and the sheet stiffness most significantly affect the crepe wavelength and the creping force. The model provides guidance in understanding and optimizing the creping process to produce high quality products.
adhesive; buckling; creping; delamination; failure; paper; softness; tissue
Structural patterns in students' conceptions in mechanics
International Journal of Science Education
21
9
903-920
1999
10.1080/095006999290228
Reports the existence of patterns of reasoning that are common to students' conceptions in different areas of mechanics. Finds that the common frameworks between different ideas have a generality level that lies between Piaget's stage theory and the approach of alternative conceptions. Contains 30 references.
A higher order model for thin-walled structures with deformable cross-sections
International Journal of Solids and Structures
51
3-4
575-598
2014
10.1016/j.ijsolstr.2013.10.023
A higher order model for the analysis of linear, prismatic thin-walled structures that considers the cross-section warping together with the cross-section in-plane flexural deformation is presented in this paper. The use of a one-dimentional model for the analysis of thin-walled structures, which have an inherent complex three-dimensional (3D) behaviour, can only be successful and competitive when compared with shell finite element models if it fulfills a twofold objective: (i) an enrichment of the model in order to as accurately as possible reproduce its 3D elasticity equations and (ii) the definition of a consistent criterion for uncoupling the beam equations, allowing to identify structural deformation modes. The displacement field is approximated through a linear combination of products between a set of linear independent functions defined over the cross-section and the associated weights only dependent on the beam axis; this approximation is not constrained by any ab initio kinematic assumptions. Towards an efficient application of the approximation procedure, the cross-section is discretized into thin-walled elements, being the displacement field approximated for each element independently of the displacement direction. The approximation is thus hp refined enhancing the "capture" of the 3D structural mechanics of thin-walled structures. The beam model governing equations are obtained through the integration over the cross-section of the corresponding elasticity equations weighted by the cross-section global approximation functions. A criterion for uncoupling the beam governing equations is established, allowing to (i) retrieve the classic equations of the thin-walled beam theory both for open and closed sections and (ii) derive a set of uncoupled deformation modes representing higher order effects. The criterion is based on the solution of the polynomial eigenvalue problem associated with the beam differential equations, allowing to quantify the Saint-Venant principle for thin-walled structures. In fact, the solution of the non linear eigenvalue problem yields a twelve fold null eigenvalue (representing polynomial solutions) that are verified to represent beam classic solutions and sets of pairs and quadruplets of non-null eigenvalues corresponding to higher order modes of deformation. © 2013 Elsevier Ltd. All rights reserved.
Distortion; Higher order deformation modes; Thin-walled structures; Warping
Pearson Education - Classical Mechanics
Pearson
638
2002
For 30 years, this book has been the acknowledged standard in advanced classical mechanics courses. This classic book enables readers to make connections between classical and modern physics — an indispensable part of a physicist's education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the book to include the latest topics, applications, and notation to reflect today's physics curriculum
0321188977; 9780321188977; Charles Poole; Classical Mechanics; Herbert Goldstein; International Edition; John Safko; Pearson; Pearson Education
Topics in statistical mechanics
Open Quantum Systems III
1–66
2005
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics. Special emphasis is put on new adiabatic theorems for steady states close to and far from equilibrium, and on investigating cyclic thermodynamic processes using an extension of Floquet theory.
Perturbation theory via Feynman diagrams in classical mechanics
European Journal of Physics
27
5
1241-1249
2006
10.1088/0143-0807/27/5/023
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.
Mechanical properties of W and W(C) thin films: Young’s modulus, fracture toughness and adhesion
Thin Solid Films
332
1-2
195-201
1998
10.1016/S0040-6090(98)01056-6
This contribution presents an investigation and the determination of the mechanical properties of tungsten (W) and tungsten-carbon (W(C)) single layer coatings deposited on steel substrates, in order to optimize a W/W(C) bilayer coating for mechanical applications. The coatings are first tested by three-point bending, to determine Young's moduli. An acoustic emission detector, adapted to the bending device, allows the detection of the first stages of cracking in the coating and furthermore, by an analytical treatment, the determination of the fracture resistance. The adhesion of the coating on this substrate is analyzed from microtensile experiments, performed with a device adapted to a scanning electron microscope. A theoretical formalism is applied to analyze the stress redistribution in the cracked coatings. The elastic moduli of W and W(C) thin films are found to be very close to the bulk values of W. The determined fracture properties (toughness) ranged from 1 to 2.5 MPa m(1/2) and from 0.2 to MPa m(1/2) for the W and the W(C) coatings, respectively. Their differences might be related to the film morphology. The adhesion of these coatings on stainless steel substrates appears good; experimentally no debonding was observed in either system. (C) 1998 Elsevier Science S.A. All rights reserved.
adhesion; carbon; s modulus; tungsten; young
Determination of material parameters for Abaqus progressive damage analysis of E-glass epoxy laminates
Composites Part B: Engineering
46
211-220
2013
10.1016/j.compositesb.2012.09.069
A methodology for determination of material parameters for the progressive damage analysis (PDA) model implemented in Abaqus is presented. The methodology is based on fitting PDA model results to available experimental data. The applicability of the PDA model is studied by comparison to a broad set of experimental data for E-glass epoxy laminates, as well as contrasting PDA with ply discount results. Also, sensitivity of the Abaqus PDA model to h- and p-refinement is studied. ?? 2012 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Transverse cracking; C. Damage mechanics; C. Finite element analysis (FEA); Parameter identification
Weinbergs nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox
Physical Review Letters
66
4
397-400
1991
10.1103/PhysRevLett.66.397
The constraints imposed on observables by the requirement that transmission not occur in the Einstein-Podolsky-Rosen (EPR) experiment are determined, leading to a different treatment of separated systems from that originally proposed by Weinberg (1989). It is found that forbidding EPR communication in nonlinear quantum mechanics necessarily leads to another sort of unusual communication: that between different branches of the wave function.
Statistical Mechanics
Statistical Mechanics
637-652
2011
10.1016/B978-0-12-382188-1.00016-5
Computer simulations play an important role in modern statistical mechanics. The history of the use of computer simulations in science parallels the history of early digital computing. Computer simulations in statistical mechanics fall into two broad classes: Monte Carlo (MC) and molecular dynamics (MD), although variants span the range between the two. Both methods involve numerically evolving simple models of materials through a set of microstates to determine the thermodynamic averages of measurable quantities. Computer simulations provide a means to study physical systems that is complementary to both experiment and theory. The goal of an MC simulation in equilibrium statistical mechanics is to use pseudorandom numbers to draw a representative sample of microstates from the equilibrium probability distribution. The purpose of a molecular dynamics simulation is to integrate Newton's equations of motion for the set of particles in the given system. One advantage of MD over MC is that it approximates the time evolution of the equations of motion of the system, so MD can be used to study a host of dynamical properties. MD is usually more efficient at simulating systems with long-range interactions since all the particles are updated together. MD is sometimes easier to implement than MC for complex systems since appropriate MC moves are sometimes difficult to derive.
AMERICA'S AUTOMOBILES PLY THE WORLD'S ROADS
New York Times (1923-Current file)
116
1929
ONE hears a great deal of the romance of American business. Seldom is it more definitely exemplified than in the extraor dinary expansion in a decade and a half of our automobile export trade. American-made cars; motor buses and motor trucks have invaded the outermost of the far places, and upon ...
Three-dimensional thin film flow over and around an obstacle on an inclined plane.
Physics of Fluids
21
3
32102
2009
10.1063/1.3082218
Steady Stokes flow driven by gravity down an inclined plane over and around an attached obstacle is considered. The effects of the obstacle are examined for various flow configurations and results produced for flow over hemispherical obstacles. Comparison is made with previously published papers that assume that the obstacle is small and/or the free surface deflection and disturbance velocity are small. Values for the unit normal and curvature of the free surface are found using both finite difference approximations and Hermitian radial basis function interpolations, with the resulting solutions compared. Free surface profiles for thin film flows over hemispherical obstacles that approach the film surface are produced and the effects of near point singularities considered. All free surface profiles indicate an upstream peak, followed by a trough downstream of the obstacle with the peak decaying in a “horseshoe” shaped surface deformation. Flow profiles are governed by the plane inclination, the Bond number, and the obstacle geometry. An extension of this approach provides a new class of solutions where a thin film flows around a cylindrical obstacle. Notably, the static contact line angle between the free surface and the obstacle is introduced as an extra flow parameter and its effect investigated for a given set of flow parameters and fixed boundary conditions. Solutions are obtained where steady flow profiles can be found both over and around a cylindrical obstacle raising the awareness of possible multiple solutions. [ABSTRACT FROM AUTHOR]
FINITE differences; FLUID dynamics; FLUID mechanics; RADIAL basis functions; STOKES flow; THIN films
Fractional statistical mechanics.
Chaos (Woodbury, N.Y.)
16
3
033108
2006
10.1063/1.2219701
The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generalization of the Hamiltonian systems is discussed. Liouville and Bogoliubov equations with fractional coordinate and momenta derivatives are considered as a basis to derive fractional kinetic equations. The Fokker-Planck-Zaslavsky equation that has fractional phase-space derivatives is obtained from the fractional Bogoliubov equation. The linear fractional kinetic equation for distribution of the charged particles is considered.
Algorithms; Kinetics; Mathematics; Models, Statistical; Models, Theoretical; Nonlinear Dynamics; Physics; Physics: methods; Systems Theory
ON THE FLUID MECHANICS OF FIRES1
Annual Review of Fluid Mechanics
33
1
67-92
2001
10.1146/annurev.fluid.33.1.67
? Abstract? Fluid mechanics research related to fire is reviewed with a focus on canonical flows, multiphysics coupling aspects, and experimental and numerical techniques. Fire is a low-speed, chemically reacting flow in which buoyancy plays an important role. Fire research has focused on two canonical flows, the reacting boundary layer and the reacting free plume. There is rich, multilateral, bidirectional coupling among fluid mechanics and scalar transport, combustion, and radiation. There is only a limited experimental fluid mechanics database for fire owing to measurement difficulties in the harsh environment and to the focus within the fire community on thermal/chemical consequences. Increasingly, computational fluid dynamics techniques are being used to provide engineering guidance on thermal/chemical consequences and to study fire phenomenology.
Microcanonical entropy and mesoscale dislocation mechanics and plasticity
Journal of Elasticity
104
Berdichevsky 1997
23-44
2011
10.1007/s10659-011-9328-3
A methodology is devised to utilize the statistical mechanical entropy of an isolated, constrained atomistic system to define constitutive response functions for the dissipative driving-force and energetic fields in continuum thermomechanics. A thermodynamic model of dislocation mechanics is discussed as an example. Primary outcomes are constitutive relations for the back-stress tensor and the Cauchy stress tensor in terms of the elastic distortion, mass density, polar dislocation density, and the scalar statistical density.
Dislocation mechanics; Entropy; Plasticity; Statistical mechanics
In situ atomic force microscopy studies on lithium (de)intercalation-induced morphology changes in LixCoO2 micro-machined thin film electrodes
Journal of Power Sources
222
417-425
2013
10.1016/j.jpowsour.2012.09.017
Structural instability due to intercalation-induced stresses in electrode materials is one of the key degradation mechanisms of Li-ion batteries. Fragmentation of material degrades structural integrity and electrical resistance, and also accelerates harmful side reactions. In situ experiments are the appropriate approach for investigating the actual time-dependent nature of the behavior changes of an electrode material while it is charged and discharged. In the current work, a unique in situ electrochemical atomic force microscopy (ECAFM) measurement is made on samples of cylindrical shape, which are micro-machined by focused ion beam (FIB) microscopy. This pre-defined geometry allows the exclusion of secondary, non-active materials from the electrochemically active material as well as the removal of any vagueness owing from the irregular geometry of particles. The experimental results are also used to validate a proposed coupled electrochemical and mechanical model for determining the stress-strain state of active electrode material during electrochemical cycling. The results produced using this model correlate strongly with the experimental data. The combined results reveal the key effects of the geometry, kinetics, and mechanics of electrode materials on the stress-strain state, which acts as a barometer of the structural stability of a material. © 2012 Elsevier B.V. All rights reserved.
AFM; Electrochemical-mechanical; Intercalation; Micro-machined; Thin film electrode; Volume change
Fluid mechanics
Physics Education
22
6
350-354
1987
10.1088/0031-9120/22/6/004
Outlines the contents of Volume II of "Principia" by Sir Isaac Newton. Reviews the contributions of subsequent scientists to the physics of fluid dynamics. Discusses the treatment of fluid mechanics in physics curricula. Highlights a few of the problems of modern research in fluid dynamics. Shows that problems still remain.
Durability mechanics of concrete and concrete structures, redefinition and a new approach
Shrinkage and Durability Mechanics of Concrete and Concrete and Concrete Structures.
2001
10.1201/9780203882955.pt9
Durability mechanics of concrete and concrete structures, redefinition and a new approach. In T.-A. Tanabe et al. Creep, Shrinkage and Durability Mechanics of Concrete and Concrete and Concrete Structures. London: Taylor & Francis Group.
Dynamic load balancing in computational mechanics
Computer Methods in Applied Mechanics and Engineering
184
2-4
485-500
2000
10.1016/S0045-7825(99)00241-8
In many important computational mechanics applications, the computation adapts dynamically during the simulation. Examples include adaptive mesh refinement, particle simulations and transient dynamics calculations. When running these kinds of simulations on a parallel computer, the work must be assigned to processors in a dynamic fashion to keep the computational load balanced. A number of approaches have been proposed for this dynamic load balancing problem. This paper reviews the major classes of algorithms and discusses their relative merits on problems from computational mechanics. Shortcomings in the state-of-the-art are identified and suggestions are made for future research directions.
Adaptive mesh refinement; Dynamic load balancing; Parallel computer
Computational biology: a statistical mechanics perspective
Chapman & Hall/CRC
11
276
2006
Quantitative methods have a particular knack for improving any field theytouch. For biology, computational techniques have led to enormous strides inour understanding of biological systems, but there is still vast territory tocover. Statistical physics especially holds great potential for elucidatingthe structural-functional relationships in biomolecules, as well as theirstatic and dynamic properties. Breaking New Ground Computational Biology: AStatistical Mechanics Perspective is the first book dedicated to the interfacebetween statistical physics and bioinformatics. Introducing both equilibriumand nonequilibrium statistical mechanics in a manner tailored to computationalbiologists, the author applies these methods to understand and model theproperties of various biomolecules and biological networks at the systemslevel. Unique Vision, Novel Approach Blossey combines his enthusiasm foruniting the fields of physics and computational biology with his considerableexperience, knowledge, and gift for teaching. He uses numerous examples andtasks to illustrate and test understanding of the concepts, and he supplies adetailed keyword list for easy navigation and comprehension. His approachtakes full advantage of the latest tools in statistical physics and computerscience to build a strong set of tools for confronting new challenges incomputational biology. Making the concepts crystal clear without sacrificingmathematical rigor, Computational Biology: A Statistical Mechanics Perspectiveis the perfect tool to broaden your skills in computational biology.
Thermal buckling of antisymmetric angle-ply laminated cylindrical shells
Composites Engineering
1
3
183-192
1991
10.1016/0961-9526(91)90018-N
This paper is aimed at the development of an analytical method to handle thermal buckling of laminated composite circular cylindrical shells. An eighth-order governing differential system for predicting this response is formulated from an energy approach. With the focus on simply-supported, antisymmetric angle-ply laminated composite cylinders subjected to circumferentially-varying temperatures, Galerkin's method is employed, where the corresponding numerical results provide insight into the response of the critical buckling temperature to such factors as lamination angles, number of layers, stacking sequence, goemetric aspect ratios and various temperature functions. For example, in the case of antisymmetric laminates, the coupling effect between bending and compression vanishes as the number of layers increases. This phenomenon is confirmed for common composite materials such as Graphite/Epoxy and Boron/Epoxy.
High-strain rate response of angle-ply glass epoxy laminates
Journal of Composite Materials
29
10
1308-1320
1995
The effects of strain rate on the mechanical behavior of Scotchply Type 1002 glass/epoxy angle-ply laminates is investigated. High strain rate tests (approximately 10(3) sec(-1)) using a direct tension split Hopkinson bar apparatus and quasi-static tests (strain rate of approximately 10(-4) sec(-1)) using a servo-hydraulic testing machine have been conducted. Results indicate that the maximum normal stress experienced by glass/epoxy laminates is higher for dynamic than for quasi-static loading conditions. Although both fibers and matrix are sensitive to the strain rate, the fibers influence laminate rate sensitivity more than the matrix.
Random response of antisymmetric angle-ply laminated plates
Structural Safety
6
2-4
115-127
1989
10.1016/0167-4730(89)90014-3
The random response of an antisymmetric angle-ply composite plate\nsubjected to random lateral load on its surface is obtained. The\nfirst-order transverse shear deformation theory, involving five coupled\npartial differential equations, is used. To evaluate the effect of\nshear deformation, anisotropy and other problem parameters on the\nresponse, the numerical results obtained with this theory are compared\nwith the results obtained by the classical plate theory. Significant\ndifferences are observed in the two sets of results obtained by the\ntwo theories especially for thick plates, thus demonstrating the\nimportance of shear deformations and need for utilization of plate\ntheories which properly account for such deformations. © 1989.
a-Si:H thin film transistors after very high strain
Journal of Non-Crystalline Solids
266-269
1320-1324
2000
10.1016/S0022-3093(99)00944-8
We fabricate amorphous silicon (a-Si:H) thin-film transistors (TFTs) on a 25 μm Kapton foil, and then bend the foil over mandrels of various radii. The bending causes tensile strain in the TFTs when they face out, and compressive strain when they face in. After bending, we measure the electrical properties of the TFTs. After ∼2% of compressive strain, there is no change in the TFT electrical performance due to bending, namely in the on-current, off-current, source-gate leakage current, mobility and the threshold voltage. In tension, no change in the TFT performance is observed up to the strain of ∼0.5%. For larger tensile strains TFTs fail mechanically by cracking of the TFT layers. These cracks run perpendicularly to the bending direction.
a200; f200; p290; t190
Large deflection vibration of angle ply laminated plates
Journal of Sound and Vibration
40
3
393-408
1975
http://dx.doi.org/10.1016/S0022-460X(75)81309-5
Large deflection vibration of unsymmetric angle ply laminated rectangular plates are studied. Two different out of plane boundary conditions considered are (a) all the edges clamped, and (b) all the edges simply supported. The dynamic analogues of Von Karman 's large deflection equations for laminated plates are used. Solutions are obtained for two in-plane boundary conditions. Non-linear frequency is obtained as a function of lamination parameter, material constants, aspect ratio, linear frequency and amplitude of vibration. Two mode analysis also is presented wherein the modal equations are solved by a perturbation technique. Non-linear frequency to linear frequency ratio amplitude curves are presented for various cases.
Knot theory and statistical mechanics
Rev. Mod. Phys.
64
4
1099-1131
1992
10.1103/RevModPhys.64.1099
This is a tutorial review on knot invariants and their construction using the method of statistical mechanics. We begin with brief reviews of the elements of knot theory and relevant results in statistical mechanics. We then show how knot invariants, including those discovered recently, can be obtained by applying techniques used in solving lattice models in lattice statistics. Our approach is based on the consideration of solvable models with strictly local Boltzmann weights. The presentation, which is self-contained and elementary, is intended for a general readership. A table of polynomial invariants for knot and links containing up to six crossings is included in the Appendix.
A rotation-free thin shell quadrilateral
Computer Methods in Applied Mechanics and Engineering
196
2631-2646
2007
10.1016/j.cma.2007.01.008
In this paper a four-node quadrilateral finite element for the analysis of smooth thin shells is presented. The main feature of the element, an extension of previous developments in triangles, is that the translational displacements of the middle surface are the only degrees of freedom. The membrane behavior results from a standard bilinear interpolation of the geometry within the element. With the aim of an efficient element in codes with explicit time integration, one point quadrature is used in the element area. To avoid spurious deformation modes (hourglass modes) membrane forces resulting from a perturbation stabilization technique are included. For the computation of the curvature tensor a patch of five elements (the element and the four adjacent elements) is defined. The curvature field, assumed constant within the element, is expressed in terms of the deformation gradient at the element boundary and is dependent on the position of the twelve nodes included in the patch. In some problems a bending deformed configuration may occur without associated energy. A cost-effective perturbation stabilization scheme is used to control it. General boundary conditions are shown to be easily implemented. The element denoted BSQ (for Basic Shell Quadrilateral) is based on a Total Lagrangian Formulation and has been implemented in codes with implicit and explicit integration. To assess the element performance and convergence properties a set of numerical examples are presented, including geometrically linear and non-linear problems with large strain plasticity. The results obtained show good convergence properties. For several examples different values of the stabilization coefficients have been considered to study the sensitivity of the results to such coefficients. In general this sensitivity appears to be low as the mesh is refined and the results are obtained with a fixed set of coefficients. ?? 2007 Elsevier B.V. All rights reserved.
Finite elements; Hourglass control; Large strains; Quadrilateral; Rotation-free; Thin shells
Assessment of the 3-D shape and mechanics of the proximal femur using a shape template and a bone mineral density image
Biomechanics and Modeling in Mechanobiology
10
4
529-538
2011
10.1007/s10237-010-0253-3
Measurement of bone mineral density (BMD) by DXA (dual-energy X-ray absorptiometry) is generally considered to be the clinical golden standard technique to diagnose osteoporosis. However, BMD alone is only a moderate predictor of fracture risk. Finite element analyses of bone mechanics can contribute to a more accurate prediction of fracture risk. In this study, we applied a method to estimate the 3D geometrical shape of bone based on a 2D BMD image and a femur shape template. Proximal femurs of eighteen human cadavers were imaged with computed tomography (CT) and divided into two groups. Image data from the first group (N = 9) were applied to create a shape template by using the general Procrustes analysis and thin plate splines. This template was then applied to estimate the shape of the femurs in the second group (N = 9), using the 2D BMD image projected from the CT image, and the geometrical errors of the shape estimation method were evaluated. Finally, finite element analysis with stance loading condition was conducted based on the original CT and the estimated geometrical shape to evaluate the effect of the geometrical errors on the outcome of the simulations. The volumetric errors induced by the shape estimation method itself were low (<0.6%). Increasing the number of bone specimens used for the template decreased the geometrical errors. When nine bones were used for the template, the mean distance difference (±SD) between the estimated and theCT shape surfaces was 1.2±0.3mm, indicating that themethodwas feasible for estimating the shape of the proximal femur. Small errors in geometry led systematically to larger errors in the mechanical simulations. The method could provide more information of the mechanical characteristics of bone based on 2D BMD radiography and could ultimately lead to more sensitive diagnosis of osteoporosis. © Springer-Verlag 2010.
Bone strength; Computed tomography; Finite element; Proximal femur; Shape estimation
Biorthogonal quantum mechanics
Journal of Physics A: Mathematical and Theoretical
47
035305
2014
10.1088/1751-8113/47/3/035305
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert space dimensionality is finite. Specifically, characterisations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.
Analysis of matrix cracking in GFRP laminates using Raman spectroscopy
Composites Science and Technology
67
1946-1954
2007
10.1016/j.compscitech.2006.10.019
A Raman spectroscopic technique was used to investigate the elastic modulus degradation and the residual strain development in cross-ply and [0/452/0]T glass fibre/epoxy laminates. Glass has a poor Raman signal and, therefore, embedded aramid fibres were used as strain sensors for mapping of the internal strain development within the 0?? ply due to matrix cracking in the off-axis ply. The elastic modulus and the residual strain were derived from the changes of the distance between well identified strain "peaks" on the aramid fibres. The elastic modulus reduction and the residual strain development are described by a closed form model. The modulus reduction predictions are accurate, whereas the experimental residual strain is higher than that predicted. Since both phenomena are governed by the same elastic parameters, the discrepancy cannot be explained by purely elastic analysis. Development of inelastic strains in the off-axis layer is suggested as a possible cause. ?? 2006 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Matrix cracking; C. Damage mechanics; C. Transverse cracking; D. Raman spectroscopy
Classical Mechanics: kinematics and statics
Textbook
2012
10.1007/978-3-642-03434-3
This is the first volume of three books by the same author, devoted\nentirely to classical mechanics. The triad of works covers different\nsubjects in classical mechanics and creates a link between them by\nderiving topics from the same root. Moreover, the author unifies\ndifferent approaches from English, Russian, Polish, and German literature\ndevoted to classical mechanics. Emphasis is placed on the study of\nelectro-magneto-mechanical systems. \n\nClassical Mechanics: Kinematics and Statics is addressed to a wide\nspectrum of undergraduate and graduate students, postgraduate students,\nresearchers, and instructors, from the fields of mechanical and civil\nengineering. This volume, which includes a wealth of worked examples\nand applications, is also intended to be used as a self-contained\nreference for researchers in applied mathematics and physical sciences.\nIt is also recommended as a supplementary textbook at the upper undergraduate\nand graduate levels.\n\nIn Chapter 1 the fundamental principles of mechanics are formulated,\nillustrated, and discussed. Chapter 2 is devoted to statics and Chapter\n3 presents the geometry of masses. Kinematics of a particle, the\ncurvilinear and normal coordinates, and kinematic pairs and chains\nare the main focus of Chapter 4. Chapter 5 studies the kinematics\nof a rigid body and a composite motion of a particle. Chapter 6 ends\nthe text with kinematics of a deformable body.
Quantum mechanics of classically non-integrable systems
Physics Reports
163
4
205-297
1988
10.1016/0370-1573(88)90130-5
In the semiclassical limit, quantum mechanics shows differences between classically integrable abd chaotic systems. Here we review recent developments in this field. Topics dealt with include formal integrability of quantum mechanics, semiclassical quantization, statistical properties of eigenvalues, semiclassical eigenfunctions, effects on the time-evolution and localization due to classical diffusion. A large bibliography supplements the text.
Rheology of model confined ultrathin fluid films .1. Statistical mechanics of the surface force apparatus experiments
Journal of Chemical Physics
106
17
7295-7302
1997
10.1063/1.473691
We have studied the behavior of confined ultrathin films of a simple model system in which the fluid and wall particles were modeled as Lennard-Jones rare gas atoms by Monte Carlo simulations. We have used a new (Grand isoforce) statistical ensemble in these simulations, with which it is possible to simulate thin films under constraints (fixed chemical potential mu, temperature T, stress tensor components T-zz, T-xz, and T-yz) that are presumably resembling the conditions under which the Surface Force Apparatus (SFA) operates. We also employ another ensemble, with fixed (mu, T, V, T-xz, T-yz), which we call ''Grand Isoshear.'' Some important features of the SFA experiments on globular, nonpolar, molecular liquids have been reproduced in the simulations. Using the new statistical ensembles we have shown that a periodic solvation force can be obtained under the operating conditions of the SFA, although some additional features may exist, but remain hidden in the experiments if located in the unstable branch of the solvation force curve. We demonstrate that epitaxy between the solid walls and the fluid molecules is not required to obtain an apparently periodic solvation force curve. (C) 1997 American Institute of Physics.
asymptotic decay; micropores; molecularly-thin-films; monte-carlo simulation; phase-transitions; pore; shear; simple classical fluid; solvation forces; stick-slip motion
Three-dimensional analysis of the spontaneous instability for soft thin viscoelastic films
Acta Mechanica
211
3
345-356
2010
10.1007/s00707-009-0245-5
Abstract Based on the continuum mechanics and the bifurcation theory, a three-dimensional theoretical model for a soft thin viscoelastic\nfilm bonded to a rigid substrate is investigated. Considering the competition among van der Waals interaction potential energy,\nstrain energy, and surface energy, three-dimensional governing equations of the spontaneous instability are derived, and the\nanalytical results of time-dependent critical conditions are obtained. Furthermore, the phase diagram of instability due to\nvan der Waals interaction and variation of the dimensionless characteristic wavenumber and the critical stiffness of interaction\nwith the critical time are discussed.
Comparing small scale plasticity of copper-chromium nanolayered and alloyed thin films at elevated temperatures
Acta Materialia
93
175-186
2015
10.1016/j.actamat.2015.04.008
The yield strengths and deformation mechanisms of Cu–Cr nanolayered and alloyed thin films were studied by microcompression testing at elevated temperatures. The mechanical response of the films with alternating layers of Cu and Cr with sub-100nm interlayer thicknesses and alloyed films of the same average composition was compared to determine the role of the interfaces on deformation. Higher resistance to plastic flow at elevated temperatures was exhibited by the nanolayered films with smaller interlayer thickness among the layered films, while the alloyed film revealed an anomalous increase in strength with temperature exhibiting a deformation mechanism similar to the pure Cr film.
Interfaces; Micromechanics; Nanostructured materials; Stress-assisted diffusion; Transmission electron microscopy
Effects of thickness and transverse shear modulus nonlinearity on the post-“yield” and post-localization response of an externally pressurized imperfect cross-ply ring
Composite Structures
88
1
83-96
2009
http://dx.doi.org/10.1016/j.compstruct.2008.02.016
The present investigation is concerned with the prediction of localization (onset of deformation softening) and post-localization and post-“yield” equilibrium paths for moderately thick and thick cross-ply [90/0/90] imperfect plane strain rings. These paths are often unstable in the presence of modal imperfections and material nonlinearity, and are considered to “bifurcate” from the primary equilibrium paths, representing periodic buckling patterns pertaining to global or structural level stability. The fully nonlinear finite element analysis, based on the total Lagrangian formulation, employs a three-dimensional theory, known as layer-wise linear displacement distribution theory (LLDT), to capture the three-dimensional interlaminar (especially, shear) deformation behavior, associated with the localized interlaminar shear-crippling failure. The combined effects of modal imperfections, interlaminar shear/normal deformation and nonlinear (hypo-elastic) material property for the transverse shear modulus, GTT, on the localization and delocalization (deformation hardening) phenomena are thoroughly investigated, and physically meaningful conclusions are drawn from these numerical results.
Compression failure; Deformation softening; Localization/delocalization; Post-buckling; Strain hardening; Thick cross-ply ring
Persistence of thin ice regions in Europa's ice crust
Geophysical Research Letters
29
22
22-25
2002
10.1029/2002GL016171
Extensive data from planetary spacecraft as well as celestial mechanics models support the existence of a subsurface ocean on Europa ~100 km thick, maintained by a tidal heat flux. Models in which the overlying ice crust is less than 20 km thick permit breaches in the ice due to impact events or thermal plumes from the tidally heated core. We apply a two-dimensional thermal model to the analysis of the refreezing of a hole in the ice crust following a breach event. Our model incorporates heat produced by tidal heating of Europa in two ways: a basal heat flux from Europa's silicate and iron core, together with volumetric heating of the ice shell. We compare our refreezing timescales to those obtained from a model where viscous flow in the base of the ice crust fills the hole. We find that catastrophic breaches in Europa's ice crust may produce regions of relatively thin ice persisting up to ~1 My. These breaches are closed by viscous flow when radii are small (<10–50 km) and by conductive refreezing for larger radii, especially if Europa's crust has a high basal heat flow due to a hot core. Detection of the ice/ocean interface by orbital detection of the temperature anomalies or radar sounding would be most probable in the vicinity of these events.
http://dx.doi.org/10.1029/2002GL016171, doi:10.102
Development of a new quadrilateral thin plate element using area coordinates
Computer Methods in Applied Mechanics and Engineering
190
979-987
2000
10.1016/S0045-7825(99)00457-0
A new quadrilateral thin plate bending element with 12 degrees of freedom, called element ACGCQ, has been developed by employing both the area coordinates and the generalized conforming approach. The deflection field of the element is expressed as a polynomial, in terms of area coordinates, which is corresponding to a fourth order polynomial in terms of Cartesian coordinates x and y. The 12 generalized conforming conditions implemented are four-point and four-line compatibility conditions for the deflection w, and four-line compatibility conditions for the normal slope ??n. Since the relation between the area and Cartesian coordinates is linear, the formulation of the element stiffness matrix is straight forward. Several numerical examples were employed to test the proposed element. The results obtained show that it possesses the advantage of high accuracy and reliability, rapid convergence and insensitivity to geometric distortion.
area coordinates; finite elements; generalized conforming approach; quadrilateral plate bending elements
Numerical simulations of stress generation and evolution in Volmer-Weber thin films
Journal of the Mechanics and Physics of Solids
2008
10.1016/j.jmps.2008.02.008
We present a detailed model of the stresses and shape changes that occur in polycrystalline thin films during Volmer-Weber growth. Our model tracks the shape of an array of islands as they grow and coalesce into a continuous film. The islands change shape as a result of the deposition flux, as well as surface and grain boundary diffusion. Stress is generated in the film as a result of forces exerted between neighboring islands as they meet to form a grain boundary. The internal stresses in the islands and the diffusive changes on their surfaces and grain boundaries are computed using a coupled finite element scheme. Interactions between neighboring islands are modeled using a cohesive zone law. Our model predicts stress-thickness vs. thickness behavior that is in excellent agreement with experiments. Specifically, we observe a three-stage growth process consisting of a stress-free pre-coalescence stage, a rapid tensile rise at coalescence, and an eventual transition to a steady-state. The steady-state stress may be tensile or compressive, depending on the deposition rate, the grain size, and the properties of the film. Detailed parametric studies are conducted to establish the influence of material properties and growth conditions on the stress history, and the results are compared with experimental observations and previous models. ?? 2008 Elsevier Ltd. All rights reserved.
Cohesive zone; Finite element analysis; Thin film stress; Volmer-Weber growth
Inertial effects in time-dependent motion of thin films and drops
Journal of Fluid Mechanics
467
1-17
2002
10.1017/S0022112002008637
Capillarity is an important feature in controlling the spreading of liquid drops and in the coating of substrates by liquid films. For thin films and small contact angles, lubrication theory enables the analysis of the motion to be reduced to single evolution equations for the heights of the drops or films, provided the inertia of the liquid can be neglected. In general, the presence of inertia destroys the major simplification provided by lubrication theory, but two special cases that can be treated are identified here. In the first example, the approach of a drop to its equilibrium position is studied. For sufficiently low Reynolds numbers, the rate of approach to the terminal state and the contact angle are slightly reduced by inertia, but, above a critical Reynolds number, the approach becomes oscillatory. In the latter case there is no simple relation connecting the dynamic contact angle and contact-line speed. In the second example, the spreading drop is supported by a plate that is forced to oscillate in its own plane. For the parameter range considered, the mean spreading is unaffected by inertia, but the oscillatory motion of the contact line is reduced in magnitude as inertia increases, and the drop lags behind the plate motion. The oscillatory contact angle increases with inertia, but is not in phase with the plate oscillation.
Review of some poroelastic effects in rock mechanics
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts
30
7
1119-1126
1993
10.1016/0148-9062(93)90081-N
This paper reviews by examples some critical pore pressure effects in rock mechanics. The influence of pore pressure on the shear, effective compressive and tensile stresses around a borehole are examined. The impact on hydraulic fracturing is also briefly explored.
Some elementary connections between curvature and mismatch strain in compositionally graded thin films
Journal of the Mechanics and Physics of Solids
44
5
723-736
1996
10.1016/0022-5096(96)00008-7
A thin film structure with through-the-thickness variation of properties and/or mismatch strain is considered. The relationship of the overall curvature of the film to the variation of properties and mismatch strain is reviewed. It is shown that, if the material properties are known, the mismatch strain distribution in the film can be expressed in terms of the dependence of curvature on film thickness. In addition, the case of film growth under conditions for which the mismatch strain of deposited material depends on the local strain conditions of the growth surface is considered. By means of an illustration, it is shown that the final state of strain within a free film following growth depends on the constraint conditions that were imposed on the film during its growth.
Fracture of anodic-bonded silicon-thin film glass-silicon triple stacks
Engineering Fracture Mechanics
75
5
1064-1082
2008
10.1016/j.engfracmech.2007.04.030
In this study we focus on the fracture behavior of two types silicon-thin film glass-silicon (Si-Glass-Si) triple stacks specimens with a sharp corner. We determine the notch stress intensity factor Kn for both specimens using a combination of the Williams eigenfunction expansion method, Stroh's sextic formalism, finite element analysis, and the path-independent H-integral. Empirical solutions of dimensionless stress intensity factors are proposed for two typical specimens, and the dependence of geometry is analyzed. Furthermore, the effect of glass thickness on stress intensity is explored for anodic-bonded Si-Glass-Si triple stacks. We discuss the feasibility of using a critical value of Kn to correlate the failure results for both specimens with various bond area and glass thickness. © 2007 Elsevier Ltd. All rights reserved.
Stress intensity factors for internal circumferential cracks in thin-and thick-walled cylinders
Engineering Fracture Mechanics
60
5-6
491–500
1998
10.1016/S0013-7944(98)00045-9
ÐThis paper addresses the calculation of mode I stress intensity factors for complete circumferential cracks on the inner surface of a hollow cylinder subjected to axisymmetric loading. The analysis based on the weight function method involves two reference sets of data. These are the stress intensity factor and the crack mouth opening displacement for a crack under uniform loading. Boundary-element computations are performed in order to extend the reference data available in the literature to include the cases of thin-walled cylinders and deep cracks. The derived weight function is valid for a wide range of cylinder inner and outer radii, 0.1RRi/RoR1, and of the relative crack depth, a/tR0.8. Its application provides the computation of stress intensity factors with an accuracy of about 3%.
boundary-element method; ðcircumferential crack; stress intensity factor; weight function
Roughening and pinning of interface cracks in shear delamination of thin films
Journal of Statistical Mechanics: Theory and Experiment
2009
11
P11009
2009
10.1088/1742-5468/2009/11/P11009
We investigate the roughening of shear cracks running along the interface between a thin film and a rigid substrate. We demonstrate that short-range correlated fluctuations of the interface strength lead to self-affine roughening of the crack front as the driving force (the applied shear stress/stress intensity factor) increases towards a critical value. We investigate the disorder-induced perturbations of the crack displacement field and crack energy, and use the results to determine the crack pinning force and to assess the shape of the critical crack. The analytical arguments are validated by comparison with simulations of interface cracking.
The determination of fluctuating velocity in air with heated thin film gauges
Journal of Fluid Mechanics
29
part 2
289 - 295
1967
10.1017/S0022112067000813
When attempts are made to use thin film anemometers in airflow to measure fluctuating velocity it is found that the dynamic sensitivity cannot be obtained from a steady-flow calibration. It is found that the dynamic sensitivity is con- siderably less than that predicted by static calibration and that the sensitivity is frequency-dependent. It is shown that thermal feedback from the substrate, on which the gauge is mounted, to the heated element is responsible for the variation of sensitivity with frequency, despite constant-temperature operation of the probe, and this variation is examined theoretically and experimentally.
Intrinsic parameter fluctuations in nanometre scale thin-body SOI devices introduced by interface roughness
Superlattices and Microstructures
34
3-6
283-291
2003
10.1016/j.spmi.2004.03.026
An investigation is presented into intrinsic parameter fluctuations in thin-body Sol MOSFETs due to local variations in body thickness as a result of interface roughness. A series of well scaled devices from 15 nm channel length down to 5 nm are investigated using three-dimensional drift-diffusion simulations which include the density gradient equation to account for quantum mechanical effects. It is shown that the intrinsic parameter variations are enhanced by the quantum mechanical confinement within the channel of the device. A comparison with parameter fluctuations due to discrete random doping in the source and drain is also presented. (C) 2004 Published by Elsevier Ltd.
fluctuations; interface roughness; MOSFETs; quantum mechanics; scaling; soi
On universal relations in continuum mechanics
Continuum Mechanics and Thermodynamics
9
2
61-72
1997
10.1007/s001610050055
This paper is devoted to a systematic study of local universal relations in continuum mechanics. We show that it is possible to determine the complete set of independent universal relations whose characterization is obtained by linear universal rules. A historical review of the literature on the topic and various significant examples are given.
Canonical relational quantum mechanics from information theory
Electronic Journal of Theoretical Physics
8
25
93-108
2011
In this paper we construct a theory of quantum mechanics based on Shannon information theory. We define a few principles regarding information-based frames of reference, including explicitly the concept of information covariance, and show how an ensemble of all possible physical states can be setup on the basis of the accessible information in the local frame of reference. In the next step the Bayesian principle of maximum entropy is utilized in order to constrain the dynamics. We then show, with the aid of Lisi's universal action reservoir approach, that the dynamics is equivalent to that of quantum mechanics. Thereby we show that quantum mechanics emerges when classical physics is subject to incomplete information. We also show that the proposed theory is relational and that it in fact is a path integral version of Rovelli's relational quantum mechanics. Furthermore we give a discussion on the relation between the proposed theory and quantum mechanics, in particular the role of observation and correspondence to classical physics is addressed. In addition to this we derive a general form of entropy associated with the information covariance of the local reference frame. Finally we give a discussion and some open problems.
03.65.ta; 03.67.-a; 03.67.bg; 03.67.mn; Information theory; Quantum mechanics; Relational quantum mechanics; Shannon information theory PACS (2010): 03.65.-w
Determination of elastic moduli of thin layers of soft material using the atomic force microscope
Biophysical Journal
82
5
2798-2810
2002
10.1016/S0006-3495(02)75620-8
We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels.
Thin-film flow of a power-law liquid falling down an inclined plate
Journal of Non-Newtonian Fluid Mechanics
122
69-78
2004
10.1016/j.jnnfm.2004.01.021
We consider the problem of a thin layer of a power-law liquid falling down an inclined plate. The corresponding nonlinear evolution equation for the film thickness is solved numerically in a periodic domain. Numerical calculations show that saturation of nonlinear interactions occurs, resulting in a finite-amplitude permanent wave. The free-surface evolution is similar to that for a Newtonian liquid, but the shape and amplitude of the permanent wave are influenced strongly by the non-Newtonian fluid behaviour. The permanent wave is nearly harmonic for initial wavenumbers just below the cut-off wavenumber or of solitary type for much smaller wavenumbers. For shear-thickening (shear-thinning) liquids, the maximum wave amplitude is always smaller (larger) than that for a Newtonian liquid. For shear-thinning liquids at low flow rates, the permanent wave remains harmonic as for a Newtonian liquid. The increase of the Reynolds number, which measures the flow rate, leads to more significant growth of the two-dimensional disturbances in the case of a shear-thinning liquid than in the case of a Newtonian liquid. ?? 2004 Elsevier B.V. All rights reserved.
Long-wavelength theory; Power-law model; Surface-wave instability
Delamination buckling in the microwedge indentation of a thin film on an elastically deformable substrate
Mechanics of Materials
39
9
881-892
2007
10.1016/j.mechmat.2007.03.003
A delamination buckling model is proposed for the assessment of the interfacial fracture toughness by the microwedge indentation delamination test on a film/substrate system. The delamination buckling model is based on Von Karman nonlinear plate theory and considers the elastic deformation in the substrate and the impression on the film. The substrate deformation is modeled by employing three-coupled springs and the effect of the impression free-surfaces is modeled by using two-coupled springs. A closed form solution is derived with the spring compliances obtained from the dimension analysis and numerical calculations. The energy release rate and the phase angle are given for a variety the elastic mismatch between the film and the substrate. The results show that in some cases, the energy release rate can be two orders in magnitude larger than that derived from the clamped end condition. ?? 2007.
Indentation test; Interface toughness; Phase angle; Residual stress; Thin film buckling
Inverse method for detection and sizing of cracks in thin sections using a hybrid genetic algorithm based signal parametrisation
Theoretical and Applied Fracture Mechanics
49
2
185-198
2008
10.1016/j.tafmec.2007.11.004
A hybrid-GA method, based on signal parameterization, has been reported here for the improved detection and sizing of surface cracks of small sizes/depths in thin sections. The method relies on parameterizing the composite reference from the defect into its individual components i.e., the crack tip diffracted echo and the corner trap echo and subsequently use the relative arrival time technique (RATT). The phased array ultrasonic technique was employed in the investigation. Both experimental and simulated signals were used in the study. It is shown through both simulations and experiments that the hybrid-GA is successful in parameterizing both non-overlapping and overlapping echoes encountered in thin sections. It is additionally shown that the hybrid-GA improves the signal to noise ratio and correct for under-sampling of data. © 2007 Elsevier Ltd. All rights reserved.
FDTD; Genetic algorithms; NDE; NDT; Phased array; Signal parameterization; Sizing; Small crack; Ultrasound
How thin is a thin bed?
Geophysics
38
6
1176-1180
1973
10.1190/1.1440403
Based on reflective properties, a thin bed may be conveniently defined as one whose thickness is less than about lambda/8 where lambda is the (predominant) wavelength computed using the velocity of the bed. The amplitude of a reflection from a thin bed is to the first order of approximation equal to 4*pi*A*b/lambda where b is the thickness of the bed and A is the amplitude of the reflection if the bed were to be very thick. The equation shows that a bed as thin as 10 ft has, for typical frequency and velocity, considerably more reflective power than is usulaly attributed to it.
Geometry andMechanics of Uniform n-Plies: from Engineering Ropes to Biological Filaments
Journal of Elasticity
69
41-72
2002
10.1023/A:1027390700610
We study the mechanics of uniform n-plies, correcting and extending previous work in the literature. An n-ply is the structure formed when n pretwisted strands coil around one another in helical fashion. Such structures are encountered widely in engineering (mooring ropes, power lines) and biology (DNA, proteins). We first show that the well-known lock-up phenomenon for n = 2, described by a pitchfork bifurcation, gets unfolded for higher n. Geometrically, n-plies with n> 2 are all found to behave qualitatively the same. Next, using elastic rod theory, we consider the mechanics of n-plies, allowing for axial end forces and end moments while ignoring friction. An exact expression for the interstrand pressure force is derived, which is used to investigate the onset of strand separation in plied structures. After defining suitable displacements we also give an alternative variational formulation and derive (nonlinear) constitutive relationships for torsion and extension (including their coupling) of the overall ply. For a realistic loading problem in which the ends are not free to rotate one needs to consider the topological conservation law, and we show how the concepts of link and writhe can be extended to n-plies.
birdcaging; constitutive relations; dna; end loads; helix; link; multi-strand plies; pling; proteins; rod mechanics; strand separation; twist-stretch cou-; wire rope; writhe
Renewable energy education for technicians/mechanics
Renewable Energy
14
1-4
393-400
1998
10.1016/S0960-1481(98)00095-0
Some of the issues relating to renewable energy education are highlighted. Outlines of proposed course curricula for certificate and Diploma level courses are briefly presented and discussed.
mechanics; renewable energy education; technicians
Mechanics of isolated horizons
Classical and Quantum Gravity
17
2
253-298
2000
10.1088/0264-9381/17/2/301
A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A space-time representing a black hole which is itself in equilibrium but whose exterior contains radiation admits such a horizon. However, the definition is applicable in a more general context, such as cosmological horizons. Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced and their properties analyzed. Although their definitions do not refer to infinity, these quantities assume their standard values in the static black hole solutions. Finally, using these definitions, the zeroth and first laws of black hole mechanics are established for isolated horizons.
Craze growth mechanics
Polymer
41
3
1119-1129
2000
10.1016/S0032-3861(99)00234-7
Crazing is an important fracture mechanism in polymers. In this paper, crazes are treated as cracks bridged by fibrils. Fibril stresses are treated as external loads on the crack flanks. This perception of a craze allows an analysis in terms of linear elastic fracture mechanics. A “Paris law” type of crack growth behaviour is adopted and the two constants for the Paris equation are estimated. The results of the approach explain experimental results from the literature, including the well-known empirical logarithmic craze growth equation. The model prediction compares favourably with craze growth data, obtained by Wales on PVC.
Craze growth rate; Paris low; Stress intensity factor
On the classical limit of Bohmian mechanics for Hagedorn wave packets
Journal of Functional Analysis
259
9
2404-2423
2010
10.1016/j.jfa.2010.07.011
We consider the classical limit of quantum mechanics in terms of Bohmian trajectories. For wave packets as defined by Hagedorn we show that the Bohmian trajectories converge to Newtonian trajectories in probability.
and phrases; bohmian mechanics; classical limit; quantum mechanics; semiclassical wave packets
C-PLY™, a new structural approach to multiaxials in composites
JEC Composites Magazine
48
68
53-54
2011
Among the first manufacturers to commit themselves to Professor Tsai's project, Chomarat accepted the challenge to convert a mass- production tool into a unique manufacturing process able to produce a new range of multiaxial materials. This range of products opens new prospects in the construction of composites by providing increased performance and weight reduction previously impossible to obtain.
Rhetoric ’ s Mechanics : Retooling the Equipment of
College Composition and Communication
60
December
366-387
2008
Teaching rhetorical production in a digital age calls for us to rethink our discipline's current distaste for writing mechanics. Yet, the digital mechanics of writing are much broader than grammatical concerns. They include production tools that allow for the invention and circulation of audio, visual, and Multigenre writing. (Contains 3 figures and 11 notes.)
Comparison of global and local response surface techniques in reliability-based optimization of composite structures
Structural and Multidisciplinary Optimization
26
5
333-345
2004
10.1007/s00158-003-0353-0
This paper discusses the development and application of two alternative strategies, in the form of global and sequential local response surface (RS) techniques, for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS), whereas the local technique uses multiple first-order RS models, with each applied to a small subregion of the FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, the thickness and orientation angle of each ply, the diameter and length of the cylinder, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of the ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with the reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of the reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy, with the sequential local RS technique having a considerably better computational efficiency.
Axial buckling of cylindrical shells; First-order reliability method; Reliability-based optimization; Response surface technique
Specific heat in transverse Ising thin films
Physica a-Statistical Mechanics and Its Applications
339
3-4
403-415
2004
10.1016/j.physa.2004.03.027
The specific heat and temperature dependence of magnetizations in transverse Ising thin films are investigated by the use of the standard mean-field theory and the effective-field theory with correlations. The exchange interaction and transverse field at the surfaces take values different from those in the bulk. Many characteristic features are obtained in the magnetic properties, depending on the thickness L of a film, the ratios of those properties between the surface and the bulk and the value of transverse field in the bulk. It is clarified that the various characteristic features in specific heat mainly come from those in Ising thin films with zero transverse field and the specific heat in Ising thin films with zero transverse field may dramatically change with the variation of L and the value of exchange interaction at the surfaces. (C) 2004 Elsevier B.V. All rights reserved.
ferroelectric-films; field; magnetization; model; phase-diagrams; specific heat; transitions; transverse ising film
Mechanics of emplacement of basic intrusions
Tectonophysics
46
1-2
41-63
1978
10.1016/0040-1951(78)90104-X
The sunken nature of many basic intrusions can be explained by simple models for flexure of the lithosphere subjected to loading by a magma. The lithosphere is divided into the strata above the magma which deforms as a stack of elastic plates, and the substratum below the magma which is modelled as an elastic plate overlying a weak fluid asthenosphere. Plane-strain plate theory is used to calculate shape and size of plutons. Significant mechanical parameters controlling the shape are: (1) depth of emplacement; (2) width of intrusion; (3) total lithospheric thickness; (4) magma density; (5) effective thickness of the overburden; and (6) magmatic pressure. In areas with lithospheric thickness of 50–100 km, basic intrusions emplaced in the upper crust (< 10 km) will be laccolithic whereas bowl-shape intrusions form in a thin lithosphere (< 50 km) or result from viscoelastic deformation subsequent to emplacement. For a thick lithosphere (100 km) emplacement of magma in the lower crust should result in thin sill-like plutons. If lithospheric thickness was 25 km and magma pressure about 1 kbar, emplacement of the Freetown basic complex at 15 km depth results in a maximum magma thickness of 10 km. The thickness of the model compares well with that determined from Bouguer gravity models. Calculated thickness from the elastic bending model for Umfraville, Thanet and Tudor gabbros, Ontario, yield values smaller than thickness determined by gravity. Progressive thickening of these plutons subsequent to emplacement may have caused the greater thickness, where the underburden, subjected to high temperatures, reacted viscoelastically. Dip of igneous layering towards the center of some intrusions may result from viscoelastic depression of the floor while the magma crystallized.
Mathematical Foundations of Quantum Mechanics
American Mathematical Monthly
72
1
96
1955
10.2307/2313034
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.
Effect of stiffness of thin reinforcing ring on the state of stress of a nonlinear elastic plate …
International Applied Mechanics
1971
Page 1. OF OF REINFORCING RING ON THE STATE OF STRESS OF A NONLINEAR ELASTIC PLATE WITH A HOLE G. G. Kuliev UDC 539.3
Adhesion of a flat punch adhered to a thin pre-stressed membrane
The Journal of Adhesion
79
2
123-140
2003
10.1080/00218460309573
The mechanics of a circular membrane delaminating from a rigid punch is derived based on linear elasticity and an energy balance approach. Both the tensile prestress and the resulting concomitant stress upon external loading are considered. A "pull-off" phenomenon is predicted when the contact circle shrinks to a critical value between 0.1945 and 0.3679 of the film diameter, depending on the critical strain energy release rate and the prestress. These asymptotic limits match exactly with the prestress dominant model by Shanahan and prestress free model by Wan. Thin film delamination from a rectangular punch is also investigated. Unlike the circular punch, the rectangular contact is expected to reduce to a line contact with zero contact area at "pinch-off." The graphs and trends shown are useful in assessing thin film delamination assisted by a prestress.
Effects of anisotropy and curvature on free vibration characteristics of laminated composite cylindrical shallow shells
Structural Engineering and Mechanics
35
4
493-510
2010
This paper presents effects of anisotropy and curvature on free vibration characteristics of cross-ply laminated composite cylindrical shallow shells. Shallow shells have been considered for different lamination thickness, radius of curvature and elasticity ratio. First, kinematic relations of strains and deformation have been showed. Then, using Hamilton's principle, governing differential equations have been obtained for a general curved shell. In the next step, stress-strain relation for laminated, cross-ply composite shells has been given. By using some simplifications and assuming Fourier series as a displacement field, differential equations are solved by matrix algebra for shallow shells. The results obtained by this solution have been given tables and graphs. The comparisons made with the literature and finite element program (ANSYS).
anisotropy; finite element method (fem); shell theory; structural composites; thin; vibration
Size effects on the plastic collapse limit load of thin foils in bending and thin wires in torsion
European Journal of Mechanics - A/Solids
30
6
854-864
2011
10.1016/j.euromechsol.2011.05.003
Following a previous paper by the author [Strain gradient plasticity, strengthening effects and plastic limit analysis, Int. J. Solids Struct. 47 (2010) 100-112], a noncon- ventional plastic limit analysis for a particular class of micron scale structures as, typically, thin foils in bending and thin wires in torsion, is here addressed. An ide- alized rigid-perfectly plastic material is considered, which is featured by a strengthening potential degree-one homogeneous function of the effective plastic strain and its spatial gradient. The nonlocal (gradient) nature of the material resides in the inherent strengthening law, whereby the yield strength is related to the effective plastic strain through a second order PDE with associated higher order boundary conditions. The peculiarity of the considered structures stems from their geome-try and loading conditions, which dictate the shape of the collapse mechanism and make the higher order boundary conditions on the (microscopically) free boundary be accommodated by means of a boundary singularity mechanism. This consists in the formation of thin boundary layers with unbounded stresses, but bounded stress resultants which --together with the regular bulk stresses-- contribute to the value of the collapse load. Closed-form solutions are provided for thin foils in pure bend- ing and thin wires in pure torsion, and in particular the limit bending and torque moments are given as functions of an adimensionalized internal length parameter.
giulio maier on the; gradient plasticity; occasion of his eightieth; plastic limit analysis; size effects; this paper is dedicated; to prof
Statistical Mechanics of Interfaces ´
Encyclopedia of Mathematical Physics
2001
55-63
2006
Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.
A computational damage mechanics model for thermomigration
Mechanics of Materials
41
3
271-278
2009
10.1016/j.mechmat.2008.10.013
Miniaturization of electronics to nanoscale leads to significantly higher current density levels and larger thermal gradients in electronics packaging. Laboratory test data show that thermomigration plays a significant role in high current density induced failure in solder joints and interconnects. In this paper, a computational damage mechanics model for thermomigration process is proposed and implemented in finite element method. This model is based on thermodynamics and formulated by continuum mechanics equations, mass transport principals and heat transfer equations. A damage evolution model using entropy production rate as a metric is utilized to evaluate the degradation in solder joints subjected to high temperature gradients. ?? 2008 Elsevier Ltd. All rights reserved.
Relativistic quantum mechanics and the Bohmian interpretation
Foundations of Physics Letters
18
6
549-561
2005
10.1007/s10702-005-1128-1
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role, provides a viable interpretation of relativistic quantum mechanics. We formulate the Bohmian interpretation of many-particle wave functions in a Lorentz-covariant way. In contrast with the nonrelativistic case, the relativistic Bohmian interpretation may lead to measurable predictions on particle positions even when the conventional interpretation does not lead to such predictions.
Bohmian interpretation; Klein-Gordon equation; Relativistic quantum mechanics
Effective behaviour of elastic heterogeneous thin structures at finite deformations
Computational Mechanics. Solids, Fluids, Engineered Materials, Aging Infrastructure, Molecular Dynamics, Heat Transfer, Manufacturing Processes, Optimization, Fracture & Integrity
41
4
595-606
2008
10.1007/s00466-007-0217-3
In this contribution the effective material behaviour of thin structures like membranes and plates consisting of heterogeneities is investigated. The diameter of typical inclusions can be in the order of magnitude of the thickness of the membrane or plate. Thus, the prerequisite for a standard homogenization procedure using representative volume elements is not fulfilled anymore, since the required size of an RVE would be larger than the thickness of the structure itself. Additionally the assumption of uniformity of the boundary conditions on the RVE would be violated especially for plates since in general the predominant deformation of such structures is bending. However, it can be shown that the effective behaviour of such heterogeneous thin structures subjected to finite deformations is still in good agreement to the results obtained for homogenized materials.
History of classical mechanics
Die Naturwissenschaften
63
3
119-130
1976
10.1007/BF00600486
Continuing the story begun in Part I, this article sketches the development of rational mechanics in the nineteenth century. Then it was taught to every physicist and, as time went on, to an ever greater proportion of engineers. Not only was it the core of their training in natural science, but also it served as the paradigm of a scientific discipline. The rise of relativity and the theory of quanta left classical mechanics the preserve of engineers for the first half of the 20th century. Recently classical mechanics, particularly in reference to severely deformable bodies, has come to be studied and developed again as a science in its own right, much as it was in the Age of Reason and the Enlightenment.
High Strain Test Method for Thin Composite Laminates
16th International Conference on Composite Structures
c
2011
This test and verification research effort focuses on evaluating thin composite laminates used in deployable space structures. A new test method has been developed to quantify the bending moment vs. curvature behavior of thin composite laminates. Equations of the test fixture mechanics and possible sources of error have been assessed. Calibration testing of a known, spring-steel was conducted showing excellent correlation to tensile test data. Composite samples of interest to the deployable space community are slated for test and evaluation.
a new test method; composite laminates; curvature behavior of thin; deployable composite structures; equations; evaluating thin composite; evaluation; has been developed to; high strain; laminates used in deployable; modeling; quantify the bending moment; research effort focuses on; space structures; summary; test; this test and verification; vs
Matrix cracking in polymeric composites laminates: Modelling and experiments
Composites Science and Technology
68
2310-2317
2008
10.1016/j.compscitech.2007.09.013
Composites ability to retain functionality in the presence of damage is a crucial safety and economic issue. Generally the first damage mode in composite laminates is matrix cracking, which affects the mechanical properties of the structure long before its load-bearing capacity is exhausted. In this paper, a detailed analysis of the effect of matrix cracking on the behaviour of cross-ply [0/90]s and unbalanced symmetric [0/45]s glass/epoxy laminates loaded statically in tension is performed. Theoretical predictions of stiffness reduction due to damage are based on the Equivalent Constraint Model (ECM), which takes into account concurrent matrix cracking in all plies of the laminate, although matrix cracking under consideration is developing only within the off-axis ply of the laminates. The longitudinal Young's modulus predictions are compared to experimentally derived data obtained using laser Raman spectroscopy (LRS). The good agreement between predicted and measured values of the reduced longitudinal Young's modulus validates the ECM model and proves that its basic assumptions are accurate. Thus, the predictions for all the mechanical properties by the ECM model are within a realistic range, while experimental evidence is required for further validation. ?? 2007 Elsevier Ltd. All rights reserved.
A. Polymer-matrix composites (PMCs); B. Matrix cracking; C. Damage mechanics; C. Transverse cracking; D. Raman spectroscopy
Effects of the top-electrode size on the piezoelectric properties (d[sub 33] and S) of lead zirconate titanate thin films
Journal of Applied Physics
96
5
2800
2004
10.1063/1.1775306
The effects of a decreasing top electrode size on the electric and piezoelectric properties of tetragonal Pb(ZrX,Ti1−X)O3 thin films are investigated. The effective piezoelectric small-signal coefficient d33,eff and the piezoelectric large signal-strain S are measured using a double-beam laser interferometer. Both properties are found to decrease rapidly with decreasing size of the used Pt top electrode for the investigated dimensions of 5 mm to 100 m edge length (square pads).While the ? loss of d33,eff is as high as 75%, the influence on the relative permittivity is only small. The source of the pad size effect on the measured piezoelectric properties is found to be the mechanics of the layered structure commonly used for piezoelectric measurements (Pt/PZT/Pt/TiO/SiO2/Si),[PZT, Pb(Zrx,Ti1−x)O3] which is verified by finite element simulations.
Determining the fracture resistance of thin sheet fiber composites - Paper as a model material
Composites Science and Technology
74
43-51
2013
10.1016/j.compscitech.2012.10.007
In nonlinear fracture mechanics testing of thin-sheet short-fiber composites, special problems occur that do not appear in other engineering materials, such as steels. The most important problem is the formation of a long process zone, where fiber pull-out, realignment and breakage occur, making an optical crack length measurement impossible. This impedes the determination of a reproducible value of the fracture toughness and the construction of a crack growth resistance curve. Two new approaches are presented to overcome this problem. In the first one, a procedure is presented to determine experimentally the cohesive zone relation on deeply-notched double-edge notch tension specimens. The cohesive zone relation enables us, together with the mechanical properties, to simulate numerically a fracture mechanics test on an arbitrary geometry and to determine a crack growth resistance curve. In the second approach, the displacements and strains around the process zone are measured during in situ experiments under an optical microscope using digital image analysis. With this local deformation analysis, a critical local strain is determined where the load bearing capacity of the material decreases to zero. The knowledge of this critical strain is used to find the location of the crack tip and to determine a crack growth resistance curve. The application of the two approaches is demonstrated on commercial printing paper as model material. It is shown that reproducible fracture toughness parameters can be determined with both procedures. ?? 2012 Elsevier Ltd.
A. Short-fiber composites; B. Fracture toughness; C. Deformation; C. Finite element analysis (FEA); Cohesive zone model
Organic molecular beam epitaxial growth of substituted phthalocyanine thin films - tetrapyridotetraazaporhyrins on alkali halide ( 100 ) surfaces
Thin Solid Films
331
17-130
1998
http://dx.doi.org/10.1016/S0040-6090(98)00908-0
Thin films of tetrapyridotetraazaporphyrinatozinc (TPyTAPZn) and of tetrapyridotetraazaporphyrinatooxovanadium (TPyTAPVO) which both can be looked at as substituted phthalocyanines Pc were prepared on the (100) surfaces of NaCl, KCl, KBr and on quartz glass under ultra high vacuum (UHV) conditions. The films were studied by reflection high energy electron diffraction (RHEED), UV-vis absorption spectroscopy, tapping mode atomic force microscopy (AFM) and modeled by molecular mechanics calculations. Highly ordered crystalline films were obtained for the first monolayers with the molecules oriented in square lattices in close relationship to the substrate crystal axes as determined by RHEED. 2√2×2√2, R=45° surface lattices were obtained for TPyTAPZn on KBr and KCl relative to the respective surface unit mesh. Somewhat distorted 2√2×2√2, R=15° and 1.25√5×1.25√5, R=18.4° surface lattices were found for TPyTAPVO on KBr and KCl, respectively, instead of high crystallinity whereas a clear √10×√10, R=18° surface lattice was obtained on NaCl. The pyrido groups in the ligand instead of the benzo groups of Pc led to these new molecular orientations by providing different interaction with the substrate surface, within the molecular plane and between layers as proven by molecular mechanics geometry optimization. Very sharp absorption bands shifted to lower transition energy also indicate crystalline growth in square lattices for thicker films. The band position and hence the size of the exciton splitting is discussed based on a point dipole model and used to estimate the vertical interaction range in the thin films. AFM allowed a detailed analysis of crystal morphology and film texture. The island growth of the organic crystals at step edges of the alkali halide substrates indicate a high mobility of molecules on terraces as well as across step edges of the substrate under deposition conditions.
atomic force microscopy; diffraction; ection high energy electron; lm; molecular mechanics calculation; molecular order; molecular semiconductor; organic molecular beam epitaxy; re; substituted phthalocyanine; thin; uv-vis absorption spectroscopy
Quantum Mechanics as Complex Probability Theory
Modern Physics Letters A
9
28
2571
1994
10.1142/S0217732394002422
We show that the phenomena explained by quantum mechanics can alternatively be explained as a breakdown of probability theory without the need for wave-particle duality or the idea that a particle does not have a unique path in space. The single-particle Lagrangian consistent with the reformulated quantum mechanics is derived and specialized to the Schrödinger and Klein-Gordon theories. The usual paradoxes of quantum mechanics are explained. A connection to gravity is proposed. Probability theory is restored in the classical limit.
Stability , Composition and Function of Palladium Surfaces in Oxidizing Environments : A First-Principles Statistical Mechanics Approach
Dissertation Freie Universität Berlin
1-179
2006
The catalytic oxidation using transition metals (TM) as the active\nmaterial is an important technological\n\nprocess, which is still not fully understood. Recently, there has\nbeen an increasing awareness that the\n\nsurface of the TM catalysts employed might be oxidized under the oxygen-rich\nconditions of the catalytic\n\nreaction (ambient pressures of O2 and other reactant gases). The resulting\nchanges in the\n\ncomposition and structure of the surface can then also strongly influence\nthe catalytic activity of the material.\n\n\n\nIn the present work the catalytic CO oxidation over the Pd(100) surface\nis studied as a model system.\n\nRecent experimental results for this system suggest that the Pd(100)\nsurface might actually be oxidized\n\nunder conditions as applied in industrial oxidation catalysis. However,\nit is still being discussed, if the\n\nobserved oxidic phase is already a thick, bulk-like oxide film or\na nanometer thin surface oxide layer, and\n\nif the actual active state of the catalyst under reaction conditions\nis then mainly dominated by a metallic\n\nor an oxidic phase.\n\n\n\nTo address this topic from a theoretical point of view a multiscale\nmodeling approach has been employed in\n\nthis work. To describe the system quantitatively on an atomic (microscopic)\nlevel density-functional theory (DFT)\n\nhas been used. The results of the DFT calculations have then been\ncombined with concepts from thermodynamics\n\nand statistical mechanics to transfer the information obtained in\nthe microscopic regime to meso- and macroscopic\n\nlength and time scales.\n\n\n\nIn a first step the atomistic thermodynamics approach is used to obtain\na large scale picture about the\n\nthermodynamic stability of different phases in a constrained thermodynamic\nequilibrium with an\n\nO2 and CO gas phase (i.e. the formation of CO2 is not considered).\n\nFocussing on temperature and pressure conditions representative of\ntechnological oxidation catalysis it\n\nis found that\n\na thin surface oxide structure or a CO covered metal surface are the\nrelevant system states under these conditions.\n\nIn a second refining step the stability of the surface oxide structure\nunder steady-state conditions\n\nis then investigated using kinetic Monte Carlo (kMC) simulations,\nnow explicitly taking into account\n\nthe on-going CO2 formation.\n\nThe result is that despite the catalytic CO oxidation reaction\n\nthe surface oxide on Pd(100) is still stable under stoichiometric\npO2/pCO\n\nratios in the gas phase at elevated temperatures.\n\nThis indicates the importance of this surface oxide and calls for\ndetailed studies evaluating its\n\ncontribution to the overall catalytic activity.
DFT; heterogeneous catalysis; s; surface chemistry
Effect of reinforcement type on high velocity impact response of GRP plates using a sharp tip projectile
International Journal of Impact Engineering
38
715-722
2011
10.1016/j.ijimpeng.2011.03.004
High velocity impact performance of glass reinforced polyester (GRP) resin composite plates with different type of reinforcement was investigated. The projectile used was a sharp tipped (30°) conical head with total length of 30 mm and shank length of 15 mm with weight of 9.74 g. Five different types of E-glass fiber reinforcement were used, including chopped strand mat (CSM), plain weave, satin weave, unidirectional and cross-ply unidirectional fiber reinforcements. A smooth barrel gas gun was used to conduct high velocity impact tests in the velocity range of 80-160 m/s. Composite plates with size of 15 cm × 15 cm were prepared in 3 and 6 mm thickness. Results showed higher ballistic limit velocity (velocity at which samples fully penetrated the target plates with zero residual velocity) for 3 mm GRP plates with cross-ply unidirectional reinforcement followed by unidirectional reinforcement and plain weave, the plates with satin weave and CSM reinforcements were almost in same level. The thicker specimens (6 mm), plates with plain weave reinforcement showed better ballistic performance towards sharp tipped conical projectile impact, followed by cross-ply unidirectional, satin weave, unidirectional and CSM reinforced plates. Experimentally determined ballistic limit velocity for all specimens correlate well with estimated ballistic limit values obtained in full perforation tests. Damage assessment conducted on all specimens indicated fiber tension and shear failure for thin-walled and sever delamination for the thick-walled specimens as the dominant failure modes. © 2011 Elsevier Ltd. All rights reserved.
Ballistic limit; Composite; High velocity impact; Sharp tip projectile
The cholesterol-dependent cytolysin pneumolysin from Streptococcus pneumoniae binds to lipid raft microdomains in human corneal epithelial cells.
PloS one
8
4
e61300
2013
10.1371/journal.pone.0061300
Streptococcus pneumoniae (pneumococcus) is an opportunistic bacterial pathogen responsible for causing several human diseases including pneumonia, meningitis, and otitis media. Pneumococcus is also a major cause of human ocular infections and is commonly isolated in cases of bacterial keratitis, an infection of the cornea. The ocular pathology that occurs during pneumococcal keratitis is partly due to the actions of pneumolysin (Ply), a cholesterol-dependent cytolysin produced by pneumococcus. The lytic mechanism of Ply is a three step process beginning with surface binding to cholesterol. Multiple Ply monomers then oligomerize to form a prepore. The prepore then undergoes a conformational change that creates a large pore in the host cell membrane, resulting in cell lysis. We engineered a collection of single amino acid substitution mutants at residues (A370, A406, W433, and L460) that are crucial to the progression of the lytic mechanism and determined the effects that these mutations had on lytic function. Both Ply(WT) and the mutant Ply molecules (Ply(A370G), Ply(A370E), Ply(A406G), Ply(A406E), Ply(W433G), Ply(W433E), Ply(W433F), Ply(L460G), and Ply(L460E)) were able to bind to the surface of human corneal epithelial cells (HCECs) with similar efficiency. Additionally, Ply(WT) localized to cholesterol-rich microdomains on the HCEC surface, however, only one mutant (Ply(A370G)) was able to duplicate this behavior. Four of the 9 mutant Ply molecules (Ply(A370E), Ply(W433G), Ply(W433E), and Ply(L460E)) were deficient in oligomer formation. Lastly, all of the mutant Ply molecules, except Ply(A370G), exhibited significantly impaired lytic activity on HCECs. The other 8 mutants all experienced a reduction in lytic activity, but 4 of the 8 retained the ability to oligomerize. A thorough understanding of the molecular interactions that occur between Ply and the target cell, could lead to targeted treatments aimed to reduce the pathology observed during pneumococcal keratitis.
Amino Acid Sequence; Animals; Bacterial Proteins; Bacterial Proteins: chemistry; Bacterial Proteins: genetics; Bacterial Proteins: metabolism; Cell Line; Cholesterol; Cholesterol: metabolism; Epithelium, Corneal; Epithelium, Corneal: cytology; Humans; Membrane Microdomains; Membrane Microdomains: metabolism; Models, Molecular; Molecular Sequence Data; Mutagenesis, Site-Directed; Mutation; Perforin; Perforin: chemistry; Perforin: genetics; Perforin: metabolism; Protein Binding; Protein Multimerization; Protein Structure, Quaternary; Protein Transport; Rabbits; Streptococcus pneumoniae; Streptococcus pneumoniae: metabolism; Streptolysins; Streptolysins: chemistry; Streptolysins: genetics; Streptolysins: metabolism
Continuum Mechanics
Architectural Engineering
56
3
B34
2003
10.1007/978-3-540-74298-2
This book presents an introduction into the entire science of Continuum Mechanics in three parts. Part I: Continuum Mechanics introduces into the Foundations using tensors in Cartesian coordinate systems, classical theory of elasticity, and fluid mechanics. Part II: Mechanics of Materials has chapters on viscoelasticity, plasticity, principles of constitutive modelling, and thermodynamics. Part III presents Tensor Analysis and fundamental equations of Continuum Mechanics in curvilinear coordinates.
Continuum Mechanics
Architectural Engineering
216
5114
518-518
2008
10.1038/216518a0
This book presents an introduction into the entire science of Continuum Mechanics in three parts. Part I: Continuum Mechanics introduces into the Foundations using tensors in Cartesian coordinate systems, classical theory of elasticity, and fluid mechanics. Part II: Mechanics of Materials has chapters on viscoelasticity, plasticity, principles of constitutive modelling, and thermodynamics. Part III presents Tensor Analysis and fundamental equations of Continuum Mechanics in curvilinear coordinates.
Fracture mechanics of diamond-like carbon (DLC) films coated on flexible polymer substrates
Surface and Coatings Technology
201
14
6423-6430
2007
10.1016/j.surfcoat.2006.12.008
Diamond-like carbon (DLC) films have been widely used for many industrial applications due to their. outstanding physical properties such as high hardness, wear resistance and biological compatibility. The DLC films coated on polymer substrates have also been extensively used and investigated because recently, quite a few applications for the use of these polymer-DLC composites have been proposed and actively discussed. The applications range from DLC-coated Polyethylene Terephthalate film (DLC-PET), through DLC-coated Polycarbonate (DLC-PC) to other DLC-coated rubbers. In this work, thin DLC films coated on several polymer substrates possessing different chemical structures and Young's moduli were introduced. The DLC-polymer films were stretched to different strains and the extended surface was investigated by optical microscopy and scanning electron microscopy (SEM) to study the fracture mechanics of the DLC-coated polymer films. Horizontally and vertically aligned micro-cracks and micro-buckling were observed, constructing periodic lattice-like fracture patterns on the surface of the extended DLC-polymer films. It was found that the lattice patterns were significantly influenced by Young's moduli of polymer substrates and DLC films, and that the patterns were also dependent on the adhesion between the DLC films and the polymers. (c) 2006 Elsevier B.V. All rights reserved.
carbon films; fracture surface; polymers
Some comments on developments in exact solutions in statistical mechanics since 1944
Journal of Statistical Mechanics: Theory and Experiment
2010
11
28
2010
10.1088/1742-5468/2010/11/P11037
Lars Onsager and Bruria Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall mention a few, and show how some of the latest work seems to be returning once again to the properties observed by Onsager and Kaufman.
On compatibility of Bohmian mechanics with standard quantum mechanics
Physics
1
2
3
2003
It is shown that the apparent incompatibility of Bohmian mechanics with standard quantum mechanics, found by Akhavan and Golshani quant-ph/0305020, is an artefact of the fact that the initial wavefunction they use, being proportional to a $\delta$-function, is not a regular wavefunction.
Quantum Physics
Generalizing Quantum Mechanics for Quantum Spacetime
Structure
31
2006
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value. This paper reviews a fully four-dimensional, sum-over-histories, generalized quantum mechanics of cosmological spacetime geometry. This generalization is constructed within the framework of generalized quantum theory. This is a minimal set of principles for quantum theory abstracted from the modern quantum mechanics of closed systems, most generally the universe. In this generalization, states of fields on spacelike surfaces and their unitary evolution are emergent properties appropriate when spacetime geometry behaves approximately classically. The principles of generalized quantum theory allow for the further generalization that would be necessary were spacetime not fundamental. Emergent spacetime phenomena are discussed in general and illustrated with the example of the classical spacetime geometries with large spacelike surfaces that emerge from the `no-boundary' wave function of the universe. These must be Lorentzian with one, and only one, time direction. The essay concludes by raising the question of whether quantum mechanics itself is emergent.
Ecological mechanics: A physical geometry for intentional constraints
Human movement science
7
155-200
1988
10.1016/0167-9457(88)90011-5
A proposal is made for a new discipline, ecological mechanics. This version of mechanics is complementary but not reducible to classical relativity, and quantum mechanics. Where traditional mechanics attempt causal analyses for all motions, ecological mechanics explicitly addresses the motions of living systems that exhibit goal-directedness. The shortcomings of the physical geometries underlying traditional mechanics are reviewed, and means are proposed for redressing their deficiencies for modeling the behaviors of intentional systems. This demands a new physical geometry that retains all the best features of the old ones but is extended to accommodate intentional acts. The new physical geometry combines a variant of Minkowski's space-time geometry with a (Cantorian) fractal geometry which reformulates Einstein's energy conversion law (E = mc2) and Planck's energy distribution law (E = fh) so that they apply, more realistically, to the scale of living systems. A new scaling technique called ecometrics, is introduced for accomplishing this feat. This approach assumes a symmetry operator which acts to ‘intentionalize’ causation and to ‘causalize’ intention so that perceptual information and action control processes are defined over a commensurate but dual measurement bases. The promise of ecological mechanics rests on the imputed discovery of a new conservation law which holds locally rather than absolutely. Empirical evidence is reviewed and graphically portrayed mathematical arguments are given that tend to support the hypothesis.
Design sensitivity of post-buckling states including material constraints
Computer Methods in Applied Mechanics and Engineering
188
665-679
2000
10.1016/S0045-7825(99)00354-0
This paper reports theoretical studies on the design sensitivity of problems with geometrically non-linear behavior leading to buckling and post-buckling of thin-walled structural members. For the class of problems considered, buckling occurs in the form of a stable bifurcation, and it is assumed that changes in the design parameters do not break the bifurcation behavior. The specific focus of the research is the first yield or first failure of the material as part of the sensitivity study of equilibrium states along the post-critical path. The investigation employs a discrete model of a structure in terms of generalized coordinates (suitable for finite element analysis) and a single load parameter; and perturbation techniques to classify the critical state and to approximate the post-critical path. The problem of material behavior is modeled by means of constraints on the post-critical path, based on a yield criterion. For simplicity, the presentation uses the von Mises yield criterion, but other more complex criteria, such as those employed in composite materials (first-ply failure) can also be represented. Two forms of the constraints are formulated, and the problem of sensitivity with respect to changes in a design parameter is discussed. A simple example of a circular plate is presented to illustrate the use of the formulation for the sensitivity with respect to a single design parameter. (C) 2000 Elsevier Science S.A. All rights reserved.
material constraint; post buckling; sensitivity
Game Mechanics, Dynamics, and Aesthetics
Library Technology Reports
51
2
17-19
2015
10.5860/ltr.51n2
The article examines game design elements in order to understand how gamification works. It adopts the definition of gamification as the use of game design elements typical for games in non-game applications. It cites examples of game elements like points, avatars and badges, game mechanics, like behavioral momentum, loss aversion and ownership, that fall into three types, namely behavioral, feedback and progression. It also discusses the mechanics, dynamics and aesthetics (MDA) framework.
AVATARS (Virtual reality); DESIGN; DYNAMICS; GAMES; GAMIFICATION
Development of High-Strength Cross-Ply "Green" Composites
Zairyo/Journal of the Society of Materials Science, Japan
52
7
857-862
2003
This paper discusses the development of high-strength biodegradable, "green", cross-ply fabric-reinforced composites. The composites were made using woven Manila hemp fibers as the reinforcement and starch-based emulsion-type biodegradable polymer as the matrix. The mechanical properties of the composites have been evaluated as a function of fiber content (20 to 75 mass%). The experimental results indicate that the composites show the flexural and tensile strength of 104 MPa and 153 MPa, respectively. Both of tensile and flexural modulus and flexural strength increased with increasing the fiber content. However, the tensile strength increased with the fiber content till 50 mass% and remained constant thereafter. This dependence on the fiber content is due to the decrease in fiber strength caused by fiber damages introduced during hot-pressing.
Bending strength; Biocomposites; Biodegradable composite material; Biodegradable composite materials; Biodegradable plastics; Biodegradation; Cross-ply; Fiber reinforced plastics; Hot pressing; Manila hemp fiber; Plastic filaments; Tensile strength
Effect of relative ply orientation on the through-thickness permeability of unidirectional fabrics
Composites Science and Technology
96
116-121
2014
10.1016/j.compscitech.2014.03.007
When unidirectional stitched fabrics are used as reinforcement in composites, plies are typically stacked on top of each other to build up the desired thickness. Strength and stiffness requirements dictate the orientation of individual layers and the accuracy of angular alignment is limited. A pressure differential across the thickness is used to distribute the resin, either from a pre-impregnated fabric or injected from a resin source, to occupy all of the empty spaces between the fibers. This process is commonly modeled using Darcy's law, which describes flow of resin through porous media in which the flow rate is directly proportional to the applied pressure differential by the through-thickness permeability of the fabric. A different orientation between layers or even a slight misalignment during the stacking can change the through-thickness permeability dramatically due the change of resin pathways. In this work, we characterize the through-thickness permeability of a series of unidirectional fabrics stacked in various orientations to address both the effect of stacking sequence and those of misalignment of the individual layers. We conduct numerical simulations to predict the effect of change in fiber orientation on the through-thickness permeability. The results from the numerical model are compared with experimental measurements. Our results show that averaging approach is not suitable to calculate the through-thickness permeability component when using unidirectional fabrics and that the stacking sequence of the unidirectional fabrics may significantly influence the through-thickness permeability. We also show that the effects of small misalignments between individual layers do not significantly modify the transverse flow. © 2014 Elsevier Ltd.
A. Textile composites; B. Transport properties
Fluid-Structure-Acoustic Interaction of the Flow Past a Thin Flexible Structure
AIAA Journal
48
4
738-748
2010
10.2514/1.40344
The acoustic field resulting from the interaction of a thin flexible structure with a turbulent flow was investigated both numerically and experimentally. Two different model configurations were considered: in one a flexible plate acted as a moving wall in a turbulent boundary layer, and in the other the flexible plate was located in the wake of a square cylinder. The fully coupled simulation of the fluid structure acoustics interaction was based on a partitioned approach employing two different simulation codes: a finite-volume flow solver of second-order accuracy in space and time and a finite-element structural-mechanics and acoustics solver. A code coupling interface was used for the exchange of data between the different discretizations. The experiments were performed in an acoustic wind tunnel employing microphone measurements of the sound pressure level. Detailed flow measurements were carried out using laser Doppler anemometry and three-component hot-wire anemometry. The flow-induced vibration of the flexible structure was measured with a laser-scanning vibrometer. Experimental and numerical results characterizing the flow field, the structural vibration, and the generated sound are presented.
The morphology and folding patterns of buckling-driven thin-film blisters
Journal of the Mechanics and Physics of Solids
42
3
531-559
1994
10.1016/0022-5096(94)90030-2
Thin films and coatings in a state of residual compression can, under appropriate conditions, decohere and buckle away from the substrate to form blisters. These blisters are often observed to adopt intricate shapes and to fold into complex patterns. In this paper, such shapes and patterns are given an energetic interpretation, i.e. they follow as energy minimizers. We formulate the energy of the film by recourse to von Kármán theory of moderate deflections of a plate. The energy functional has the following key properties : it contains two terms, namely, the membrane and bending energies, the latter being a singular perturbation of the former; and the membrane energy functional is nonconvex and, consequently, its infimum is generally not attained. In keeping with the conventional mathematical treatment of these problems, we construct solutions by a matched asymptotic expansion. The outer solution follows by membrane energy minimization and determines the essential folding pattern of the film. The inner solution is obtained by fitting boundary layers at sharp edges in the membrane solution. The film deflections thus constructed are found to match, in surprising detail, the observed complex folding patterns adopted by delaminated films. In addition, the boundary layer analysis permits one to accord a well-defined line tension to sharp edges in the membrane solution, and, in particular, to the boundary of the blister. This provides a simple device for assessing the configurational stability of some blister morphologies. In particular, the analysis predicts the transition from straight-sided to telephone-cord morphologies at a critical mismatch strain.
Stationary nonequilibrium statistical mechanics
Encyclopedia of Mathematical Physics ed JP Francoise GL Naber TS Tsun
3
1-17
2005
A brief review on the dynamical systems approach to nonequilibrium statistical mechanics and chaotic dynamics
Modeling and Fracture Prediction of Single Ply Cord-Rubber Composites
Journal of Composite Materials
26
2
152-170
1992
10.1177/002199839202600201
This paper presents finite element and experimental results for single ply strips of unidirectional cord-rubber composite using two types of finite elements: rubber elements and cord-rubber elements. The finite element model takes into account the large strain and nonlinear behavior of the rubber material, bimodular material behavior and geometrical nonlinear behavior due to reorientations of the cords. To illustrate the be havior of strips of single ply composites, results are presented in the form of load- displacement, deformed shapes and cord strains for three polyester cord rubber composite specimens. It is shown that the rubber between cords may contract or bulge, depending on the cord angle. The effect of the material models for rubber material and cord-rubber com posite material on the load displacement behavior is also presented. Utilizing this finite el ement model and critical tearing energy criterion, an attempt is made to predict the critical loads for crack growth initiation and final fracture for four cracked rubber composite spec imens. All the finite element results are compared to experimental data with relatively good agreement.
Effectively Emergent Quantum Mechanics
Outlook
1
5
8-10
2008
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently flat. In other words, quantum mechanics might play no role when and where the space-time geometry is highly curved. We study the first two simple models of Effectively Emergent Quantum Mechanics(EEQM): R-dependent EEQM and G-dependent EEQM where R is the Ricci scalar and G is the Gauss-Bonnet Lagrangian density. We discuss that these EEQM theories might be fine tuned to remain consistent with all the implemented experiments and performed observations. In particular, we observe that G-dependent EEQM softens the problem of quantum gravity.
Application of a continuum dislocation-based model to a tensile test on a thin film
Materials Science and Engineering: A
400-401
443-447
2005
10.1016/j.msea.2005.03.059
Plastic deformation on the microscale shows a significant size effect in the sense that plastic response is stronger than that of macroscopic bulk materials. This effect is often ascribed to the deposition of misfit dislocations, to the presence of geometrically necessary dislocations or to bowing-out of discrete dislocations. The models based upon these assumptions do predict the size effect, but they are not completely satisfactory. This paper discusses an alternative model, based upon the continuum-theory of dislocations, which ascribes size effects to the bowing of continuously distributed dislocations, treated within a rigorous continuum mechanics framework. Results are compared to those of tensile tests on thin Cu-films, presented in the literature. A quantitative agreement is found concerning the size effect and the influence of grain orientation. (c) 2005 Elsevier B.V. All rights reserved.
2005; 401; 443; 447; a 400; application of a continuum; dislocation-based model; erials science and engineering; on a thin film; to a tensile test
A cohesive zone finite element approach to model tensile cracks in thin film coatings
Journal of Mechanics of Materials and Structures
2
7
1231-1247
2007
A two-dimensional finite element model using cohesive zone elements was developed to predict cracking in thin film coating-interlayer-substrate systems that are subjected to tensile loading. The constitutive models were chosen to represent a metal carbide/diamond-like carbon composite coating with a titanium interlayer and a steel substrate. Material properties of the coating and interlayer along with the cohesive finite element parameters were varied to study effects on stress distributions and coating cracking. Stress distributions were highly nonuniform through the coating thickness. Thus the initiation and arrest of tensile cracks differed from what is predicted by simple shear-lay theory. Intercrack spacing distributions resulting from the variation of different parameters were quantified and compared with those from experiments.
Cohesive zone finite element modeling; Intercrack spacing; Tensile cracking; Thin film coatings
Boundary control of free and forced oscillation of shearable thin-walled beam cantilevers
European Journal of Mechanics - A/Solids
17
4
687-700
1998
http://dx.doi.org/10.1016/S0997-7538(99)80028-X
This paper deals with the problem of controlling the bending oscillations of cantilevers subjected to harmonic time-dependent excitations and with that of enhancing their eigenvibration response characteristics. The structural model consisting of a thin-walled beam of arbitrary cross-section includes a number of nonclassical effects, such as transverse shear, secondary warping and heterogeneity. The control is achieved via the action of a bending moment applied at the tip of the structure. A dynamic feedback control law relating the boundary bending moment to the angular velocity at the tip of the structure is implemented and its implications upon the closed-loop eigenvalues and dynamic response to harmonic excitations are revealed. A computational methodology based on the extended Galerkin's technique aimed at determining the closed-loop response characteristics is used and numerical results revealing the efficiency of the adopted control methodology are displayed.
boundary control; closed-loop eigenvalues; oscillation; response; thin-walled beam
Application of the Island Blister Test for Thin Film Adhesion Measurement
The Journal of Adhesion
29
1-4
219-231
1989
10.1080/00218468908026488
Abstract The island blister test has recently been proposed as an adhesion test which allows the peel of thin, well-adhered films without exceeding the tensile strength of the film. The island blister test site is a modification of the standard blister test site, consisting of a suspended membrane of film with an ?island? of substrate at the film center. The membrane support and island are secured to a rigid plate and the film is pressurized, peeling the film inward off the island. A model for this inward or ?annular? peel indicates that even for systems of good adhesion, peel can be initiated at low enough pressures to prevent film failure by making the center island sufficiently small relative to the size of the film. We have fabricated island blister test sites using micromachining techniques and have used them to measure the debond energy of polymer films on various substrates. The peel data obtained from these island sites match well to the behavior predicted by a simple fracture mechanics analysis. This paper reports the fabrication of the island test sites, the experimental verification of the test, and the results of application of the test to polyimide films on metallic and polymeric substrates.\nAbstract The island blister test has recently been proposed as an adhesion test which allows the peel of thin, well-adhered films without exceeding the tensile strength of the film. The island blister test site is a modification of the standard blister test site, consisting of a suspended membrane of film with an ?island? of substrate at the film center. The membrane support and island are secured to a rigid plate and the film is pressurized, peeling the film inward off the island. A model for this inward or ?annular? peel indicates that even for systems of good adhesion, peel can be initiated at low enough pressures to prevent film failure by making the center island sufficiently small relative to the size of the film. We have fabricated island blister test sites using micromachining techniques and have used them to measure the debond energy of polymer films on various substrates. The peel data obtained from these island sites match well to the behavior predicted by a simple fracture mechanics analysis. This paper reports the fabrication of the island test sites, the experimental verification of the test, and the results of application of the test to polyimide films on metallic and polymeric substrates.
Aspects of supersymmetric quantum mechanics
Annals of Physics
146
2
262-288
1983
10.1016/0003-4916(83)90034-9
We review the properties of supersymmetric quantum mechanics for a class of models proposed by Witten. Using both Hamiltonian and path integral formulations, we give general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations. The spectrum of states is discussed, and a virial theorem is derived for the energy. We also show that the euclidean path integral for supersymmetric quantum mechanics is equivalent to a classical stochastic process when the supersymmetry is unbroken (E0 = 0). By solving a Fokker-Planck equation for the classical probability distribution, we find Pc(y) is identical to |Ψ0(y)|2 in the quantum theory.
Symplectic geometry and quantum mechanics
Operator theory, advances and applications
166
367 p.
2006
This book is devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a rigorous presentation of the basics of symplectic geometry and of its multiply-oriented extension. Further chapters concentrate on Lagrangian manifolds, Weyl operators and the Wigner-Moyal transform as well as on metaplectic groups and Maslov indices. Thus the keys for the mathematical description of quantum mechanics in phase space are discussed. They are followed by a rigorous geometrical treatment of the uncertainty principle. Then Hilbert-Schmidt and trace-class operators are exposed in order to treat density matrices. In the last chapter the Weyl pseudo-differential calculus is extended to phase space in order to derive a Schrödinger equation in phase space whose solutions are related to those of the usual Schrödinger equation by a wave-packet transform. The text is essentially self-contained and can be used as basis for graduate courses. Many topics are of genuine interest for pure mathematicians working in geometry and topology.
Boundary value problems Weyl theory.; Quantum theory.; Symplectic geometry.
Geometry, Mechanics, and Dynamics
Fields Institute Communications
73
285-317
2015
10.1007/978-1-4939-2441-7
In this paper, we introduce local expressions for discrete Mechanics. To apply our results simultaneously to several interesting cases, we derive these local expressions in the framework of Lie groupoids, following the program proposed by Alan Weinstein (Fields Inst Commun 7:207–231, 1996). To do this, we will need some results on the geometry of Lie groupoids, as, for instance, the construction of symmetric neighborhoods or the existence of local bisections. These local descriptions will be particularly useful for the explicit construction of geometric integrators for mechanical systems (reduced or not), in particular, discrete Euler-Lagrange equations, discrete Euler-Poincaré equations, discrete Lagrange-Poincaré equations: : : These topics are closely related with a part of Marsden’s work. In addition, the results contained in this paper can be considered as a local version of the study that we have started in Marrero et al. (Nonlinearity 19(6):1313–1348, 2006), on the geometry of discrete Mechanics on Lie groupoids.
Grain size effects on the adhesion of thin ductile films
Mechanical Properties Derived from Nanostructuring Materials. Symposium, 22-25 April 2003
221-226
2003
Grain size can be controlled by varying the process conditions used to deposit the film and post growth processing. This study examines how the grain size will impact the mechanical properties, hardness and adhesion, of thin ductile films on brittle substrates. The grain structures of copper and tin films were examined using OIM and AFM. The interfacial fracture toughness of each film was calculated using a tungsten overlayer and mechanics based models. The hardnesses of the films were correlated to the measured interfacial fracture toughness, and demonstrate that increased hardness correlates to an increased sensitivity to the Mode II component of loading
adhesion; atomic force microscopy; copper; ductility; fracture toughness; grain size; hardness; metallic thin films; tin; tungsten
Bending of fibre-reinforced composite thin-walled tubes
Composites
21
5
431-438
1990
10.1016/0010-4361(90)90443-Z
The present paper reports on the bending of thin-walled fibre-reinforced composite circular tubes under certain end-clamping conditions, simulating the oblique collision of structural elements of impacted vehicles. The fracture mechanism of the crushed composite tubes is quite different from that of metallic components loaded under the same conditions. Energy absorption in the present case is achieved by material fragmentation; i.e., the mechanism of fracture dominates the phenomenon, rather than plastic deformation. The effect of clamping conditions on the energy absorbing efficiency of the shell is also examined. © 1990.
Complementarity in Categorical Quantum Mechanics
Foundations of Physics
42
7
856-873
2012
10.1007/s10701-011-9585-9
We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a `point-free' definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.
Boolean lattice; Classical structure; Complementarity; Dagger kernel monoidal category; Orthomodular lattice; Orthonormal basis; von Neumann algebra
Mechanics of encapsulated droplets
Progr Colloid Polym Sci
111
58-64
1998
10.1007/BFb0118110
ARCHIVED States that the deformation of the capsule increases with the increase of the capillary number until a critical value is reached, where the capsule bursts. Refers to her previous work in 1991 for the details in bursting prediction.
capsule - interface; mechanics - interfacial; polymerization - deformation
Some open problems in granular matter mechanics
Progress in Natural Science
19
5
523-529
2009
10.1016/j.pnsc.2008.06.023
Granular matter is a large assemblage of solid particles, which is fundamentally different from any other type of matters, such as solid and liquid. Most models presented for granular matter are phenomenological and are only suitable for solving engineering problems. Many fundamental mechanical problems remain open. By analyzing characteristics of internal state structure, we propose that granular matter is intrinsically multiscale, i.e. microscale of particle size, mesoscale of force chain, and macroscale of the bulk of granular matter. The correlations among difference scales would be crucial. The mesoscale force chain network is determined by both particle properties and macroscopic boundary conditions. The evolution of the force the chain network contributes to macroscopic mechanical properties of granular matter. In addition, we discuss the drawbacks in simplifying contact forces in the current models, and the difficulties in analyzing the interaction of interstitial fluid in wet granular matter. As an appropriate application of granular matter, debris flow can be studied with granular matter mechanics; meanwhile, debris flow brings more challenges which certainly motivate future studies on granular matter. ©2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.
Contact mechanics; Debris flow; Force chain; Granular matter; Multiscale mechanics
Microstructure evolution of gold thin films under spherical indentation for micro switches contact applications
European Materials Research Society
1-9
2010
10.1007/s10853-011-5575-8
RF MEMS (Radio Frequency Micro Electro Mechanical System) switches are promising devices but their gold-on-gold contacts, assimilated for this study to a sphere/plane contact, represent a major reliability issue. A first step toward understanding failure mechanisms is to investigate the contact metal microstructure evolution under static and cyclic loading. After static and cyclic loading of sputtered gold thin films under spherical indentation, high-resolution Electron Back Scatter Diffraction (EBSD) is used to investigate the contact area. Grain rotation against {111} fiber texture of 1-lm-thick sputtered gold thin film is a signature of plastic deformation. Grain rotation is observed above 1.6 mN under static loading using a spherical diamond indenter with 50-lm tip radius. The heterogeneity in grain rotation observed corresponds to a greater plastic deformation in the middle of the indent than at the edge. A 30° grain rotation due to cyclic work hardening is observed for a half-million mechanical cycles under 300 lN load using a spherical gold tip (20 lm radius). The same test in hot switching mode induces a grain growth in the contact area. Therefore, thermal effects occurring during hot switching are underlined. © Springer Science+Business Media, LLC 2011.
contact mechanics; ebsd; microstructure; micro-switch reliability; nano-indentation
Role of oxide thickening in fatigue crack initiation in LIGA nickel MEMS thin films
Materials Science and Engineering: A
561
434-440
2013
10.1016/j.msea.2012.10.057
This paper presents the results of a combined experimental and theoretical study of the fatigue crack initiation in LIGA Ni thin films with a thickness of 270 μ m . The potential roles of surface oxide thickening and slip bands are explored for fatigue crack initiation. Surface oxides and roughness are characterized using X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). The underlying crack driving forces associated with pop-in in surface oxide layers are then compared to those associated with the early stages of fatigue crack growth. The implications of the results are discussed for the modeling of fatigue in LIGA Ni micro-electro-mechanical-systems (MEMS) structures.
Statistical mechanics of the XY model. III
Physical Review A
3
6
2137-2140
1971
10.1103/PhysRevA.3.2137
We continue the considerations of the first paper in this series by studying the time dependenceof the spin-correlation functions in response to a step-function change in the external magnetic field. We find that these correlation functions exhibit nonergodic behavior.
Crack initiation in ultra thin patterned films
Proceedings of the 11th International Conference on Fracture
2005
We present an investigation of the unique cracking problems associated with patterned thin film devices fabricated via soft lithographic methods. Decohesion and fracture of the patterned films is dominated by two key properties: interfacial failure strength and processing induced stresses/shrinkage. We utilize several experimental methods for characterizing these properties and their relationship to cracking in patterned films. Thin film interfacial strength is measured using a laser induced pulsed loading technique. Laser pulse absorption generates a high amplitude, short duration stress waves from the substrate side of the sample, providing a loading force that does not damage or otherwise affect the test film before the failure event occurs. The rapid, high strain-rate loading minimizes inelastic deformation in the films, providing an intrinsic estimate of the interfacial strength. Processing induced residual stress in the films is determined by in situ laser reflectance measurements of wafer curvature. A dynamic edge delamination test is underdevelopment to obtain the fracture toughness of the interface. The link to meaningful fracture parameters is achieved with the aid of appropriate analytical and numerical tools to support the experiments.
Exact 3D piezoelasticity solution of hybrid cross-ply plates with damping under harmonic electro-mechanical loads
Journal of Sound and Vibration
282
3-5
617-634
2005
10.1016/j.jsv.2004.03.030
Three-dimensional (3D) piezoelasticity solution is presented for the steady-state forced response of simply supported hybrid cross-ply rectangular plates with embedded or surface-bonded piezoelectric layers under electromechanical harmonic excitation with damping. For each layer, all the entities are expanded in Fourier series to satisfy the boundary conditions at the edges. The governing equations reduce to ordinary differential equations in the thickness coordinate with constant coefficients. Their general solution is obtained using state-space technique. A transfer matrix approach is presented to obtain these from the electromechanical boundary conditions at the top and bottom of the plate, the conditions of prescribed potentials and the conditions of continuity/jump at the layer interfaces. Results for the amplitude and phase lag of the central deflection are presented for an elastic plate and for hybrid composite and sandwich plates. The reduction of deflection response by actuation of a piezoelectric layer is illustrated. The present benchmark solution would help assess 2D plate theories for damped response under harmonic loads. ?? 2005 Elsevier Ltd. All rights reserved.
The effect of stiffeners on the optimal ply orientation and buckling load of rectangular laminated plates
Computers and Structures
80
27-30
2229-2239
2002
10.1016/S0045-7949(02)00265-1
Optimal designs of symmetrically laminated rectangular plates with different stiffener arrangements are presented. The plates are subject to a combination of simply supported, clamped and free boundary conditions, and the design objective is the maximisation of the biaxial buckling load. This is achieved by determining the fibre orientations optimally with the effects of bending-twisting coupling taken into account. Square tubing is used as stiffeners, and the finite element method coupled with an optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of the stiffener arrangement and boundary conditions on the optimal ply angles and the buckling load are numerically studied. It is demonstrated that in some cases, stiffeners can sometimes reduce, rather than increase the buckling strength of an optimally designed plate. © 2002 Civil-Comp Ltd. and Elsevier Science Ltd. All rights reserved.
Accurate prediction of free-edge and electromechanical coupling effects in cross-ply piezoelectric laminates
Composite Structures
113
308-315
2014
http://dx.doi.org/10.1016/j.compstruct.2014.03.027
Abstract 3D hybrid analyses on the interlaminar stresses near the free edges of piezoelectric laminated plates are presented on the basis of three-dimensional piezoelasticity. The state space equations for cross-ply piezoelectric laminates subjected to a uniform axial extension are obtained by considering all the independent elastic and piezoelectric constants. With the application of the transfer matrix and recursive solution approach, the equations satisfy the traction-free and open-circuit boundary conditions at free edges and the continuity conditions across the interfaces between material layers. Three-dimensional exact solution is sought and validated by comparing the present analytical results with those from existing approximate and finite element models. The singularities of interlaminar stresses near free edges are observed and the significant electromechanical influence on the free-edge effect is found.
Coupling effect; Exact solution; Free-edge; Interlaminar stress; Laminated plate; Piezoelasticity
Delamination identification of cross-ply graphite/epoxy composite beams using electric resistance change method
Composites Science and Technology
62
5
629-639
2002
10.1016/S0266-3538(02)00013-1
Detection of delaminations is a difficult task for visual inspections. Difficulty of detection underlines the importance of development of smart structures for monitoring delaminations of graphite/epoxy laminated composites. This study employs an electric resistance change method for identification of delamination location and size; applicability of the method is investigated experimentally using beam-type specimens fabricated from cross-ply laminates. On the specimen surface, multiple electrodes are mounted by co-curing copper foil to measure electric resistance changes. Interlamina shear tests are conducted to create a practical delamination crack in a beam-type specimen. Five beam specimen types were made and tested. A large number of tests were conducted to obtain a data set for solving inverse problems to estimate delamination location and size from measured electric resistance changes. Response surfaces are employed for a solver of inverse problems instead of well-known artificial neural networks. As a result, the method successfully identifies delamination location and size for these beam type specimens. To obtain practically efficient estimation performance, at least five electrodes are indispensable for these beam type specimens.
A. Smart materials; C. Delamination; Graphite fibres
Transverse cracking in CFRP cross-ply laminates with interlaminar resin layers
Advanced Composite Materials
7
347-363
1998
10.1163/156855198X00246
In recent years, interlaminar-toughened laminates have been developed in which resin rich layers are placed in interlaminar regions in order to enhance the interlaminar fracture toughness of CFRP laminates. In the present study, a predictive method is developed for transverse cracking in CFRP cross-ply laminates with interlaminar resin layers at 0/90° interfaces under static tensile loading. The analysis is based on a two-dimensional approximate elastic analysis considering the interlaminar resin layers and thermal residual stresses. To predict transverse cracking, both energy and stress criteria are used. The change in thermoelastic properties of a laminate due to transverse cracking is also predicted. To investigate the validity of the analysis, loading-unloading tests are performed to obtain Young's modulus reduction as a function of the transverse crack density. The predictions of transverse crack density as a function of the laminate strain are compared with our previous experimental results. A good agreement is obtained which implies the validity of the present analysis.
On the physical relation between the Dirac equation and the generalized mKdV equation on a thin elastic rod
Physics Letters A
189
1-2
27-31
1994
10.1016/0375-9601(94)90813-3
Recently the physical meaning of quantum mechanics in soliton physics was revealed through the consideration of the Dirac equation on a thin elastic rod embedded in 2 and 3 space. In this article, we generalize this to that on a thin rod in n and consider the relation between the Dirac equation and the generalized mKdV equations.
The Friction Characteristics and Microscopic Properties of Composite Electroplating Thin Films
Applied Mechanics and Materials
479-480
60-63
2013
10.4028/www.scientific.net/AMM.479-480.60
With the vast improvement of nanoscale science and technology, mechanical properties of nanoscale materials become more and more important. In this paper, the plastic and elastoplastic properties of composite electroplating thin films were examined using nano-indentation methods. Both experimental and simulation techniques were performed, and the results were mapped to determine the strength coefficient and strain hardening factor of SiC/Ni and Al2O3/Ni thin films. © (2014) Trans Tech Publications, Switzerland.
Composite electroplating films; Nanoindentation; Strain hardening
Ultra-thin Chip Technology and Applications
Technology
13-19
2011
10.1007/978-1-4419-7276-7
Ultra-thin chips are the 'smart skin' of a conventional silicon chip. This book shows how very thin and flexible chips can be fabricated and used in many new applications in microelectronics, Microsystems, biomedical and other fields. It provides a comprehensive reference to the fabrication technology, post processing, characterization and the applications of ultra-thin chips.
The sensitivity of a polarimetric sensor embedded in unidirectional and cross-ply composite laminates
Smart Materials and Structures
16
3
642
2007
10.1088/0964-1726/16/3/011
Matrix cracking in composite laminates is the first macroscopic damage mode to be readily detected. Polarimetric sensors embedded in composite laminates can detect the development of this damage and they have an advantage over other sensors in being able to sense damage over long gauge lengths (potentially, many metres). In this paper, the sensitivity of a polarimetric sensor manufactured from Hi-Bi PANDA fibre has been measured experimentally and a phase-strain model available in the literature has been used to determine the characteristic parameters of the sensor. The sensitivity of such sensors embedded in unidirectional composites is shown to be in good agreement with theoretical predictions, allowing for material non-uniformity. In the case of cross-ply laminates, which are transversely anisotropic, it is shown that sensor sensitivity is dependent on the relationship of the sensor axes to the composite axes, as well as on the degree of sensor twist. Maximum sensitivity is obtained for a combination of low twist angle and congruence between the sensor optical axes and the composite axes. Twist angles of greater than 90° give rise to sensitivities, which, although lower, are reasonably constant and approximately the same as the sensitivity of the sensor in a unidirectional composite.
Imaging microstructure and stress fields within a cross-ply composite laminate
Composites Science and Technology
69
5
567-574
2009
10.1016/j.compscitech.2008.11.037
Microfocus X-ray diffraction can be used in a scanning acquisition mode to image a fibre reinforced composite material in terms of a range of different parameters. This includes microstructural information, as well as detail of emerging stress fields around open hole geometries. In this study, the in situ deformation of a cross-ply laminate specimen is investigated. The results show a number of interesting phenomena related to stress transfer in such systems. This includes stress concentrations in fibres adjacent to the open hole and local shear forces acting upon fibres perpendicular to the deformation axis. In addition to imaging the sample, the technique also allows a number of mechanical parameters to be estimated. This includes transverse strain and longitudinal stiffness. Using isotropic elasticity theory, the stress concentration tangential to the open hole can be determined analytically. ?? 2008 Elsevier Ltd. All rights reserved.
Vibration analysis of angle-ply laminated composite plates with an embedded piezoceramic layer.
IEEE transactions on ultrasonics, ferroelectrics, and frequency control
50
9
1084-99
2003
An optical full-field technique, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), is used in this study to investigate the force-induced transverse vibration of an angle-ply laminated composite embedded with a piezoceramic layer (piezolaminated plates). The piezolaminated plates are excited by applying time-harmonic voltages to the embedded piezoceramic layer. Because clear fringe patterns will appear only at resonant frequencies, both the resonant frequencies and mode shapes of the vibrating piezolaminated plates with five different fiber orientation angles are obtained by the proposed AF-ESPI method. A laser Doppler vibrometer (LDV) system that has the advantage of high resolution and broad dynamic range also is applied to measure the frequency response of piezolaminated plates. In addition to the two proposed optical techniques, numerical computations based on a commercial finite element package are presented for comparison with the experimental results. Three different numerical formulations are used to evaluate the vibration characteristics of piezolaminated plates. Good agreements of the measured data by the optical method and the numerical results predicted by the finite element method (FEM) demonstrate that the proposed methodology in this study is a powerful tool for the vibration analysis of piezolaminated plates.
Similitude and Physical Modeling for Buckling and Vibration of Symmetric Cross-Ply Laminated Circular Cylindrical Shells
Journal of Composite Materials
37
19
1697-1712
2003
10.1177/002199803035191
The similitude invariant and the scaling laws of the symmetric cross-ply laminated circular cylindrical shells for buckling and free vibration problems are derived by applying the similitude transformation to the governing differential equations directly. The scaling laws obtained by this approach are unique because they are forced by the governing differential equations. In the absence of the experimental data, the validity of the scaling laws is verified by numerical experiments. This is done by calculating theoretically the buckling loads and fundamental frequencies for free vibration of the model and substituting into the scaling laws. The predicted values of the prototype from the scaling laws are then compared with those values from the closed-form solution. Examples for the complete similitude cases with various stacking sequences, number of plies, and radius ratios show exact agreement. The presented relationships between the model and prototype will greatly facilitate and reduce the costly experiment. In reality, it may not be feasible to construct the model to fulfill the similarity requirements completely. Several cases of partial similitude are investigated and verified numerically. Modeling with distortion in stacking sequences is recommended, but model with distortion in material properties yields moderately high percent of discrepancy.
Buckling; Laminated cylindrical shells; Physical modeling; Scaling laws; Similitude invariants; Vibration
Vibration of anti-symmetric angle-ply composite plates under random excitation
Aircraft Engineering and Aerospace Technology
79
475-484
2007
10.1108/00022660710780605
Purpose - The transverse shear deformation and rotary inertia effects need to be included for an accurate analysis in the response of the relatively thick plates, This paper seeks to use, one of the refined theories which takes into account those effects, The First Order Shear Deformation Theory; to obtain linear and non-linear responses for anti-symmetric angle-ply composite plates under random excitation. Design/methodology/approach - The random excitation is assumed to be stationary; ergodic and Gaussian with zero-mean. A Monte Carlo Simulation of stationary random process is used. A multi-mode Galerkin approach and numerical integration procedure are employed to find linear and non-linear response solutions. Laminated composite plate is taken to be simply-supported along four edges. Findings - The vibration of composite plates at elevated temperatures is also investigated. The linear and non-linear deflections root-mean-square (RMS) are obtained for various input levels, the different lamination angles and the number of layers. Practical implications - Further, case studies might lead to a lighter design of thick panels used in high-performance systems such as aerospace structures. Originality/value - The paper provides information on the linear and more realistic non-linear vibrations of thick composite plates in time domain so that it would be possible to obtain key statistical information directly from time-response history.
The behavior of angle-ply laminated cylindrical shells with viscoelastic interfaces in cylindrical bending
Composite Structures
78
4
551-559
2007
10.1016/j.compstruct.2005.11.017
The behavior of a simply supported angle-ply laminated cylindrical shell in cylindrical bending with viscoelastic interfaces is studied. The Kelvin-Voigt model is adopted to represent the character of interfaces. State-space formulations are developed based on the exact elasticity equations, and in particular, a variable substitution technique is used to derive the state equations with constant coefficients. Since the behavior of this structure under static loading is time-dependent, the power series expansion technique is used to approximate the variations of physical variables with time. The response for a laminated shell with viscous interfaces is also investigated as a particular case. Results show that the displacements as well as the maximum stresses in the panel increase rapidly with time. Thus, the imperfect bonding properties should be considered carefully in the design of laminated structures. ?? 2005 Elsevier Ltd. All rights reserved.
Cylindrical shell; Kelvin-Voigt model; Power series expansion; State-space method; Variable substitution technique
Powder mechanics in tribology
Powder Technology
37
1
155-167
1984
Recently considerable progress has been made in understanding the interactions between a surface and a solid lubricant layer deposited or formed by various physical and chemical methods. Very few studies have been conducted on how these films lubricate and fail from a microscopic point of view. In some of them it has been observed that lubrication and failure criteria are usually arbitrary and that particle interactions play a fundamental role as constituent elements of lubricant layers or as wear debris. To understand these mechanisms, "lubricating" and "abrasive" powders were studied from tribological and rheological point of view. Via classical mechanics, the flow properties of micronized powders were analysed in terms of size, shape and stress-strain relations. Starting from the cumminution process, crushing and grinding phenomena were analysed to determine experimentally through packing, cohesion and consolidation and ultimate shear strength and to predict the boundary friction coefficient in powder lubrication. The rupture surface and instability phenomena were involved for cohesive and noncohesive, "lubricating" and "abrasive" powders. The librication process was found to be very instable, consisting of the plastic flow of thin laminated films formed of coalesced fine particles and reactive films. The effect of substrate surface finish in terms of statistical moments criteria was demonstrated. The tribological process, analysed as particle mechanics of wear debris and as lubricating or abrasive powder interactions, was elucidated.
Yield stress in thin layers of ferrofluids
Physica A: Statistical Mechanics and its Applications
365
2
265-281
2006
10.1016/j.physa.2005.09.071
We present results of theoretical study of quasielastic behavior of ferrofluid filling a thin flat gap, placed into perpendicular magnetic field. When the field exceeds a certain critical magnitude, magnetic particles form dense discrete domains, elongated along the field, and linking the gap boundaries. Due to these bridges between the gap boundaries, the ferrofluid exhibits quasielastic properties with respect to shear strain in the plane of the gap. We estimated the elastic modules as well as the yield stress of the system, depending on magnetic field and concentration of magnetic particles in the ferrofluid. Analysis shows that there are at least two microscopical mechanisms of transition from the elastic to fluid behavior of the ferrofluid. The first one is connected with the loss of the mechanical equilibrium of the domains, slopped, under the shear stress, with respect to applied magnetic field. The second mechanism is connected with breakup of the "bridge" into two separate drops, when the shear strain exceeds some critical magnitude. Estimates show that for real ferrofluids the second mechanism is more probable. ?? 2005 Elsevier B.V. All rights reserved.
ferrofluids; heterogeneous aggregates; phase transitions
Effects of thermal and mechanical fatigue on flexural strength of G40-600/PMR-15 cross-ply laminates
Journal of Applied Polymer Science
51
February
1107-1118
1994
10.1002/app.1994.070510617
The effects of thermal and mechanical fatigue on the flexural strength of G40-600/PMR-15 cross-ply laminates with ply orientation of (0(2),90(2))2S and (90(2),0(2))2S are examined. The relative importance of shear and tensile stresses is examined by varying the span-to-depth ratios of flexural test specimens from 8 to 45. Acoustic emission signals are measured during the flexural tests in order to monitor the initiation and growth of damage. Optical microscopy is used to examine specimens for resin cracking, delamination, and fiber breaks after testing. Transverse matrix cracks and delaminations occur in all specimens, regardless of ply orientation, span-to-depth ratio, or previous exposure of specimens to thermal and mechanical fatigue. A small amount of fiber tensile fracture occurs in the outer 0 deg ply of specimens with high span-to-depth ratios. Because of the complex failure modes, the flexural test results represent the 'apparent' strengths rather than the true flexural or shear strengths for these cross-ply laminates. Thermal cycling of specimens prior to flexural testing does not reduce the apparent flexural strength or change the mode of failure. However, fewer acoustic events are recorded at all strains during flexural testing of specimens exposed to prior thermal cycling. High temperature thermal cycling (32 to 260 C, 100 cycles) causes a greater reduction in acoustic events than low temperature thermal cycling (-85 to +85 C, 500 cycles). Mechanical cycling (0 to 50 percent of the flexural strength, 100 cycles) has a similar effect, except that acoustic events are reduced only at strains less than the maximum strain applied during flexural fatigue.
Thin-Film Encapsulation of Thin-Cathode Organic Light-Emitting Devices
Japanese Journal of Applied Physics
46
No. 11
7432-7435
2007
10.1143/JJAP.46.7432
We have developed a novel thin-film encapsulation method for thin-cathode\norganic light-emitting devices (OLEDs) by introducing organic (not\npolymer)/inorganic multiple thin films to protect devices, which\nis shown to slow down the permeation rate of moisture and oxygen.\nFrom the stability test of devices, the projected lifetime of thin-cathode\nOLEDs with thin-film encapsulation was similar to that of thin-cathode\nOLEDs with glass lid encapsulation.
Damage characteristics of cross ply GFRP and woven AFRP under various impact velocities
Key Engineering Materials
334-335 I
409-412
2007
Ankle Foot Orthosis (A.F.O) should endure the uncountable repeating impact and fatigue loadings due to the gait characteristics. This study investigated the impact deflection and relationship between the absorbed energy and the residual strength rate using the cross ply GFRP (glass/epoxy) and the woven AFRP (aramid/epoxy) for the leaf spring in A.F.O. In conclusion, the equation was suggested to evaluate the absorbed energy and the residual strength rate by the different impact velocities. When the cross ply GFRP and the woven AFRP was selected for the leaf spring in A.F.O, it was reasonable to use the cross ply GFRP for the parts subject to the large impact and the woven AFRP for the parts to require the high elastic energy such as the large deformation.
Ankle foot orthosis; Ankle foot orthosis (A.F.O); Aramid/epoxy; Deflection; Delamination; Elastic energy; Energy absorption; Glass/epoxy; Glass fiber reinforced plastics; Impact energy; Impact load; Impact loads; Impact testing; Indentation; Rebound energy; Residual strength rate; Strength of materials
Modal interpretations of Quantum Mechanics
Stanford Encyclopedia of Philosophy
21
2012
10.1016/j.shpsb.2006.05.005
The original “modal interpretation” of non-relativistic quantum theory was born in the early 1970s, and at that time the phrase referred to a single interpretation. The phrase now encompasses a class of interpretations, and is better taken to refer to a general approach to the interpretation of quantum theory. We shall describe the history of modal interpretations, how the phrase has come to be used in this way, and the general program of (at least some of) those who advocate this approach.
Perspectives in experimental solid mechanics
International Journal of Solids and Structures
37
1-2
251-266
2000
10.1016/S0020-7683(99)00092-X
The role of experiments in the interaction with theory is reviewed in the context of developing improved procedures in the evolutionary process of establishing engineering principles and design tools. The exceptional benefits derived from the increasing computational capabilities of the past decades are examined, as well as associated impediments to advancing mechanics objectives. Significant needs derive from these observations which command continuing or even increased commitments to supporting experimental efforts in mechanics. A summary of the salient methods in experimental research currently available is supplemented by perceived additional instrumentation needs and related tools that are required to address problems associated with emerging technologies. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.
but; experiment micromechanics; known; nanomechanics; nothing can be adequately; not know any science; not know mathematics does; plasticity; the scholar who does; without experiment
Vascular mechanics, mechanobiology, and remodeling.
Journal of mechanics in medicine and biology
9
2
243-257
2009
10.1142/S021951940900295X
Arteries exhibit a remarkable ability to adapt in response to sustained alterations in hemodynamic loading as well as in response to disease, injury, and clinical treatment. A better understanding of such adaptations will be aided greatly by formulating, testing, and refining appropriate theoretical frameworks for modeling the biomechanics and associated mechanobiology. The goal of this brief review is to highlight some recent developments in the use of a constrained mixture theory of arterial growth and remodeling, with particular attention to the requisite constitutive relations, and to highlight future directions of needed research.
Mechanics of thick-skinned Variscan overprinting of Cadomian basement (Iberian Variscides)
Comptes Rendus - Geoscience
341
2-3
127-139
2009
10.1016/j.crte.2008.12.003
Remnants of the Cadomian basement can be found in the Iberian Variscides (IBVA) in several key sectors of its autochthonous units (composed of Neoproterozoic to Lower Palaeozoic metasedimentary sequences) and within the Continental Allochthonous Terrane (CAT). Comprehensive characterization of these critical exposures shows that the prevailing features are related to major geological events dated within the age range of 620-540 Ma. Indeed, near the Cambrian-Ordovician boundary, the IBVA Internal Zones experienced pervasive basement thinning and cover thickening, reflecting diffusive displacement of intracratonic rifting that continued until Lower Devonian times. In the thick-skinned Internal Zones, Helvetic/Penninic style nappes were generated, whereas flower upright axial structures developed along transpressive, intraplate shear zones. These features contrast with those preserved in the thin-skinned IBVA External Zones, dominated by décollements above (un-)deformed Palaeozoic and Cadomian basement. The inferred attenuation of rheological contrast between Cadomian basement and Palaeozoic cover can be explained by inherited fabrics due to thermal softening operated during the Cambrian-Lower Devonian extensional regime. Deeper décollements (and subsequent strain partitioning) are also expected to develop at the upper-lower crust (and at the Moho?) transition, as imaged by the available seismic profiling and MT surveys. The whole data implies a significant discontinuity between Cadomian and Variscan Cycles that should have constrained subsequent lithospheric evolution. © 2008 Académie des sciences.
Cadomian basement; Iberian Variscides; Thick-skinned tectonics
Super classical quantum mechanics: The best interpretation of nonrelativistic quantum mechanics
American Journal of Physics
69
4
413
2001
10.1119/1.1349542
It has been shown that Newtonian classical mechanics (NCM) suffers from several kinds of chaotic indeterminacies. That means, a large set of problems treated with NCM gives results which are in wild disagreement with observation. In the present paper, these shortcomings are repaired in a simple, obvious, and essentially unique manner. The NCM theory is thereby transformed into a new theory which is fully equivalent to the Heisenberg, Schrödinger, and Dirac nonrelativistic quantum mechanics, with the vital addition of Born’s probabilistic interpretation of the wave function built in from the start. I call this new theory “super classical quantum mechanics” (SCQM). Using Ehrenfest’s theorem of 1927, the classical limit of the new theory, SCQM, is seen to give exactly the results expected of the repaired Newtonian theory of classical mechanics.
Mechanics of the nucleus.
Comprehensive Physiology
1
2
783-807
2011
10.1002/cphy.c100038
The nucleus is the distinguishing feature of eukaryotic cells. Until recently, it was often considered simply as a unique compartment containing the genetic information of the cell and associated machinery, without much attention to its structure and mechanical properties. This article provides compelling examples that illustrate how specific nuclear structures are associated with important cellular functions, and how defects in nuclear mechanics can cause a multitude of human diseases. During differentiation, embryonic stem cells modify their nuclear envelope composition and chromatin structure, resulting in stiffer nuclei that reflect decreased transcriptional plasticity. In contrast, neutrophils have evolved characteristic lobulated nuclei that increase their physical plasticity, enabling passage through narrow tissue spaces in their response to inflammation. Research on diverse cell types further demonstrates how induced nuclear deformations during cellular compression or stretch can modulate cellular function. Pathological examples of disturbed nuclear mechanics include the many diseases caused by mutations in the nuclear envelope proteins lamin A/C and associated proteins, as well as cancer cells that are often characterized by abnormal nuclear morphology. In this article, we will focus on determining the functional relationship between nuclear mechanics and cellular (dys-)function, describing the molecular changes associated with physiological and pathological examples, the resulting defects in nuclear mechanics, and the effects on cellular function. New insights into the close relationship between nuclear mechanics and cellular organization and function will yield a better understanding of normal biology and will offer new clues into therapeutic approaches to the various diseases associated with defective nuclear mechanics.
Animals; Cell Differentiation; Cell Nucleus; Cell Nucleus: pathology; Cell Nucleus: physiology; Cell Nucleus: ultrastructure; Humans; Neoplasms; Neoplasms: pathology
Fracture Mechanics ch10
Fracture Mechanics
247-285
2012
10.1016/B978-0-12-385001-0.00010-9
This chapter briefly introduces some special topics in fracture mechanics, including fracture of anisotropic solids, fracture of nonhomegenous matertials, and dynamic fracture mechanics. Fracture mechanics of nonhomogeneous materials has applications in macroscopically heterogeneous materials, such as functionally graded materials (FGMs), which have been developed to meet the increasing multifunctional structural performance requirements in engineering applications. Prediction of crack initiation and propagation in a dynamically loaded structure is based on dynamic fracture mechanics, which generally considers both inertia effects on the stresses and displacements, and loading rate effects on the constitutive responses of materials. This chapter also focuses on the fracture of fiber-reinforced materials. Composite materials, or simply composites, include fiber- and particulate-reinforced materials. Composites are heterogeneous materials at the microscopic scale. In continuum mechanics, properties of a composite are homogenized at the macroscopic level and the material is treated as a macroscopically, or statistically homogeneous material. The most successful composites for aerospace and other engineering applications have been fiber-reinforced polymer matrix materials. Fiber composites are usually modeled as anisotropic materials with three mutually orthogonal planes of symmerty.
dynamic fracture; fracture of anisotropic materials; fracture of nonhomogeneous materials; impact load; rapid crack propagation
Statistical Mechanics in Collective Coordinates
Journal of Statistical Physics
110
497-502
2003
10.1023/A:1022191214859
We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker-Planck equation in terms of the collective coordinates. Simple approximations, leading to Debye-Huckel theory and to the hard sphere Percus-Yevick equation are discussed.
Collective coordinates; Fokker-Planck equation; Jacobian; Statistical mechanics
Dynamical ensembles in statistical mechanics
Physica A: Statistical Mechanics and its Applications
240
1-2
43-53
1997
10.1016/S0378-4371(97)00129-5
A distribution function, using dynamical weights, proposed previously to describe statistical mechanical systems in stationary states, is discussed from a physical point of view. The distribution function correctly describes certain large current fluctuations far from equilibrium, observed in two computer simulations, which model a shearing fluid and a conducting solid, respectively.
doi:10.1103/PhysRevLett.74.2694 url:http://dx.doi.
Multiscale computational analysis in mechanics using finite calculus: An introduction
Computer Methods in Applied Mechanics and Engineering
192
28-30
3043-3059
2003
10.1016/S0045-7825(03)00340-2
The paper introduces a general procedure for computational analysis of a wide class of multiscale problems in mechanics using a finite calculus (FIC) formulation. The FIC approach is based in expressing the governing equations in mechanics accepting that the domain where the standard balance laws are established has a finite size. This introduces naturally additional terms into the classical equations of infinitesimal theory in mechanics which are useful for the numerical solution of problems involving different scales in the physical parameters. The discrete nodal values obtained with the FIC formulation and the finite element method (FEM) can be effectively used as the starting point for obtaining a more refined solution in zones where high gradients of the relevant variables occur using hierarchical or enriched FEM. Typical multiscale problems in mechanics which can be solved with the FIC method include convection-diffusion-reaction problems with high localized gradients, incompressible problems in solid and fluid mechanics, localization problems such as prediction of shear bands in solids and shock waves in compressible fluids, turbulence, etc. The paper presents an introduction of the treatment of multiscale problems using the FIC approach in conjunction with the FEM. Examples of application of the FIC/FEM formulation to the solution of simple multiscale convection-diffusion problems are given. ?? 2003 Elsevier B.V. All rights reserved.
Computational analysis of progressive failure in a notched laminate including shear nonlinearity and fiber failure
Composites Science and Technology
70
4
692-700
2010
10.1016/j.compscitech.2010.01.003
A computational model for mesolevel analysis of progressive laminate failure is presented. A previously developed discrete model for mesh independent representation of matrix cracks is combined with continuum descriptions for fiber failure and matrix nonlinearity. For fiber failure, a continuum damage model is introduced and a phenomenological damage/plasticity law is used for the shear nonlinearity. Special attention is paid to the application of the dissipation based arclength method to these models, where the presence of residual stresses is also taken into account. With the analysis of a notched cross-ply laminate the importance of the different components of the model to capture the complete failure process correctly is exemplified.
A. Laminate; B. Fracture; B. Nonlinear behavior; C. Computational mechanics; C. Damage mechanics
Intrusive gravity currents propagating along thin and thick interfaces
Journal of Fluid Mechanics
586
109
2007
10.1017/S0022112007007288
Inviscid gravity currents released from a finite-length lock are known to propagate at a constant speed to a predicted finite distance before decelerating. By extension this should occur in a two-layer fluid with equal upper- and lower-layer depths for an intrusion having the average density of the ambient. The experiments presented here show this is not necessarily the case. The finite-depth thickness of the interface non-negligibly influences the evolution of the intrusion so that it propagates well beyond the predicted constant-speed limit; it propagates without decelerating beyond 22 lock lengths in a rectilinear geometry and beyond 6 lock radii in an axisymmetric geometry. Experiments and numerical simulations demonstrate that the intrusion speed decreases to half the two-layer speed in the circumstance in which the interface spans the domain. The corresponding long mode-2 interfacial wave speed increases rapidly with interfacial thickness, becoming comparable with the intrusion speed when the interfacial thickness is approximately one-quarter the domain height. For somewhat thinner interfacial thicknesses, the intrusion excites solitary waves that move faster than the long-wave speed. The coupling between intrusions and the waves they excite, together with reduced mixing of the current head, result in constant-speed propagation for longer times.
Functional concepts in continuum mechanics
Meccanica
33
5
433-444
1998
10.1023/A:1004304224398
This paper is an attempt to give a concise presentation of the main concepts of continuum mechanics and to show their articulation. Functional definitions have been favoured. The first section is devoted to a review of continuum mechanics. The second section deals with the mechanics of materials. Constitutive equations of the material are given first by equations of state and then by complementary equations written in order to fulfil the fundamental inequality concerning the production of entropy and the physical properties of the material (viscosity, plasticity, damage etc.). Section 3 gives the Lagrangian and the Hamiltonian formulations for a moving body. Section 4 is devoted to the motion of surfaces through which discontinuities appear, to show briefly two examples of application of the previous concepts. One can easily define the source of intrinsic inhomogeneity, of heat, of irreversible entropy on a surface of phase transition and also for a shockwave.
analytical continuum mechanics; continuum thermodynamics; fluid mechanics; virtual power
The influence of peel angle on the mechanics of peeling flexible adherends with arbitrary load-extension characteristics
Tribology International
38
11-12 SPEC. ISS.
951-958
2005
10.1016/j.triboint.2005.07.024
The peel test is commonly used to determine the strength of adhesive joints. In its simplest form, a thin flexible strip which has been bonded to a rigid surface is peeled from the substrate at a constant rate and the peeling force which is applied to the debonding surfaces by the tension in the tape is measured. Peeling can be carried out with the peel angle, i.e. the angle made by the peel force with the substrate surface, from any value above about 10?? although peeling tests at 90 and 180?? are most common. If the tape is sufficiently thin for its bending resistance to be negligibly small then as well as the debonding or decohesion energy associated with the adhesive in and around the point of separation, the relation between the peeling force and the peeling angle is influenced both by the mechanical properties of the tape and any pre-strain locked into the tape during its application to the substrate. The analytic solution for a tape material which can be idealised as elastic perfectly-plastic is well established. Here, we present a more general form of analysis, applicable in principle to any constitutive relation between tape load and tape extension. Non-linearity between load and extension is of increasing significance as the peel angle is decreased: the model presented is consistent with existing equations describing the failure of a lap joint between non-linear materials. The analysis also allows for energy losses within the adhesive layer which themselves may be influenced by both peel rate and peel angle. We have experimentally examined the application of this new analysis to several specific peeling cases including tapes of cellophane, poly-vinyl chloride and PTFE. ?? 2005 Elsevier Ltd. All rights reserved.
Adherends; Load and extension; Peel angle
Quasi-static and high strain rate properties of a cross-ply metal matrix composite
Materials Science and Engineering: A
507
1-2
93-101
2009
10.1016/j.msea.2008.12.021
A series of compression tests has been carried out at quasi-static and high strain rates on cylindrical samples of an alumina fiber/Al-6061 metal matrix composite. The composite plates were prepared with fibers in the 0, 0/90 and 45 orientations. It was found that the mechanical properties were strongly dependent upon the imposed strain rate, with fracture stress increases of 50% being noted for several orientations at high strain rates: these increases are not believed to be related to strain rate sensitivity of either the matrix or fibers but to arise from the inertia of fragments which remain in place after fracture and continue to bear load. Also, and in contradiction to behavior anticipated from the rule of mixtures, it was found that 0/90 samples exhibited properties superior to those of 0 unidirectional samples. High-speed photography was used to confirm the sequence of deformation and fracture events at high strain rate. 2008 Elsevier B.V. All rights reserved.
metal matrix composite
Effects of glass fiber size composition (film-former type) on transverse cracking in cross-ply laminates
Composites Part A: Applied Science and Manufacturing
31
1083-1090
2000
10.1016/S1359-835X(00)00065-8
Transverse cracking is an important phenomenon in the context of fluid leakage in pipes and pressure vessels. Multiple transverse cracking in [0/90]s glass-fiber-reinforced vinylester and epoxy laminates with six different fiber surface treatments (size) is examined. Film-former composition is the variable since this component can be easily changed also in commercial size formulations. The influence of the film-former polymer on transverse cracking is significant in epoxy laminates and very strong in vinylester laminates. Both onset of transverse cracking and slope of crack density vs. strain are influenced. Remarkably low crack densities were observed in some vinylester laminates. Micromechanisms of cracking are interpreted. Correlation is established between transverse cracking behavior and interfacial shear strength measured by single fragmentation tests. The strong film-former effect is proposed to be due to a combination of improved interfacial adhesion and the plasticizing effect from the film-former on the interphase region.
b; film-former polymer; transverse cracking
The cross-ply arrangement of collagen fibres in the submucosa of the mammalian small intestine.
Cell and tissue research
248
3
491-7
1987
Whole-mount preparations of the submucosa were made from the small intestine of rats, guinea-pigs, rabbits and sheep. In the distended intestine the collagen fibres ran straight and approximately parallel to the serosal surface. They formed a characteristic lattice, with two arrays of fibres running diagonally in a clockwise and an anticlockwise direction, and making an angle of 50 degrees-55 degrees with the longitudinal axis of the intestine. This collagen-fibre lattice was flexible and changed with the movements of the intestinal wall; when the radial distension predominated, the angle between collagen fibres of the submucosa and longitudinal axis of the intestine increased to 60 degrees-65 degrees, and when the longitudinal distension predominated the angle decreased to about 30 degrees.
Animals; Collagen; Collagen: analysis; Guinea Pigs; Intestinal Mucosa; Intestinal Mucosa: cytology; Intestinal Mucosa: ultrastructure; Intestine, Small; Intestine, Small: cytology; Intestine, Small: ultrastructure; Microscopy, Electron; Rabbits; Rats; Sheep; Species Specificity
Mechanics of endothelial cell architecture and vascular permeability
Crit Rev Biomed Eng
29
2
247-278
2001
10.1615/CritRevBiomedEng.v29.i2.20
Blood vessel walls form a selective barrier to the transport of materials between blood and tissue, and the endothelium contributes significantly to this barrier function. The role of the endothelium is particularly important in thin-walled vessels, such as venules, because during tissue inflammation the endothelial junctions widen in localized areas and gaps form, thus compromising the barrier function. The mechanisms of endothelial gap formation are still under question. In this review we describe what is known about the structure of endothelial cell-cell junctions and how this structure can change during inflammation. We then consider two possible mechanisms by which endothelial gaps are formed: active endothelial cell contraction or breakdown of the junctional complex, followed by passive recoil. Using measured values of the mechanical properties of endothelial cells, and the forces to which they are subjected, we calculate that gap formation by breakdown of cellular adhesion, followed by passive recoil, is a feasible mechanism. Finally, since endothelial cell surfaces, including junctions, are coated with a glycocalyx, we consider the question of whether changes in the glycocalyx can markedly increase endothelial permeability. We conclude that gap formation can occur by active contraction or by breakdown of adhesion, depending on the inflammatory mediator, and that the responses of the glycocalyx may also play an important role in the regulation of microvascular permeability.
Actins/physiology; Animal; Biomechanics; Blood Proteins/physiology; Cadherins/physiology; Capillary Permeability/*physiology; Cell Adhesion/physiology; Endothelium, Vascular/*cytology/*physiology; Glycocalyx/physiology; Histamine/physiology; Human; Intercellular Junctions/physiology/ultrastructure; Thrombin/physiology; Vasoconstriction/physiology
Videogame Mechanics in Games for Health
Games for Health Journal
2
4
194-204
2013
10.1089/g4h.2013.0617
Game mechanics have been identified as ?methods invoked by agents for interacting with the game world.?1 They are elements of game play that provide a primary source of interactivity and structure how videogames proceed. Many kinds of game mechanics have been generated. Some provide fun or enjoyment, others may provide excitement or even suspense (i.e., emotional aspects of game play), whereas some are guided by principles of behavior change theory. Game mechanics that succeed in off-the-shelf entertainment videogames, however, may not work in serious games, such as games for health (G4H). Although game mechanics are key to a serious videogame's success, maintaining a balance between the serious intent of the game while keeping it fun, there has been little attention to game mechanics in the academic G4H literature. Several eminent games for health developers (academics and nonacademics) were asked to share their experiences in regard to game mechanics in the serious videogames they have developed.
Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets
Geophysical Journal International
172
2
817-841
2008
10.1111/j.1365-246X.2007.03671.x
Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in the flexure mechanism. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However local studies of gravity and topography data suggest large variations in the thickness of the lithosphere. In this article we obtain the scalar flexure equations governing the deformations of a thin spherical shell with variable thickness or variable Young's modulus. The resulting equations can be solved in succession, except for a system of two simultaneous equations, the solutions of which are the transverse deflection and an associated stress function. In order to include bottom loading generated by mantle convection, we extend the method of stress functions to include loads with a toroidal tangential component. We further show that toroidal tangential displacement always occurs if the shell thickness varies, even in the absence of toroidal loads. We finally prove that the degree-one harmonic components of the transverse deflection and of the toroidal tangential displacement are independent of the elastic properties of the shell and are associated with translational and rotational freedom. The flexure equations for a shell of variable thickness are useful not only for the prediction of the gravity signal in local admittance studies, but also for the construction of stress maps in tectonic analysis.
Elasticity and anelasticity; Lithospheric flexure; Mechanics, theory, and modelling; Planetary tectonics
A co-rotational formulation for thin-walled beams with monosymmetric open section
Computer Methods in Applied Mechanics and Engineering
190
8-10
1163-1185
2000
10.1016/S0045-7825(99)00471-5
A consistent co-rotational total Lagrangian finite element formulation and numerical procedure for the geometric nonlinear buckling and postbuckling analysis of thin-walled beams with monosymmetric open section is presented. The element developed here has two nodes with seven degrees of freedom per node. The element nodes are chosen to be located at the shear centers of the end cross-sections of the beam element and the shear center axis is chosen to be the reference axis. The deformations of the beam element are described in the current element coordinate system, which is constructed at the current configuration of the beam element. In element nodal forces, all coupling among bending, twisting, and stretching deformations of the beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, the third-order term of the twist rate of the beam axis is considered in element nodal forces. An incremental-iterative method based on the Newton–Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. A parabolic interpolation method of the arc length is used to find the buckling load. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.
Buckling; Co-rotational formulation; Geometric nonlinearity; Thin-Walled beam
Giant stretchability of thin gold films on rough elastomeric substrates
Acta Materialia
61
2
540-547
2013
10.1016/j.actamat.2012.10.001
Stretching metallic conductors to large deformations while maintaining a low and constant electrical resistance is one of the main challenges in stretchable electronics technologies. Here, we report the conservation of conductivity for deformations of up to 100% in 80 and 500 nm thick gold films deposited on rough polydimethylsiloxane (PDMS) substrates. The roughness is produced by curing PDMS on sand-blasted or surface-etched masters. Under stretching, roughness creates a fine-scale inhomogeneous stress state within the film and a non-percolating crack pattern develops, preserving the conductivity. Compared to smooth surfaces, the strain corresponding to electrical failure is increased by a factor >50. By combining the roughness effect with prestretching of the substrate during deposition, a fine-scale random wrinkling morphology develops and the stretchability is enhanced even further. The stretchability is finally improved by increasing the thickness of the film. These synergistic effects can be explained based on fracture mechanics arguments. Finally, a high number of large deformation cycles can be accommodated without electrical failure. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Ductility; Electrical conductivity; Fracture; Roughness; Stretchable electronics
Study of Thin Sandwich Beams With Steel Faces and Perforated Polymer Core in Bending Loading: Experiments and Simulations
Journal of Applied Mechanics
78
1
14504
2011
10.1115/1.4002364
The mechanical behavior of thin sandwich beams with steel faces and porous polymer core have been investigated using quasistatic four-points bending. Classic sandwich models predicting the behavior and the failure modes are improved to fit the particular configuration of the structure. Numerical simulations were set up in order to investigate damage at large strain. Macroscopic results are compared with analytical models and numerical simulations. Two numerical models of the core allowed confrontation of local behavior with experiments. Criteria for localization and damaging depending on core architecture are proposed. [{DOI}: 10.1115/1.4002364]
A combined mesh and model adaptive strategy for the scaling issues in the numerical modelling of the ductile damage in thin panels
Computer Methods in Applied Mechanics and Engineering
192
3285-3300
2003
10.1016/S0045-7825(03)00351-7
In this paper, a combined model and mesh adaptive computational approach is presented for the numerical modelling of ductile damage in thin panels. The aim of such a strategy is to be able to compute with the finite element techniques, the damage tolerance of large structures, such as a fuselage, in a fully coupled way, taking into account the multiscale character of the problem. In a sole computation, both global structural features at the macroscale level-such as fasteners, stiffeners and joint configuration-and a realistic material damage behaviour at the microscale level are treated in a coherent way. ?? 2003 Elsevier B.V. All rights reserved.
Adaptive finite elements; Damage; Model error; Residual methods
A two-ply polymer-based flexible tactile sensor sheet using electric capacitance.
Sensors (Basel, Switzerland)
14
2
2225-38
2014
10.3390/s140202225
Traditional capacitive tactile sensor sheets usually have a three-layered structure, with a dielectric layer sandwiched by two electrode layers. Each electrode layer has a number of parallel ribbon-like electrodes. The electrodes on the two electrode layers are oriented orthogonally and each crossing point of the two perpendicular electrode arrays makes up a capacitive sensor cell on the sheet. It is well known that compatibility between measuring precision and resolution is difficult, since decreasing the width of the electrodes is required to obtain a high resolution, however, this may lead to reduction of the area of the sensor cells, and as a result, lead to a low Signal/Noise (S/N) ratio. To overcome this problem, a new multilayered structure and related calculation procedure are proposed. This new structure stacks two or more sensor sheets with shifts in position. Both a high precision and a high resolution can be obtained by combining the signals of the stacked sensor sheets. Trial production was made and the effect was confirmed.
capacitive tactile sensor; conductive rubber; flexible sensor; polymer; screen printing; tactile sensor
Development of a specialised finite element for the analysis of composite structures with ply drop-off
Composite Structures
46
1-16
1999
10.1016/S0263-8223(99)00013-6
A global–local approach for the analysis of tapered laminated composites is presented. The method is considerably more economical than existing techniques. A new drop-off element that is degenerated from a 2-dimensional (2-D) drop-off element is introduced to carry out the global analysis. The drop-off element accommodates the termination of plies within the element and therefore, the size of the stiffness matrix reduces. At the vicinity of the drop-off where the stress concentration is high a local analysis with a refined mesh is performed with the results of the global analysis. Since a fine mesh is to be adopted only near the drop-off there is substantial economy in the computational effort and time as compared to the conventional analysis models. The present method has been validated extensively against published results. A discussion of the stress/strain distribution at different locations has been presented.
Linear stability analysis of thin leaky dielectric films subjected to electric fields
Journal of Non-Newtonian Fluid Mechanics
102
233-250
2002
10.1016/S0377-0257(01)00180-X
An intriguing process, known as lithographically induced self-assembly (LISA), is initiated by positioning a template parallel to a flat silicon wafer-coated with a thin polymeric film and then raising the temperature above the glass transition/melting temperature of the film. Electric fields exert a force on charges induced at the polymer-air interface, placing the film in tension. The static equilibrium that results is unstable to disturbances with wavelengths for which the electrostatic force overcomes the surface tension. Flow ensues, generating a pattern in the film with periodicity reflecting the characteristic length of the instability. Though the initiation of the process as outlined above is generally accepted, the forces guiding the evolution of the film into the remarkably periodic microstructures observed are not. Our goal here is to create a sound understanding of the mechanism through quantitative modeling to facilitate the conversion of these microstructures into nano-structures. Given the apparent importance of conductivity in the film we adopt the "leaky dielectric model", which also allows for re-distribution of charges on the interfaces, and undertake a linear stability analysis to explore the effects of various process parameters, particularly the conductivity and the film thickness. The linear stability analysis with the leaky dielectric model for the polymer film yields growth exponents and characteristic wavenumbers much larger than that for the perfect dielectric model. The differences are striking in that the slightest conductivity increases the growth exponent by a factor of 2-20 and decreases the fastest growing wavelength by a factor of 2-4. © 2002 Elsevier Science B.V. All rights reserved.
Conductivity; Dielectric film; Electric field; Leaky dielectric; Linear stability analysis
Introduction to Quantum Mechanics
Nature
155
3948
11
2008
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
Implications of quantum theory in the foundations of statistical mechanics
Quantum
1-19
2001
An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time.
WIND EFFECTS ON SINGLE-PLY ROOFING SYSTEMS
J. Struct. Eng.
116
1
177-187
1990
A failure mechanism for single-ply roofing systems is formulated that accounts for air infiltration into the space underneath the inflated membrane and the billowing of the membrane with the fluctuations of wind pressure on the roof. The governing differential equation, expressed in terms of the pressure underneath the inflated membrane, is derived and solved numerically for a range of material, geometric, and wind parameters. The results are expressed in terms of a transient response factor (TRF), which is equal to the ratio of the fluctuating component of pressure across the membrane thickness to the fluctuating component of wind pres- sure. The results show that TRF increases with the rate of air infiltration into the space underneath the inflated membrane, the stiffness of the membrane, the mag- nitude of the fluctuating component of wind pressure, and the size of the inflated membrane. The inadequacies of the present empirical design procedures are discussed.
Modal decomposition of thin-walled member collapse mechanisms
Thin-Walled Structures
74
269-291
2014
10.1016/j.tws.2013.10.002
Following recent investigations on the decomposition of elastic buckling modes into combinations of structurally meaningful deformation modes, this work presents a novel extension of the above procedure to elastic–plastic collapse mechanisms and highlights the relevant role that this concept may play in the mechanical knowledge/interpretation of thin-walled member failures. In order to achieve the sought decomposition, a code based on a Generalised Beam Theory (GBT) formulation developed to perform first-order elastic–plastic analyses of thin-walled members is employed. Five illustrative examples are presented and discussed, and the results displayed, namely load-deflection curves, deformed configurations and stress contours, are validated through the comparison with values provided by shell finite element analyses. The most relevant modal results addressed consist of (i) load-deflection curves determined on the basis of pre-selected deformation mode sets, (ii) modal participation diagrams and (iii) modal amplitude functions. These results make it easy to characterise and interpret the mechanics associated with the thin-walled member elastic–plastic failures (as well as with the various loading stages), which may be of great importance in the improvement/development of existing/new design methods (e.g, yield-line theory, direct strength method).
Elastic–plastic strength reserve; First-order inelastic failures; Generalised Beam Theory (GBT); Local/global deformation modes; Thin-walled steel members; Yield-line mechanisms
Glass-modified stress waves for adhesion measurement of ultra thin films for device applications
Journal of the Mechanics and Physics of Solids
51
8
1395-1412
2003
10.1016/S0022-5096(03)00057-7
Laser-generated stress wave profiles with rarefaction shocks (almost zero post-peak decay times) have been uncovered in different types of glasses and presented in this communication. The rise time of the pulses was found to increase with their amplitude, with values reaching as high as 50 ns. This is in contrast to measurements in other brittle crystalline solids where pulses with rise times of 1-2 ns and post-peak decay times of 16-20 ns were recorded. The formation of rarefaction shock is attributed to the increased compressibility of glasses with increasing pressures. This was demonstrated using a one-dimensional nonlinear elastic wave propagation model in which the wave speed was taken as a function of particle velocity. The technological importance of these pulses in measuring the tensile strength of very thin film interfaces is demonstrated by using a previously developed laser spallation experiment in which a laser-generated compressive stress pulse in the substrate reflects into a tensile wave from the free surface of the film and pries off its interface at a threshold amplitude. Because of the rarefaction shock, glass-modified waves allow generation of substantially higher interfacial tensile stress amplitudes compared with those with finite post-peak decay profiles. Thus, for the first time, tensile strengths of very strong and ultra thin film interfaces can be measured. Results presented here indicate that interfaces of 185-nm-thick films, and with strengths as high as 2.7 GPa, can be measured. Thus, an important advance has been made that should allow material optimization of ultra thin layer systems that may form the basis of future MEMS-based microelectronic, mechanical and clinical devices. ?? 2003 Elsevier Science Ltd. All rights reserved.
Adhesion; Interface strength; Interferometery; Laser-generated stress waves; Multilayers; Nonlinear elastic; Rarefaction shock; Spallation; Thin films
The nonlinear dynamics of pendent drops on a thin film coating the underside of a ceiling
Journal of Fluid Mechanics
647
239
2010
10.1017/S002211201000008X
This paper considers the dynamics of a thin film of viscous liquid of density ρ coating the underside of a horizontal rigid boundary under the action of surface tension σ and gravity g, and in the lubrication limit. Gravitational instability for inverse wavenumbers larger than the capillary length ℓ = (σ/ρg)1/2) leads to the formation of quasi-static pendent drops of radius ≈3.83ℓ. If the boundary conditions are such as to pin the positions of the drops then the drops slowly drain fluid from the regions between them through thin annular trenches around each drop. A similarity solution is derived and verified numerically in which the film thickness in the intervening regions scales like t−1/4 and that in the trenches like t−1/2. A single drop placed far from boundaries on an otherwise uniform film, and given an initial perturbation, undergoes self-induced quasi-steady translation during which it grows slowly in amplitude by leaving a wake where the film thickness is reduced by an average of 90. It is driven by release of gravitational potential energy as fluid is collected from the film into the lower lying drop. Analysis of Landau–Levich regions around the perimeter of the translating drop predicts its speed and the profile of the wake. Two translating drops may coalesce if they collide, in contrast with the non-coalescence of colliding collars in the analogous one-dimensional problem (Lister et al., J. Fluid Mech. vol. 552, 2006b, p. 311). Colliding drops may also bounce off each other, the outcome depending on the angle of incidence through complex interactions between their surrounding capillary wave fields.
Review of stochastic mechanics
Journal of Physics: Conference Series
361
1
012011
2012
10.1088/1742-6596/361/1/012011
Stochastic mechanics is an interpretation of nonrelativistic quantum mechanics in which the\r trajectories of the configuration, described as a Markov stochastic process, are regarded as\r physically real. The natural stochastic generalization of classical variational principles leads to\r a derivation of the Schrödinger equation. A brief review of the successes and failures of the theory\r is given, with references.
Basic-deformed quantum mechanics
Quantum
34
10
2009
Starting on the basis of q-symmetric oscillator algebra and on the associate q-calculus properties, we study a deformed quantum mechanics defined in the framework of the basic square-integrable wave functions space. In this context, we introduce a deformed Schroedinger equation, which satisfies the main quantum mechanics assumptions and admits, in the free case, plane wave functions that can be expressed in terms of the q-deformed exponential, originally introduced in the framework of the basic-hypergeometric functions.
The hydrodynamic stability of a thin film of liquid in uniform shearing motion
Journal of Fluid Mechanics
8
04
593-610
1960
10.1017/S0022112060000827
The stability problem for a thin film of liquid having a linear mean-velocity profile and bounded by a fixed wall and free surface is solved asymptotically for large values of the Reynolds number R. The analysis is similar to that for plane Couette flow, but instability occurs for sufficiently large values of R in accordance with Heisenberg's criterion that neutral disturbances having finite wave numbers and phase velocities for R = [infty infinity] are necessarily unstable as R [rightward arrow] [infty infinity]. It is found that a sufficient condition for stability is W < 3, where W is the Weber number based on the mean speed at the free surface and the depth of the film. The minimum critical Reynolds number, also based on free surface speed and film depth, is found to be R = 203. This last figure is in order-of-magnitude agreement with observation, but there remains considerable uncertainty as to whether the observed instability corresponds to that considered here. Neutral stability curves are presented in an R vs α (= wave-number) plane with W as the family parameter. Brief consideration also is given to the time-rate-of-growth of unstable disturbances and to the lighter fluid that, in actual configurations, is responsible for the shear in the film. An appendix gives extended and more accurate results for the function F(z), introduced and calculated previously by Tietjens (1925) and Lin (1955).
Phenomenological invariant-based finite-element model for geometrically nonlinear analysis of thin shells
Computer Methods in Applied Mechanics and Engineering
196
49-52
4952-4964
2007
10.1016/j.cma.2007.06.015
A Kirchhoff-Love type curved triangular finite element is proposed for geometrically nonlinear analysis of elastic isotropic shells undergoing small strains but large displacements. The finite-element formulation is based on the expression of the strain energy in terms of invariants of the strain and curvature-change tensors of the shell middle surface. The element sides are chosen as three independent directions for determining the strains and curvature changes. The emphasis is put on improvement of the bending behavior of the element so that the element is able to undergo finite curvature changes. Recursive relations are obtained for exactly calculating the coefficients of the first- and second-order variations of the strain energy of the finite element which are necessary to formulate the equilibrium and stability conditions of the discrete model of a shell. A shell finite element with 15 degrees of freedom is developed and tested. Numerical examples are presented to demonstrate the accuracy and mesh convergence of the finite-element solutions. © 2007 Elsevier B.V. All rights reserved.
Finite element; Invariants; Large rotations; Stability; Thin shell
On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells
Computational Mechanics
16
5
341-359
1995
10.1007/BF00350723
A simple non-linear stress resultant four node shell finite element is presented. The underlying shell theory is developed from the three dimensional continuum theory via standard assumptions on the displacement field. A model for thin shells is obtained by approximating terms describing the shell geometry. In this work the rotation of the shell director is parameterized by the two Euler angles, although other approaches can be easily accomodated. A procedure is provided to extend the presented approach by including the through-thickness variable material properties. These may include a general non-linear elastic material with varied degree of orthotropy, which is typical for fibre reinforced composites. Thus a simple and efficient model suitable for analysis of multilayered composite shells is attained. Shell kinematics is consistently linearized, leading to the Newton-Raphson numerical procedure, which preserves quadratic rate of asymptotic convergence. A range of linear and non-linear tests is provided and compared with available solutions to illustrate the approach.
Numerical simulations of island formation in a coherent strained epitaxial thin film system
Journal of the Mechanics and Physics of Solids
47
11
2273-2297
1999
10.1016/S0022-5096(99)00026-5
Three dimensional finite element computations are used to predict the formation of quantum dot arrays in a strained epitaxial thin film system. The film is idealized as an initially planar, isotropic elastic layer with isotropic surface energy, which is coherently bonded to an elastic, lattice mismatched substrate. A small, doubly sinusoidal variation in film thickness, intended to represent the dominant wavelength of surface roughness, is introduced to trigger island formation. The film continues to roughen due to strain induced surface diffusion and eventually breaks up into arrays of discrete islands. The conditions necessary for island formation are identified, and are shown to differ significantly from the conditions necessary for spontaneous roughening of a strained layer. A detailed parametric study is conducted to determine the influence of the properties of film and substrate, film thickness, and surface roughness on the resulting island morphologies. In particular, our simulations show that there exists a critical range of surface roughness wavelength which leads to the formation of perfectly periodic island arrays. Finally, our predictions are compared with existing experimental measurements.
c; finite elements; quantum dot; strained layer; surface di; surface roughening; usion
A two-scale modeling of motion-induced fluid release from thin fibrous porous media
Chemical Engineering Science
64
9
2067-2075
2009
10.1016/j.ces.2009.01.048
In this work, a two-scale two-phase modeling methodology is presented for studying fluid release from saturated/unsaturated thin fibrous media when brought in contact with a moving solid surface. Our macroscale model is based on the Richards’ equation for two-phase fluid transport in porous media. The required constitutive relationships, capillary pressure and relative permeability as functions of medium's saturation, are obtained through microscale modeling. At microscales, a 3-D model based on fiber diameter, fiber orientation, and medium's solid volume fraction (SVF), is generated to resemble the internal structure of the fibrous sheets and be used in full-morphology analysis as well as microscale permeability simulation. A mass convection boundary condition is considered here to model the fluid transport at the boundary in contact with the target surface. It was shown that the mass convection coefficient, kf, plays a significant role in determining the release rate and is expected to be in the range of 10-6<kf<10-9, depending on the properties of the fluid, fibrous sheet, the target surface as well as the speed of the relative motion, and remains to be determined experimentally.
Convective transport; Fibrous media; Fluid mechanics; Microstructure; Multiphase flow; Porous media; Transport processes
Charpy Impact of Sandwich Structural Composites (CFRP/PC/CFRP) of Polycarbonate (PC) Cores Covered with Carbon Fiber Cross Textile Reinforced Epoxy Polymer (CFRP) Thin Sheets as a Function of Temperature
MATERIALS TRANSACTIONS
53
7
1288-1294
2012
10.2320/matertrans.M2011357
The purpose of this study is to investigate a lighter, cheaper and possibly stronger alternative to CFRP, by obtaining the Charpy impact values (a(uc)) of a sandwich structural composite (CFRP/PC/CFRP) constructed of a polycarbonate (PC) core between two thin plies of carbon cross textile fiber/epoxy (CFRP) within the temperature range of aircraft operation, from 200 to 403 K below the glass transition temperature of PC (T-g = 422 K). The a(uc) of CFRP/PC/CFRP were compared with a 2.0 mm thick 12-ply CFRP laminate. Results showed overall, the CFRP/PC/CFRP had higher a(uc) than the CFRP at each fracture probability (P-f) from 300 to 373 K except at 200 K with low Pf and 403 K with high Pf. Specifically, although the volume fraction of carbon fiber (12%) of CFRP/PC/CFRP was much smaller than that (60%) of the CFRP, the a(uc) at room temperature (300 K) of CFRP/PC/CFRP was approximately 64% higher than that of CFRP at mid-fracture probability (P-f) of 0.50. Fracture modes of CFRP/PC/CFRP were explained by delamination between PC core and the CFRP thin sheet surfaces, bending plastic deformation, and CFRP fracture. The highest Weibull coefficient (n) was obtained at 323 K. Based on the 3-parameter Weibull equation, the limiting impact value (a(s)) also exhibited the highest value at 323 K. In addition, the cost of CFRP/PC/CFRP was 40% lower than that of CFRP at the time of this study. Since the use of PC resin as the core enhanced the safety design at low cost, practical use of sandwich structural composites of CFRP/PC/CFRP is possible. {[}doi:10.2320/matertrans.M2011357]
carbon fiber reinforced polymer (CFRP); Charpy impact test; delamination; epoxy; polycarbonate; sandwich structure
Two-dimensional pitting corrosion of aluminium thin layers
Physica A: Statistical Mechanics and its Applications
217
3-4
319-338
1995
10.1016/0378-4371(95)00048-C
The influence of Cl- and Fe3+ ions on the morphology of pits grown in aluminium thin films was investigated. Under open circuit conditions various morphologies ranging from percolation-cluster-like patterns to dense holes with smooth perimeters were observed. Temporal fluctuations in the free corrosion potential did not reflect significant differences in pit shapes. The growth of two-dimensional pits is likely to be influenced by two main factors: (a) local fluctuation in the electrolyte aggressiveness due to copious hydrogen bubbling at dissolution sites; (b) global restriction of pit growth imposed by the cathodic reactions occurring on the oxidised surface. A spreading percolation model with feed-back is able to reproduce all the morphologies observed and provides a possible explanation to the 1/f2 character of the potential noise.
Open or closed? Dirac, Heisenberg, and the relation between classical and quantum mechanics
Studies in History and Philosophy of Science Part B: …
35
3
1-31
2004
10.1016/j.shpsb.2003.11.002
This paper describes a long-standing, though little-known, debate between Paul Dirac and Werner Heisenberg over the nature of scientific methodology, theory change, and intertheoretic relations. Following Heisenberg’s terminology, their disagreements can be summarized as a debate over whether the classical and quantum theories are “open” or “closed.” A close examination of this debate sheds new light on the philosophical views of two of the great founders of quantum theory.
classical mechanics; closed theory; dirac; heisenberg; intertheoretic relations; quantum mechanics
Mechanics of elastomer-shim laminates
Cmc-Computers Materials & Continua
5
1
11-29
2007
The mechanics of laminates of elastomer and shims of high modulus material are reviewed. Such structures are often built to provide engineering components with specified, and quite different, stiffnesses in different modes of deformation. The shims may either be rigid or flexible, flat or curved, but are usually close to inextensible, being made of a high modulus material such as steel. On the other hand, rubber has an exceptionally low shear modulus, about one thousandth of its bulk modulus, so that shear of the rubber layers and flexure of the high modulus layers (if thin) are the dominant mechanisms of deformation of the composite. In comparison, extension of the layers and changes to their separation are highly constrained. Modes of failure are addressed as well as force-deformation behaviour. For compression normal to the laminations, the shear in the rubber results in in-plane tension in the shims, possibly leading to tensile failure. For tension normal to the laminations, the elastomer can cavitate, which would relieve the shear in it and hence the in-plane compressive stress applied to the shim. In flexure, shear in the rubber can apply in-plane compressive stress to the shims and cause buckling failure.
bearings; bonded rubber blocks; buckling; cavitation; compression; damping; elastic stability; fracture; instability; laminates; nonlinear behavior; rubber; shape factor; shear; springs; stiffness
Radiographic Investigation of the Effects of Ply Modification on Damage Development in Laminates Containing Circular Holes
Journal of Composite Materials
42
20
2143-2161
2008
10.1177/0021998308094552
The goal of this research was to evaluate possible damage suppression in multi-directional notched laminates through the use of slightly off-axis longitudinal plies. These 'non-traditional' laminates were compared to laminates with 08 longitudinal plies for quasi-isotropic and hard lay-ups, for open hole tension, filled hole tension, and single-shear bearing loadings. In-situ radiographic inspections were performed to evaluate damage initiation, progression, and suppression. In notched tension, the non-traditional laminates were less strong and stiff than their traditional counterparts, but X-ray images clearly showed the suppression of longitudinal splitting and delamination. Under single-shear bearing loads, the non-traditional laminates demonstrated increased bearing resistance compared to traditional laminates, and the non-traditional laminates were less prone to damage in the longitudinal plies.
Molecular motors: single-molecule mechanics.
Current biology : CB
6
4
392-394
1996
10.1016/S0960-9822(02)00504-3
Novel techniques are revealing the movements and forces associated with single interactions of motor proteins, such as myosin and kinesin, and also of processive enzymes, such as RNA polymerase.
Chemical and morphological properties of (Ti-Zr)N thin films grown in an arc pulsed system
Microelectronics Journal
39
11
1379-1381
2008
10.1016/j.mejo.2008.01.067
Due to its extensive field of application in different areas, including mechanics, electronics, tribology and optics the last decade has seen a large interest the study of titanium-zirconium-nitride (Ti-Zr)N thin films grown by different techniques. We had produced (Ti-Zr)N thin films and in this work chemical, morphological and electronics analysis are presented. Thin films were produced by the PAPVD (plasma assisted physics vapor deposition) technique, by pulsed arc in a mono-vaporizer system using a titanium-zirconium target with 99.99% purity. Argon-nitrogen mixture for the discharge was used. For the analyses X-ray photoelectron spectroscopy (XPS) and scanning probe microscopy (SPM) techniques were used, XPS results shown the chemical composition of the films. Films were morphologically and tribologically characterized using SPM, obtaining grain size and friction coefficient. ?? 2008 Elsevier Ltd. All rights reserved.
Arc pulsed; SPM; (Ti-Zr)N; XPS
Microscratch analysis of the work of adhesion for Pt thin films on NiO
Journal of Materials Research
7
1126-1132
1992
10.1557/JMR.1992.1126
The adhesion of as-sputtered Pt thin films to NiO single crystals has been characterized by a continuous microscratch technique. In these experiments, a conical indenter was driven into a 1.2 μm thick Pt film at a rate of 15 nm/s, and across the sample surface at a rate of 0.5 μm/s, until a load drop was observed indicating that the film had delaminated. Using the width of the scratch track at the point at which the film delaminated from the substrate, the critical load required for delamination, and the area of the delaminated region, a model has been developed to determine the work of adhesion of the Pt/NiO system. This model uses an elastic contact mechanics approach to relate the stresses acting in a scratch experiment to the strain energy released during film delamination. Using this model, the work of adhesion and hence the interfacial fracture toughness have been determined to be 0.023-0.06 J/m2 and 0.07-0.11 MPa rootm, respectively. These values are in reasonable agreement with those determined by other methods for metal-ceramic systems.
Effects of substrate compliance on circular buckle delamination of thin films
Engineering Fracture Mechanics
74
15
2334-2351
2007
10.1016/j.engfracmech.2006.11.007
The present work analyzes circular delamination buckling in a film/substrate system based on the Von Karman nonlinear plate theory with the consideration of elastic deformation of the substrate. Due to the axisymmetry of circular buckling, the substrate deformation is modeled by coupled springs and the spring compliances are determined from the dimension analysis and finite element calculations. The numerical shooting method is used to solve the nonlinear post-buckling problem. The stress intensity factors, the energy release rate, and the phase angle are given here for a variety of the elastic mismatch between the film and the substrate. The results show that in some cases, the energy release rate can be several times larger than that derived from the widely used clamped edge condition. ?? 2006 Elsevier Ltd. All rights reserved.
Circular delamination; Energy release rate; Phase angle; Residual stress; Thin film buckling
A full-scale numerical study of interfacial instabilities in thin-film flows
Journal of Fluid Mechanics
325
163-194
1996
10.1017/S0022112096008075
Surface wave instabilities in a two-dimensional thin draining film\nare studied by a direct numerical simulation of the full nonlinear\nsystem. A finite element method is used with an arbitrary {LagrangianâEulerian}\nformulation to handle the moving boundary problem. Both temporal\nand spatial stability analysis of the finite-amplitude nonlinear\nwave regimes are done. As the wavenumber is decreased below the linear\ncut-off wavenumber, supercritical sinusoidal waves occur as reported\nearlier from weakly nonlinear analysis and experiments. Further reduction\nin wavenumber makes the Fourier spectrum broad-banded resulting in\nsolitary humps. This transition from nearly sinusoidal permanent\nwaveforms to solitary humps is found to go through a quasi-periodic\nregime. The phase boundaries for this quasi-periodic regime have\nbeen determined through extensive numerical parametric search. Complex\nwave interaction processes such as wave merging and wave splitting\nare discussed. In the exhaustive numerical simulations performed\nin this paper, no wave-breaking tendency was observed, and it is\nspeculated that the complex wave-interaction processes such as wave\nmerging and wave splitting curb the tendency of the film to break.
cfd; krishnamoorthy
Modern fracture mechanics
Philosophical Magazine
93
28-30
3893-3906
2013
10.1080/14786435.2013.812811
Alan Cottrell had a unique ability to impact the metallurgical/materials research community via his fundamental approaches at various length scales and by providing micromechanistic approaches to fracture in crystalline materials, culminating in the macro-mechanics of large-scale engineering structures. His concepts/techniques/analyses have been successfully applied to a range of structural materials and are being applied to an ever-increasing range of more complicated materials systems, ranging from ferrous-based crystalline systems to amorphous metals and biological systems. The field of Modern Fracture Mechanics requires an increasingly complex set of experimental and computational tools to capture material deformation, damage accumulation and failure across multiple size and time scales and builds directly from some of the earliest works and desires of Sir Alan, as reviewed herein.\nAlan Cottrell had a unique ability to impact the metallurgical/materials research community via his fundamental approaches at various length scales and by providing micromechanistic approaches to fracture in crystalline materials, culminating in the macro-mechanics of large-scale engineering structures. His concepts/techniques/analyses have been successfully applied to a range of structural materials and are being applied to an ever-increasing range of more complicated materials systems, ranging from ferrous-based crystalline systems to amorphous metals and biological systems. The field of Modern Fracture Mechanics requires an increasingly complex set of experimental and computational tools to capture material deformation, damage accumulation and failure across multiple size and time scales and builds directly from some of the earliest works and desires of Sir Alan, as reviewed herein.
Generalized statistical mechanics of cosmic rays
Physica A: Statistical Mechanics and its Applications
331
1-2
10
2003
10.1016/j.physa.2003.09.025
We consider a generalized statistical mechanics model for the creation process of cosmic rays which takes into account local temperature fluctuations. This model yields Tsallis statistics for the cosmic ray spectrum. It predicts an entropic index q given by q=11/9 at largest energies (equivalent to a spectral index of alpha=5/2), and an effective temperature given by (5/9)TH, where kTH approximately equal to 180 MeV is the Hagedorn temperature measured in collider experiments. Our theoretically obtained formula is in very good agreement with the experimentally measured energy spectrum of primary cosmic rays.
1; 2; 3; applied a; cosmic ray energy spectrum; further developed many; hagedorn temperature; have recently been successfully; idea; introduced tsallis; maximize more general entropy; more general versions; nonextensive statistical mechanics; others; statistical mechanics; systems; variety complex physical
Some remarks on the history of fracture mechanics
Proceedings of the 3rd International Conference on Applied Mathematics, Simulation, Modelling, Circuits, Systems and Signals
122-131
2009
This paper is an essay over the evolution of fundamental ideas of fracture mechanics. This evolution is described from an historical point of view following three major directions: experimental methods, numerical methods and analytical methods. It starts from the observation of Leonardo da Vinci from the fifteenth century and goes until the present time, pointing out the most important moments and ideas in the evolution of fracture mechanics.
fracture mechanics; history; history of mathematics
Geometric and material nonlinearity during the deformation of micron-scale thin-film bilayers subject to thermal loading
Journal of the Mechanics and Physics of Solids
52
9
2101-2126
2004
10.1016/j.jmps.2004.02.003
We study, by experiments and modeling, the linear and geometric nonlinear\nbehavior of thin-film bilayer mechanical structures subjected to\nthermal loading due to combined creep and stress relaxation. On the\nexperimental side, we designed and fabricated a series of micron-scale\ngold (0.5 mum thick)/polysilicon(1.5 and 3.5 pm thick) beams and\nplates and initially thermal cycled them between room temperature\nand 190degreesC to stabilize the gold microstructure over this temperature\nrange. After the initial thermal cycle, they are heated to 190degreesC\nwhere they are relatively flat, and then cooled to 120degreesC. During\nthis temperature drop the thin film structures undergo linear and\npossibly geometrically nonlinear deformation depending on their size.\nThey are then held at 120degreesC for about four weeks. During the\nthermal loading history we measured, using interferometry, full-field\ndeformed shapes of the structures, from which curvature was determined.\nDuring the isothermal hold, creep and stress relaxation are observed\nin all of the structures, as manifested in significant curvature\nchanges. We observe that both material and structural phenomena contribute\nto the observed deformation response. The interplay between the two\nis apparent in the plates where the initial cooling caused them to\nbuckle, but the creep and stress relaxation then caused them to substantially\nunbuckle. We attempted to model the inelastic deformation by assuming\nsimple power-law creep in the gold (ε) over circle = Asigma(n),\nand assuming that the polysilicon did not relax at the modest temperature\nof 120degreesC. In order to accurately account for the dependence\nof curvature and stress on position, we carried out the calculations\nusing the finite element method. We find that with such a simple\nmodel we can qualitatively describe all of the observed phenomena,\nhowever, some quantitative discrepancies exist. Finally, we carried\nout a parametric study of the effects of the structure shape and\nthe power-law creep constants on the deformation, and studied the\nevolution of the stress state in the films both through the thickness\nand in the plane of the beams and plates. Regarding the stress state,\ninitially a significant stress gradient exists through the thickness\nof the films. Over time it becomes more uniform, and nearly constant\nin the creeping/relaxing metal film, but the gradient remains in\nthe polysilicon film (that does not creep or relax). (C) 2004 Elsevier\nLtd. All rights reserved.
Creep; Geometric nonlinearity; Microelectrochemical Systems (MEMS); Stress relaxation; Thin film bilayer
On the shape of Cables, Arches, Vaults and Thin Shells
University of Cambridge
1-7
2009
In the Structural Mechanics course, you are taught the basics of the equilibrium shape of a cable under its self-weight. The course material only covers the analysis of cables under a load that is uniformly distributed along the horizontal span of the cable. This assumption holds for shallow cables, i.e. when the span to height ratio is large, and results in a quadratic equation for the equilibrium shape. In reality, however, the shape of a cable is described by a catenary. The calculations for the shape of the catenary of a cable are somewhat involved and will not be discussed here; a derivation is given in Meriam and Kraige (1998, pp. 303). Let it suffice to say that for large span/height ratios, the equations taught in Part IA Structural Mechanics are sufficiently accurate and the shape of shallow cables can be described using a quadratic equation.
FRACTURE TESTING OF NANOSCALE THIN FILMS INSIDE THE TRANSMISSION ELECTRON MICROSCOPE
International Journal of Applied Mechanics
2
4
745-758
2010
10.1142/s1758825110000731
To visualize the fracture mechanisms in nanoscale thin films while measuring their fracture properties, we developed an experimental setup to carry out the experiments in-situ in the transmission electron microscope. The setup includes a 3 mm x 5 mm micro-electromechanical testing chip with actuators and sensors to measure fracture toughness of notched specimens. Fracture experiments were performed on about 125 nm thick freestanding aluminum thin film specimens with average grain size of about 50 nm. The specimens fractured at uniform far field stress of 470 MPa with stress intensity factor of 0.8-1.1 MPa m(1/2). Commonly cited deformation mechanisms, such as dislocation-based plasticity and grain boundary sliding processes were not observed even at the notch tip, where the calculated stress considering the concentration factor exceeded 4 GPa. We propose that for grain sizes below 50 nm, dislocation motion confined at grain boundaries and grain rotation emerge to be significant processes in thin film deformation.
Analytical mechanics of solids
Springer Handbook of Experimental Solid Mechanics
3-15
2008
10.2116/analsci.8.687
In this chapter we consider certain useful fun- damental topics from the vast panorama of the analytical mechanics of solids, which, by itself, has been the subject of several handbooks. The spe- cific topics that are briefly summarized include: elementary theories of material response such as elasticity, dynamic elasticity, viscoelasticity, plas- ticity, viscoplasticity, and creep; and some useful analytical results for boundary value problems in elasticity.
Microcomputer Quantum Mechanics
The Mathematical Gazette
69
448
153
1985
10.2307/3616960
Microcomputer Quantum Mechanics combines the teaching of computing skills with depth of mathematical understanding. This practical text demonstrates how computation can be integrated with theoretical analysis as part of a unified attack on problems in one of the most interesting areas of modern physics. The author discusses the mathematical principles behind the programs and actually creates new methods to facilitate the application of microcomputers in quantum mechanics.
Solving classical mechanics problems by numerical integration of Hamilton's equations.
Am. J. Phys.
54
12
1096+
1986
10.1119/1.14722
The numerical solution of classical mechanics problems is described. The method of solution is by application of a Runge–Kutta formula to Hamilton's equations. Two problems, the elastic pendulum and the compound pendulum, are considered as examples. The use of numerical solutions in teaching mechanics is discussed.
mechanics; numerics; theory
Deformation analysis of thin plate with distributed load by triple-reciprocity boundary element method
Engineering Analysis with Boundary Elements
36
5
772-778
2012
10.1016/j.enganabound.2011.10.008
In general, internal cells are required to solve the deformation of a thin plate with an arbitrary distributed load using a conventional boundary element method (BEM). However, in this case, the merit of the BEM, which is the easy preparation of data, is lost. In this paper, it is shown that the deformation analysis of a thin plate with an arbitrary distributed load can be performed without the use of internal cells using the triple-reciprocity BEM. The distribution of an arbitrary load is interpolated using boundary integral equations. The problem of the thin plate, in accordance with Kirchhoffs theory, is formulated by means of two coupled Poisson equations, which are expressed in integral form using the second theorem of Green in the classical way. A new computer program was developed and applied to several problems. ?? 2011 Elsevier Ltd. All rights reserved.
Boundary element method; Computational mechanics; Shell structure; Thin plate
Molecular Mechanics Calculations and Metal Ion Recognition
Accounts of chemical research
23
13
253-257
1990
10.1021/ar00176a003
A review with 39 refs. The results of authors studies on the relation between the cations size and the stability of a complex with a tetraaza microcycle were examd. and compared with results of mol. mechanics calcns.
Quaternionic quantum mechanics allows non-local boxes
arXiv
1-9
2009
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows one to rule out quaternionic quantum mechanics using assumptions about communication complexity or information causality.
Quantum Physics
Torque-induced deformations of charged elastic DNA rods: thin helices, loops, and precursors of DNA supercoiling.
Journal of biological physics
37
2
227-38
2011
10.1007/s10867-010-9211-7
We study the deformations of charged elastic rods under applied end forces and torques. For neutral filaments, we analyze the energetics of initial helical deformations and loop formation. We supplement this elastic approach with electrostatic energies of bent filaments and find critical conditions for buckling depending on the ionic strength of the solution. We also study force-induced loop opening, for parameters relevant for DNA. Finally, some applications of this nano-mechanical DNA model to salt-dependent onset of the DNA supercoiling are discussed.
buckling instability; dna elasticity; dna electrostatics; dna supercoiling
Interfacial discontinuity relations for coupled multifield phenomena and their application to the modeling of thin interphases as imperfect interfaces
Journal of the Mechanics and Physics of Solids
59
7
1413-1426
2011
10.1016/j.jmps.2011.04.004
Interfacial continuity and discontinuity relations are needed in dealing with a variety of mechanical and physical phenomena in heterogeneous media. The present work consists of two parts. In the first part concerned with perfect interfaces, two orthogonal projection operators reflecting the interfacial continuity and discontinuity of the field variables of coupled mechanical and physical phenomena are introduced and some coordinate-free interfacial relations involving the surface decomposition of a generic linear constitutive law are deduced. In the second part dedicated to the derivation of a general imperfect interface model for coupled multifield phenomena by applying Taylor's expansion to a 3D curved thin interphase perfectly bonded to its two neighboring phases, the interfacial operators and relations given in the first part are used directly so as to render the derivation more direct and to write the final interfacial jump relations characterizing the model in a unified and compact way. The general imperfect interface model obtained in the present work includes as special cases all the relevant ones reported in the literature. © 2011 Elsevier Ltd. All rights reserved.
Adhesion and adhesives; Anisotropic material; Asymptotic analysis; Inhomogeneous material; Interface
Semi-continuous approach for the modeling of thin woven composite panels applied to oblique impacts on helicopter blades
Composites Part A: Applied Science and Manufacturing
43
6
871-879
2012
10.1016/j.compositesa.2012.01.020
In aeronautics, passenger safety and reliability of structures are essential aspects. In the specific case of helicopters, blades are subjected to impact loadings. Modeling these phenomena continue to be difficult and experimental tests often replace the prediction. The following work will focus on the experimental and numerical study of an oblique impact on the skin of the blade. It is equivalent in a first approach to an impact on a sandwich panel made up of a foam core and a thin woven composite skin. The objectives are to identify the mechanisms of damage in the skin for this kind of loading and to develop a representative modeling of the chronology of damage adapted to the modeling of the complete structure. Thus, a semi-continuous F.E. explicit modeling has been developed. It relies on the development of a specific damageable element at the bundles scale. Satisfactory numerical results are obtained. They allow the identification of the damage mechanism of the woven skin. © 2012 Elsevier Ltd. All rights reserved.
A. Fabrics/textiles; B. Impact behavior; C. Damage mechanics; C. Finite element analysis (FEA)
Substrate effects on indentation plastic zone development in thin soft films
Journal of Materials Research
16
11
3150-3157
2001
10.1557/JMR.2001.0434
Plastic zone evolution in Al-2 wt% Si metal films on silicon and sapphire substrates was studied using nanoindentation and atomic force microscopy (AFM). AFM was used to measure the extent of plastic pileup, which is a measure of the plastic zone radius in the film. It was found that the plastic zone size develops in a self-similar fashion with increasing indenter penetration when normalized by the contact radius, regardless of film hardness or underlying substrate properties. This behavior was used to develop a hardness model that uses the extent of the plastic zone radius to calculate a core region within the indenter contact that is subject to an elevated contact pressure. AFM measurements also indicated that as film thickness decreases, constraint imposed by the indenter and substrate traps the film thereby reducing the pileup volume.
deformation; hardness; load; mechanical-properties; microindentation mechanics; microscopy; silicon; single-crystal; wear-resistant coatings; wt-percent-si
'Many Minds'. Interpretations of Quantum Mechanics
The British Journal for the Philosophy of Science
47
2
159-188
1996
10.1093/bjps/47.2.159
Seventy years after the discovery of modern quantum mechanics , there is still no consensus as to how the theory should be understood. The philosophies of Niels Bohr and of the logical positivists, which once served to deter physicists and philosophers from asking ...
Energy–vorticity theory of ideal fluid mechanics
Journal of Atmos. Phys
66
7
2073-2083
2010
Doi 10.1175/2008jas2897.1
... In conclusion, it is argued that on the basis of the energy – vorticity theory of ideal fluid mechanics , new numerical schemes can be constructed, which might be of importance for modeling coherent structures in long-term ... Email: peter . nevir @met.fu-berlin.de. 1. Introduction. ...
Supersymmetry and the quantum mechanics of spin
Nuclear Physics B
314
3
557-586
1989
10.1016/0550-3213(89)90408-2
Bohr-Sommerfeld quantization is exact for a spin in a magnetic field. This well-known result is connected with the existence of a hidden supersymmetry. I discuss the supersymmetry and, in a broader context, the semiclassical quantum-mechanical interpretation of the Weyl character formula for compact, semisimple Lie groups.
Reliability predictions of laminated composite plates with random system parameters
Probabilistic Engineering Mechanics
15
327-338
2000
10.1016/S0266-8920(99)00034-X
Reliability predictions of laminated composite plates with random system parameters subjected to transverse loads are performed using different methods. System parameters such as material properties, layer thicknesses, and lamina strengths of a laminated composite plate are treated as base-line random variables and an appropriate failure criterion is used to construct the limit state equation of the plate in the reliability analysis. Based on the statistics of the base-line random variables obtained from experiments, different methods, namely, Monte Carlo method, ?? method, and first-order second moment, are used to calculate the reliability of the laminated composite plates. In the first-order second moment method, the stochastic finite element method is used to derive for the statistics of the first-ply failure load of the laminated composite plates from those of the base-line random variables. The reliability of the laminated plate is then computed using the theoretically determined statistics together with an assumed probability distribution of the first-ply failure load. The feasibility and accuracy of the different methods are studied by means of the experimental data of centrally loaded laminated composite plates with different lay-ups. The suitability of several commonly used failure criteria for reliability analysis of laminated composite plates is also investigated by means of several examples.
b method; composite laminates; first-ply failure; monte carlo; reliability; stochastic finite element method
Probabilistic Fracture Mechanics Methodology Applied To Pipes Subjected To
Volume 4: Materials Technology; Ocean Engineering
1-8
2007
10.1115/OMAE2007-29345
A probabilistic fracture mechanics procedure for performing the structural reliability analysis of tubes subjected to multiple reeling cycles was developed. This procedure was based on a fracture mechanics approach, a fatigue formulation and the Monte Carlo method. This methodoloy allows the determination of more realistic maximum tolerable defect sizes than those provided by available methodologies presented in standards and recommended practices.
crack growth; fatigue; fracture; mechanics; reeling; structural reliability
Analogy between thermodynamics and mechanics
American Journal of Physics
47
6
488
1979
10.1119/1.11788
We note that equations of state—by which we mean identical relations among the thermodynamic variables characterizing a system—are actually first‐order partial differential equations for a function which defines the thermodynamics of the system. Like the Hamilton‐Jacobi equation, such equations can be solved along trajectories given by Hamilton’s equations, the trajectories being quasistatic processes which obey the given equation of state. This gives rise to the notion of thermodynamic functions as infinitesimal generators of quasistatic processes, with a natural Poisson bracket formulation. This formulation of thermodynamic transformations is invariant under canonical coordinate transformations, just as classical mechanics is, which is to say that thermodynamics and classical mechanics have the same formal structure, namely a symplectic structure.
Isogeometric analysis and Genetic Algorithm for shape-adaptive composite marine propellers
Computer Methods in Applied Mechanics and Engineering
284
835-860
2015
10.1016/j.cma.2014.10.028
This paper presents a layup optimisation algorithm for composite marine propellers, including the hygrothermal effects, using Non-Uniform Rational B-Splines (NURBS) based FEM coupled with real-coded Genetic Algorithm (GA). The use of Iso-Geometric Analysis (IGA) enables accurate representation of complex marine propeller blades, coupled with GA for both continuous and mixed integer ply angle optimisation. The optimisation scheme was further investigated multi-objective, multi-material and multiple layer thickness optimisation scenarios. Furthermore, the IGA-FEM solver was constructed based on constitutive equations that take into account the hygrothermal effects that must be addressed to enable the optimisation of non-symmetric layups. Such non-symmetric layup patterns are proposed to be used to create extension-twist coupling to gain further control in layup optimisation. The optimisation technique is presented here as a method to widen the efficiency envelope of marine propellers. However, the same approach can potentially be adopted to cater many other practical applications such as composite wind turbine blades, aircraft propellers and other general composite ply angle optimisation scenarios. The paper discusses the proposed framework for optimisation of marine propeller, numerical tools used in the process and results under different conditions.
Composite ply optimisation; Genetic Algorithm; Hygrothermal effects; Isogeometric analysis; Marine propeller
Secondary instability and mode jumping analysis of deep hygrothermally buckled cross-ply laminated plates
Composite Structures
117
244-254
2014
10.1016/j.compstruct.2014.06.037
An analytical investigation is performed to study the secondary instability and dynamic aspects of the mode jumping in hygrothermally buckled cross-ply laminated plates. The governing partial differential equations (PDEs) and constitution relations are derived rigorously from an asymptotically correct, geometrically nonlinear theory. A novel and relatively simpler solution approach is developed to solve the two coupled fourth-order PDEs, namely, the compatibility equation and the dynamic governing equation. The von Kàmàn plate equation, namely, the coupled nonlinear governing equation, is reduced to a system of nonlinear ordinary differential equations (ODEs) by expressing the transverse deflection as a series of linear buckling modes. The ODEs, combined with the non-linear algebraic constraint equations obtained from in-plane boundary conditions, are then solved numerically under the parametric variation of the temperature and moisture. The comparison between the present method and the FEA shows that the secondary bifurcation point of the hygrothermally loaded plate is far beyond the primary buckling point, and the jump behavior cannot be predicted correctly without sufficient assumed modes, while the present method has the capability of exploring deeply into the post-secondary buckling realm and capturing the mode jumping phenomenon for various combinations of plate configurations boundary conditions. Furthermore, by monitoring free vibration along the stable primary postbuckling and the jumped equilibrium paths, we find that a mode shifting phenomenon (the exchange of vibration modes) exists in the primary post-buckling regime.
Deep hygrothermally buckled; Laminated plates; Mode jumping; Secondary instability; Variational asymptotic method
Modeling the plastic response of thin metal membranes
Journal of the Mechanics and Physics of Solids
54
11
2474-2494
2006
10.1016/j.jmps.2006.04.010
Using a dislocations-based model of slip and crystal plasticity, we show by illustrative examples that the experimentally observed increase in the yield stress of very thin metallic membranes most likely is due to the variation of grain orientations through the thickness of the membrane, as well as the surface hardness due to oxidation or contamination, both of which generally are insignificant when there is a sufficient number of interior crystals through the membrane thickness; the overall effect may well be produced by a combination of these two causes. We show that crystal plasticity models can account for such size effects without a need for resorting to phenomenological strain-gradient models. We illustrate this using Nemat-Nasser's dislocations-based slip-induced crystal plasticity model that inherently includes length scales, although other rate-dependent slip models, e.g., the classical power-law slip model, most likely would qualitatively produce similar results. Our numerical results, based on the experimentally supported dislocation-induced slip model and the values of the model parameters given in Nemat-Nasser and Li [1998. Flow stress of F.C.C. polycrystals with application to OFHC Cu. Acta Mater. 46, 565-577], correlate well, both qualitatively and quantitatively, with the experimental results reported by Hommel and Kraft [2001. Deformation behavior of thin copper films on deformable substrates. Acta Mater. 49, 3935-3947] and Espinosa et al. [2004. Plasticity size effect in free-standing submicron polycrystalline FCC films subjected to pure tension. J. Mech. Phys. Solids 52, 667-689] for thin copper membranes, suggesting that, for submicron-sized samples, the classical crystal plasticity with slip models, does qualitatively account well for the small-size effects, and that quantitative predictions are obtained when, in addition, a physics-based dislocation model that includes length scales, is used. It is thus concluded that the length-scale effect and the size effect are two separate issues in metal plasticity, both of which are nicely accounted for by physics-based dislocation models of crystal plasticity without a need to include the plastic strain gradient.
Crystal plasticity; Metallic membranes; Polycrystalline material; Size effect
Experimental considerations for indentation-induced adhesion measurement of multilayered thin films
Materials Research Society Symposium - Proceedings
522
Warrendale, PA, United States
365-370
1998
Nanoindentation of thin films is an especially attractive technique for the quantitative assessment of the adhesion energy of thin films, in that the film can be measured in the as-processed condition with almost no sample preparation. Linear elastic fracture mechanics calibrations have been previously developed to quantify the strain energy release rate as a function of film properties, film residual stress and indentation volume. However, this test is limited by the practical difficulty of producing a suitable delamination for either strong interfaces or ductile films. Modified mechanics suitable for a multilayer film have recently been developed. One particularly useful application of this calibration is discussed, namely the use of a highly stressed refractory superlayer that acts to promote delamination of the underlying film (assuming said interface is the weaker). Delamination is ensured by triggering the fracture process through nanoindentation. Such superlayers can be deposited over the as-processed film of interest, producing no significant changes in that film's microstructure or interfacial character. Experimental results using this method are reviewed with particular attention to experimental consideration, along with recent results using copper and tungsten thin films on SiO2.
Adhesion; Delamination; Elasticity; Fracture mechanics; Interfaces (materials); Microstructure; Multilayers; Nanoindentation; Residual stresses; Strain rate; Thin films
The application of a homogenized overall and local anisotropic damage constitutive model to unidirectional and cross-ply CFCC with oblique loading directions
Composite Structures
68
309-317
2005
10.1016/j.compstruct.2004.03.024
A homogenized anisotropic damage constitutive model is proposed to describe the mechanical behavior of continuous fiber-reinforced ceramic matrix composites (CFCC) for different loadings direction and laminate stacking sequences. An overall fourth-order damage effect tensor is introduced to account for the overall damage of the composites. In addition, two local (matrix and fiber) fourth-order damage effect tensors are introduced to analyze the local effects of damage experienced in both matrix and fibers. The overall and local damage tensors are correlated through a homogenization procedure. New expressions are derived for the stress and strain concentration factors of the damaged composite. The model is simulated by macro-microscopic finite element method (FEM). As applications of the model, unidirectional and cross-ply CFCC laminates with oblique loading directions are analysed to discuss the effects of fiber arrangement and orientation on the macroscopic mechanical behavior. ?? 2004 Elsevier Ltd. All rights reserved.
Anisotropic damage; Continuous fiber-reinforced ceramic matrix composi; Homogenization theory
Mechanical properties and oxidation resistance of C-B-Si coated silicon nitride fiber reinforced Si-N-C composites with cross-ply structure
Composites Part A: Applied Science and Manufacturing
30
577-581
1999
10.1016/S1359-835X(98)00152-3
To enhance the oxidation resistance of a ceramic matrix composite, a C-B-Si interface layer was applied between the fiber and the matrix. The layer was deposited on the fiber by chemical vapor deposition. Three types of coatings were prepared: A1, A2 (multilayers of graphite layer/B-C-Si crystalline layer/graphite layer) and B1 (monolayer of B and C containing graphite). The multilayer coated CMC retained 88-97% of the original strengths after oxidation at 1523 K for 36 ks. The monolayer coated CMC degraded to 55% of its original strength after oxidation, but had a high fracture toughness (28 MPa m\n 1/2) before oxidation. The differences of the oxidation resistance and fracture toughness were discussed in relation to the microstructure of the coatings.
amorphous si; b; c; ceramic composite; cross-ply structure; mechanical properties; n; oxidation resistance
Exact vibration solutions for cross-ply laminated plates with two opposite edges simply supported using refined theories of variable order
Journal of Sound and Vibration
333
8
2347-2359
2014
http://dx.doi.org/10.1016/j.jsv.2013.12.007
This paper presents exact solutions for free vibration of rectangular cross-ply laminated plates with at least one pair of opposite edges simply supported using refined kinematic theories of variable order. Exact natural frequencies are obtained using an efficient and unified formulation where the solving set of second-order differential equations of motion and related boundary conditions are expressed at layer level in terms of so-called fundamental nuclei having invariant properties with respect to the order of the plate theory. The nuclei are then appropriately expanded according to the number of layers and the order of the theory and the resulting equations are transformed into a first-order model whose solution is obtained by using the state space concept. In this way, the mathematical effort needed to derive analytical solutions is highly reduced. Both higher-order equivalent single-layer and layer-wise theories are considered in this study. Comparisons with other exact solutions are presented and useful benchmark frequency results for symmetric and un-symmetric cross-ply laminates are provided.
A QUICKSTEP-based quantum mechanics/molecular mechanics approach for silica.
The Journal of chemical physics
124
15
154707
2006
10.1063/1.2187485
Quantum mechanics/molecular mechanics (QM/MM) approaches are currently used to describe several properties of silica-based systems, which are local in nature and require a quantum description of only a small number of atoms around the site of interest, e.g., local chemical reactivity or spectroscopic properties of point defects. We present a QM/MM scheme for silica suitable to be implemented in the general QM/MM framework recently developed for large scale molecular dynamics simulations, within the QUICKSTEP approach to the description of the quantum region. Our scheme has been validated by computing the structural and dynamical properties of an oxygen vacancy in alpha-quartz, a prototypical defect in silica. We have found that good convergence in the Si-Si bond length and formation energy is achieved by using a quantum cluster of only eight atoms in size. We check the suitability of the method for molecular dynamics and evaluate the Si-Si bond frequency from the velocity-velocity correlation function.
A model to predict the planar electrical potential distribution in cross-ply carbon-fiber composites subjected to alternating magnetic fields
Composites Science and Technology
49
71-80
1993
10.1016/0266-3538(93)90023-A
Mechanisms of heat generation and distribution in carbon-fiber-based composites subjected to an alternating magnetic field are considered. A model is developed and verified which predicts the strength and distribution of these mechanisms in the plane of cross-ply laminates. In this analysis, the fibers in a cross-ply laminate are treated as a grid of conductive loops in the plane. Each such conductive loop uses the alternating magnetic field to produce a rotational electromotive force that induces electric fields in the polymeric regions. Induced electromagnetic energy is converted into thermal energy through dielectric losses in polymeric regions between the carbon fibers in the adjacent orthogonal plies that comprise the conductive loops. Each possible conductive loop is accounted for and the resulting superposition of potential differences at the nodes leads to the in-plane profile of the electric field in the polymeric regions. Data from AS4-graphite-reinforced poly(ether ether ketone) laminate surface temperature measurements using liquid crystal sheets are compared qualitatively with the theory.
carbon fiber; composites; dielectric heating; ether ether ketone; induction heating; laminated; modelling; poly
High-performance two-ply yarn supercapacitors based on carbon nanotube yarns dotted with Co3 O4 and NiO nanoparticles.
Small (Weinheim an der Bergstrasse, Germany)
11
7
854-61
2015
10.1002/smll.201401862
Yarn supercapacitors are promising power sources for flexible electronic applications that require conventional fabric-like durability and wearer comfort. Carbon nanotube (CNT) yarn is an attractive choice for constructing yarn supercapacitors used in wearable textiles because of its high strength and flexibility. However, low capacitance and energy density limits the use of pure CNT yarn in wearable high-energy density devices. Here, transitional metal oxide pseudocapacitive materials NiO and Co3 O4 are deposited on as-spun CNT yarn surface using a simple electrodeposition process. The Co3 O4 deposited on the CNT yarn surface forms a uniform hybridized CNT@Co3 O4 layer. The two-ply supercapacitors formed from the CNT@Co3 O4 composite yarns display excellent electrochemical properties with very high capacitance of 52.6 mF cm(-2) and energy density of 1.10 μWh cm(-2) . The high performance two-ply CNT@Co3 O4 yarn supercapacitors are mechanically and electrochemically robust to meet the high performance requirements of power sources for wearable electronics.
Fatigue behavior of cross-ply glass-fiber epoxy composites including the effect of fiber-matrix interphase
Composite Interfaces
7
4
287-299
2000
10.1163/156855400750244996
The effect of glass-fiber epoxy interface in cross-ply reinforced composites on the fatigue behavior is studied throughout this paper. The sensitivity of the interphase on fatigue life of cross-ply laminates is shown by a shift of the S-N curve to approx. 30% higher applied maximum loads for the composites with well-bonded fibers. Further, the damage as measured by stiffness reduction is more significant for the composites with poor bonded and commercial sized fibers than was found for EP sized ones. The loss energy is shown to be a sensitive tool to characterize the nature of fiber-matrix adhesion. The loss energy for composites with poor adhesion between fiber and matrix results in significantly higher amounts of consumed energy during a single stress-strain than those composites containing well-bonded fibers.\nThe effect of glass-fiber epoxy interface in cross-ply reinforced composites on the fatigue behavior is studied throughout this paper. The sensitivity of the interphase on fatigue life of cross-ply laminates is shown by a shift of the S-N curve to approx. 30% higher applied maximum loads for the composites with well-bonded fibers. Further, the damage as measured by stiffness reduction is more significant for the composites with poor bonded and commercial sized fibers than was found for EP sized ones. The loss energy is shown to be a sensitive tool to characterize the nature of fiber-matrix adhesion. The loss energy for composites with poor adhesion between fiber and matrix results in significantly higher amounts of consumed energy during a single stress-strain than those composites containing well-bonded fibers.
Thin Shock-Layer Theory Revisited
4th AIAA Theoretical Fluid Mechanics Meeting
AIAA 2005-5194
2005
During the hypersonics activities of the 1960s, thin shock-layer theory was developed as a First-order correction to Newtonian theory, in the hope of gaining insightinto effcient lift at very high speeds. The wings are limited to conical geometry, but can have arbitrary transverse camber. Good predictions were made of the forces generated by delta and caret wings, but no optimization studies were carried out. This paper collects together some old results, including some that were not widely published, establishes a parameter that measures hypersonic lifting effciency, and presents a wing design that achieves a very high value of that parameter.
Direct method for life prediction of fibre reinforced polymer composites based on kinematic of damage potential
International Journal of Fatigue
70
289-296
2015
10.1016/j.ijfatigue.2014.10.004
In this paper, a direct computational method of life prediction for fibre-reinforced polymers (FRP) is developed. This approach is based on a simplified direct method (SDM) which allows to predict the life from the stabilized damage state. The SDM is extended to the case of anisotropic continuous damage mechanics of FRP. It is shown that damage processes in composite material subjected to fatigue load can reach stabilized damage state. Damage state and thermodynamic forces associated with damage mechanisms at the stabilized state are related to life. Experimental validation was done on the standard glass-fibre/epoxy angle-ply and cross-ply laminate plates subjected to fatigue loading with different load ratios (R=0.1,0.5).
matrix composites; pmcs; polymer
Fatigue simulation for titanium/CFRP hybrid laminates using cohesive elements
Composites Science and Technology
69
11-12
1968-1973
2009
10.1016/j.compscitech.2009.04.020
Hybrid laminates made of polymer matrix composite plies with a metal sheet are called fiber metal laminates (FMLs). This study presents a new numerical approach for examining the fatigue damage progress in FMLs. A layer-wise finite element along with a cohesive element are used to predict the fatigue damage progress for splitting, transverse cracking and delamination. Four-node cohesive elements are introduced to express 0 degrees ply splitting and transverse cracking. Eight-node cohesive elements are inserted into the ply interfaces to represent delamination. The most important character of this model is that the proposed simulation introduces a damage-mechanics concept into the degradation process in cohesive elements in order to express the damage progress due to cyclic loading. This enables us to address the complicated fatigue damage process observed in a FML. We applied this model to titanium/glass fiber-reinforced plastic (Ti/GFRP) laminates and compared the simulated results with the experiment data reported in the references. We confirmed that this model can reproduce the fatigue damage process in a FML. The effect of the parameters of the cohesive element on Ti crack growth and the delamination profile were also investigated. The Ti crack-growth rate was found to be strongly associated with the delamination profile near the crack tip. (C) Koninklijke Brill NV, Leiden, 2010
a; hybrid composites
A spectrally formulated plate element for wave propagation analysis in anisotropic material
Computer Methods in Applied Mechanics and Engineering
194
42-44
4425-4446
2005
10.1016/j.cma.2004.12.003
A new spectrally formulated plate element is developed to study wave propagation in composite structures. The element is based on the classical lamination plate theory. Recently developed method based on singular value decomposition (SVD) is used in the element formulation. Along with this, a new strategy based on the method of solving polynomial eigenvalue problem (PEP) is proposed in this paper, which significantly reduces human intervention (and thus human error), in the element formulation. The developed element has an exact dynamic stiffness matrix, as it uses the exact solution of the governing elastodynamic equation of plate in frequency-wavenumber domain as the interpolating functions. Due to this, the mass distribution is modeled exactly, and as a result, a single element captures the exact frequency response of a regular structure, and it suffices to model a plate of any dimension. Thus, the cost of computation is dramatically reduced compared to the cost of conventional finite element analysis. The fast Fourier transform (FFT) and Fourier series are used for inversion to time-space domain. This element is used to model plate with ply drops and to capture the propagation of Lamb waves. ?? 2004 Elsevier B.V. All rights reserved.
CLPT; High frequency; Lamb wave; PEP; Ply-drop; SVD
Supersymmetric Mechanics - Vol. 2
Nature
21
529
viii, 243
2006
10.1038/021153a0
This is the first volume in a series of books on the general theme of Supersymmetric Mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the INFN-Laboratori Nazionali di Frascati. This volume supplies a pedagogical introduction, at the non-expert level, to the attractor mechanism in space-time singularities. After a qualitative overview, explicit examples realizing the attractor mechanism are treated at length.
Statistical mechanics of a nonlinear model for DNA denaturation
Physical Review Letters
62
23
2755-2758
1989
10.1103/PhysRevLett.62.2755
We investigate the statistical mechanics of a simple lattice model for the denaturation of the DNA double helix.
Overview of interfacial fracture energy predictions for stacked thin films using a four-point bending framework
Surface and Coatings Technology
237
333-340
2013
10.1016/j.surfcoat.2013.06.127
Developing a robust predicting methodology on the interfacial fracture energy of dissimilar materials is urgently needed to meet the mechanical strength requirements for investigating novel materials and subsequent device structures with the bonded types of multi thin films. Thus, this paper provides an overview of useful approaches according to linear-elastic interfacial fracture mechanics, such as J-integral method, modified virtual crack closure technique (MVCCT), and analytical solutions derived from the relationship between the stress field of delaminated tip and crack tip opening displacements to compare their estimated capability of cracking energy. A popular technique for determining the interface adhesion of thin coatings is the four-point bending test (4-PBT). The testing vehicles of 4-PBT allow a more thorough validation of the foregoing predicted approaches based on finite element analysis compared with the simulated results with related experimental data. The critical energies of 18J/m2, 78.53J/m2, 52.01J/m2, and 71.02J/m2 for the bonded interfaces of SiO2/SiLK, Ta/SiLK, TaN/SiLK, and Si3N4/SiLK stacked nano-scaled thin films are precisely judged, respectively. The predicted results of the J-integral method match well with the MVCCT estimation. The results reveal that the opening fractured mode is dominant at the beginning of the crack advances along the bonded interface of Ta/SiLK, TaN/SiLK, and Si3N4/SiLK stacked films as the interfacial crack length increases. Moreover, the essential trends of dependences for the modulus ratio and thickness ratio of stacked thin films on interfacial energy release rate are logically identified and investigated. Therefore, this paper could be regarded as a design guideline of interfacial fracture behavior for stacked films utilized in the development of advanced device technologies. ?? 2013 Elsevier B.V.
Finite element analysis (FEA); Four-point bending test; Interfacial adhesion; J-integral; Virtual crack closure technique
Concrete-filled thin-walled steel SHS and RHS beam-columns subjected to cyclic loading
Thin-Walled Structures
41
9
801-833
2003
10.1016/S0263-8231(03)00030-2
The flexural force-deformation behavior of concrete-filled thin-walled steel SHS and RHS beam-columns was experimentally investigated and the results presented in this paper. The parameters in the study included the depth-to-width ratio (??), the core concrete strength (fcu), and the axial load level (n). Thirty concrete-filled thin-walled steel SHS and RHS beam-column specimens were tested under constant axial load and cyclically increasing flexural loading. A mechanics model is developed in this paper for concrete-filled steel SHS and RHS columns subjected to constant axial load and cyclically increasing flexural loading, and is a development of the analysis used for monotonically loading condition (Han et al., 2001). The predicted cyclic responses for the composite columns are in good agreement with test results. Based on the theoretical model, parametric analysis was performed on the behaviors of moment (M) versus curvature (??) response, lateral load (P) versus lateral displacement (??) relationship, as well as ductility coefficient (??) for the composite beam-columns. Finally, simplified models for the moment (M) versus curvature (??) response, and the lateral load (P) versus lateral displacement (??) relationship were suggested. Formula should be suitable for incorporation into building code, for the calculation of the ductility coefficient (??) of the composite beam-columns under constant axial load and cyclically increasing flexural loading was developed. ?? 2003 Elsevier Science Ltd. All rights reserved.
Composite beam-columns; Concrete; Cyclic load; Ductility; Hollow sections; Hysteresis models; Seismic design; Strength; Thin-walled structure
Statistical Mechanics: Theory and Molecular Simulation
New York
713
2010
Statistical mechanics is a theoretical framework that aims to predict the observable static and dynamic properties of a many-body system starting from its microscopic constituents and their interactions. Its scope is as broad as the set of “many-body” systems is large: as long as there exists a rule governing the behavior of the fun- damental objects that comprise the system, the machinery of statistical mechanics can be applied. Consequently, statistical mechanics has found applications outside of physics, chemistry, and engineering, including biology, social sciences, economics, and applied mathematics. Because it seeks to establish a bridge between the microscopic and macroscopic realms, statistical mechanics often provides a means of rationalizing observed properties of a system in terms of the detailed “modes of motion” of its basic constituents.
Computational fracture mechanics: research and application
Engineering Fracture Mechanics
50
5-6
653–670
1995
10.1016/0013-7944(94)E0051-H
This paper focuses on the impact of computational methodology on furthering the understand- ing of fundamental fracture phenomena. The current numerical approaches to the solution of fracture mechanics problems, e.g. finite element (FE) methods, finite difference methods and boundary element methods, are reviewed. The application of FE methods to the problems of linear elastic fracture problems is discussed. Particular emphases are placed on the stress intensity factors, energy release rate in mixed mode fracture and dynamic crack propagation. Numerical solutions of ductile fracture problems are surveyed. A special focus is placed on stable crack growth problems. The need for further research in this area is emphasized. The importance of large strain phenomena and accurate modeling of non-linearities is highlighted. An expanded version of fracture mechanics methodology is given by Liebowitz [Advances in Fracture Research 3. Pergamon Press, Oxford (1989)]; additional treatment is given in this paper to numerical results incorporating error estimates and algorithms for mesh design into the FE code. The adaptive method involves various stages which includes FE analysis, error estimation/indication, mesh refinement and fracture/failure analysis iteratively. Reference is made to integrate expert knowledge and a hierarchial, rule-based, decision process to fracture mechanics for the purpose of designing practical fracture-proof engineering products. Some further areas of research in adaptive finite element analysis are discussed.
Classical mechanics
American Journal of Physics
2002
The section on the formulation has been shortened. I anticipate continuing to refer students to Slater and Frank’s for a lucid
Viscoelastic free surface flows: thin film hydrodynamics of Hele-Shaw and dip coating flows
Journal of Non-Newtonian Fluid Mechanics
57
2–3
203-225
1995
http://dx.doi.org/10.1016/0377-0257(94)01329-G
The effect of elasticity on the meniscus shape and film thickness for the free boundary creeping flow created by injecting air to a Hele-Shaw cell initially filled with a viscoelastic fluid is studied theoretically. The theory is developed with the assumptions that the displaced viscoelastic fluid wets the walls and that capillary number Ca and the local Weissenberg number We are both small. The transition region between the advancing meniscus and the entrained film is where the fluid rheology has its greatest effect. The Oldroyd-B constitutive equation is used to model the viscoelastic fluid. The theory is formulated as a double expansion in Ca13 and WeCa13. According to our asymptotic analysis, as the fluid becomes more viscoelastic, the film thickness decreases and the pressure drop at the meniscus tip increases. A detailed analysis shows that the dominant mechanisms are the resistance to stream-wise strain, tending to lower the film thickness, and the buildup of shear stress, tending to raise the film thickness, with the former being the numerically larger of the two. Our theory leads to the prediction that as viscoelasticity comes to dominate the shear resistance, the film thickness will scale with U43. The effects of shear thinning and normal stress thinning are analyzed by adapting an approximate model obtained by retaining only the dominant terms in the force balance. Our Hele-Shaw cell theory is extended to dip coating and soap film forming flows. Our theoretical results pertaining to the effects of viscoelasticity on the thickness of the film are in qualitative agreement with recent experimental data.
Thin film hydrodynamics; Viscoelastic free surface flows
The mechanics of human smooth pursuit eye movement
The Journal of physiology
180
3
569-591
1965
VL - 180
Page 1. ;180;569-591 . . DA movement. The mechanics of human smooth pursuit eye This information is current as of March 10, 2008
Effect of a hard coat layer on buckle delamination of thin ITO layers on a compliant elasto-plastic substrate: An experimental-numerical approach
Engineering Fracture Mechanics
78
6
877-889
2011
10.1016/j.engfracmech.2011.01.013
Layer buckling and delamination is a common interfacial failure phenomenon in thin film multi-layer structures that are used in flexible display applications. Typically, the substrate is coated on both sides with a hybrid coating, called a hard coat (HC), which acts as a gas barrier and also increases the scratch resistance. In this paper 250nm thick indium tin oxide (ITO) layers have been deposited on a 200μm thick high temperature aromatic polyester substrate (AryliteTM), with and without a 3μm HC. In order to study the influence of this HC layer on delamination phenomena, two-point bending experiments are performed from which buckle width and height values are measured after straightening of the sample. An analytical model and a finite element (FE) model are developed to estimate the adhesion properties from the measured buckle geometries. In the numerical model, the initiation and propagation of the delamination process is described by cohesive zone elements, of which the parameters are extracted from response surface model (RSM) results. Furthermore, the numerical model is used to illustrate the significant change in buckle geometry upon load reversal, i.e. from loaded to straightened state, which is governed by the elasto-plastic behavior of the substrate material. It is concluded that the addition of a HC layer significantly decreases the adhesion of the ITO layer. The latter is determined as function of the actual mode angle. © 2011 Elsevier Ltd.
Buckling; Cohesive zone modeling; Delamination; Finite element analysis; Flexible electronics; Interface adhesion; Thin films
Statistical mechanics of random graphs
Physica A: Statistical Mechanics and its Applications
344
56-61
2004
10.1016/j.physa.2004.06.087
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications. © 2004 Elsevier B.V. All rights reserved.
Clustering; Complex networks; Monte Carlo method
Bohmian mechanics and the meaning of the wave function
arXiv preprint quant-ph/9512031
1-15
1995
We outline how Bohmian mechanics works: how it deals with various issues in the foundations of quantum mechanics and how it is related to the usual quantum formalism. We then turn to some objections to Bohmian mechanics, for example the fact that in Bohmian mechanics there is no back action of particle configurations upon wave functions. These lead us to our main concern: a more careful consideration of the meaning of the wave function in quantum mechanics, as suggested by a Bohmian perspective. We propose that the reason, on the universal level, that there is no action of configurations upon wave functions, as there seems to be between all other elements of physical reality, is that the wave function of the universe is not an element of physical reality. We propose that the wave function belongs to an altogether different category of existence than that of substantive physical entities, and that its existence is nomological rather than material. We propose, in other words, that the wave function is a component of physical law rather than of the reality described by the law.
The specific heat of thin films near the λ-transition: a Monte Carlo study of an improved three-dimensional lattice model
Journal of Statistical Mechanics: Theory and Experiment
2009
10
P10006
2009
10.1088/1742-5468/2009/10/P10006
We study the finite size scaling behaviour of the specific heat of thin films in the neighbourhood of the λ-transition. To this end we have simulated the improved two-component ##IMG## [http://ej.iop.org/icons/Entities/phi.gif] {phi} 4 model on the simple cubic lattice. We employ free boundary conditions in the short direction to mimic the vanishing order parameter at the boundaries of a 4 He film. Most of our simulations are performed for the thicknesses L 0 = 8, 16 and 32 of the film. It turns out that one has to take into account corrections ##IMG## [http://ej.iop.org/images/1742-5468/2009/10/P10006/jstat331836ieqn1.gif] {{\propto } L_0^{-1}} to obtain a good collapse of the finite size scaling functions obtained from different L 0 . Our results are compared with those obtained from experiments on thin films of 4 He near the λ-transition, from field theory and from previous Monte Carlo simulations.
0904; 1535; arxiv eprint; classical monte carlo simulations; classical phase transitions; finite-size scaling; surface effects; theory
A local point interpolation method for static and dynamic analysis of thin beams
Computer Methods in Applied Mechanics and Engineering
190
42
5515-5528
2001
10.1016/S0045-7825(01)00180-3
The local point interpolation method (LPIM) is a newly developed truly meshless method, based on the idea of meshless local Petrov–Galerkin (MLPG) approach. In this paper, a new LPIM formulation is proposed to deal with fourth-order boundary-value and initial-value problems for static and dynamic analysis (stability, free vibration and forced vibration) of beams. Local weak forms are developed using weighted residual method locally. In order to introduce the derivatives of the field variable into the interpolation scheme, a technique is proposed to construct polynomial interpolation with Kronecker delta function property, based only on a group of arbitrarily distributed points. Because the shape functions so-obtained possess delta function property, the essential boundary conditions can be implemented with ease as in the conventional finite element method (FEM). The validity and efficiency of the present LPIM formulation are demonstrated through numerical examples of beams under various loads and boundary conditions.
Dynamic analysis; Meshless method; Static analysis; Strong formulation; Weak formulation
Buckling of composite columns of lipped-channel and hat sections with web stiffener
Thin-Walled Structures
47
11
1149-1160
2009
10.1016/j.tws.2009.04.011
The buckling of thin-walled composite columns in hat sections and lipped-channel sections reinforced with web stiffener is studied. The columns were composed of symmetric angle-ply laminates. The finite element method was used to investigate the buckling behaviour of the columns. Bifurcation analyses were carried out to obtain the buckling load and mode shapes of the columns. Load-deflection analyses were performed to study the post-buckling behaviour of the columns. The results showed significant effects of ply angle and geometric parameters on the buckling and post-buckling behaviour of the columns. This research provides a guide for improving the loading capacity of composite columns.
Buckling; Composite column; Finite element method; Ply angle; Web stiffener
Understanding Quantum Mechanics
American Journal of Physics
37
11
1165
1969
10.1119/1.1975253
Here Roland Omnès offers a clear, up-to-date guide to the conceptual framework of quantum mechanics. In an area that has provoked much philosophical debate, Omnès has achieved high recognition for his Interpretation of Quantum Mechanics (Princeton 1994), a book for specialists. Now the author has transformed his own theory into a short and readable text that enables beginning students and experienced physicists, mathematicians, and philosophers to form a comprehensive picture of the field while learning about the most recent advances. This new book presents a more streamlined version of the Copenhagen interpretation, showing its logical consistency and completeness. The problem of measurement is a major area of inquiry, with the author surveying its history from Planck to Heisenberg before describing the consistent-histories interpretation. He draws upon the most recent research on the decoherence effect (related to the modern resolution of the famous Schrödinger's cat problem) and an exact formulation of the correspondence between quantum and particle physics (implying a derivation of classical determinism from quantum probabilism). Interpretation is organized with the help of a universal and sound language using so-called consistent histories. As a language and a method, it can now be shown to be free of ambiguity and it makes interpretation much clearer and closer to common sense.
A failure model for the analysis of thin woven glass composite structures under impact loadings
Computers & Structures
79
8
785-799
2001
10.1016/S0045-7949(00)00190-5
A progressive damage model for a woven glass fibre fabric reinforced with epoxy composite was developed and implemented into a well known explicit Lagrangian finite element code. The approach uses a novel damage mechanics formulation to predict in-plane damage in a woven fabric composite defined by matrix cracks and fibre fracture in the warp and weft directions. The model uses a stress based energy dissipation approach and an advanced post failure strain softening methodology. Strain-rates effects, which are commonly observed for woven glass composites are modelled using a damage lag formulation within the constitutive model. Results are compared with laboratory experiments and full-scale tests. The comparisons indicate that the damage model can predict with reasonable accuracy the damage modes observed in both the laboratory and full-scale experiments. Conclusions are presented also on the logical extensions to the damage formulation.
Statistical mechanics of multipartite entanglement
Distribution
42
2
2-5
2008
We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.
Information Theory and Statistical Mechanics
The Physical Review
108
2
171–190
1957
Information Theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on a given information; i.e., it is maximally noncomittal with regard to missing information.
Buckle-driven delamination of thin film and the influence of the Casimir or van der Waals force interaction
HDP'04
128-133
2004
10.1109/hpd.2004.1346685
Indentation test is becoming increasingly used to quantitatively assess the thin film interfacial adhesion for its simplicity and ability to mechanically probe the smallest of solids. The conventional technique is based on the analysis of a combination of Linear Elastic Fracture Mechanics (LEFM) and simplified post-buckling theory. In this paper a full post-buckling response of thin film is investigated by FEM calculation; the contributions of double-buckling to the indenatation test is discussed. The results show that the double-buckling needs more energy than single-buckling case thus lead to a greater value of strain energy release rate. Finally, the influences of the Casimir or can der Waals interaction on the post-buckling behavior between the thin film and substrate are considered.
buckling; crack; Delamination; fracture mechanics; indentation test; interface; model
TRAPPED WAVES OVER SYMMETRICAL THIN BODIES
JOURNAL OF FLUID MECHANICS
223
509-519
1991
Explicit relations are derived for the dependence of the longshore wavenumber on the wave frequency of symmetric trapped waves or edge waves travelling near the cutoff frequency over submerged horizontally symmertric thin bodies or near-vertical Results for particular geometries are presented and shown to agree with certain explict solutions for edge waves over sloping beaches or trapped waves over a submerged narrow shelf, or a semicircular mound on the sea bed. Similar results are obtained for thin bodies extending vertically throughout the depth in open channels or for thin cross-sections in an acoustic wave guide.
SURFACE-WAVES
Quantum mechanics is about quantum information
Foundations of Physics
35
4
541-560
2005
10.1007/s10701-004-2010-x
I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive -- just as, following Einstein's special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right.
Entanglement; Foundations of quantum mechanics; Quantum information; Quantum measurement
Fatigue crack constraint in plain-woven CFRP using newly-developed spread tows
International Journal of Fatigue
28
10 SPEC. ISS.
1248-1253
2006
10.1016/j.ijfatigue.2006.02.010
This paper discusses the fatigue behavior of a new type plain-woven CF/epoxy composite (CFRP) using very thin and wide tows called as "spread tows". Tension-tension fatigue tests were conducted and internal damage was observed by using an optical microscope. The experimental results showed that the fatigue lives of plain-woven CFRP using spread tows were longer than those of conventional plain-woven CFRP. As the fatigue tests were conducted at cyclic maximum stress of 600 MPa, we could not observe any crack in the new type plain-woven CFRP subjected to 106 cyclic loads. At cyclic maximum stress of 800 MPa, we could not observe any crack at the narrow weft part (about 0.05 mm thickness). It was found that fatigue crack formation and propagation criterion was affected by tow thickness. The cross-over point between the spread tows was regarded as (0/90)s cross-ply laminate and the ply failure strain was calculated. As a calculation result, it was clarified that fatigue crack formulation and propagation was constrained by using spread tows. Thereby, fatigue lives of the composites were improved compared with those of conventional plain-woven fabric composites. ?? 2006 Elsevier Ltd. All rights reserved.
CFRP; Composites; Fatigue; Fatigue crack constraint; Plain-woven fabric; Spread tow
Human respiratory mechanics demonstration model.
Advances in physiology education
33
1
53-59
2009
10.1152/advan.90177.2008
Respiratory mechanics is a difficult topic for instructors and students alike. Existing respiratory mechanics models are limited in their abilities to demonstrate any effects of rib cage movement on alveolar and intrapleural pressures. We developed a model that can be used in both large and small classroom settings. This model contains digital pressure displays and computer integration for real-time demonstration of pressure changes that correspond to the different phases of breathing. Moving the simulated diaphragm and rib cage causes a volume change that results in pressure changes visible on the digital sensors and computer display. Device testing confirmed the model's ability to accurately demonstrate pressure changes in proportion to physiological values. Classroom testing in 427 surveyed students showed improved understanding of respiratory concepts (P < 0.05). We conclude that our respiratory mechanics model is a valuable instructional tool and provide detailed instructions for those who would like to create their own.
Arrival time in quantum mechanics
Physics Reports
338
4
353-438
2000
10.1016/S0370-1573(00)00047-8
The arrival time is a simple classical concept, very common in laboratory practice. This review describes theoretical problems encountered in trying to obtain a quantum mechanical counterpart and the solutions proposed. A summary of current experimental techniques is also included.
Research directions in computational mechanics
Computer Methods in Applied Mechanics and Engineering
192
7-8
913-922
2003
10.1016/S0045-7825(02)00616-3
This article is derived from a report prepared by the US National Committee on Theoretical and Applied Mechanics. It is part of that committee's agenda to develop position papers on research directions in various areas of mechanics. This is the most recent work devoted to computational mechanics. The report was authored by a subcommittee consisting of Tinsley Oden (Chair), Ted Belytschko, Ivo Babuska and Thomas Hughes. It also incorporates suggestions made by the USNCTAM at large.
Variation of PEEK matrix crystallinity in APC-2 composite subjected to large shearing deformations
Composites Science and Technology
60
4
605-612
2000
10.1016/S0266-3538(99)00169-4
This paper presents an experimental investigation of matrix cracking and microstructure variations in order to evaluate their relative contributions to the shear stiffness loss of AS4/PEEK composite material subjected to large shear deformations. Specimen observations by X-radiography allow us to characterize the matrix cracking, and measurements of the matrix crystallinity at different levels of loading give information on the microstructure alteration of the PEEK matrix. These measurements have been performed by using three different methods that have been compared: wide-angle X-ray scattering (WAXS), conventional differential scanning calorimetry (DSC) and modulated differential scanning calorimetry (MDSC). The relationship between the matrix cracking development, the change in the PEEK crystallinity and the secant shear stiffness variation is discussed. This study shows that, neither the presence of inter- or intra-ply cracks nor the decrease of the PEEK matrix crystallinity degree, are sufficient to induce the significant loss of the ply shear stiffness measured in [±45]2s APC-2 laminates tested in tension.
A. Polymer-matrix composites; B. Non-linear behaviour; C. Damage mechanics; D. Differential scanning calorimetry; D. X-ray diffraction
Stokes flow past bubbles and drops partially coated with thin films. Part 2. Thin films with internal circulation – a perturbation solution
Journal of Fluid Mechanics
132
237-250
1983
10.1017/S0022112083001627
In the present study we examine the steady axisymmetric creeping flow due to the motion of a liquid drop or a bubble which is partially covered by a thin immiscible fluid layer or film. The analysis is based on the assumption that surface-tension forces are large compared with viscous forces which deform the drop, and that the circulation in the film is weak. The latter assumption is satisfied provided that the film-fluid viscosity is not too small. A perturbation scheme based on the thinness of the fluid layer is used to construct the solution. One of the principal results is an expression for the drag force on the complex drop. We also find that the extent to which the drop or bubble is covered the film has a maximum value depending on the magnitude of the driving force on the film. In addition, we find the rather interesting result that when the ratio of the primary drop viscosity and bulk fluid viscosity is greater than ½, the circulation within the film may have a double-cell structure.
Deriving Landauer's erasure principle from statistical mechanics
ArXiv e-prints
3
2005
We present a concise derivation of Landauer's erasure principle from the postulates of statistical mechanics, along with a small number of additional but uncontroversial axioms.
John Bell's varying interpretations of quantum mechanics
Arxiv preprint
13 pages
2014
Various interpretations of quantum mechanics, favored (or neglected) by John Bell in the context of his non-locality theorem, are compared and discussed.
Trace inequalities in nonextensive statistical mechanics
Entropy
1-8
2005
10.1016/j.laa.2006.03.015
In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized Golden-Thompson inequality.
Statistical Mechanics
Operator methods in classical mechanics
American Journal of Physics
70
9
951
2002
10.1119/1.1485713
By taking into account that the equations of motion of classical mechanics can be expressed in terms of differential operators in phase space, we develop a simple method for obtaining exact solutions for several models in one and more dimensions. We also propose a simple procedure for the systematic construction of exactly solvable models in one dimension.
Effect of residual stress on ferroelectric properties of PZT thin film prepared by metalorganic decomposition
Mechanics and Material Engineering for Science and Experiments
259-262
2003
In the paper, ferroelectric thin films Pb(Zr0.58Ti 0.42)O3 were prepared by metalorganic decomposition (MOD). The residual stress in thin film was tested by two methods, which were x-ray diffractometer (XRD) and indentation fracture. In the indentation fracture method, two models including GLFW model and ZCF model were adopted. The results measured by ZCF model were closer to the results measured by XRD. The relationship of properties such as microstructures, ferroelectric response with residual stress was discussed.
Decomposition; Ferroelectricity; Indentation fracture; Lead compounds; MOD; PZT thin film; Residual stress; Residual stresses; Thin films; X ray diffraction analysis; XRD
Emergent Probabilities in Quantum Mechanics
arXiv
2006
The transition from the quantum to the classical is governed by randomizing devices (RD), i.e., dynamical systems that are very sensitive to the environment. We show that, in the presence of RDs, the usual arguments based on the linearity of quantum mechanics that lead to the measurement problem do not apply. RDs are the source of probabilities in quantum mechanics. Hence, the reason for probabilities in quantum mechanics is the same as the reason for probabilities in other parts of physics, namely our ignorance of the state of the environment. This should not be confused with decoherence. The environment here plays several, equally important roles: it is the dump for energy and entropy of the RD, it puts the RD close to its transition point and it is the reason for probabilities in quantum mechanics. We show that, even though the state of the environment is unknown, the probabilities can be calculated and are given by the Born rule. We then discuss what this view of quantum mechanics means for the search of a quantum theory of gravity.
Synthetic Mechanics Revisited
Journal of Philosophical Logic
20
2
121-130
1991
papers2://publication/uuid/F1335C85-8A64-4476-8F40-574EC1A6E5BE
Earlier results on eliminating numerical objects from physical theories are extended to results on eliminating geometrical objects.
Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
ESAIM: Mathematical Modeling and Numerical Analysis
39
797-826
2005
10.1051/m2an
In order to describe a solid which deforms smoothly in some region,\nbut non smoothly in some other region, many multiscale methods have\nbeen recently proposed that aim at coupling an atomistic model (discrete\nmechanics) with a macroscopic model (continuum mechanics). We provide\nhere a theoretical basis for such a coupling in a one-dimensional\nsetting, in the case of convex energy.
and phrases; continuum mechanics; discrete mechanics; multiscale methods; variational problems
Mixed stabilized finite element methods in nonlinear solid mechanics
Computer Methods in Applied Mechanics and Engineering
199
37-40
2559-2570
2010
10.1016/j.cma.2010.04.006
Computer Methods in Applied Mechanics and Engineering, 199 (2010) 2559-2570. 10.1016/j.cma.2010.04.006
algebraic sub-grid scales; mixed finite element interpolations; stabilization methods
Nonlinear large deflection of thin film overhung on compliant substrate using shaft-loaded blister test
Journal of Applied Mechanics
82
9
091001
2015
10.1115/1.4030739
This paper presents the nonlinear large deflection of the thin film and the effect of substrate deformation on the thin film deflection through the shaft-loaded blister test. The blister of thin film can be divided into two parts, namely, the annular contact brim and the central noncontact bulge. A two-coupled line spring model is developed to describe the deformation of the contact part, and Föppl–Hencky equations are employed to study the constitutive relation between the applied load and the central deflection. The analytical and numerical solutions for the constitutive relation between the applied load and the deflection of thin film with considering the deformation of substrate are derived.
Fracture mechanics using a 3D composite element
Composite Structures
45
1
29-39
1999
10.1016/S0263-8223(99)00011-2
The formulation of a 3D composite element and its use in a mixed-mode fracture mechanics example is presented. This element, like a conventional 3D finite element, has three degrees of freedom per node although, like a plate element, the...
Effects of surface tension and intraluminal fluid on mechanics of small airways.
Journal of applied physiology (Bethesda, Md. : 1985)
82
1
233-239
1997
Airway constriction is accompanied by folding of the mucosa to form ridges that run axially along the inner surface of the airways. The mucosa has been modeled (R. K. Lambert. J. Appl. Physiol. 71:666-673, 1991) as a thin elastic layer with a finite bending stiffness, and the contribution of its bending stiffness to airway elastance has been computed. In this study, we extend that work by including surface tension and intraluminal fluid in the model. With surface tension, the pressure on the inner surface of the elastic mucosa is modified by the pressure difference across the air-liquid interface. As folds form in the mucosa, intraluminal fluid collects in pools in the depressions formed by the folds, and the curvature of the air-liquid interface becomes nonuniform. If the amount of intraluminal fluid is small, < 2% of luminal volume, the pools of intraluminal fluid are small, the air-liquid interface nearly coincides with the surface of the mucosa, and the area of the air-liquid interface remains constant as airway cross-sectional area decreases. In that case, surface energy is independent of airway area, and surface tension has no effect on airway mechanics. If the amount of intraluminal fluid is > 2%, the area of the air-liquid interface decreases as airway cross-sectional area decreases. and surface tension contributes to airway compression. The model predicts that surface tension plus intraluminal fluid can cause an instability in the area-pressure curve of small airways. This instability provides a mechanism for abrupt airway closure and abrupt reopening at a higher opening pressure.
Quantum Mechanics Without Observers
arXiv preprint arXiv:1302.4156
1-40
2013
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process theory and utilizing methods from combinatorial games, interpolation theory and complex systems theory results in a novel realist version of quantum mechanics incorporating quasi-local, nondeterministic hidden variables that are compatible with the no-hidden variable theorems and relativistic invariance, and reproduce the standard results of quantum mechanics to a high degree of accuracy without invoking observers.
causal tapestries; hidden variables; measurement problem; reality game
Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell-II: Finite element modeling and application
Acta Mechanica Solida Sinica
22
3
197-205
2009
10.1016/S0894-9166(09)60266-4
Based on the generalized variational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established (see, Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell-I), the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones. ?? 2009 The Chinese Society of Theoretical and Applied Mechanics.
ferromagnetic thin shell; finite element method; magneto-thermo-elasticity; nonlinear coupling
Refined methods in photoelastic stress analysis with applications to fracture mechanics
Optics and Lasers in Engineering
14
3
185-202
1991
10.1016/0143-8166(91)90048-X
A combined Tardy and photoelastic fringe multiplication methodology is reviewed for three-dimensional stress freezing photoelasticity. Specifically, the investigation concerns the thin transitional region near the free surface-crack front intersection in a finite body. The photoelastic data are combined with moiré interferometry to provide stress and displacement fields surrounding a crack tip. Experimental methodology involving refined thin slicing techniques, enhanced photoelastic fringe constant determination and photoelastic data interpretation is presented.
Cyberspatial mechanics.
IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society
38
3
629-44
2008
10.1109/TSMCB.2008.916309
In support of a generalization of systems theory, this paper introduces a new approach in modeling complex distributed systems. It offers an analytic framework for describing the behavior of interactive cyberphysical systems (CPSs), which are networked stationary or mobile information systems responsible for the real-time governance of physical processes whose behaviors unfold in cyberspace. The framework is predicated on a cyberspace-time reference model comprising three spatial dimensions plus time. The spatial domains include geospatial, infospatial, and sociospatial references, the latter describing relationships among sovereign enterprises (rational agents) that choose voluntarily to organize and interoperate for individual and mutual benefit through geospatial (physical) and infospatial (logical) transactions. Of particular relevance to CPSs are notions of timeliness and value, particularly as they relate to the real-time governance of physical processes and engagements with other cooperating CPS. Our overarching interest, as with celestial mechanics, is in the formation and evolution of clusters of cyberspatial objects and the federated systems they form.
Algorithms; Computer Communication Networks; Computer Simulation; Cybernetics; Cybernetics: methods; Information Storage and Retrieval; Information Storage and Retrieval: methods; Mechanics; Models, Theoretical
Coordinate mapping of hyolaryngeal mechanics in swallowing.
Journal of visualized experiments : JoVE
87
2014
10.3791/51476
Characterizing hyolaryngeal movement is important to dysphagia research. Prior methods require multiple measurements to obtain one kinematic measurement whereas coordinate mapping of hyolaryngeal mechanics using Modified Barium Swallow (MBS) uses one set of coordinates to calculate multiple variables of interest. For demonstration purposes, ten kinematic measurements were generated from one set of coordinates to determine differences in swallowing two different bolus types. Calculations of hyoid excursion against the vertebrae and mandible are correlated to determine the importance of axes of reference. To demonstrate coordinate mapping methodology, 40 MBS studies were randomly selected from a dataset of healthy normal subjects with no known swallowing impairment. A 5 ml thin-liquid bolus and a 5 ml pudding swallows were measured from each subject. Nine coordinates, mapping the cranial base, mandible, vertebrae and elements of the hyolaryngeal complex, were recorded at the frames of minimum and maximum hyolaryngeal excursion. Coordinates were mathematically converted into ten variables of hyolaryngeal mechanics. Inter-rater reliability was evaluated by Intraclass correlation coefficients (ICC). Two-tailed t-tests were used to evaluate differences in kinematics by bolus viscosity. Hyoid excursion measurements against different axes of reference were correlated. Inter-rater reliability among six raters for the 18 coordinates ranged from ICC = 0.90 - 0.97. A slate of ten kinematic measurements was compared by subject between the six raters. One outlier was rejected, and the mean of the remaining reliability scores was ICC = 0.91, 0.84 - 0.96, 95% CI. Two-tailed t-tests with Bonferroni corrections comparing ten kinematic variables (5 ml thin-liquid vs. 5 ml pudding swallows) showed statistically significant differences in hyoid excursion, superior laryngeal movement, and pharyngeal shortening (p < 0.005). Pearson correlations of hyoid excursion measurements from two different axes of reference were: r = 0.62, r(2) = 0.38, (thin-liquid); r = 0.52, r(2) = 0.27, (pudding). Obtaining landmark coordinates is a reliable method to generate multiple kinematic variables from video fluoroscopic images useful in dysphagia research.
Modeling of mixed-mode crack growth in ductile thin sheets under combined in-plane and out-of-plane loading
Engineering Fracture Mechanics
78
17
3082-3101
2011
10.1016/j.engfracmech.2011.09.004
This paper describes a modeling approach for analyzing mixed-mode crack growth events in ductile thin-sheet materials under large deformation and combined in-plane and out-of-plane loading conditions. The remote mixed-mode I/III loading leads to local mixed-mode I/II/III fields near the crack front. Making use of full-field surface deformation measurements, finite element models of mixed-mode I/III stable tearing events in thin-sheet specimens have been developed. Model predictions have been compared with experimental measurements (a) just prior to initial crack growth and (b) during stable tearing crack growth. Analyses of curvilinear crack growth events are carried out using a nodal release option or a local re-meshing option and using a generalized CTOD parameter with experimentally measured critical CTOD values. Results of this study suggest that the modeling approach can be employed to numerically re-construct experimental crack growth events in thin plate specimens. This offers a viable means of analyzing and understanding the mixed-mode crack growth events and provides a tool for further investigations of 3D crack front fields (which are otherwise unavailable experimentally) and for the study of fracture criteria for stable tearing events. © 2011 Elsevier Ltd.
Crack growth; Fracture; Mixed mode; Modeling; Simulation; Stable tearing
Finite element modelling of the mechanism of deformation and failure in metallic thin-walled hollow spheres under dynamic compression
Mechanics of Materials
54
43-54
2012
10.1016/j.mechmat.2012.06.002
Recent interest in lightweight metallic hollow sphere foams for aerospace applications requires a better physical understanding of dynamic properties of single spheres. Finite element modelling supported by high rate experiments was developed to investigate the underlying deformation and failure mechanisms of electrodeposited nickel thin-walled hollow spheres. Parametric simulation was performed to further explore the effect of sphere geometry (wall thickness to diameter ratio) and loading rate. It was found that decreasing the ratio of wall thickness to diameter tends to transit the side wall failure mode from bending to buckling. For a thin-walled sphere (the thickness to diameter ratio less than a critical value), the macroscopic dynamic behaviour is primarily dominated by the two deformation and failure mechanisms: (1) buckling failures of wall materials and (2) self-contacts of wall surfaces and wall-anvil contacts. At higher impact velocity (greater than a critical velocity), inertia effect due to dynamic localisation of wall crushing arises and significantly influences the deformation/failure mode of the sphere, resulting in an increased initial crushing strength and asymmetric deformation. Finally, the behaviour of hollow spheres was correlated to explore the power law behaviour of bulk foams with respect to the relative density; it was found that metallic thin-walled hollow sphere foams can be better approximated as open-cell rather than closed-cell foams. ?? 2012 Elsevier Ltd. All rights reserved.
Dynamic phenomena; Failure mode; Finite element model; Foams; Hollow spheres; Rate dependency
The regular hybrid boundary node method in the bending analysis of thin plate structures subjected to a concentrated load
European Journal of Mechanics - A/Solids
38
79-89
2013
10.1016/j.euromechsol.2012.10.001
This paper proposes a computational procedure based on the regular hybrid boundary node method (RHBNM) for solving the thin plate subjected to a concentrated load. The solution is decomposed into the particular solution arising from the concentrated load and the complementary solution for the homogeneous equation. In the solution procedure, the particular solution is first obtained by the fundamental solution. For the latter, we employ the RHBNM to solve. The RHBNM is a promising boundary type meshless method based on a modified variational principle and the moving least squares (MLS) approximation, and exploits the meshless attributes of the MLS and the reduced dimensionality advantages of the boundary element method (BEM). In this paper, a modified variational functional of the thin plate is developed, in which the independent variables are the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain. The MLS method is employed to approximate the boundary variables whereas the domain variables are interpolated by a linear combination of fundamental solutions of both the biharmonic equation and Laplace's equation. Some numerical tests illustrate the validity and efficiency of the present method.
Meshless method; Regular hybrid boundary node method; Thin plate bending
Degrees of freedom (mechanics)
Wikipedia.org
2014
In mechanics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration. Degree of freedom is a fundamental concept central to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering. It is the number of parameters that determine the state of a physical system.
A coupled theory of damage mechanics and finite strain elasto-plasticity—II. Damage and finite strain plasticity
International Journal of Engineering Science
28
6
505-524
1990
10.1016/0020-7225(90)90053-L
A constitutive model is formulated here for anisotropic continuum damage mechanics using finite strain plasticity. The formulation is given in spatial coordinates (Eulerian reference frame) and incorporates both isotropic and kinematic hardening. The von Mises yield criterion is modified to include the effects of damage through the use of the hypothesis of elastic energy equivalence. A modified elasto-plastic stiffness tensor that includes the effects of damage is derived within the framework of the proposed model. Numerical implementation of the proposed model includes the finite element formulation where an Updated Lagrangian description is used. The basic example of finite simple shear is solved. The problem of crack initiation is also solved for a thin elasto-plastic plate with a center crack that is subjected to inplane tension. This problem is solved in the companion paper using the coupled theory of elasticity with damage.
U-type piezoelectric thin-film microactuator for hard disk drives
IEEE Transactions on Magnetics
41
11
4309-4314
2005
10.1109/TMAG.2005.854235
We have designed, fabricated, and investigated a new dual-stage actuator system based on a thin-film lead-zirconate-titanate (PZT) microactuator and a voice coil motor for positioning a magnetic head in a high-density hard disk drive (HDD). We made the PZT microactuator by using a modified sol-gel technique to deposit PZT thin film and applying reactive ion etching processes to shape the device. We studied the crystalline structure and growth behavior of the piezoelectric films by X-ray diffraction and scanning electron microscopy and found that the PZT material preferably has a composition of Pb(Zr<sub>0.52</sub>Ti<sub>0</sub>.48)O<sub>3</sub>. We also tested and simulated the U-type SUS304 substrate integrated with two single-layer PZT elements in order to investigate the driving mechanics. The device performance is outstanding. With the peak-to-peak head displacement of 1.08 μm at the applied voltage of ±20 V and the suspension response frequency higher than 12 kHz, both displacement/voltage sensitivity and resonant frequency are high enough for the device to be used in future high-density HDDs.
Hard disk drives; Piezoelectric elements; PZT thin film; U-type microactuator
On the behaviour of thin-walled steel regular polygonal tubular members
Thin-Walled Structures
62
191-205
2013
10.1016/j.tws.2012.08.006
This paper presents an investigation concerning the mechanics of deformation of thin-walled steel tubular members with single-cell regular polygonal cross-sections, such as those employed to build transmission line structures, towers, antennas and masts. This type of cross-sections exhibit rotational symmetry of order equal to the number of walls, which leads to remarkable peculiarities concerning the cross-section in-plane and out-of-plane (warping) deformation. The investigation is based on a specialization of Generalised Beam Theory (GBT), aiming at fully uncoupling the main cross-section deformation mode sets, which makes it possible to obtain analytical results and thus extract in-depth information concerning the structural behaviour of this type of members. Several illustrative examples, employing both analytical and numerical (using GBT-based beam finite elements) strategies, are presented throughout the text. For validation and comparison purposes, results obtained with standard shell finite element models are also provided. © 2012 Elsevier Ltd. All rights reserved.
Cross-section deformation; Generalised Beam Theory (GBT); Regular polygonal cross-sections; Thin-walled members
Semiclassical mechanics with molecular applications
SIAM review
27
4
485-504
1991
Semiclassical mechanics relates Newton's classical theory to modern quantum mechanics in a manner designed for the interpretation of the most recent experimental evidence. The theory is physically intuitive and computationally accurate, and is particularly powerful for large quantum numbers - hence it has special reference to atomic, nuclear, and molecular physics. It also proves to be remarkably accurate even for the lowest quantum states. This book gives a comprehensive account of the application of the theory to molecular systems, with particular attention paid to the problems of non-separability. Spectroscopy is addressed in addition to collision theory. Although it is primarily a research monograph, the inclusion of problems at the end of each chapter makes this book equally applicable as a graduate text.
quantum conditions
Streaming-potential phenomena in the thin-Debye-layer limit. Part 2. Moderate Péclet numbers
Journal of Fluid Mechanics
704
109-136
2012
10.1017/jfm.2012.221
Macroscale description of streaming-potential phenomena in the thin-double-layer limit, and in particular the associated electro-viscous forces, has been a matter of long-standing controversy. In part 1 of this work (Yariv, Schnitzer & Frankel, J. Fluid Mech., vol. 685, 2011, pp. 306–334) we identified that the product of the Hartmann () and P´eclet (Pe) numbers is O.2/, being the dimensionless Debye thickness. This scaling relationship defines a one-family class of limit processes appropriate to the consistent analysis of this singular problem. In that earlier contribution we focused on the generic problems associated with moderate and large Pe, where the streaming-potential magnitude is comparable to the thermal voltage. Here we consider the companion generic limit of moderate P´eclet numbers and large Hartmann numbers, deriving the appropriate macroscale model wherein the Debye-layer physics is represented by effective boundary conditions. Since the induced electric field is asymptotically smaller, calculation of these conditions requires higher asymptotic orders in analysing the Debye-scale transport. Nonetheless, the leading-order electro-viscous forces are of the same O.2/ relative magnitude as those previously obtained in the large-Pe limit. The structure of these forces is different, however, first because the small Maxwell stresses do not contribute at leading order, and second because salt polarization results in a dominant diffuso-osmotic slip. Since the salt distribution is governed by an advection–diffusion equation, this slip gives rise to electro-viscous forces which are nonlinear in the driving flow. The resulting scheme is illustrated by the calculation of the electro-viscous excess drag in the prototype problem of a translating sphere
A possible role of the pleura in lung mechanics.
Journal of biomechanics
20
8
773-7
1987
The pressure-volume behavior of excised visceral pleura is studied. The pleura is modeled as a thin incompressible membrane, and the requisite membrane tension is determined from a pseudostrain-energy function. Results are compared to pressure-volume behavior of saline-filled and air-filled parenchyma and to experimental pleural data from the literature. Results suggest that the pleura may play a role as a volume limiter of lung expansion although the need for more detailed analysis is discussed.
Animals; Biomechanics; Elasticity; Lung; Lung: physiology; Lung Volume Measurements; Models, Biological; Models, Theoretical; Pleura; Pleura: physiology; Pressure
Thrust and Torque Prediction in Drilling From a Cutting Mechanics Approach
CIRP Annals-Manufacturing Technology
87-91
1979
A thin shear-zone analysis is developed for the relevant operation, coupled with a means of obtaining cutting data for use in the model. The lips and chisel edge are considered as a number of elemental single edge and orthogonal cuts, respectively. Allowance is made for the variable cutting conditions within and between drills. Predicted and measured thrusts and torques for the whole drill for 65S-T6 and a steel are tabulated. Good predictions are provided for a wide range of drill specifications and cutting conditions
Al Mg Si Cu wrought alloys; Can wrought alloy 65S; Drilling; Forces; Forecasting; Thrust; Torque
Synchrotron X-ray microdiffraction reveals rotational plastic deformation mechanisms in polycrystalline thin films
Acta Materialia
57
13
3738-3753
2009
10.1016/j.actamat.2009.04.024
Understanding the mechanical response of polycrystalline materials on the mesoscopic scale remains a challenge as it is largely determined by grain-to-grain interactions and the discrete underlying microstructure. We conducted in situ synchrotron Laue microdiffraction experiments to map local strain tensors and orientations over polycrystalline thin gold films for different applied biaxial strain states. The experimental results demonstrate stress relaxation to be accompanied by cooperative transport of dislocation density leading to rotational plastic deformation heterogeneities. We propose a disclination model of closed dislocation walls and consider the geometry of transformations corresponding to a Burgers circuit enclosing the multipole disclination configuration. The observed stress-driven rotational deformation of the grain is shown to be described by the change in rotational closure failure associated with a Burgers circuit around the multipole disclination configuration. This concept is further advanced in a non-Euclidian geometry to demonstrate that the observed microrotation is captured by higher-order gradients in a micropolar continuum theory. © 2009 Acta Materialia Inc.
Dislocation mechanics; Mesoscopic; Microdiffraction; Micropolar
Modelling of the interface between a thin film and a substrate within a strain gradient plasticity framework
Journal of the Mechanics and Physics of Solids
55
939-955
2007
10.1016/j.jmps.2006.11.001
Interfaces play an important role for the plastic deformation at the micron scale. In this paper, two types of interface models for isotropic materials are developed and applied in a thin film analysis. The first type, which can also be motivated from dislocation theory, assumes that the plastic work at the interface is stored as a surface energy that is linear in plastic strain. In the second model, the plastic work is completely dissipated and there is no build-up of a surface energy. Both formulations introduce one length scale parameter for the bulk material and one for the interface, which together control the film behaviour. It is demonstrated that the two interface models give equivalent results for a monotonous, increasing load. The combined influence of bulk and interface is numerically studied and it is shown that size effects are obtained, which are controlled by the length scale parameters of bulk and interface. ?? 2006 Elsevier Ltd. All rights reserved.
Constitutive behaviour; Dislocations; Strain gradient plasticity
Fracture mechanics analysis of coating/substrate systems
Engineering Fracture Mechanics
65
5
595-607
2000
10.1016/S0013-7944(99)00142-3
A finite fracture mechanics model is used to predict the development of multiple cracks in the coating layer of coating/substrate systems. The stresses in a cracked coating are evaluated by a variational mechanics approach. These stresses are then used to calculate the total energy released due to the formation of a complete crack in the coating layer. The analysis can handle tensile loads or bending loads and includes the effect of residual thermal stresses. By assuming the next coating crack forms when the energy released due to the formation of a complete microcrack equals the in situ fracture toughness of coating, it is proposed that one can predict the number of coating cracks as a function of applied strain. Alternatively, it is proposed that experimental data for number of cracks vs. strain can be fit to the fracture analysis and be used to determine an in situ coating fracture toughness.
Coatings; Fracture mechanics; Paints; Variational mechanics
Plastic buckling and collapse of thin shell structures, using layered plastic modeling and co-rotational ANDES finite elements
Computer Methods in Applied Mechanics and Engineering
198
5-8
785-798
2009
10.1016/j.cma.2008.10.013
This study reveals an analysis of plastic buckling and collapse of thin shell structures. For this purpose, the co-rotational and layered plastic model as well as ANDES (Assumed Natural Deviatoric Strain) finite element formulations are used. The co-rotational kinematics formulation splits the translational and rotational deformations in a small deformation analysis. The ANDES finite element is modified to elastoplastic ANDES finite element by the introduction of the von Mises yield criterion elastoplastic formulation on its original deformation model. In order to accommodate the plasticity formulation, the Gauss point layered integration is inserted through of thickness of the element to produce the internal force vector and material stiffness matrix. Special effort is devoted to maintain the consistency of the internal forces and tangent stiffness as well as to enhance the robustness of element level computations. The arc-length method is used to follow the postbuckling equilibrium path. Results are presented for several benchmark elastoplastic shell problems available in the present literature, which are generally in agreement with the present work. © 2008 Elsevier B.V.
ANDES finite element; Buckling and collapse; Co-rotational formulation; Layered plastic model; Shell structures
Estimating the conditions for polariton condensation in organic thin-film microcavities
Journal of Chemical Physics
136
3
034510
2012
10.1063/1.3678015
We examine the possibility of observing Bose condensation of a confined two-dimensional polariton gas in an organic quantum well. We deduce a suitable parameterization of a model Hamiltonian based upon the cavity geometry, the biexciton binding energy, and similar spectroscopic and structural data. By converting the sum-over-states to a semiclassical integration over $d$-dimensional phase space, we show that while an ideal 2-D Bose gas will not undergo condensation, an interacting gas with the Bogoliubov dispersion $H(p)\approx s p$ close to $p=0$ will undergo Bose condensation at a given critical density and temperature. We show that $T_c/\sqrt{\rho_c}$ is sensitive to both the cavity geometry and to the biexciton binding energy. In particular, for strongly bound biexcitons, the non-linear interaction term appearing in the Gross-Pitaevskii equation becomes negative and the resulting ground state will be a localized soliton state rather than a delocalized Bose condensate.
Quantum mechanics
Nature
478
7367
47-8
2011
10.1038/478047a
We investigate the effect of systematically applying molecular dynamics (MD) and quantum mechanics/molecular mechanics (QM/MM) to docked poses in an attempt to improve the correspondence between theoretical prediction and experimental observation. The proposed scheme involves running a short time scale MD simulation on a docked ligand pose (and any known structurally important crystal structure waters in the active site), followed by QM/MM minimization. Both of these steps are relatively fast for moderately sized ligands; longer time scale MD involving the protein is not found to improve the results. The final binding energy is given in terms of the QM/MM total energy, a van der Waals correction, and a term to account for desolvation effects. This methodology is first tested with a trypsin inhibitor, for which we establish the importance of running MD before reoptimizing with QM/MM. The method is then applied to cytochrome c peroxidase using a set of binders and decoys. In this example, the proposed methodology affords much better discrimination between binders and decoys than the traditional docking approach used. For both systems presented, application of this protocol results in a significantly better energetic ranking and a smaller root mean squared deviation from known crystallographic ligand poses. This work highlights the importance of including polarization effects through QM/MM and of sampling with MD to refine a set of initial docked poses.
Asymptotic model of fields in a thin-walled structure with crack-like defects
Quarterly Journal of Mechanics & Applied Mathematics
62
1
1-18
2009
10.1093/qjmam/hbn023
The transition from two-dimensional (2D) wave propagation through the square periodic structure in anti-plane shear time-harmonic case to a discretised model of a 2D lattice with masses connected by springs is considered. A model of a defect in the middle part of the thin-walled bridges is presented. As a first part of the asymptotic model, the effective transmission condition in the vicinity of the transverse cut of the thin-walled bridges is discussed. Then, a boundary layer determining the asymptotic expansion of the field near the tip of the crack is constructed. Stress intensity factors are evaluated for deep cracks in the junction regions. The corresponding boundary layer analysis is non-trivial and has not been attempted elsewhere. [ABSTRACT FROM PUBLISHER] Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
BOUNDARY layer (Aerodynamics); ELASTIC wave propagation; SHEAR (Mechanics); SHEAR waves; STRAINS & stresses (Mechanics)
Nonlinear parametrically excited surface waves in surfactant-covered thin liquid films
Journal of Fluid Mechanics
520
243-265
2004
10.1017/S0022112004001600
The effect of gravity modulation on the nonlinear evolution of long-wavelength disturbances at the free surface of a surfactant-covered thin liquid layer is studied. The surfactants, which are assumed to be insoluble, give rise to interfacial concentration gradients and associated Marangoni flow in the underlying liquid film. A coupled system of lubrication-theory-based evolution equations for the film height and surfac- tant concentration is solved numerically using spectral methods. Previous work using Floquet theory had determined that small-amplitude long-wavelength disturbances are destabilized by gravity modulation in the presence of surfactant; uncontaminated films were found to be linearly stable. Our numerical results indicate that uncontaminated free surfaces are destabilized by nonlinearities and exhibit a harmonic response. The interface exhibits complex dynamics during a forcing cycle, characterized by numerous coalescence events between thickened fluid ridges leading to coarsening. The presence of surfactant-induced Marangoni flow gives rise to a harmonic response, larger scale fluid structures of reduced amplitude, less frequent coalescence events, and less complicated film dynamics.
Mechanics of food handling by fluid-feeding insects
Regulatory Mechanisms in Insect Feeding
32-73
1995
10.1007/978-1-4615-1775-7_2
24 Kingsolver, J.G. and Daniel, T.L. (1995) Mechanics of food handling by fluid-feeding insects. In Regulatory Mechanisms in Insect Feeding (Chapman, R.F. and De Boer, G., eds), pp. 32–73, Chapman & Hall
Applications of fracture mechanics numerical modelling in rock engineering
First Break
28
March
53-62
2010
10.3997/1365-2397.2010008
Discontinuities are an important feature of rock and rock mass. They control the hydraulic properties by connected fracture networks and also govern the mechanical behaviour. Rock fracture mechanics is the explicit analysis of fracture propagation. Fracture mechanics is based on physical principles, rather than empirical relationships as employed in classical rock mechanics. Here the basic relations and laboratory techniques in rock fracture mechanics are summarized and applications of fracture-mechanics-based numerical codes on rock mechanics issues are highlighted, such as borehole stability and hydraulic fracturing. Nowadays, the propagation of fractures and generation of fracture networks can be simulated satisfactorily in two dimensions. Outstanding difficulties which are not yet resolved are anisotropic behaviour, extension to three spatial dimensions, and inclusion of realistic fracture sets in the models. The potential of fracture-mechanics-based numerical modelling for meeting challenges in different industries is outlined. Such software tools might help, for example, in analysing the risk of a thermo/hydraulic short circuit in geothermal projects, in identifying the factors influencing borehole instability or sand production in reservoir geomechanics, or in improving hydraulic stimulation campaigns to optimize the connection of an existing fracture network to the wellbore. © 2010 EAGE.
The ultraviolet photoconductive detector based on Al-doped ZnO thin film with fast response
Science China Physics, Mechanics and Astronomy
54
1
102-105
2010
10.1007/s11433-010-4203-y
We report fabrication and characterization of metal-semiconductor-metal photoconductive detectors based on Al-doped ZnO thin films fabricated by radio frequency magnetron sputtering. Optical and structural properties of the thin films were charac- terized using various techniques. At 6 V bias, a responsivity higher than 4 A/W in the wavelength shorter than 350 nm was ob- tained, and this responsibility dropped quickly and reached the noise floor in the visible region. Transient response measure- ment revealed that the detector had a fast photoresponse with a rise time of 9 ns and a fall time of 1.2 μs.
photoconductive detector; ultraviolet photodetector; ZnO; ZnO:Al
Coupled deflection analysis of thin-walled Timoshenko laminated composite beams
Computational Mechanics
43
4
493-514
2008
10.1007/s00466-008-0324-9
For the deflection analyses of thin-walled Timoshenko laminated composite\nbeams with the mono- symmetric I-, channel-, and\n\nL-shaped sections, the stiffness matrices are derived based on the\nsolutions of the simultaneous ordinary differential equations.\n\nA general thin-walled composite beam theory considering shear deformation\neffect is developed by introducing Vlasov’s assumptions.\n\nThe shear stiffnesses of thin-walled composite beams are explicitly\nderived from the energy equivalence. The equilibrium equations\n\nand force-deformation relations are derived from energy principles.\nBy introducing 14 displacement parameters, a generalized\n\neigenvalue problem that has complex eigenvalues and multiple zero\neigenvalues is formulated. Polynomial expressions are assumed\n\nas trial solutions for displacement parameters and eigenmodes containing\nundetermined parameters equal to the number of zero\n\neigenvalues are determined by invoking the identity condition to\nthe equilibrium equations. Then the displacement functions\n\nare constructed by combining eigenvectors and polynomial solutions\ncorresponding to nonzero and zero eigenvalues, respectively.\n\nFinally, the stiffness matrices are evaluated by applying the member\nforce-displacement relations to the displacement functions.\n\nIn addition, the finite beam element formulation based on the classical\nLagrangian interpolation polynomial is presented.\n\nIn order to verify the validity and the accuracy of this study, the\nnumerical solutions are presented and compared with the\n\nfinite element results using the isoparametric beam elements and\nthe detailed three-dimensional analysis results using the\n\nshell elements of ABAQUS. Particularly the effects of shear deformations\non the deflection of thin-walled composite beams\n\nwith the mono-symmetric I-, channel-, and L-shaped sections with\nvarious lamination schemes are investigated.
analysis; composite beam; deflection; shear deformation; stiffness matrix; thin-walled
Multi-scale detection of failure in planar masonry thin shells using computational homogenisation
Engineering Fracture Mechanics
76
4
479-499
2009
10.1016/j.engfracmech.2008.10.003
This paper presents a computational homogenisation-based technique for localisation detection in planar masonry shells. A computational homogenisation procedure is used for the in-plane and the out-of-plane behaviour of masonry walls taking the periodicity of the material into account. The quasi-brittle nature of the masonry constituents results in initial and damage-induced (evolving) anisotropy properties with localisation of damage at both the structural and fine scales. Using a closed-form damage model at the mesoscopic scale, it is shown that a structural scale localisation criterion based on the acoustic tensor adapted to shell kinematics allows to detect the structural scale localisation. This detection identifies average preferential cracking orientations consistent with the stacking mode of masonry for both in-plane and out-of-plane failure. This approach is illustrated by examples of bed joint and stair-case failure, and its subsequent integration in multi-scale nested computational schemes is discussed.
computational homogenisation; masonry planar shells
The Rise of Quantum Mechanics
Arxiv
June
20
2008
The rise of quantum mechanics is reviewed with special attention to the development between June 1925 and October 1927 when the Copenhagen interpretation was proposed.
Atomic Physics; History of Physics
Experiments in statistical mechanics
American Journal of Physics
68
2000
1073
2000
10.1119/1.1315604
We present experiments designed to illustrate the basic concepts of statistical mechanics using a gas of “motorized molecules.” Two molecular motion machines are constructed. The pressure fluctuation machine (mechanical interaction simulator) is a working model of two gases separated by a movable piston. The Boltzmann machine (canonical simulator) is a working model of a two-level quantum system in a temperature bath. Dynamical probabilities (fraction of time) are measured using mechanical devices, such as stop watches and motion sensors. Statistical probabilities (fraction of states) are calculated using physical statistics, such as microcanonical and canonical statistics. The experiments enable one to quantitatively test the fundamental principles of statistical mechanics, including the fundamental postulate, the ergodic hypothesis, and the statistics of Boltzmann.
Study on Thin Extended Octagonal Ring Elastomer
Frontiers of Manufacturing and Design Science, Pts 1-4
44-47
2208-2212
2011
DOI 10.4028/www.scientific.net/AMM.44-47.2208
In order to optimize octagonal ring elastomer, the structure and work principle of thin extended octagonal ring elastomer is briefly presented, the corresponding model is established by material mechanics, the analysis of stress and strain is discussed by finite element and the critical parameters is found. It is practical for octagonal ring elastomer improving the performance.
ansys; finite element; octagonal ring; optimal design
Adaptive mesh refinements for thin shells whose middle surface is not exactly known
Computer Methods in Applied Mechanics and Engineering
197
51-52
4789-4811
2008
10.1016/j.cma.2008.07.001
A strategy concerning mesh refinements for thin shells computation is presented. The geometry of the shell is given only by the reduced information consisting in nodes and normals on its middle surface corresponding to a coarse mesh. The new point is that the mesh refinements are defined from several criteria, including the transverse shear forces which do not appear in the mechanical energy of the applied shell formulation. Another important point is to be able to construct the unknown middle surface at each step of the refinement. For this, an interpolation method by edges, coupled with a triangle bisection algorithm, is applied. This strategy is illustrated on various geometries and mechanical problems. © 2008 Elsevier B.V. All rights reserved.
Adaptive mesh refinement; A posteriori error estimation; Geometry approximation; Mixed finite elements method; Shell
Molecular dynamics of dewetting of ultra-thin water films on solid substrate
Applied Mathematics and Mechanics
28
12
1555-1559
2007
10.1007/s10483-007-1201-z
Molecular dynamics simulation is applied to study the instability and rupture process of ultra-thin water films on a solid substrate. Results show the small disturbance of the film will develop linearly due to the spinodal instability, whereas the interaction between solid and liquid has less influences on the initial growth. Then the rupture occurs and the rim recedes with a dynamic contact angle. The radius of the rim varies with time as the square root of t, which is consistent with the macroscopic theory available. Stronger interaction between solid and liquid will postpone rupture time, decline the dynamic contact angle and raise the density of water near the interface between solid and liquid.
2; 2000 mathematics subject classification; 76d45; chinese library classification o363; dewetting; molecular dynamics simulation; ultra thin liquid film
Incorporation of wall finite relative rotations in a geometrically exact thin-walled beam element
Computational Mechanics
48
2
229-244
2011
10.1007/s00466-011-0593-6
In this paper, a large displacement and finite rotation thin-walled beam element previously developed by the authors, which accounts for cross-section deformation, is extended by including finite relative rotations of the beam walls in the in-plane kinematic description of the cross-sections. The inclusion of these relative rotations is motivated by the fact that it enables a simple and meaningful representation of the cross-section in-plane distortion and allows for a co-rotational description of the wall "local-plate" behavior, which leads to a computationally efficient numerical implementation. The present extension preserves all features of the original formulation, namely the geometrically exact description of the beam mid-surface and the allowance for arbitrary cross-section deformation modes complying with Kirchhoff's assumption. The efficiency of the resulting beam finite element is demonstrated by means of numerical examples, which include comparisons with solutions obtained by means of the previous beam finite element and standard shell finite elements. © 2011 Springer-Verlag.
Beam finite elements; Cross-section deformation; Finite rotations; Large displacements; Thin-walled members
X-ray diffraction measurement of residual stress in epitaxial ZnO/α-Al2O3 thin film
Mechanics Research Communications
6-11
2011
10.1016/j.mechrescom.2011.02.008
Piezoelectric thin films on high acoustic velocity non piezoelectric substrates, such as ZnO and AlN, deposited on diamond or sapphire substrates, are attractive for high frequency and low-loss surface acoustic wave devices. In this work, ZnO films were epitaxialy grown on R-Al2O3 and C-Al2O3 substrates using plasma- assisted molecular beam epitaxy (MBE). The surface roughness of the ZnO layers is about 0.2nm for a 2m×2m AFM scan area. The absolute epitaxial relationships between ZnO films and - plane sapphire are investigated by X-ray diffraction techniques. The resulting relationships for ZnO films on R-Al2O3 and C-Al2O3 substrates are found to be (11 ¯ 20)[0001]ZnO//(01 ¯ (0001)[10 ¯ 10]ZnO//(0001)[2 ¯ 10]C-Al2O3 1 ¯ 12)[0 ¯ 111]R-Al2O3 and , respectively. An analytical technique to determine residual strain in epitaxial ZnO films by X-ray diffraction (XRD) was studied. Based on piezoelectric constitutive equations and Bragg law,weapplied an extended model, in which the elastic, piezoelectric and dielectric constants are introduced, to evaluate the residual stress in these films.
Epitaxial thin film X-ray diffraction Residual Str; MBE
Interface energy and its influence on interface fracture between metal and ceramic thin films in nanoscale
Journal of Applied Physics
108
8
84317
2010
10.1063/1.3501090
A theoretical model about the size-dependent interface energy between two thin films with different materials is developed by considering the chemical bonding contribution based on the thermodynamic expressions and the structure strain contribution based on the mechanical characteristics. The interface energy decreases with reducing thickness of thin films, and is determined by such available thermodynamic and mechanical parameters as the melting entropy, the melting enthalpy, the shear modulus of two materials, etc. The predicted interface energies of some metal/MgO and metal/Al2O3 interfaces based on the model are consistent with the results based on the molecular mechanics calculation. Furthermore, the interface fracture properties of Ag/MgO and Ni/Al2O3 based on the atomistic simulation are further compared with each other. The fracture strength and the toughness of the interface with the smaller structure interface energy are both found to be lower. The intrinsic relations among the interface energy, the interface strength, and the fracture toughness are discussed by introducing the related interface potential and the interface stress. The microscopic interface fracture toughness is found to equal the structure interface energy in nanoscale, and the microscopic fracture strength is proportional to the fracture toughness. (C) 2010 American Institute of Physics. doi:10.1063/1.3501090
Three attempts at two axioms for quantum mechanics
Arxiv preprint arXiv:1011.5322
1-15
2010
The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field h e r e may act on an electron t h e r e. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?
Quantum Physics
Semiclassical Mechanics
SIAM Review
27
4
485-504
1985
Classical mechanics and the quantum conditions of\nPlanck, Bohr, Sommerfeld, Wilson and Einstein are\npresented. The virtues and defects of this `old quantum\ntheory' are pointed out. Its replacement by quantum\nmechanics id is described, leading to the Schroedinger\nequation for the wave function and the corresponding\nenergy eigenvalues. For separable systems, the\nreduction of this equation to ordinary differential\nequations and their asymptotic solution by the WKB\nmethod are described, as well as the resulting\ncorrected quantum conditions with integer or\nhalf-integer quantum numbers. For nonseparable systems,\nthe analogous asymptotic solution constructed by the\nauthor is described, together with the corrected\nquantum conditions to which it leads. Examples of the\nuse of these conditions in the solution of eigenvalue\nproblems are presented. It is explained that\ndifficulties arise in using this method when the\nclassical motion is stochastic or chaotic. Suggestions\nfor overcoming these difficulties are mentioned.
asymptotic analysis; eigenvalue problems; mathemat
Nano and Cell Mechanics: Fundamentals and Frontiers
Nano and Cell Mechanics: Fundamentals and Frontiers
2012
Research in nano and cell mechanics has received much attention from the scientific community as a result of society needs and government initiatives to accelerate developments in materials, manufacturing, electronics, medicine and healthcare, energy, and the environment. Engineers and scientists are currently engaging in increasingly complex scientific problems that require interdisciplinary approaches. In this regard, studies in this field draw from fundamentals in atomistic scale phenomena, biology, statistical and continuum mechanics, and multiscale modeling and experimentation. As a result, contributions in these areas are spread over a large number of specialized journals, which prompted the Editors to assemble this book.Nano and Cell Mechanics: Fundamentals and Frontiers brings together many of the new developments in the field for the first time, and covers fundamentals and frontiers in mechanics to accelerate developments in nano- and bio-technologies.Key features:• Provides an overview of recent advances in nano and cell mechanics.• Covers experimental, analytical, and computational tools used to investigate biological and nanoscale phenomena.• Covers fundamentals and frontiers in mechanics to accelerate developments in nano- and bio-technologies.• Presents multiscale-multiphysics modeling and experimentation techniques.• Examines applications in materials, manufacturing, electronics, medicine and healthcare.Nano and Cell Mechanics: Fundamentals and Frontiers is written by internationally recognized experts in theoretical and applied mechanics, applied physics, chemistry, and biology. It is an invaluable reference for graduate students of nano- and bio-technologies, researchers in academia and industry who are working in nano and cell mechanics, and practitioners who are interested in learning about the latest analysis tools. The book can also serve as a text for graduate courses in theoretical and applied mechanics, mechanical engineering, materials science, and applied physics.
Continuum Damage Mechanics: Part I - General Concepts
Journal of Applied Mechanics
55
1
59
1988
10.1115/1.3173661
ContinuumDamage Mechanics (C.D.M.) has developed continuously since the early worksof Kachanov and Rabotnov. It constitutes a practical tool totake into account the various damaging processes in materials andstructures at a macroscopic continuum level. The main basic featuresof C.D.M. are considered in the first part together withits present capabilities, including damage definitions and measures, and itsincorporation into a thermodynamic general framework. Practical damage growth equationswill be reviewed in the second part of the paper. 1988 ASME
Molecular Mechanics Applied to Single-Walled Carbon Nanotubes 2 . Literature Review 3 . Molecular Mechanics Modeling
Material Researh
11
3
325-333
2008
10.1590/S1516-14392008000300016
Single-walled carbon nanotubes, with stiffness of 1.0 TPa and strength of 60 GPa, are a natural choice for high strength materials. A problem, however, arises when experimental data are compiled. The large variability of experimental data leads to the development of numerical models denominated molecular mechanics, which is a “symbiotic” association of molecular dynamics and solid mechanics. This paper deals with molecular mechanics simulations of single-walled carbon nanotubes. To be able to evaluate the molecular mechanics model, the three major carbon nanotube configurations (armchair, zigzag and chiral) were simulated. It was proven that the carbon nanotube configuration has influence on stiffness. By varying the radius, hence the curvature, the Young’s modulus changed from 0.95 TPa to 5.5 TPa, and the Poisson’s ratio ranged from 0.15 to 0.29. The numerical simulations were in good agreement with those presented in the literature
mechanical; molecular mechanics; numerical simulation; single-walled carbon nanotubes
Fatigue life prediction of cross-ply composite laminates
Materials Science and Engineering: A
238
2
329-335
1997
10.1016/S0921-5093(97)00427-9
To predict the fatigue life of fiber reinforced composites, fatigue process of CFRP laminates of [0°/90°]s is investigated and the influence of damages occurring at fiber, matrix and fiber/matrix interface on the various critical strengths and the relationship between residual critical strength and failure are discussed. As a result, it was shown that fatigue strength (i.e. fatigue life) consisted of residual critical strength and stresses occurring at each layer (0° and 90° layers) and interlayer. Moreover, the fatigue failure occurred because the residual critical strength of each layer and interlayer decreased with dependence of their microdamage densities, so that the fatigue life can be predicted by evaluating microdamage behavior in fatigue process.
90; cfrp laminates of; crack density; fatigue life; number of cycles; residual critical strength; s; stress amplitude ratio
On the transient response of cross-ply laminated circular cylindrical shells
International Journal of Impact Engineering
9
4
475-484
1990
10.1016/0734-743X(90)90036-U
Transient response of simply-supported circular cylindrical shells\nis investigated using a higher-order shear deformation theory (HSDT).\nThe theory is a modification of the Sanders' shell theory and accounts\nfor parabolic distribution of the transverse shear strains through\nthickness of the shell and tangential stress-free boundary conditions\non the bounding surfaces of the shell. The results obtained using\nthe classical shell theory (CST) and the first-order shear deformation\ntheory (FSDT) are compared with those obtained using the higher-order\ntheory. The state-space approach is used to develop the analytical\nsolutions to the equations of motion of the three theories. © 1990.
PEC defect automated classification in aircraft multi-ply structures with interlayer gaps and lift-offs
NDT and E International
53
39-46
2013
10.1016/j.ndteint.2012.10.007
Current pulsed eddy current (PEC) defect classification method requires highly trained personnel and the results are usually influenced by subjectivity of human perception. Lift-off effect and interlayer air gaps are the main obstacles in eddy current defect classification in multi-layer structures. Therefore, automated defect classification in multi-layer structures is very desirable and stringent. In this work, principal component analysis (PCA) and support vector machine (SVM) are investigated for defect automated classification under different interlayer gaps and lift-off effects. The experimental classification and predicting results show that 1st-layer surface defects, 1st-layer sub-surface defects, 2nd-layer surface defects, and 2nd-layer sub-surface defects can be classified satisfactorily when air gap and lift-off vary from 0 to 1.4 mm through the proposed methods, which has the potential for automatic defect in-situ classification for multi-layer aircraft structures. © 2012 Elsevier Ltd.
Air gap; Classification; Lift-off; Principal component analysis; Pulsed eddy current; Support vector machine
N.N. Bogolyubov and statistical mechanics
Russian Mathematical Surveys
49
5
19
1994
10.1070/RM1994v049n05ABEH002419
CONTENTS §1. Introduction §2. Theory of open systems §3. Kinetic\ntheory and hydrodynamics §4. Quantum statistical mechanics References
STA
100 Volumes of ‘Notes on numerical fluid mechanics’: 40 years of numerical fluid mechanics and aerodynamics in retrospect
100 Volumes of ‘Notes on numerical fluid mechanics’: 40 years of numerical fluid mechanics and aerodynamics in retrospect
xviii + 503
2009
10.1007/978-3-540-70805-6
This volume contains 37 invited contributions, collected to celebrate one hundred volumes of the NNFM Series. After a general introduction overviews are given in five parts of the developments in numerical fluid mechanics and related fields. In the first part information about the series is given, its origins are discussed, as well as its environment and the German and European high-performance computer scene. In Part II the co-editors of the series give short surveys over developments in their countries. Current applications, mainly in the aerospace sector, but also in the automotive sector, are discussed in Part III. Applications to flow problems in engineering and physics, ranging from hydraulic machinery to astrophysics, are the topics of Part IV. Algorithms, computer science, commercial CFD, public partnerships in high-performance computing, and hardware development up to petaflops computers are treated in Part V. All volumes, which were published in the series finally are listed in Part VI.
aerodynamics; computational fluid dynamics; computational methods; fluid mechanics; notes on numerical fluid mechanics; numerical fluid mechanics; numerical methods
Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical–cylindrical shells
International Journal of Solids and Structures
43
16
4810-4829
2006
10.1016/j.ijsolstr.2005.07.025
Here, the nonlinear thermo-elastic buckling/post-buckling characteristics of laminated circular conical–cylindrical/conical–cylindrical–conical joined shells subjected to uniform temperature rise are studied employing semi-analytical finite element approach. The nonlinear governing equations, considering geometric nonlinearity based on von Karman’s assumption for moderately large deformation, are solved using Newton–Raphson iteration procedure coupled with displacement control method to trace the pre-buckling/post-buckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deformation. The study is carried out to highlight the influences of semi-cone angle, material properties and number of circumferential waves on the nonlinear thermo-elastic response of the different joined shell systems.
Dynamics of polymeric liquids. Vol. 1, 2nd Ed. : Fluid mechanics
Related Information: Fluid Mechanics. Dynamics of Polymeric Liquids. Volume 1. 2nd Edition
Medium: X; Size: Pages: 784
1987
This book examines Newtonian liquids and polymer fluid mechanics. It begins with a review of the main ideas of fluid dynamics as well as key points of Newtonian fluids. Major revisions include extensive updating of all material and a greater emphasis on fluid dynamics problem solving. It presents summaries of experiments describing the difference between polymeric and simple fluids. In addition, it traces, roughly in historical order, various methods for solving polymer fluid dynamics problems.
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHE; 42 ENGINEERING; CALCULATION METHODS; FLUID FLOW; FLUID MECHANICS; FLUIDS; LIQUID FLOW; LIQUIDS; MECHANICS; POLYMERS
On the curvature effect of thin membranes
Journal of Computational Physics
233
449-463
2013
10.1016/j.jcp.2012.09.001
We investigate the curvature effect of a thin, curved elastic interface that separates two subdomains and exerts a pressure due to a curvature effect. This pressure, which we refer to as interface pressure, is similar to the surface tension in fluid mechanics. It is important in some applications, such as the canopy of parachutes, biological membranes of cells, balloons, airbags, etc., as it partially balances a pressure jump between the two sides of an interface. In this paper, we show that the interface pressure is equal to the trace of the matrix product of the curvature tensor and the Cauchy stress tensor in the tangent plane. We derive the theory for interfaces in both 2-D and 3-D, and present numerical discretizations for computing the quality over triangulated surfaces.
curvature effect; elastic membrane; generalized young–laplace equation; interface pressure; numerical discretizations; stress
Quantum mechanics and mixed quantum mechanics/molecular mechanics simulations of model nerve agents with acetylcholinesterase
Theoretical Chemistry Accounts
109
2003
160-168
2003
10.1007/s00214-002-0424-0
The accurate modeling of biological processes presents major computational difficulties owing to the inherent complexity of the macromolecular systems of interest. Simulations of biochemical reactivity tend to require highly computationally intensive quantum mechanical methods, but localized chemical effects tend to depend significantly on properties of the extended biological environment - a regime far more readily examined with lower-level classical empirical models. Mixed quantum/classical techniques are gaining in popularity as a means of bridging these competing requirements. Here we present results comparing two quantum mechanics/molecular mechanics implementations (the SIMOMM technique of Gordon et al. as implemented in GAMESS, and the ONIOM technique of Morokuma et al. found in Gaussian 98) as performed on the enzyme acetylcholinesterase and model nerve agents. This work represents part of the initial phase of a DoD HPCMP Challenge project in which we are attempting to reliably characterize the biochemical processes responsible for nerve agent activity and inhibition, thereby allowing predictions on compounds unrelated to those already studied.
Acetylcholinesterase; IMOMM; Nerve agent; Simulation
Fracture energy of automotive clearcoats—I. Experimental methods and mechanics
Polymer Degradation and Stability
60
291-299
1998
The fracture energy of five automotive clearcoats was measured using fracture mechanics methods originally developed for measuring the fracture energy of brittle inorganic thin films. The fracture energy of the clearcoats ranged from 12 J m-2 to 140 J m-2. A discrepancy between the actual fracture energy and the [`]apparent' fracture energy was observed and attributed to differences in the tensile stress-strain behavior of the materials, in particular the yield strength. Correcting for differences in their tensile stress-strain behavior, the apparent fracture energy of the films ranged from 13 J m-2 to 330 J m-2. Contrary to expectations, the fracture energy of the clearcoats did not decrease with increasing cross-link density. This was ascribed to differences in chemical architecture and additives in these commercial materials. Measuring the toughness in this manner shows promise for evaluating the long-term cracking resistance of automotive clearcoats.
Short-term plyometric training improves running economy in highly trained middle and long distance runners
Journal of strength and conditioning research / National Strength & Conditioning Association
20
4
947-954
2006
10.1519/R-18235.1
Fifteen highly trained distance runners VO(2)max 71.1 +/- 6.0 ml.min(-1).kg(-1), mean +/- SD) were randomly assigned to a plyometric training (PLY; n = 7) or control (CON; n = 8) group. In addition to their normal training, the PLY group undertook 3 x 30 minutes PLY sessions per week for 9 weeks. Running economy (RE) was assessed during 3 x 4 minute treadmill runs (14, 16, and 18 km.h(-1)), followed by an incremental test to measure VO(2)max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km.h(-1) (4.1%, p = 0.02), but not at 14 or 16 km.h(-1). This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p = 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p = 0.09), and a lower VO(2)-speed slope (14%, p = 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or VO(2)max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics.
Adult; Analysis of Variance; Humans; Lactates/bloo
Selectivity in asymmetric synthesis from QM-guided molecular mechanics
Journal of Molecular Structure: THEOCHEM
506
9-16
2000
10.1016/S0166-1280(00)00398-5
The QM-guided molecular mechanics method (Q2MM) is introduced and defined as a transition state force field model based on modified QM data. Applications to selectivity predictions in asymmetric synthesis are demonstrated. The methodology is compared to the popular QM/MM method. (C) 2000 Elsevier Science B.V.
Asymmetric synthesis; Force fields; Molecular mechanics; Parameterization; Transition state modelling
Delamination of thin bonded cement-based overlays: analytical analysis
Materials and Structures
44
1
43-51
2011
10.1617/s11527-010-9607-7
This paper deals with an analytical approach for the prediction of\ndebonding initiation between cement-based overlay and old concrete\nsubstrate under monotonous mechanical loading. Based on the linear\nelastic fracture mechanics, an available analytical model has been\nused. The calculations take into account the interlocking between two\ncrack surfaces in the overlay. To validate the model, three point\nstatic bending tests on composite specimens were carried out. Assuming\nthat the debonding initiation just occurs after the crack cutting the\noverlay layer reaches the overlay-substrate interface, the stress\nintensity factor of the debonding tip can be calculated, allowing\nprediction of stress fields near the interface debonding tip. Then with\na criterion of debonding initiation and propagation depending on the\ninterface tensile strength, the load associated could be determined and\nmight be interesting for the design of thin bonded cement-based\noverlays. The adequateness of this analytical approach was verified by\nboth experimental data and finite element calculations.
á a; debonding á; durability á; interlocking á analytical approach; q; repairs á interface á; -t; thin bonded overlays á; toumi; tran á a; turatsinze
The Central Mystery of Quantum Mechanics
Arxiv Preprints
24
2009
A critical re-examination of the double-slit experiment and its variants is presented to clarify the nature of what Feynmann called the "central mystery'' and the "only mystery'' of quantum mechanics, leading to an interpretation of complementarity in which a 'wave and particle' description rather than a 'wave or particle' description is valid for the same experimental set up, with the wave culminating in the particle sequentially in time. This interpretation is different from Bohr's but is consistent with the von Neumann formulation as well as some more recent interpretations of quantum mechanics.
complementarity; wave-particle duality
Fracture mechanics analysis of the dentine-luting cement interface
Proceedings of the Institution of Mechanical Engineers Part H-Journal of Engineering in Medicine
216
H4
271-276
2002
10.1243/09544110260138763
The objectives of this study were to determine the fracture toughness of adhesive interfaces between dentine and clinically relevant, thin layers of dental luting cements. Cements tested included a conventional glass-ionomer, F (Fuji I), a resin-modified glass-ionomer, FP (Fuji Plus) and a compomer cement, D (DyractCem). Ten miniature short-bar chevron notch specimens were manufactured for each cement, each comprising a 40 mum thick chevron of lute, between two 1.5 mm thick blocks of bovine dentine, encased in resin composite. The interfacial K-IC results (MN/m(3/2)) were median (range): F, 0.152 (0.14-0.16), FP; 0.306 (0.27-0.37), D; 0.351 (0.31-0.37). Non-parametric statistical analysis showed that the fracture toughness of F was significantly lower (p < 0.05) than those of FP or D, and all were significantly lower than values for monolithic cement specimens [26]. Scanning electron microscopy of the specimens suggested crack propagation along the interface. However, energy dispersive X-ray analysis indicated that failure was cohesive within the cement. It is concluded that the fracture toughness of luting cement was lowered by cement-dentine interactions.
adhesion; bond strength measurements; bovine; compomer; dental glass; dentine adhesion; fluoride release; fracture toughness; glass-ionomer cement; glass-ionomer cements; layer thickness; shear; tests; toughness
More clarity on the concept of material frame-indifference in classical continuum mechanics
Acta Mechanica
202
213-246
2009
10.1007/s00707-008-0028-4
There was and still is a considerable amount of confusion in the community of classical continuum mechanics on the concept of material frame-indifference. An extensive review is presented which will point out and try to resolve various misconceptions that still accompany the literature of material frame-indifference. With the tools of differential geometry a precise terminology is developed ending in a consequent mathematical framework, in which not only the concept of material frame-indifference can be formulated naturally, but showing advantages that go beyond all conventional considerations on invariance used so far in classical continuum mechanics. As an exemplification the Navier-Stokes equations and the corresponding Reynolds averaged equations are written in a general covariant form within Newtonian mechanics.
Circulation around a thin zonal island
Journal of Fluid Mechanics
437
301-323
2001
10.1017/S0022112001004402
Laboratory and numerical experiments are used to study flow of a uniform-density fluid on the beta -plane around a thin zonally elongated island (or ridge segment in the abyss). This orientation is chosen specifically to highlight the roles of the zonal boundary layer dynamics in controlling the circulation around the island. There are examples of deep ocean topography that fall into this category which make the work directly applicable to oceanic flows. Linear theory for the transport around the island and the flow structure is based on a modification of the Island Rule (Pedlosky et al. 1997; Pratt & Pedlosky 1999). The linear solution gives a north-south symmetric flow around the island with novel features, including stagnation points which divide the zonal boundary layers into eastward and westward flowing zones, and a western boundary layer of vanishing length, and zonal jets. Laboratory experiments agree with the linear theory for small degrees of nonlinearity, as measured by the ratio of the inertial to Munk boundary layer scales. With increasing nonlinearity the north-south symmetry is broken. The southern stagnation point (for anticyclonic forcing) moves to the eastern tip of the island. The flow rounding the eastern tip from the northern side of the island now separates from the island. Time-dependence emerges and recirculation cells develop on the northern side of the island. Mean transport around the island is relatively unaffected by nonlinearity and given to within 20% by the modified Island Rule. Numerical solutions of the shallow water equations are in close agreement with the laboratory results. The transition from zonal to meridional island orientation occurs for island inclinations from zonal greater than about 20 degrees.
Fractional quantum mechanics
Physical Review E
62
3
3135
2000
10.1103/PhysRevE.62.3135
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the L\'evy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the L\'evy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schr\"odinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.
Fluid mechanics of slot-coating in photopolymer-based rapid composites manufacturing
Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science
217
1
65-79
2003
10.1243/095440603762554622
This paper describes the fluid mechanics of the slot-coating process in the context of rapid layered manufacturing. It has been conjectured that slot-coating would successfully address a number of common difficulties encountered in the formation of thin layers from a highly viscous fibre-photopolymer composite liquid. The objective of the present study was therefore the development of an engineering analysis tool to assist with the design of a slot-coating-based liquid layer formation mechanism for use as an integral part of a lithography-based rapid layered composite parts manufacturing (RLCM) system. In addition to an analytical model, the paper presents a numerical model based on a volume-of-fluid (VOF) algorithm. This algorithm allows (a) solution of non-steady-state problems, (b) tracking of the free surface of the fluid undergoing large deformations and (c) easy modification of the model's domain to facilitate experimentation with coater geometry. Results from a set of simulated experiments establish a relationship between the liquid-coat height and several design and process parameters. Physical examination of cross-sections of several test parts built on an RLCM prototype system in the authors' laboratory confirmed the ability of the new coater design to form solid layers of good quality, as predicted by the numerical simulations.
fibres; finite-element method; flow; fluid mechanics; photopolymers; rapid manufacturing; slot-coating; volume tracking
Fisher Information and Statistical Mechanics
Entropy
5
2-4
2012
Fisher information is an important concept in statistical estimation theory and information theory, but it has received relatively little consideration in statistical physics. In order to rectify this oversight, in this brief note I will review the correspondence between Fisher information and fluctuations at thermodynamic equilibrium, and discuss various applications of Fisher information to equilibrium and non-equilibrium statistical mechanics.
Game mechanics for classroom engagement
Cutting-Edge Technologies in Higher Education
6 Part C
PARTC
67-94
2012
10.1108/S2044-9968(2012)000006C006
Gamification, the integration of game mechanics to influence behavior and engagement, is a much-touted method of improving participant action. Characteristics of online video games (e.g., World of Warcraft, Farmville, The Sims) have been shown to improve motivation, sustain learner engagement, and increase satisfaction. Gamification is used in websites, businesses, medicine, law enforcement, and increasingly in education. However, gamification is only beneficial to an activity if the relationship between the activity and the final goal are understood. This chapter looks at the gamification in education, in particular second language acquisition, and examines seven basic game mechanics: achievement, appointment, rewards, leaderboards, privacy, social engagement loops (or viral mechanics), and modifiers. The discussion describes implementation of game mechanics and potential pitfalls of gamification. Copyright © 2012 by Emerald Group Publishing Limited.
Co-rotational finite element formulation for thin-walled beams with generic open section
Computer Methods in Applied Mechanics and Engineering
195
19-22
2334-2370
2006
10.1016/j.cma.2005.05.011
A consistent co-rotational total Lagrangian finite element formulation for the geometric nonlinear buckling and postbuckling analysis of thin-walled beams with generic open section is presented. The element developed here has two nodes with seven degrees of freedom per node. The element nodes are chosen to be located at the shear centers of the end cross-sections of the beam element and the shear center axis is chosen to be the reference axis. The deformations of the beam element are described in the current element coordinate system constructed at the current configuration of the beam element. The element nodal forces are derived using the virtual work principle. The virtual rigid body motion corresponding to the virtual nodal displacements is excluded in the derivation of the element nodal forces. A procedure is proposed to determine the virtual rigid body motion. The way used to determine the element coordinate system and element nodal deformations corresponding to the virtual nodal displacements and that corresponding to the incremental nodal displacement are consistent. In element nodal forces, all coupling among bending, twisting, and stretching deformations of the beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. In the derivation of the element tangent stiffness matrix, the change of element nodal forces induced by the element rigid body rotations should be considered for the present method. Thus, a stability matrix is included in the element tangent stiffness matrix. An incremental-iterative method based on the Newton–Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. Numerical examples are presented to investigate the accuracy and efficiency of the proposed method. The effect of the terms in the element nodal force and tangent stiffness matrix, which will converge to zero with the decrease of element size, on the convergence rate of solution and accuracy for the buckling load and nonlinear behavior of three dimensional beam structures are also investigated through numerical examples.
Buckling; Co-rotational formulation; Geometric nonlinearity; Thin-walled beam
Sir James Lighthill and modern fluid mechanics - A memorial tribute
Advances in Fluid Mechanics Iii
26
1-10
2000
10.1155/S0161171299226671
This memorial tribute commemorates Sir James Lighthill the man and the mathematical scientist. A brief biographical information is presented with my personal reminiscences. He is one of the most brilliant; and influential applied mathematicians of the twentieth century. By ally standards, his legacy of research and publications of six books and one hundred fifty papers in fluid mechanics and applied mathematics will remain forever as a remarkable example of scholarly work.
Fatigue and fracture of a Ni-P amorphous alloy thin film on the micrometer scale
Fatigue and Fracture of Engineering Materials and Structures
28
8
703-710
2005
10.1111/j.1460-2695.2005.00923.x
Fracture and fatigue tests have been performed on micro-sized specimens for microelectromechanical systems (MEMS) or micro system technology (MST) applications. Cantilever beam type specimens with dimensions of 10 × 12 × 50 μm3, approximately 1/1000th the size of ordinary-sized specimens, were prepared from a Ni–P amorphous thin film by focused ion beam machining. Fatigue crack growth and fracture toughness tests were carried out in air at room temperature, using a mechanical testing machine developed for micro-sized specimens. In fracture toughness tests, fatigue pre-cracks were introduced ahead of the notches. Fatigue crack growth resistance curves were obtained from the measurement of striation spacing on the fatigue surface, with closure effects on the fatigue crack growth also being observed for micro-sized specimens. Once fatigue crack growth occurs, the specimens fail within one thousand cycles. This indicates that the fatigue life of micro-sized specimens is mainly dominated by a crack initiation process, also suggesting that even a micro-sized surface flaw may be an initiation site for fatigue cracks which will shorten the fatigue life of micro-sized specimens. As a result of fracture toughness tests, the values of plane strain fracture toughness, KIC, were not obtained because the criteria of plane strain were not satisfied by this specimen size. As the plane strain requirements are determined by the stress intensity, K, and by the yield stress of the material, it is difficult for micro-sized specimens to satisfy these requirements. Plane-stress- and plane-strain-dominated regions were clearly observed on the fracture surfaces and their sizes were consistent with those estimated by fracture mechanics calculations. This indicates that fracture mechanics is still valid for such micro-sized specimens. The results obtained in this investigation should be considered when designing actual MEMS/MST devices.
Durability; Fatigue; Fracture; MEMS; Microscale testing; MST; Reliability
Prognostication in thin cutaneous melanomas
Archives of Pathology and Laboratory Medicine
134
12
1758-1763
2010
10.1043/2009-0653-RAR.1
While most patients diagnosed with thin cutaneous melanoma will have a good prognosis, nearly 5% will die of their disease. Thin melanomas are common and approximately one-quarter of all melanoma-related deaths result from thin primary tumors. Patients with thin melanoma commonly have sentinel lymph node biopsies that are uncommonly positive.
Some observations on the early history of equilibrium Statistical mechanics
Journal of statistical physics
110
March
475-496
2003
10.1023/A:1022139230789
The article begins with some personal comments by the author on the outstanding contributions of Michael Fisher to statistical mechanics and critical phenomena. Its major aim is to trace the contributions of a number of pioneering personalities to the early history of equilibrium statistical mechanics. Four different areas are considered: (1) Classical Statistical Mechanics, (2) Quantum Statistical Mechanics, (3) Interacting Systems, and (4) The Ising Model. The article is concerned with the development and applications of statistical mechanics when certain basic assumptions are made. It does not deal with the justification of these assumptions which is a sophisticated discipline of its own.
critical phenomena; history; pioneers; statistical mechanics
Electrically driven cracks in piezoelectric ceramics: experiments and fracture mechanics analysis (vol 50, pg 2333, 2002)
Journal of the Mechanics and Physics of Solids
51
5
977
2003
Pii S0022-5096(02)00118-7
Piezoelectric systems like multilayer actuators are susceptible to damage by crack propagation induced by strain incompatibilities. These can arise under electric fields for example between the electroded and external regions. Such incompatibilities have been realised in thin rectangular model specimens from PZT-piezoelectric ceramics with top and bottom electrodes only close to one edge. Under an electric field, controlled crack propagation has been observed in situ in an optical microscope. The crack paths are reproducible with very high accuracy. Small electrode widths lead to straight cracks with two transitions between stable and unstable crack growth regions, while large electrode widths result in curved cracks with four transitions. Fracture mechanics analysis is able to explain the different crack paths. An iteration method is developed to simulate the curved crack propagation also for strong curvature of the crack paths using the finite element method. The computed crack contours exhibit excellent quantitative agreement with the experiment with respect to their shape, the Stages of stable and unstable crack propagation and the transitions between them. Finally, also the crack length as a function of the electric field can be predicted. (C) 2002 Elsevier Science Ltd. All rights reserved.
a; b; c; compatibility; crack propagation and arrest; delamination; finite elements; piezoelectric material; strain
Quantum mechanics/molecular mechanics restrained electrostatic potential fitting
Journal of Physical Chemistry B
117
48
14960-14966
2013
10.1021/jp409568h
We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pKa values for almost all of the residues considered.
Short-term plyometric training improves running economy in highly trained middle and long distance runners
J Strength Cond Res
20
4
947-954
2006
10.1519/r-18235.1
Fifteen highly trained distance runners VO(2)max 71.1 +/- 6.0 ml.min(-1).kg(-1), mean +/- SD) were randomly assigned to a plyometric training (PLY; n = 7) or control (CON; n = 8) group. In addition to their normal training, the PLY group undertook 3 x 30 minutes PLY sessions per week for 9 weeks. Running economy (RE) was assessed during 3 x 4 minute treadmill runs (14, 16, and 18 km.h(-1)), followed by an incremental test to measure VO(2)max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km.h(-1) (4.1%, p = 0.02), but not at 14 or 16 km.h(-1). This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p = 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p = 0.09), and a lower VO(2)-speed slope (14%, p = 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or VO(2)max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics.
Adult; Analysis of Variance; Humans; Lactates/blood; Male; Muscle Strength/*physiology; Oxygen Consumption/*physiology; Physical Education and Training/*methods; Physical Endurance/*physiology; Running/*physiology
Stress state characterization of delamination cracks in [0/90] symmetric laminates by BEM
International Journal of Solids and Structures
45
1632-1662
2008
10.1016/j.ijsolstr.2007.10.013
The presence in a laminate of plies oriented at 90° with respect to the preferred direction of load generates almost immediately the appearance in these plies of cracks transverse to the load (parallel to the fibres in the lamina). These cracks reach the interface with the neighbouring ply, which in this paper will be considered oriented 0° with respect to the direction of the load. This may cause the bifurcation of the crack, which now appears propagating as a delamination crack between the two plies. The objective of this study is to characterize the stress state at the tip of both, the transverse crack in the 90° ply reaching the interface with the 0° ply, and the delamination crack for different lengths of the debonding. The analysis is performed by means of the Boundary Element Method allowing contact, without or with friction, to take place between the faces of the crack. The plies are considered as equivalent homogeneous bodies under a generalized plane strain state. The results are compared with those predicted by the open and contact models of Interfacial Fracture Mechanics. Accurate knowledge of the stress state at the neighbourhood of the tips of the cracks studied is necessary to generate failure criteria based on Fracture Mechanics parameters to predict the appearance and growth of the type of damage described. © 2007 Elsevier Ltd. All rights reserved.
Boundary Element Method; Contact; Delamination; Fibre reinforced composite; Interface crack; Laminate; Transverse crack
Measuring the elastic modulus of soft thin films on substrates
Experimental and Applied Mechanics, Vol 6
6
741-747
2011
10.1007/978-1-4419-9792-0
The use of instrumented indentation to measure the mechanical properties of thin films supported on substrates where the Young's modulus of the film (E1) is substantially less than that of the Young's modulus of the substrate (E2) with modulus ratios from E1/E2 = 0.0001 to 1 is important for investigating materials such as soft polymers, cellulosic sheets, and biological materials. Most existing models for determining the elastic properties of films or sheets on substrates from indentation measurements were developed for the analysis of metal and dielectric films on semiconductor substrates and thus have been used in cases where E1/E2 is ~0.01 to ~10. In the present work, flat punch indentation of systems with E1/E2 = 0.0001 to 1 is investigated via finite element (FE) modeling and experiments. A FE parametric study in which E1/E2 was varied from 0.0001 to 1 was performed to quantify the effect of substrate stiffness on the measurement of the elastic film properties. A semi-analytical model that treats the thin film and substrate as two springs in series was fit to the FE results to allow for use of the results presented. Preliminary experiments, in which a series of film/substrate systems with various modulus mismatch (E1/E2 from ~0.0005 to ~1) were characterized using instrumented indentation, were performed to evaluate the effectiveness of the model for extracting films properties from indentation measurements. The results of the parametric FE study show that for very stiff substrates, the measured stiffness becomes insensitive to changes in substrate modulus. The analytical model and FE model agree to within 7% for E1/E2 values between 0.0001 to 1 and a/t ratios from 1 to 100. Comparison of the preliminary experimental results and FE model show reasonable agreement, but further investigation is required to obtain better correlation.
Simulation of instabilities in thin nanostructures by a perturbation approach
Computational Mechanics
53
4
739-750
2013
10.1007/s00466-013-0927-7
A new numerical method is proposed to simulate instabilities in thin atomistic structures in quasi-static regime. In contrast with previous approaches based on energy minimization or Newton-Raphson methods, the present technique uses a series expansion of atomistic displacements with respect to a loading path parameter, truncated at high orders. The nonlinear set of equations defined by minimizing the potential energy of the discrete system with respect to nuclei positions is then transformed into a sequence of linear sets of equations, which can be solved efficiently. The solution can be described along very large loading steps without correction, resulting in a significant reduction of matrices to be inverted. Finally, the treatment of limit points and snap-back/snap-through arising when instabilities occur is simplified due to a continuous description with respect to the loading path parameter. The method is applied to the analysis of single carbon atom layers nanostructures like graphene sheets or nanotubes in traction or compression regimes. Accuracy and efficiency of the technique is demonstrated by comparisons with iterative Newton procedures.
ALGORITHMS; Asymptotic numerical method; ASYMPTOTIC-NUMERICAL-METHOD; BUCKLING ANALYSIS; ELEMENT; Graphene; Instabilities; MECHANICS; MINIMIZATION; Molecular statics; MULTIWALLED CARBON NANOTUBES; Nanotubes; NONLINEARITIES; ROTATIONS; UNILATERAL CONTACT
Mechanics of metal cutting
International Journal of Machine Tool Design and Research
1
1-2
89-97
1961
10.1016/0020-7357(61)90046-4
IN PRACTICE, three dimensions are usually needed to specify the geometry of the tool cutting edge relative to the direction of cutting, and the geometry of chip formation (metal removal) is extremely complex, with not even the direction of chip flow given by simple geometrical considerations. It is therefore not surprising that research in mechanics of metal cutting has usually been limited to the relatively simple two dimensional case of orthogonal cutting in which the cutting edge is parallel to the work surface and perpendicular to the direction of cutting. If the depth of cut is small compared to its width the problem is then essentially one of plane strain.\nThe cutting process taking place is characterized by the type of chip produced which following the well known Ernst [i] definition can either be discontinuous, that is, made up of segments as a result of fracture; continuous, that is, formed by a continuous plastic flow; or continuous but with a "built-up edge" which builds-up and breaks-down in a cyclic fashion. Only the second of these processes cart be regarded as a steady motion problem and it is therefore again not surprising that attention has been concentrated on cutting with this type of chip under plane strain conditions.
mechanics; metal cutting
A statistical mechanics-based model for cubic and mixed-anisotropy ferromagnetic systems
Journal of Magnetism and Magnetic Materials
320
3-4
276-278
2008
10.1016/j.jmmm.2003.11.267
A model based on classical statistical mechanics is used to calculate magnetization curves for cubic and mixed-anisotropy systems. Our results on Fe, Ni and SmFe2 are in agreement with measurements on bulk single crystals of these materials. For example, the easy axes of magnetization at room temperature for Fe and Ni are [ 1 0 0] and [ 1 1 1], respectively. For SmFe2, the easy magnetization directions at 77 K and room temperature are [ 1 1 0] and [ 1 1 1], respectively, in agreement with experiment. For the mixed-anisotropy case, we study two model systems in which both uniaxial and biaxial anisotropies are present. In the easy-[1 0 0] system, a magnetization jump to saturation is found if both anisotropies are of the same order of magnitude in contrast to easy-[ 1 1 0] systems where magnetization jumps are found even if the biaxial anisotropy is negligible. Examples of mixed-anisotropy material systems that exhibit a discontinuous jump in magnetization, demonstrated by our calculation, are ultra-thin films of Co/Cu and Fe on stepped Ag(0 0 1) substrates. (c) 2007 Elsevier B.V. All rights reserved.
Local kinetic energy in quantum mechanics
Journal of Chemical Physics
70
788-789
1979
10.1063/1.437511
The question of local kinetic energy in quantum mechanics is considered by using the phase space formulation of quantum mechanics. All quantum mech. expressions are derived for local kinetic energy and give a subset which satisfy Bader's criterion. The different definitions that various authors have used are directly related to particular quasiprobability distributions and correspondence rules.
1306; energy; kinetic; local; mechanics; quantum
Fracture mechanics in railway applications - an overview
Engineering Fracture Mechanics
72
2
163-194
2005
10.1016/j.engfracmech.2003.11.010
This paper gives a general introduction to fracture mechanics application to railway components as well as to the papers within this special issue. It is preluded by a brief discussion of various fracture control concepts such as safe-life, fail-safe and damage tolerance. Following this, an introduction to the most important damage tolerance issues of safety relevant railway components such as axles, wheels and rails is provided. (C) 2004 Elsevier Ltd. All rights reserved.
damage tolerance; fatigue crack extension; fracture mechanics; rails; railway axles; railway wheels
Plane behaviour at high strain rates of a quasi-unidirectional E-glass/polyester composite: application to ballistic impacts
European Journal of Mechanics a-Solids
17
3
461-477
1998
Doi 10.1016/S0997-7538(98)80055-7
Dealing with the plane behaviour of a composite quasi-unidirectional elementary ply made of E glass/polyester, this paper contributes to the study of impact phenomena on ceramic/composite bi-layered targets. Firstly, a quasistatic characterization of the ply in plane tensile and plane shear is carried out. After these tests, an elastoviscoplastic constitutive model with kinematic hardening is derived using the "bi-material" concept. It allows good description of the residual strains, of stiffness losses and of strain rates sensitivities. The second part presents a new fixing method for testing orthotropic materials with the tensile Hopkinson bars apparatus. Then, the elementary ply is tested at high strain rates and these tests are simulated with the constitutive model. Impact simulations incorporating a proposed failure criterion are performed, and then compared with experimental. (C) Elsevier, Paris.
composite; damage; dynamic tensile tests; impact
Near-surface,“thin skin” reverse faulting stresses in the Southeastern United States
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts
7
965-971
1993
10.1016/0148-9062(93)90053-g
Hydraulic fracturing stress measurements have been conducted in crystalline rock at two locations within the southeastern United States at depths from 50 meters to more than one kilometer. Stress orientations are similar to those obtained from other local and regional stress indicators and are consistent with a ridge-push source of intraplate stress. High horizontal stress magnitudes (with respect to the vertical stress) are found only in the near-surface. Thus, although relatively shallow stress orientation measurements appear to be reliable indicators of the stress orientation at greater depth, stress magnitudes cannot be extrapolated quantitatively beyond the depth range of the measurements.
The elastic-plastic mechanics of crack extension
International Journal of Fracture Mechanics
4
1
41-47
1968
10.1007/BF00189145
This paper briefly reviews progres~ in the elastic plastic analysis of crack extension. Analytical results for plane strain and plane stress deformation fields are noted, and elastic-plastic fracture instability as well as transitional behavior and combined rate and thermal effects are discussed.
Stress intensity solutions of thermal fatigue induced cracks in a thin plate hot spot using LEFM and finite element analysis
Engineering Fracture Mechanics
75
10
2826-2841
2008
10.1016/j.engfracmech.2008.01.009
The chief aim of this research is to marry elegant LEFM methods, published material data, and a commercially available FEA code together to represent complex crack growth and arrest phenomena in a thin plate with residual viscoplastic stresses. Additionally, representing the variation in these stress intensities across a thermal gradient to include ultimate fatigue crack arrest is of specific interest. To the authors' knowledge, modeling fracture mechanics due to these hot spots with viscoplastic residual stresses using LEFM methods on this type structure has not been achieved. With these stress intensities, predictions are to be made regarding not only the FCG rate but the probable radial arrest distance of a nominal crack from the hot spot center. © 2008 Elsevier Ltd. All rights reserved.
FEA; Hot spot; LEFM; Stress intensity solution; Stress relaxation; Thermal fatigue; Thermal gradient
Shape memory effect and magnetostriction of sputtered NiMnGa thin films
Smart Structures and Materials 2003: Active Materials: Behavior and Mechanics
5053
191-199
2003
Doi 10.1117/12.484689
NiMnGa thin films have been deposited by magnetron sputtering on Mo substrates using a Ni50Mn30Ga20 Powder metallurgical target. Independent from variation of substrate temperature during the sputtering process the deposited films are found to be polycrystalline. X-ray diffraction patterns show a decreasing peak width and a shift to slightly higher Bragg angles with increasing substrate temperature during sputtering, which is even amplified when subsequent rapid thermal annealing is applied. Annealing temperatures above 500degreesC lead to a remarkable enhancement of the shape memory effect as well as of the magnetostriction. Temperature induced martensitic transformations have been measured by a cantilever deflection technique and a cantilever resonance method. Martensitic start temperatures (M-s) range between 50 and 90degreesC depending on composition and annealing temperature. Stress relief Deltasigma upon the martensitic transformation ranges between 200 and 300 MPa whereas the magnetostrictive coupling constant b is about 2 MPa. Magnetization measurements and Curie temperature determination reveal ferromagnetic behavior within the temperature range of the martensitic transformation.
cantilever deflection; field-induced strain; fmsma; magnetostriction; ni2mnga; nimnga; ni-mn-ga; phase; shape memory alloys
Unsteady 3D Nonlinear Kutta-Joukowski Condition for Thin Lifting Surfaces
Computation Mechanics
24
138-147
1999
10.1007/s004660050446
Considering unsteady potential flows, the fluid velocity regularity\ncondition at a wake shedding edge --often referred to as the Kutta-Joukovski\ncondition-- has been clarified in the 2D nonlinear and 3D linearized\ncases only, and the usual nonlinear direct numerical approaches,\nas they are built on an already discretised view of the problem,\nskip over the theoretical question. A nonlinear Kutta-Joukovski condition\nis proposed here for unsteady 3D flows around thin airfoils, for\nwhich the body and its trailing-edge-shed wake are represented by\ndouble layers. The fluid velocity field, deriving from the potential\nfunction, is expressed using the two usual terms, relating to the\nedge of the sheet and its surface. Removing the singularity for the\nfirst term leads to the well-known condition for the potential jump\nacross the shedding edge to be continuous from the body to the wake.\nFor the second, works by Legras, for the steady case --and readily\nextendible to the unsteady one-- exhibit its logarithmic singular\nbehavior and allow to derive a regularity condition that deals with\nthe surface gradient of the potential jump across the shedding edge.\nLastly, implemented in a general non linearized situation, these\nconditions lead to an expression relating the geometric and doublets\ndistribution characteristics of the two surfaces (wing and wake).
Assembling Structure of Single-Walled Carbon Nanotube Thin Bundles
The Journal of Physical Chemistry C
113
19
8132–8135
2009
10.1021/jp901303b
Atomic force microscopy (AFM), high resolution transmission electron\nmicroscopy, and Raman spectroscopy were used to study the assembling\nstructure of thin bundles containing only a few single-walled carbon\nnanotubes (SWCNTs). The normal close-packed bundles as well as two\nnovel kinds of bundles including spiral bundles and the ribbon-like\nbundles were observed for both free-standing SWCNTs and SWCNTs on\nsubstrates. Molecular mechanics calculation was employed to study\nthe energetic competition between these three types of bundles. It\nwas found that the free-standing spiral bundles and ribbon-like bundles\nare metastable compared with the close-packed bundles. However, ribbon-like\nbundles are more likely to be formed on substrates. This indicates\nthat it is not reliable to assess whether the tested nanotube is\nindividual through the height profile of the AFM image.
Nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method
Computer Methods in Applied Mechanics and Engineering
196
2242-2251
2007
10.1016/j.cma.2006.11.009
The geometric nonlinear buckling problem of a thin doubly curved shallow shell with all edges hinged is complicated and difficult to obtain an exact analytical solution. Thus, differential equations are solved incrementally by using the differential quadrature method in this paper. Detailed formulations are worked out. Convergence study is performed. Several examples with various material properties, curvatures and dimensions are investigated. Comparisons are made with existing semi-analytical data or finite element data. It is shown that the critical loads are lower than the data obtained by either so-called Adjacent Equilibrium Method or Partitioned Solution Method. The possible reasons to cause the difference are discussed. ?? 2006 Elsevier B.V. All rights reserved.
Differential quadrature method; Doubly curved; Shallow shell; Stability
Measuring the adhesion of diamond thin films to substrates using the blister test
Proceedings of the 1995 MRS Spring Meeting
383
Generic
197-207
1995
It is shown that the blister testing technique can be used to measure the adhesion of thin films to their substrates. A brief discussion of blister test mechanics is presented here, leading to a simple equation relating adhesion to the height of the blister and the pressure causing it to grow. Blister test data for plasma-enhanced CVD diamond films on Si substrates have been analyzed using this relation. The tests show adhesion energies of 1.8-2.6 J/m2.
Adhesion; Adhesion energy; Blister testing techniques; Calculations; Chemical vapor deposition; Diamond films; Film-substrate interface; Free-standing film window; Growth temperature; Mechanical testing; Mechanical variables measurement; Plasmas; Pressure effects; Silicon; Substrates
Influence of surface roughness on the electrical conductivity of semiconducting thin films
Physica A: Statistical Mechanics and its Applications
392
14
3008-3017
2013
10.1016/j.physa.2013.03.007
The Green function solution of the Boltzmann transport equation has been applied in case of no magnetic field by ignoring any volume impurities. Gaussian, exponential and power law models for the surface roughness correlation function have been studied and the results have been compared with the ones obtained by other methods. It has been found that the electrical conductivity σ increases with increasing correlation length l for the first two models, while for the third model σ value is of the same order as the first two models. Therefore we show that the shape of the surface roughness can strongly influence the electrical properties. © 2013 Elsevier B.V. All rights reserved.
Boltzmann transport equation; Conductivity; Roughness scattering; Semiconducting thin film
Thoughness and Contact Behavior of Conventional and Low-k Dielectric Thin Films
Mat. Res. Soc. Symp. Proc.
795
1-12
2004
A comprehensive indentation fracture mechanics framework is established that allows the fracture properties of thin films to be determined. The framework is composed of four stress-intensity factors characterizing the stress fields arising from (i) elastic contact, (ii) wedging, (iii) residual elastic-plastic mismatch and (iv) pre-existing film stress. The amplitudes of the stress-intensity factors depend on the deformation properties of the film and vary throughout the indentation cycle. The toughness values of a PVD alumina, for which (iii) and (iv) are dominant, and a low-k film, for which (i), (ii) and (iv) are dominant, are evaluated.
Marangoni instability of a thin liquid film heated from below by a local heat source
Journal of Fluid Mechanics
475
377-408
2003
10.1017/S0022112002003014
We consider the motion of a liquid film falling down a\nheated planar substrate. Using the integral-boundary-layer\napproximation of the Navier-Stokes/energy equations and\nfree-surface boundary conditions, it is shown that the problem is\ngoverned by two coupled nonlinear partial differential equations\nfor the evolution of the local film height and temperature\ndistribution in time and space. Two-dimensional steady-state\nsolutions of these equations are reported for different values of\nthe governing dimensionless groups. Our computations demonstrate\nthat the free surface develops a bump in the region where the wall\ntemperature gradient is positive. We analyse the linear stability\nof this bump with respect to disturbances in the spanwise\ndirection. We show that the operator of the linearized system has\nboth a discrete and an essential spectrum. The discrete spectrum\nbifurcates from resonance poles at certain values of the wavenumber\nfor the disturbances in the transverse direction. The essential\nspectrum is always stable while part of the discrete spectrum\nbecomes unstable for values of the Marangoni number larger than a\ncritical value. Above this critical Marangoni number the growth\nrate curve as a function of wavenumber has a finite band of\nunstable modes which increases as the Marangoni number increases.
High-fidelity ultrasonic pulse-echo scheme for detecting delaminations in composite laminates
Composites Part B: Engineering
30
433-441
1999
10.1016/S1359-8368(99)00017-7
Conventional ultrasonic pulse echo imaging techniques, typically processed in the time domain, are generally limited by the large pulse widths, resulting in inaccurate and confusing B-scan images. This paper deals with a high fidelity ultrasonic pulse-echo signal processing technique suitable for detecting delaminations in thin composite laminates. In this processing scheme, broadband pulse-echo A-scan signals are reconstructed in the transform domain using complex cepstrum and homomorphic deconvolution techniques. The technique is implemented for 8-ply and 16-ply quasi-isotropic graphite/epoxy laminates with embedded Teflon film patches and damage induced by low velocity impact loading. The technique shows excellent improvement in the time resolution so that it can be used effectively for extracting exact time-of-flight information and then constructing accurate B-scan and three-dimensional images of defects in thin composites. Moreover, the approach automatically measures the time delay from the front surface, i.e., it follows the front face, making it useful for inspecting slightly warped laminates or the parts with irregular surfaces.
b; d; delamination; homomorphic deconvolution; ultrasonics
Work-related musculoskeletal symptoms among car mechanics: a descriptive study.
Occupational medicine (Oxford, England)
46
6
407-413
1996
A questionnaire concerning musculoskeletal symptoms (MSS) and working environment was answered by 100% of 103 car mechanics in 12 different garages. Almost all the mechanics had been troubled with MSS at work the past year. The most common MSS were symptoms from the low back, neck, head and shoulders. When asked which symptoms had been most troublesome at work most mechanics reported symptoms from the low back, upper back, shoulders and neck. Symptoms from the shoulders, low back and upper back were associated with absence from work due to MSS (OR = 4.2, 2.3 and 2.1 respectively). Mechanics between the ages of 30 and 40 reported significantly more shoulder symptoms than both younger and older colleagues (p < 0.001). It seems that symptoms from the back and shoulders restrain car mechanics, work more than any other MSS. The mechanics' most common working postures may contribute to the development of back and shoulder symptoms.
absence from work; car mechanics; ergonomics; work-related musculoskeletal
Fluid Mechanics
Image Rochester NY
6
1
539
1987
10.1007/b138775
Mjog god kennslubok. Agaet fyrir byrjendur sem og lengra komna
Impulsively actuated jets from thin liquid films for high-resolution printing applications
Journal of Fluid Mechanics
709
341-370
2012
10.1017/jfm.2012.337
Blister-actuated laser-induced forward transfer (BA-LIFT) is a versatile printing technique in which fine jets of ink are ejected from a thin donor film onto an acceptor substrate, enabling high-resolution patterns to be formed. Fluid ejections are initiated by the rapid expansion of micrometre-sized blisters that form on a polymer film underneath the ink layer. Recent work has demonstrated that these ejections exhibit novel flow phenomena due to the unique dimensions and geometry of the BA-LIFT configuration. In this work, we study the dynamics of BA-LIFT printing using a computational model in which fluid is forced by a boundary that deforms according to experimental time-resolved measurements of an expanding blister profile. This allows the model’s predictions to be unambiguously correlated with experimental blister-actuated ejections without any fitting parameters. First, we validate the model’s predictive capabilities against experimental results, including the ability to accurately reproduce the size, shape and temporal evolution of the jet as well as the total volume of ink released. The validated model is then used to interrogate the flow dynamics in order to better understand the mechanisms for fluid ejection. Finally, parametric studies are conducted to investigate the influence of ink density, surface tension, viscosity and film thickness as well as the size of the blister used. These results provide key insights into avenues for optimization and better control of the BA-LIFT process for improved resolution and repeatability of the printed features.
Tissue Mechanics - Chapter 14 - Cartilage
Tissue Mechanics
471-505
2007
10.1007/978-0-387-49985-7_14
“... After a half a century of research on diarthroidal joint lubrication, the enigma still remains, namely, how can fluid film lubrication be achieved in a diarthroidal joint to provide (such) extraordinary low coefficients of friction?” (From Mow et al., 1992)
Quantum Mechanics: From Realism to Intuitionism
arXiv
128
2010
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable models; models that allow a realist interpretation. In this thesis some of these proofs are discussed, like von Neumann's Theorem, the Kochen-Specker Theorem and the Bell-inequalities. Some more recent developments are also investigated, like Meyer's nullification of the Kochen-Specker Theorem, the MKC-models and Conway and Kochen's Free Will Theorem. This last one is taken to suggest that the problems that arise for certain interpretations of quantum mechanics are not limited to realist interpretations only, but also affect certain instrumentalist interpretations. It is argued that one may arrive at a more satisfying interpretation of quantum mechanics if one adopts a logic that seems more compatible with the instrumentalist viewpoint namely, intuitionistic logic. The motivations for adopting this form of logic rather than classical logic or quantum logic are linked to some of the philosophical ideas of Bohr. In particular a new interpretation of Bohr's notion of complementarity is proposed. Finally some possibilities are explored for linking the intuitionistic interpretation of quantum mechanics to the mathematical formalism of the theory.
Quantum Physics
Holism, physical theories and quantum mechanics
Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics
35
4
693-712
2004
10.1016/j.shpsb.2004.08.001
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.
Classical physics; Entanglement; Holism; Quantum mechanics; Supervenience
Homogenization and two-scale convergence for a Stokes or Navier-Stokes flow in an elastic thin porous medium
Mathematical Models & Methods in Applied Sciences
6
7
941-955
1996
In the general framework of the homogenization method we study the behavior of a thin elastic periodic structure immersed in a viscous fluid. After the proof of the convergence of the homogenization process by using the two-scale convergence method it is possible to take the limit as delta --> 0, the small parameter which represents the thickness of the solid part. We obtain a viscoelastic medium with fading memory. We consider two cases: the one in which we have a Stokes flow in the fluid part and the other one when we have a Navier-Stokes flow in the fluid part.
mechanics
Numerical study of a thin liquid film on a disk under non-uniform rotation - thermocapillary effects
Fluid Dynamics Research
37
3
154-172
2005
DOI 10.1016/j.fluiddyn.2005.03.003
The axisymmetric flow of a viscous heat conducting uniform liquid film on a rotating disk is considered and the governing equations are solved numerically. The model described highlights the effects of thermocapillary force and the effects of different spin-up protocols on the rate of thinning of the film on a rotating disk. (c) 2005 Published by The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.
asymptotic solution; deformable free-surface; evaporation; flow; layer; nonuniform rotation; stationary convection; thermocapillary effects; thin liquid film
Nucleation of interfacial shear cracks in thin films on disordered substrates
Journal of Statistical Mechanics-Theory and Experiment
2009
02
P02047
2009
10.1088/1742-5468/2009/02/P02047
We formulate a theoretical model of the shear failure of a thin film tethered to a rigid substrate. The interface between film and substrate is modeled as a cohesive layer with randomly fluctuating shear strength/fracture energy. We demonstrate that, on scales large compared with the film thickness, the internal shear stresses acting on the interface can be approximated by a second-order gradient of the shear displacement across the interface. The model is used to study one-dimensional shear cracks, for which we evaluate the stress-dependent probability of nucleation of a critical crack. This is used to determine the interfacial shear strength as a function of the film geometry and statistical properties of the interface.
fracture; fracture (theory); heterogeneous materials (theory)
Complex variable boundary element method for potential flow with thin objects
Computer Methods in Applied Mechanics and Engineering
192
1421-1433
2003
10.1016/S0045-7825(02)00647-3
A complex variable boundary element method (CVBEM) is developed for potential flow in the presence of thin objects. Singularities caused by such objects are expressed analytically through the conformal mapping technique, and the resultant singular solution is coupled with the CVBEM by the principle of superposition. This can be done by virtue of the semi-analytic nature of the CVBEM. The numerical results for example problems including flow barriers and high-conductivity fractures confirm that the proposed model yields accurate solutions of the velocity potential and the stream function within the flow domain. © 2003 Elsevier Science B.V. All rights reserved.
Boundary element method; Complex variable; Fracture; Singularity programming
Degrees of Freedom: An Essay on Competitions between Micro and Macro in Mechanics
Philosophy and Phenomenological Research
59(1)
1
1-39
1999
This paper argues that the doctrines of determinism and\nsupervenience, while logically independent, are importantly\nlinked in physical mechanics--and quite interestingly so.\n(edited)
dependence; freedom; mechanics; mind; science
Econophysics: From Game Theory and Information Theory to Quantum Mechanics
Physica A: Statistical Mechanics and its Applications
348
2005
505-543
2005
10.1016/j.physa.2004.09.029
Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the Quantum Mechanics principles using Information and Game Theory. ?? 2004 Elsevier B.V. All rights reserved.
Energy; Information; Optimal laws; Quantum mechanic laws; Rationality
Hamilton-Jacobi/action-angle quantum mechanics
Physical Review D
28
2491-2502
1983
10.1103/PhysRevD.28.2491
A quantum mechanics is constructed which is patterned on classical Hamilton-Jacobi theory. The dynamical basis of the theory is a quantum Hamilton-Jacobi equation with accompanying physical boundary conditions.
Entropic Functionals in Quantum Statistical Mechanics
Arxiv preprint
8 pages
2013
We describe quantum entropic functionals and outline a research program dealing with entropic fluctuations in non-equilibrium quantum statistical mechanics.
Contact buckling and postbuckling of thin rectangular plates
Journal of the Mechanics and Physics of Solids
49
2
209-230
2001
10.1016/S0022-5096(00)00038-7
A combined experimental/finite element effort is carried out to elucidate the post buckling response of unilaterally constrained plates under monotonically increasing edge thrust. Real time observations, together with a wide range of plate aspect ratio and a large load level facilitate deep physical insight into the general behavior of this class of problems. The interaction of the plate with the rigid restraining plane following buckling leads to interesting deformation sequences, characterized by the development of asymmetric bulges and contact zones following by a possible plate snapping. The latter is motivated by a secondary buckling evolving gradually from a contact zone(s) or a bulge(s). These two instability mechanisms are competitive, being dictated by the plate aspect ratio and other system parameters. The critical load for plate snapping agrees well with a finite element prediction based on an asymmetric deformation choice that minimizes the strain energy in the plate. A semi analytic relation for predicting the onset of secondary instability in the contact area and subsequent plate snapping is developed based on the numerical results. Finally, the present work seems to add a new dimension into the fracture of coatings and laminated composites containing near-surface defects.
A. Buckling; B. Contact mechanics; B. Elastic materials; B. Plates; C. Stability and bifurcation
Quantum Mechanics with Constraints
Ann Phys
63
586-591
1971
10.1016/0003-4916(71)90031-5
The classical motion of a particle on a surface is simulated in quantum mechanics by forcing the particle to move between two parallel surfaces with distance d. In the limit d --f 0 one obtains an equation which differs from the equation proposed originally by Schriidinger by an additional potential depending on the curvature of the surface.
Mechanics of Schrodinger mechanics
Arxiv
7
2004
Small perturbations of ideal turbulence obey the Schrodinger equation. Microscopically, the perturbation of turbulence corresponds to formation of small amplitude helices on straight vortex filaments. A helix behaves in the vorticity field of the fluid as a spin particle in the Stern-Gerlach experiment. Taking into account elastic properties of the filament leads to the Klein-Gordon equation.
General Physics; Physics Education
The Effect of Isothermal Aging on Transverse Crack Development in Carbon-Fiber-Reinforced Cross-Ply Laminates
Polymer Composites
16
2
154-160
1995
Doi 10.1002/Pc.750160207
An investigation into the effect of isothermal aging on the development of transverse cracks in cross-ply laminates of two high temperature composite systems was performed. The composite materials investigated were BASF X5260/640-800 and DuPont Avimid K/IM6. Changes in the glass transition temperature, composite weight loss, crack density, and mode I intralaminar fracture toughness were monitored during isothermal aging in air at 177 degrees C for up to 2232 h. The two laminate configurations used in this study include two variations of the generic cross-ply configuration [O-2/90(n)](s), in which n equals 1 and 2. The results of this investigation show that a layer of degraded material forms at the surface of the X5260/640-800 bismaleimide laminates and that the thickness of the degraded layer increases with aging time. After 744 h of aging, transverse cracks form in the surface plies and an increasing crack density evolves as aging time is increased; however, transverse cracks do not form in the inner 90 degrees ply groups with aging during the time period investigated. The Avimid K/IM6 thermoplastic polyimide laminates, which show evidence of cracking prior to aging, do not exhibit any significant change in crack density with aging. The results of the aging experiments also show that the bismaleimide system exhibits a weight loss of 1.5% and an increase in glass transition temperature from 250 degrees C to 300 degrees C after 2232 h of aging at 177 degrees C, while the thermoplastic polyimide system shows a weight loss of only 0.05% and an increase in glass transition temperature from 280 to 285 degrees C after 2232 h. Changes in the resistance to crack formation are also seen in these materials during aging. The mode I intralaminar fracture toughness, a measure of resistance to transverse crack formation, shows a 50% decrease after aging for 2232 h for the bismaleimide system, while the behavior exhibited by the thermoplastic polyimide shows little evidence of a reduction.
The Mechanism of Camber Thrust Generation in a Bias-ply Motorcycle Tire
Vehicle System Dynamics
13
October 2014
173-186
1984
10.1080/00423118408968774
A finite element model suitable for camber thrust analysis is formed. By inclining and pressing this finite element model onto the road plane, the forces prevailing in the contact patch of an inclined standing tire are calculated and the asymmetry-dependent mechanism of camber thrust generation is analyzed. By rotating the inclined standing tire at a constant vertical deflection, the roll-distance-dependent mechanism of camber thrust generation is analyzed.
Examining the differential effects of feedback in ply-form and track-form on staff training of consumers in a sheltered workshop.
Dissertation Abstracts International: Section B: The Sciences and Engineering
56
11-B
6434
1996
The field of organizational behavior management (OBM) utilizes behavioral principles to produce improvement and efficiency in organizations. This work has primarily been applied with little evaluation of its theoretical significance. The purpose of the present research was to investigate the probability that staff would engage their consumers in training in a community work setting for individuals with developmental disabilities as affected by the interaction between the presence of the manager with performance feedback provided to workshop staff in ply-form versus track-form. The effects these types of contingencies have on engaging consumers in training activities were also examined. Results indicate that both types of feedback increased staff training time. For three of the five staff, differential effects were seen between ply-form and track-form feedback phases in the manager absent conditions. The increases in training time were accompanied by increases in consumer on-task behavior. Acceptability data suggested that staff were receptive to the feedback and found it helpful for themselves and their consumers. The theoretical and applied relevance of these findings are discussed. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Consumer Behavior; Employee Interaction; Feedback; feedback in ply-form vs track-form phases; Organizational Behavior; Personnel Training; sheltered workshop staff & consumers; staff training of consumers
Nuclear mechanics in cancer.
Advances in experimental medicine and biology
773
435-70
2014
10.1007/978-1-4899-8032-8_20
Despite decades of research, cancer metastasis remains an incompletely understood process that is as complex as it is devastating. In recent years, there has been an increasing push to investigate the biomechanical aspects of tumorigenesis, complementing the research on genetic and biochemical changes. In contrast to the high genetic variability encountered in cancer cells, almost all metastatic cells are subject to the same physical constraints as they leave the primary tumor, invade surrounding tissues, transit through the circulatory system, and finally infiltrate new tissues. Advances in live cell imaging and other biophysical techniques, including measurements of subcellular mechanics, have yielded stunning new insights into the physics of cancer cells. While much of this research has been focused on the mechanics of the cytoskeleton and the cellular microenvironment, it is now emerging that the mechanical properties of the cell nucleus and its connection to the cytoskeleton may play a major role in cancer metastasis, as deformation of the large and stiff nucleus presents a substantial obstacle during the passage through the dense interstitial space and narrow capillaries. Here, we present an overview of the molecular components that govern the mechanical properties of the nucleus, and we discuss how changes in nuclear structure and composition observed in many cancers can modulate nuclear mechanics and promote metastatic processes. Improved insights into this interplay between nuclear mechanics and metastatic progression may have powerful implications in cancer diagnostics and therapy and may reveal novel therapeutic targets for pharmacological inhibition of cancer cell invasion.
Cell Compartmentation; Cell Nucleus; Cell Nucleus: physiology; Humans; Neoplasms; Neoplasms: pathology
Phase space quantum mechanics
Annals of Physics
327
2
167-211
2012
10.1016/j.aop.2011.09.006
This paper develops an alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative *-product and the deformation of the Poisson bracket to an appropriate Lie bracket are the key elements in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding *-products contains as a special case all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of *-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the *-multiplication. The most important result of the paper shows that developed formalism is more fundamental than the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally. In addition, examples of a free particle and a simple harmonic oscillator illustrating the formalism of the deformation quantization and its classical limit are given. © 2011 Elsevier Inc.
Deformation quantization; Moyal product; Quantum mechanics; Star product; Wigner function
Canonical transformation in quantum mechanics
American Journal of Physics
58
5
439
1990
10.1119/1.16475
The phase‐space picture of quantum mechanics and some examples illustrating it are presented. Since the position and momentum are c numbers in this picture, it is possible to introduce the concept of phase space in quantum mechanics. The uncertainty relation is stated in terms of an area element in phase space, whose minimum size is Planck’s constant. Area‐preserving canonical transformations in phase space are therefore uncertainty‐preserving transformations. The wave‐packet spread, coherent‐state representation, and squeezed states of light are discussed as illustrative examples.
Electrified viscous thin film flow over topography
Journal of Fluid Mechanics
597
449-475
2008
10.1017/S002211200700986X
The gravity-driven flow of a liquid film down an inclined wall with periodic indentations in the presence of a normal electric field is investigated. The film is assumed to be a perfect conductor, and the bounding region of air above the film is taken to be a perfect dielectric. In particular, the interaction between the electric field and the topography is examined by predicting the shape of the film surface under steady conditions. A nonlinear, non-local evolution equation for the thickness of the liquid film is derived using a long-wave asymptotic analysis. Steady solutions are computed for flow into a rectangular trench and over a rectangular mound, whose shapes are approximated with smooth functions. The limiting behaviour of the film profile as the steepness of the wall geometry is increased is discussed. Using substantial numerical evidence, it is established that as the topography steepness increases towards rectangular steps, trenches, or mounds, the interfacial slope remains bounded, and the film does not touch the wall. In the absence of an electric field, the film develops a capillary ridge above a downward step and a slight depression in front of an upward step. It is demonstrated how an electric field may be used to completely eliminate the capillary ridge at a downward step. In contrast, imposing an electric field leads to the creation of a free-surface ridge at an upward step. The effect of the electric field on film flow into relatively narrow trenches, over relatively narrow mounds, and down slightly inclined substrates is also considered.
Quaternionic quantum mechanics and quantum fields
International series of monographs on physics
xii, 586 p.
1995
It has been known since the 1930s that quantum mechanics can be formulated in quaternionic as well as complex Hilbert space. But systematic work on the quaternionic extension of standard quantum mechanics has scarcely begun. Authored by a world-renowned theoretical physicist, this book signals a major conceptual advance and gives a detailed development and exposition of quaternionic quantum mechanics for the purpose of determining whether quaternionic Hilbert space is the appropriate arena for the long sought-after unification of the standard model forces with gravitation. Significant results from earlier literature, together with many new results obtained by the author, are integrated to give a coherent picture of the subject. The book also provides an introduction to the problem of formulating quantum field theories in quaternionic Hilbert space. The book concludes with a chapter devoted to discussions on where quaternionic quantum mechanics may fit into the physics of unification, experimental and measurement theory issues, and the many open questions that still challenge the field. This well-written treatise is a very significant contribution to theoretical physics. It will be eagerly read by a wide range of physicists.
Mathematical physics.; Quantum field theory.; Quantum theory.; Quaternions.
Bell’s theorem: Does quantum mechanics contradict relativity?
American Journal of Physics
55
8
696
1987
10.1119/1.15059
Special relativity demands a locality principle (no instantaneous action at a distance); locality implies Bell’s theorem; quantum mechanics violates Bell’s inequality, therefore, quantum mechanics contradicts relativity! Or so it would seem. It is shown, however, that the locality principle needed for Bell’s theorem is stronger than the simple locality that is needed to satisfy the demands of relativity and that quantum mechanics satisfies the latter. The stronger locality principle is equivalent to the conjunction of simple locality and predictive completeness, and it is the latter principle that fails. The notion of predictive completeness is weaker than, and is implied by, the completeness criterion of Einstein, Podolsky, and Rosen. But the quantum mechanical state description is not only incomplete but incompletable, for any local complete state description would satisfy Bell’s inequality and disagree with experiment.
Hierarchical models of thin elastic structures: Overview and recent advances in error estimation and adaptivity
Computer Methods in Applied Mechanics and Engineering
196
3508-3523
2007
10.1016/j.cma.2006.10.021
In the numerical approximation of hierarchical models of thin bodies, there are two separate contributions to the total error: (a) modeling error is the error due to dimensional reduction, and (b) discretization error is the error due to the numerical approximation. Traditionally, estimation of these errors has been performed in terms of abstract quantities like the global energy norm, which does not give a clear representation of the error in the local features of the solution. Recently, a new class of finite element error estimation techniques has emerged wherein errors in a simulation are measured not in norms but in quantities of interest to the analyst. Following a brief overview of the literature, we focus on extending the theory of a posteriori estimation of the modeling error to local quantities of interest that have physical meaning. Independent estimates are obtained for the modeling and discretization errors in quantities of interest. These local estimates are used to develop goal-oriented adaptive modeling strategies in which the model is automatically adapted by controlling the two errors independently and effectively to obtain local quantities of interest to within a preset level of accuracy. Numerical examples are presented to demonstrate the accuracy of the error estimates and the adaptive strategy. ?? 2007 Elsevier B.V. All rights reserved.
Dimensional reduction; Finite element method; Goal-oriented adaptivity; Hierarchical modeling; Modeling error estimation
Static and vibration analysis of thin plates by using finite element method of B-spline wavelet on the interval
Structural Engineering and Mechanics
25
5
613-629
2007
10.12989/sem.2007.25.5.613
A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.
B-spline wavelet on the interval; Finite element method; Modal analysis; Thin plate analysis
Longwave stability of three-layer plane Poiseuille flow with an inner thin layer. Application to the coextrusion of polymers
Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy
327
2–3
201-206
1999
http://dx.doi.org/10.1016/S1287-4620(99)80056-8
This paper deals with the longwave stability of three-layer plane Poiseuille flow of Oldroyd-B fluids. The thickness of the inner layer is assumed to be very thin with respect to the outer layers. The stability is given by two eigenvalues: one corresponds to that obtained for the two-layer flow composed by the two outer layers, whereas the other one expresses the effect of the thin layer. In this way, simple conditions on the rheological properties of the inner layer are given so that the stability is given only by the eigenvalue associated to the two large layers.
interface; longues ondes; longwave; multicouche; multifluid; Oldroyd-B; Poiseuille; stabilité; stability
Uniformly valid asymptotic solutions of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate of four clamped edges with variable thickness
Applied Mathematics and Mechanics-English Edition
25
7
817-826
2004
By using "the method of modified two-variable", "the method of mixing perturbation" and introducing four small parameters, the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied. And the uniformly valid asymptotic solution of Nth- order for epsilon(1) and Mth-order for epsilon(2) of the deflection functions and stress function are obtained.
four clampled edge; method of mixing perturbation; method of modified two-variable; nonlinear unsymmetrical bending; orthotropic rectangular thin plate with variable t; uniformly valid asymptotic solution
Classical superstring mechanics
Nuclear Physics B
263
93-104
1986
We describe the classical mechanics of the superstring in both hamiltonian and lagrangian formulations, including massless external fields. The formulation is a modification of that of Green and Schwarz that allows supersymmetric Lorentz covariant quantization.
Ductile steel fibre composites with brittle and ductile matrices
Composites Part A: Applied Science and Manufacturing
61
235-244
2014
10.1016/j.compositesa.2014.02.006
Due to the intrinsic brittleness of high performance fibres, traditional structural fibre-reinforced composites have limited ductility and toughness. In the present work a new class of fibres is explored for the reinforcement of polymers: continuous stainless steel fibres that simultaneously possess a high stiffness and a high strain-to-failure. The fibres are combined with brittle and ductile matrix systems (epoxy and PA-6) to produce unidirectional and cross-ply composites. The composites are investigated in quasi static tensile tests accompanied with acoustic emission registration. The steel fibre composites are found to exhibit a 3–4times higher strain-to-failure than typical carbon or glass fibre composites.
A. Fibres; B. Mechanical properties; B. Micro-mechanics; B. Plastic deformation
Temperature gradient mechanism in laser forming of thin plates
Optics and Laser Technology
39
4
858-863
2007
10.1016/j.optlastec.2005.12.006
To obtain further insight into the deformation of a plate in the laser forming process, the temperature gradient mechanism (TGM) is studied. Through the investigation, it can be found that, under the processing conditions of TGM, the plate not only bends about the x-axis but also about the y-axis. An analytical model estimate of the bending angle about the y-axis is constructed based on the theories of heat transfer and the mechanics of elastoplasticity. Numerical simulations are carried out to investigate the deformation of the plate about the y-axis by choosing the different process parameters. The analytically based estimate is used to suggest suitable starting values for the simulation process of calculated results. The study of the bending about the y-axis may describe more fully the deformation of a plate, which is helpful in high-precision forming. ?? 2006 Elsevier Ltd. All rights reserved.
Analytical model; Laser forming; Temperature gradient mechanism
Quantum mechanics: Passage through chaos
Nature
461
7265
736-737
2009
10.1038/461736a
A quantum system can undergo tunnelling even without a barrier to\ntunnel through. The latest experiments visualize this process in\nexquisite detail, completely reconstructing the state of the evolving\nsystem.
Shear Moduli of Structural Composites from Torsion Tests
Journal of Composite Materials
36
10
1151-1173
2002
10.1177/0021998302036010486
A combined experimental/analytical approach for effective evaluation of in-plane and out-of-plane shear moduli of structural composite laminates from torsion is presented. The test samples are produced by pultrusion and consist of E-glass fiber systems and vinylester resin. Three types of rectangular samples are used: unidirectional samples cut from plates; angle-ply and angle/cross ply samples cut from wide-flange beams. The shear moduli are obtained from the experimental torsional stiffnesses (T/φ) and data reduction techniques based on torsion solutions by Lekhnitskii and Whitney. The classical approach of usingpaired samples of different widths but same material orientation can grossly underestimate out-of- plane shear moduli. Thus, to overcome this problem, samples with material orientations normal to each other are used, and to obtain samples of larger dimensions than the available thicknesses of the material, the pultruded laminates are bonded flat-wise, from which transverse strips of different widths are cut. Consistent results are obtained by the two data reduction techniques, and the experimental values are compared to predictions by micro/macro-mechanics models
Cracking resistance of thin-bonded overlays using fracture test, numerical simulations and early field performance
International Journal of Pavement Engineering
03 Aug 2012
1-13
2012
10.1080/10298436.2012.711474
Thin-bonded bituminous overlays are becoming an increasingly popular pavement maintenance treatment, which can be used to restore smoothness, seal and renew the pavement surface and increase skid resistance. Thin-bonded overlays (TBOs) are constructed using a specialised type of paving equipment called a ‘spray paver’.Aspray paver combines the operation of applying a tack coat and laying down asphalt concrete in a single pass. This allows for the application of a high rate of polymer-modified asphalt emulsion tack coat. Due to reduced thickness, cracking distress is more of a concern in this type of system. This paper describes a new approach for the evaluation of the cracking performance of TBO systems through fracture mechanics-based testing of laboratory and field specimens. Computer simulations and early field performance data are also used in the evaluation. This study is conducted in the context of three field projects which encompass seven different pavement test sections. The test sections allowed a number of variables to be studied, including type and application rate of tack coat emulsion and type of hot-mix asphalt gradation structure (gap graded vs. dense graded). Comparisons are also made between overlays constructed using spray paver and conventional paving process. All seven sections were computationally simulated to evaluate their performance in the context of thermal and reflective cracking potential. Fairly good agreement is observed between laboratory tests, computer simulations and field performance data. The results indicate that good thermal and reflective cracking resistance are expected from TBOs. Furthermore, it was observed that the cracking performance of TBOs depends on the type of gradation for the overlay mixture and the tack coat emulsion type and its application rate.
A scaled thickness conditioning for solid- and solid-shell discretizations of thin-walled structures
Computer Methods in Applied Mechanics and Engineering
200
9-12
1301-1310
2011
10.1016/j.cma.2010.11.001
The numerical discretization of thin shell structures yields ill-conditioned stiffness matrices due to an inherent large eigenvalue spectrum. Finite element parametrization that depends on shell thickness, like relative displacement shells, solid shells and other solid finite elements even add to the ill-conditioning by introducing high eigenmodes. To overcome this numerical issue we present a scaled thickness conditioning (STC) approach, a mechanically motivated preconditioner for thin-walled structures discretized with continuum based element formulations. The proposed approach is motivated by the scaled director conditioning (SDC) method for relative displacement shell elements. In contrast to SDC, the novel STC approach yields a preconditioner for the effective linear system. It is applicable independently of element technology employed, coupling to other physical fields, boundary conditions applied and additional algebraic constraints and can be easily extended to multilayer shell formulations. The effect of the proposed preconditioner on the conditioning of the effective stiffness matrix and its eigenvalue spectrum is studied. It is shown that the condition number of the modified system becomes almost independent from the aspect ratio of the employed elements. The improved conditioning has a positive influence on the convergence behavior of iterative linear solvers. In particular, in combination with algebraic multigrid preconditioners the number of iterations could be decreased by more than 85% for some examples and the computation time could be reduced by about 60%.
T-stress effects on steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modeling
Engineering Fracture Mechanics
78
6
1182-1200
2011
10.1016/j.engfracmech.2010.11.018
The non-singular T-stress provides a first-order estimate of geometry and loading mode, e.g. tension vs. bending, effects on elastic-plastic, crack-front fields under mode I conditions. The T-stress has a pronounced effect on measured crack growth resistance curves for ductile metals - trends most computational models confirm using a two-dimensional setting. This work examines T-stress effects on three-dimensional (3D), elastic-plastic fields surrounding a steadily advancing crack for a moderately hardening material in the framework of a 3D, small-scale yielding boundary-layer model. A flat, straight crack front advances at a constant quasi-static rate under near invariant local and global mode I loading. The boundary-layer model has thickness B that defines the only geometric length-scale. The material flow properties and (local) toughness combine to limit the in-plane plastic-zone size during steady growth to at most a few multiples of the thickness (conditions obtainable, for example, in large, thin aluminum components). The computational model requires no crack growth criterion; rather, the crack front extends steadily at constant values of the plane-stress displacements imposed on the remote boundary for the specified far-field stress intensity factor and T-stress. The specific numerical results presented demonstrate similarity scaling of the 3D near-front stresses in terms of two non-dimensional loading parameters. The analyses reveal a strong effect of T-stress on key stress and strain quantities for low loading levels and less effect for higher loading levels, where much of the plastic zone experiences plane-stress conditions. To understand the combined effects of T-stress on stresses and plastic strain levels, normalized values from a simple void-growth model, computed over the crack plane for low loading, clearly reveal the tendency for crack-front tunneling, shear-lip formation near the outside surfaces, and a minimum steady-state fracture toughness for T= 0 loading. ?? 2010 Elsevier Ltd.
Constraint effects; Ductile void growth; Fracture mechanics; Non-dimensional scaling; Steady crack growth; Three-dimensional effects; T-stress
Quantum mechanics for space applications
Applied Physics B: Lasers and Optics
84
4
545-550
2006
10.1007/s00340-006-2412-x
Abstract~~This paper is an introduction to the following articles in the scope of quantum mechanics for space study initiated by ESA and lead by ONERA. The context of quantum mechanics for space is summarised, and the fields under development are briefly introduced. Technological applications of quantum mechanics in space are explored and some tests of quantum mechanics are outlined. We also give a brief presentation of the opto-electronic section of the European Space Agency, and the technology development activities it carries out, with particular emphasis on those activities related to the topics of interest of the quantum mechanics in space workshop. As an example, a summary of two ESA studies on gravity gradiometry and their relevance to the field of atomic interferometry is given. In view of the scientific requirements, derived for both Earth observation and planetology for future space missions, atom interferometry shows promise and may provide an advantage over currently available accelerometer and inertial sensor systems.
Interaction of highly nonlinear solitary waves with thin plates
International Journal of Solids and Structures
49
13
1463-1471
2012
10.1016/j.ijsolstr.2012.02.013
We investigate the reflection of highly nonlinear solitary waves in one-dimensional granular crystals interacting with large plates. We observe significant changes in the reflected waves' properties in terms of wave amplitude and time of flight in association with the intrinsic inelasticity of large plates, which are governed by the plate thickness and the size of the granular constituents. We also study the effects of fixed plate boundaries in the formation of reflected waves, and find the existence of a critical distance, within which the interaction between the granular chain and plate is strongly modified. We explain the effects of intrinsic inelasticity and of boundaries in the large plates by using plate theory and the contact mechanics between a plate and a spherical striker. We find that experimental results are in excellent agreement with the analytical predictions and numerical simulations based on the combined discrete element and spectral element models. The findings in this study can be useful for the nondestructive evaluation of plate structures using granular crystals, which can improve the resolution of in-situ, portable measurement instruments leveraging high acoustic energy and sensitivity of solitary waves. ?? 2012 Elsevier Ltd. All rights reserved.
Granular crystals; Impact; Nondestructive evaluation; Solitary waves
Twyman effect mechanics in grinding and microgrinding.
Applied optics
35
28
5704-13
1996
10.1364/AO.35.005704
In the Twyman effect (1905), when one side of a thin plate with both sides polished is ground, the plate bends: The ground side becomes convex and is in a state of compressive residual stress, described in terms of force per unit length (Newtons per meter) induced by grinding, the stress (Newtons per square meter) induced by grinding, and the depth of the compressive layer (micrometers). We describe and correlate experiments on optical glasses from the literature in conditions of loose abrasive grinding (lapping at fixed nominal pressure, with abrasives 4-400 μm in size) and deterministic microgrinding experiments (at a fixed infeed rate) conducted at the Center for Optics Manufacturing with bound diamond abrasive tools (with a diamond size of 3-40 μm, embedded in metallic bond) and loose abrasive microgrinding (abrasives of less than 3 μm in size). In brittle grinding conditions, the grinding force and the depth of the compressive layer correlate well with glass mechanical properties describing the fracture process, such as indentation crack size. The maximum surface residual compressive stress decreases, and the depth of the compressive layer increases with increasing abrasive size. In lapping conditions the depth of the abrasive grain penetration into the glass surface scales with the surface roughness, and both are determined primarily by glass hardness and secondarily by Young's modulus for various abrasive sizes and coolants. In the limit of small abrasive size (ductile-mode grinding), the maximum surface compressive stress achieved is near the yield stress of the glass, in agreement with finite-element simulations of indentation in elastic-plastic solids.
deterministic microgrinding; fracture toughness; hardness; lapping; loose abrasive grinding; optics manufacturing; surface stress; twyman effect
Frequency response of bimodular cross-ply laminated cylindrical panels
Journal of Sound and Vibration
327
1-2
55-69
2009
10.1016/j.jsv.2009.05.026
With the in-plane inertia, the response of bimodular material laminated cylindrical panels computed using direct time integration shows numerical instability. This instability is due to the sudden change in the restoring force from positive/negative half cycle to negative/positive half cycle. The sudden change in restoring force with in-plane inertia excites higher harmonics at every instant of a cycle change leading to numerical instability. This numerical instability can be eliminated if the switch over from positive to negative half cycle or vice versa is exactly at the instant when restoring force is zero. However all the elements of restoring force vector do not become zero simultaneously when direct time integration is performed. Thus it is not possible in the numerical time integration approach to find time instant when restoring force vector becomes a null vector. Therefore, an approach based on Galerkin method in time domain is proposed for the steady-state response of bimodular material structures that eliminates the instability. Its efficacy is demonstrated for the first time for frequency response of bimodular material laminated cylindrical panels modelled using finite element based on Bert's constitutive model. ?? 2009 Elsevier Ltd. All rights reserved.
General relativistic statistical mechanics
Physical Review D
87
8
084055
2013
10.1103/PhysRevD.87.084055
Understanding thermodynamics and statistical mechanics in the fully general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the nonrelativistic limit but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer and is given by kT=ℏdτ/ds, with k the Boltzmann constant, ℏ the Planck constant, ds proper time and dτ the equilibrium thermal time.
Laminate mechanics for balanced woven fabrics
Composites Part B: Engineering
37
2-3
108-116
2005
10.1016/j.compositesb.2005.08.004
Laminate mechanics equations are presented for composites with balanced woven fabric reinforcements. It is shown that mimicking these textile composites with equivalent transversely isotropic ('unidirectional') layers requires disputable manipulations. Various micromechanics predictions of textile composite properties are currently available, however. These can be applied directly to generate the required material property data for the woven fabric laminate mechanics. The commonly used quasi-isotropic laminates with balanced woven fabric reinforcement are subsequently analysed. Closed form expressions are derived for the inplane and out-of-plane elastic properties of these quasi-isotropic laminates, which slightly differ from previous results for unidirectional reinforcement. ?? 2005 Elsevier Ltd. All rights reserved.
Elasticity; Laminate mechanics; Laminates
Electromagnetic interference (EMI) shielding of thin graphite/epoxy composite plates.
International SAMPE Electronics Conference
6
Crit. Mater. Processes Changing World
82-94
1992
Samples of several material combinations were tested for EMI shielding effectiveness over the frequency range 0.2-40 GHz using a dual chamber test method. The samples tested consisted of 203 mm (8 in.) square panels. The materials tested were, a solid Al plate 0.76 mm thick for control and thin (3 ply) graphite/epoxy fabric laminates that were: (1) plated with 0.051 mm Ni, (2) cocured with an outer layer of Cu mesh on each side, (3) cocured with an outer layer of Al mesh on each side, (4) cocured with an outer layer of Ni-coated graphite fiber mat on each side, and (5) cocured with an outer layer of Ag-coated graphite fiber mat on each side. A 19 mm wide area along all edges of the samples (2-5) was abraded to expose the outer layer of conductive material, where elec. contact with the metal test fixture was needed. All samples exhibited min. shielding effectiveness level ≥65 dB at 0.3-40 GHz. The Ni-plated composite had shielding effectiveness ∼ equal to that of the solid Al plate over the entire frequency range. Al and Cu mesh samples had the highest overall contact resistance at the abraded edge and the lowest shielding effectiveness. When tests were repeated at a later time the shielding effectiveness of the Al and Cu mesh decreased due to the formation of oxide layers on the abraded surface. [on SciFinder(R)]
electromagnetic shield graphite epoxy
Boltzmann and Statistical Mechanics
Dynamics: Models and Kinetic Methods for Non-equilibrium Many Body Systems
May 1994
221-238
2000
10.1007/978-94-011-4365-3_13
Lecture given at the International Meeting ``Boltzmann's Legacy - 150 Years after his Birth'', organized by the Accademia Nazionale dei Lincei, 25 - 28 May 1994, in Rome, to be published in: ``Atti dell"Accademia Nazionale dei Lincei'', 1997.
Generalizations of Quantum Mechanics
Arxiv Preprints
15
2005
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their extension to 'quantum nonequilibrium', and we consider the continuous spontaneous localization model of wave function collapse. Other models are briefly discussed.
On the Weak Measurement of Velocity in Bohmian Mechanics
Journal of Statistical Physics
134
5
13
2008
10.1007/s10955-008-9674-0
In a recent article (New Journal of Physics 9, 165, 2007), Wiseman has proposed the use of so-called weak measurements for the determination of the velocity of a quantum particle at a given position, and has shown that according to quantum mechanics the result of such a procedure is the Bohmian velocity of the particle. Although Bohmian mechanics is empirically equivalent to variants based on velocity formulas different from the Bohmian one, and although it has been proven that the velocity in Bohmian mechanics is not measurable, we argue here for the somewhat paradoxical conclusion that Wiseman's weak measurement procedure indeed constitutes a genuine measurement of velocity in Bohmian mechanics. We reconcile the apparent contradictions and elaborate on some of the different senses of measurement at play here.
Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators
Communications in Mathematical Physics
164
60
1999
10.1007/s002200000216
We study the model of a strongly non-linear chain of particles coupled to two heat baths at different temperatures. Our main result is the existence and uniqueness of a stationary state at all temperatures. This result extends those of Eckmann, Pillet, Rey-Bellet to potentials with essentially arbitrary growth at infinity. This extension is possible by introducing a stronger version of H\"ormander's theorem for Kolmogorov equations to vector fields with polynomially bounded coefficients on unbounded domains.
Is String Interactions the Origin of Quantum Mechanics?
arXiv preprint arXiv:1407.6833
1
14
2014
10.1016/j.physletb.2014.10.053
String theory developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend open string field theory is a fully consistent definition of the theory - it is at least a self consistent sector. Then we find in its structure that the rules of quantum mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions, thus deriving rather than assuming the quantum commutation rules among the usual canonical quantum variables for all physical systems derivable from open string field theory. Morally we would apply such an argument to M-theory to cover all physics. If string or M-theory theory really underlies all physics, it seems that the door has been opened to an understanding of the origins of quantum mechanics.
Star Operation in Quantum Mechanics
arXiv
hep-th
2000
We outline the description of Quantum Mechanics with noncommuting coordinates within the framework of star operation. We discuss simple cases of integrability.
hep-th
Unraveling a classical mechanics brain twister
American Journal of Physics
79
12
1250
2011
10.1119/1.3636655
We present a comprehensive analysis of an intriguing classical mechanics problem involving the coupled motion of two blocks. The problem illustrates fundamental physics concepts and theoretical techniques. We solve the equations of motion numerically and gain insight into common misconceptions about this system. The problem provides rich opportunities for student investigations using analytical and numerical methods.
Hybrid cavity mechanics with doped systems
Physical Review A
90
3
033820
2014
10.1103/PhysRevA.90.033820
We investigate the dynamics of a mechanical resonator in which is embedded an ensemble of two-level systems interacting with an optical cavity field. We show that this hybrid approach to optomechanics allows for enhanced effective interactions between the mechanics and the cavity field, leading for instance to ground state cooling of the mechanics, even in regimes, like the unresolved sideband regime, in which standard radiation pressure cooling would be inefficient.
Statistical Mechanics of Powder Mixtures
Physica A
157
1091-1100
1989
http://dx.doi.org/10.1016/0378-4371(89)90035-6
In this paper we use a new formulation of the statistical mechanics of powders to develop a theory for a mixture of grains of two different sizes. We map this problem onto the spin formulation of the eight-vertex model and reproduce the features of the phase separation diagram of the powder mixture that we would intuitively be led to expect. Finally, we discuss the insight afforded by this solution on the “thermodynamic” quantities of interest in the powder mixture.
Synthesis of Lithium Thin Film by Electrodeposition from Ionic Liquid
Applied Mechanics and Materials
217-219
1049-1052
2012
10.4028/www.scientific.net/AMM.217-219.1049
The synthesis of metallic lithium thin film from two ionic liquids, 1-ethyl-3-methylimidazoliuom bis(trifluoromethylsulfonyl) imide ({[}EMIM]Tf2N) and 1-methyl-1-propylpiperidinium bis(trifluoromethanesulfonyl) amide (PP13Tf(2)N) with lithium bis(trifluoromethanesulfonyl) imide (LiTFSI) as the lithium source was investigated. Cyclic voltammograms on a gold electrode showed the possibility of the electrodeposition of metallic lithium, and the reduction current in {[}EMIM]Tf2N was higher than the value in PP13Tf(2)N. The metallic lithium thin film could be synthesized on the gold electrode under potentiostatic conditions as confirmed by various analytical techniques including X-ray diffraction and scanning electron microscopy with energy-dispersive spectroscopy. The electrodeposited lithium surface was uniform without dendritic structures, no impurities were detected except for trace oxygen introduced during handling for the analyses.
1-ethyl-3-methyl-; abstract; amide; and 1-methyl-1-propylpiperi-; deposition; dinium bis; electrolysis; emim; imidazoliuom bis; imide; lithium; lithium thin film from; nonaqueous electrolyte; pp13tf 2 n; tf 2 n; the synthesis of metallic; thin-film; trifluoro-; trifluoromethanesulfonyl; trifluoromethylsulfonyl; two ionic liquids; with lithium bis
Mechanical behavior of thin-film coating/substrate systems under nanoindentation
Studies in Applied Mechanics
Volume 46
287-302
1998
This paper investigates the mechanical behavior of thin-film coating/substrate systems under nanoindentation testing. Experimental results have demonstrated the different failure mechanisms of material systems consist of hard-coating on soft substrate and soft-coating on hard substrate. An analytical model using Hankel's transform method is introduced to examine the displacement and stress fields of a thin-film coating/substrate system with perfect interfacial bonding under an axisymmetrical compressive loading on the coating surface. The present analysis can account for the influence of the film thickness and the material properties of the substrate. This knowledge of the stress fields provides the basis of understanding of the failure mechanisms of thin-film coating/substrate systems. Finally, the influence of Poisson's ratios of the film and the substrate are discussed in detail.
Axial collapse of thin-walled fibreglass composite tubular components at elevated strain rates
Composites Engineering
4
6
653-677
1994
10.1016/0961-9526(94)90107-4
In the present paper, we deal with the crush behaviour of axisymmetric composite structures consisting of circular tubes and frusta made from a chopped-strand glass mat and polyester resin and subjected to dynamic axial compression exerted by a drop-hammer. The effect of specimen geometry and loading rate on the energy-absorbing efficiency is studied in detail. Attention is also directed towards the mechanics of the axial crumpling process from the macroscopic point of view, and the systematic study of the microfailure process and understanding of the crack propagation mechanism during the stable collapse of the shell. This gives a somewhat more complete aspect on the actual fracture mechanics during the failure of the composite material tested. Finally, the dynamically obtained experimental results are compared with the static ones for shells of similar geometry, and useful semi-empirical relations concerning the amount of energy absorbed and the post-crushing loading are derived for the material tested. © 1994.
Generation of plastic influence functions for J-integral and crack opening displacement of thin-walled pipes with a short circumferential through-wall crack
International Journal of Pressure Vessels and Piping
117-118
17-24
2014
10.1016/j.ijpvp.2013.10.005
Fracture mechanics parameters such as the J-integral and crack opening displacement (COD), are necessary for Leak-Before-Break (LBB) evaluation. The famous two estimation methods, the GE/EPRI and the Reference Stress Method (RSM), have their applicability limit with regard to the ratio of a pipe mean radius to thickness (Rm/t). In order to extend their applicability limit to a thin walled pipe, several finite element analyses are performed for the J-integral and COD, and then new plastic influence functions are developed for thin-walled pipes with a short circumferential through-wall crack. With the newly generated plastic influence functions, the GE/EPRI and the RSM give closer results with those obtained from detailed finite element analyses. In addition, C*-integral and COD rate are estimated by using the new plastic influence functions and they are well matched with elastic–creep finite element analysis results under the power-law creep condition. Since the LBB concept can be applied to a piping system in a Korean Sodium-cooled Fast Reactor (SFR) which is designed to have thin-walled pipes and to operate in high temperature enough to cause creep, this paper can be applied for the LBB assessment of thin-walled pipes with a short through-wall crack in the SFR.
C*-integral; Crack opening displacement; GE/EPRI method; J-integral; Reference stress method; Thin-walled pipe
Simulation and measurements of the piezoelectric properties response (d33) of piezoelectric layered thin film structures influenced by the top-electrode size
14th IEEE International Symposium on Applications of Ferroelectrics, 2004. ISAF-04. 2004
00
c
7-10
2004
10.1109/ISAF.2004.1418325
The properties of piezoelectric thin film layered structures are in the focus of many investigations. Significant decreasing piezoelectric properties have been observed with decreasing top-electrode size. These results are obtained by measurements of the effective piezoelectric small-signal coefficient d<sub>33,eff</sub> and the piezoelectric large signal-strain S using a double-beam laser interferometer. Samples are investigated with squared top-electrodes with dimensions of 0.1 mm to 1 mm edge length. The loss of d<sub>33,eff</sub> is as high as 50 %, whereas the influence on the relative permittivity is only small. This work investigates this behaviour by calculating the influence of varying elastic and geometrical properties of substrate, electrodes, and piezoelectric thin film on the effective piezoelectric small-signal coefficient d<sub>33,eff</sub> by means of finite element simulations. Beside the clamping effect of the substrate under electrical operating conditions also the influence of thermally induced mechanical stresses after cooling from 4000°C to room temperature is calculated. From measurements and simulations it can be concluded that the source of the pad size effect on the measured piezoelectric properties can he attributed to the mechanics of the layered structure.
Universal Local Symmetries and Nonsuperposition in Classical Mechanics
Physical Review Letters
105
15
150604
2010
10.1103/PhysRevLett.105.150604
In the Hilbert space formulation of classical mechanics, pioneered by Koopman and von Neumann, there are potentially more observables than in the standard approach to classical mechanics. In this Letter, we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the Koopman and von Neumann formulation is extended to include the evolution of differential forms. Because of their noninvariance, those extra observables have to be removed. This removal makes the superposition of states in the Koopman and von Neumann formulation, and as a consequence also in classical mechanics, impossible.
Analysis and tests of flexibly connected thin-walled channel frames
Structural Engineering and Mechanics
2
3
269-284
1994
10.1061/(ASCE)0733-9445(1986)112:7(1573)
The analysis and tests of thin-walled channel frames including nonlinear flexible or semi-rigid connection behaviour is presented. The semi-rigid connection behaviour is modelled using a mathematical approximation of the connection flexibility-moment relationship. Local instability such as local buckling and torsional flexural buckling of the member are included in the analysis. The full response of the frame, up to the collapse load, can be predicted. Experimental investigation was carried out on a series of simple double storey symmetrical frames with the purpose of verifying the accuracy and validity of the analysis. Agreement between the theoretical and experimental results is acceptable. The investigation also shows that connection flexibility and local instability such as local buckling and torsional flexural buckling can affect the behaviour and strength of thin-walled frames significantly. The results can also provide further insight into the advanced study of practical structures where interaction between flexible connections and phenomenon associated with thin-walled members are present
A semi-analytical approach for the nonlinear two-dimensional analysis of fluid-filled thin-walled pliable membrane tubes
European Journal of Mechanics - A/Solids
28
3
626-637
2009
http://dx.doi.org/10.1016/j.euromechsol.2008.11.006
Pliable tubes are tubular membranes of low rigidity and may collapse or substantially deform easily. The governing equations of these tubes are nonlinear because the tube shape depends on the internal pressure and the deformation of the tube can be very large. In the present study, a semi-analytical approach for the nonlinear analysis of the fluid-filled thin-walled pliable tubes with different load distributions and boundary conditions is developed. Both geometric and equilibrium relations of the tube element are used to obtain the tube profile in explicit closed form. Several applications of the pliable tubes are considered and the equilibrium shape and wave propagation velocity in these tubes are also obtained. The validity of the present semi-analytical approach is confirmed by comparing the results with those obtained from the literature. It is shown that the present formulation is an appropriate method and a new approach to predict the nonlinear behavior of the pliable tubes with a good accuracy.
Inflatable geomembrane tubes; Thin-walled pliable tubes
From the Boltzmann equations to the equations of incompressible fluid mechanics, I
Archive for Rational Mechanics and Analysis
158
3
173-193
2001
10.1007/s002050100144
We consider here the problem of deriving rigorously from Boltzmann's equation, globally in time and for general initial conditions, fluid mechanics equations such as the Navier-Stokes or Euler equations.
compactness; dynamic limits; fourier integral-operators; kinetic-equations
Fracture Mechanics Ch09
Fracture Mechanics
227-246
2012
10.1016/B978-0-12-385001-0.00009-2
The cohesive zone fracture model was introduced partially to remove the stress singularity in the classical continuum crack model and partially to incorporate the physically more realistic material separation mechanisms at the atomic scale. The cohesive zone model adds a zone of vanishing thickness ahead of the crack tip with the intention of describing more realistically the fracture process without the use of stress singularity. The cohesive zone is idealized as two cohesive surfaces, which are held together by a cohesive traction. The material failure is characterized by the complete separation of the cohesive surfaces and the separation process is described by a cohesive law that relates the cohesive traction and the relative displacement of the cohesive surfaces. Hence, a physical crack extension occurs when the separation displacement at the tail of the cohesive zone (physical crack tip) reaches a critical value. One of the key advantages offered by the cohesive zone model is that it has an intrinsic fracture energy dissipation mechanism in contrast to the classical continuum based fracture mechanics for which such a mechanism is absent.
Barenblatt model; cohesive energy density; cohesive law; cohesive traction; cohesive zone
Survey of modern trends in analysis of continuum damage mechanics
Task Quarterly
10
4
437-457
2006
A brief review of the damage mechanics literature is given. As this area of scientific research is very modern, the authors have restricted themselves to about 100 most important books and papers. Basic equations to introduce the isotropic model in the framework of thermodynamics are given in a form easily applicable in numerical symulations.
continuum damage mechanics; ductile damage; fatigue damage; viscoplasticity
Continuum damage mechanics and local approach to fracture: Numerical procedures
Computer Methods in Applied Mechanics and Engineering
92
2
141-155
1991
10.1016/0045-7825(91)90236-Y
In this paper, continuum damage mechanics is applied to the prediction of the failure of structures. The numerical implementation of this theory within the framework of the finite element method is described in details for both initiation and propagation problems. Practical examples are given to demonstrate the usefulness of this so-called ‘local approach to fracture’ in the case of creep and ductile damages.
A computer-based course in classical mechanics
Computers and Education
4
15-36
1980
10.1016/0360-1315(80)90006-8
Plato mechanics course is an early version of model tracing. Lots of real world experiences reported.
Perspectives in statistical mechanics
Construction
1-23
2006
Without attempting to summarize the vast field of statistical mechanics, we briefly mention some of the progress that was made in areas which have enjoyed Barry Simon's interests. In particular, we focus on rigorous non-perturbative results which provide insight on the spread of correlations in Gibbs equilibrium states and yield information on phase transitions and critical phenomena. Briefly mentioned also are certain spinoffs, where ideas which have been fruitful within the context of statistical mechanics proved to be of use in other areas, and some recent results which relate to previously open questions and conjectures.
Quantum Mechanics in the Light
Proc. of the 3rd Int. Symposium on Foundations of Quantum Mechanics
321-343
1989
Although classical probability theory, as it is encapsulated in the axioms of Kolmogorov and in his criterion for the independence of two events, can consistently be employed in quantum mechanics, this can only be accomplished at an exorbitant price. By considering first the classic two-slit experiment, and then the passage of one photon through three polarizers, the applicability of Kolmogorov's last axiom is called into question, but the standard rebuff of the Copenhagen interpretation is shown to be adequate to this challenge. (edited)
The mechanics of axially symmetric liposomes.
Journal of biomechanical engineering
115
2
149-59
1993
Hotani has filmed morphological transformations in unilamellar liposomes, starting from a spherical shape, when the interior volume decreases steadily. Hotani's liposomes showed no evidence of general thermal fluctuations. We use a finite-deformation theory of axisymmetric, quasi-static thin shells to analyze theoretically bifurcations and changes of shape in liposomes under decreasing volume. The main structural action in a lipid bilayer is generally agreed to be its elastic resistance to bending, and it is usual to regard surface deformation as being like that of a two-dimensional liquid. We find, however, that some in-plane shear elasticity is also needed in order to produce the observed post-bifurcation behavior. Such an elasticity would be difficult to measure directly.
Biomechanical Phenomena; Biophysical Phenomena; Biophysics; Elasticity; Evaluation Studies as Topic; Liposomes; Mathematics; Mechanical; Models; Molecular; Osmolar Concentration; Pressure; Stress; Surface Properties; Tensile Strength; Thermodynamics; Videotape Recording
Quantum chaos in elementary quantum mechanics
European Journal of Physics
26
3
29
2004
10.1088/0143-0807/26/3/009
We introduce an analytical solution to the one of the most familiar problems from the elementary quantum mechanics textbooks. The following discussion provides simple illustrations to a number of general concepts of quantum chaology, along with some recent developments in the field and a historical perspective on the subject.
Crystallite coalescence during film growth based on improved contact mechanics adhesion models
Journal of Applied Physics
96
3
1348-1359
2004
10.1063/1.1766099
Intrinsictensile stress, which can lead to problems in deposited thinfilms such as cracking, peeling, and delamination, often develops duringthe early stages of thin film growth. Many attempts havebeen made to estimate the tensile stress during crystallite coalescence,both experimentally and analytically. Most recently, using a combination ofHertzian contact mechanics and elasticity theory, Freund and Chason appliedthe Johnson-Kendall-Roberts (JKR) theory to account for adhesion between crystallitesunder specific conditions. Other existing contact mechanics models that naturallyaccount for adhesion include the improved Derjaguin-Muller-Toporotov and Maugis-Dugdale theories.The objective of this study is to provide useful analyticaland numerical techniques based on these contact mechanics theories fora wide range of conditions that accurately approximate the intrinsictensile stress that develops during crystallite coalescence. As an analyticalmethod, the Maugis-Dugdale model is proposed as a more generalalternative to the JKR model. Parameters such as the contactradius and "net" adhesive force are computed as a functionof the relative separation between two adjacent crystallites in athin gold film. Another useful parameter known as the "jump-to-contact"separation is also calculated by the Maugis-Dugdale and JKR models.For comparison to the analytical models, a finite element methodis used to simulate the crystallite coalescence problem. The numericaltechnique is based on a nonlinear surface interaction element developedto approximate van der Waals adhesion, and allows for full-fieldanalysis of stress and displacement in crystallites. Two different boundaryconditions are used, for which corresponding contact radius and tensilestress are computed and compared to the analytical results. Asa further study, the length scale effect is also investigatedby varying the radius of individual crystallites from 20 nm to300 nm. It is concluded that in order to estimate theaverage tensile stress accurately using analytical models, the radius ofindividual crystallites must be large compared to the contact radius.For small length scales, the finite element approach is moreappropriate.\n\n \n ©2004 American Institute of Physics
adhesion; delamination; elasticity; finite element analysis; gold; internal stresses; mechanical contact; metallic thin films
Non-linear thermal effects on the bending response of cross-ply laminated plates using refined first-order theory
Composite Structures
49
3
257-267
2000
10.1016/s0263-8223(99)00137-3
Based on the representation of the displacement field proper to the first-order transverse shear deformation theory, and using Reissner's mixed variational principle modified as to include thermoelastic effects, an equivalent single-layer model of composite laminated plates is presented including the geometric non-linearity. In contrast to the usual approach of such models, the present model has the advantage of eliminating the need of the inclusion of a shear correction factor. Moreover, this model predicts continuous stress distributions through the laminate thickness. The equations of motion, the constitutive equations and the required boundary conditions are obtained. Based on the obtained equations, linear and non-linear numerical results on the static state of stresses and displacements of cross-ply symmetric and antisymmetric laminated plates are supplied. To assess the present model, some of the obtained linear results are compared with their counterparts in the literature. The effect of the geometric non-linearity on the thermal response of the laminate is investigated. (C) 2000 Elsevier Science Ltd. All rights reserved.
Three-dimensional elasticity solution of cross-ply shallow and non-shallow panels with piezoelectric sensors under dynamic load
Composite Structures
80
3
429-439
2007
10.1016/j.compstruct.2006.05.027
Dynamic response of cross-ply laminated shallow and non-shallow panels with a piezoelectric layer is studied. Three-dimensional elasticity solution is presented for finitely long, simply-supported, orthotropic, shell panel under dynamic pressure excitation. The exact solution for non-shallow panels and an approximate method for shallow panel solution (Soong) are considered and compared with each other. The highly coupled partial differential equations (p.d.e.) are reduced to ordinary differential equations (o.d.e.) with variable coefficients for non-shallow panel and constant coefficients for shallow shell panel by means of trigonometric function expansion in circumferential and longitudinal directions. The resulting ordinary differential equations are solved by Galerkin finite element method. Numerical examples are presented for [0/90/P] lamination and the results of the shallow and non-shallow panels are discussed. ?? 2006 Elsevier Ltd. All rights reserved.
Composite; Orthotropic; Panel; Piezoelectric; Sensor; Shallow; Three-dimensional
Quantum mechanics and stochastic mechanics for compatible observables at different times
Annals of Physics
296
2
371–389
2002
10.1006/aphy.2002.6236
Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum Mechanics in presence of non-interacting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary states agree with Quantum Mechanics only in the case of product wave functions. By appropriate Bell-like inequalities it is shown that no classical theory, in particular no stochastic process, can reproduce the quantum mechanical correlations of position variables of non interacting systems at different times.
A non-linear model for the dynamics of open cross-section thin-walled beams - Part I: Formulation
International Journal of Non-Linear Mechanics
38
7
1067-1081
2003
10.1016/S0020-7462(02)00053-7
A non-linear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an open cross-section is developed. Non-linear in-plane and out-of-plane warping and torsional elongation effects are included in the model. By using the Vlasov kinematical hypotheses, together with the assumption that the cross-section is undeformable in its own plane, the non-linear warping is described in terms of the flexural and torsional curvatures. Due to the internal constraints, the displacement field depends on three components only, two transversal translations of the shear center and the torsional rotation. Three non-linear differential equations of motion up to the third order are derived using the Hamilton principle. Taking into account the order of magnitude of the various terms, the equations are simplified and the importance of each contribution is discussed. The effect of symmetry properties is also outlined. Finally, a discrete form of the equations is given, which is used in Part II to study dynamic coupling phenomena in conditions of internal resonance. ?? 2002 Elsevier Science Ltd. All rights reserved.
Beams; Flexural-torsional dynamics; Non-linear resonances; Open cross-section; Warping non-linear effects
PDMS-Glass Interface Adhesion Energy Determined Via Comprehensive Solutions for Thin Film Bulge/Blister Tests
Journal of Applied Mechanics
77
3
031007
2010
10.1115/1.4000428
Thispaper provides comprehensive relationships for pressure, deflection, energy release rate,and phase angle for bulge testing, which are valid forall combinations of the testing length-scales (film thickness, debond size,and bulge height) and materials. These solutions can be usedto design experiments that vary relative contributions of opening andsliding displacements at the crack tip by modulating the filmthickness, debond size, and bulge volume. Their closed-form nature greatlyfacilitates property extraction via regression, e.g., modulus from experimental pressure/deflectiondata or interface toughness from debond size/injected volume data. Thisis illustrated using experiments to quantify the interfacial adhesion energybetween an initially dry polydimethylsiloxane-glass interface via bulge testing undercontrolled volume injection. The results indicate that the mode-mixity hasno effect on the energy required for debonding, which suggeststhat wetting of the crack faces behind the debonding fronteliminates friction. \n\t\t\n\t\t\t ©2010 American Society of Mechanical Engineers
bulge testing; interface adhesion; mode-mixity; pdms
Pattern instability of a soft elastic thin film under van der Waals forces
Mechanics Of Materials
38
1-2
88-99
2006
10.1016/j.mechmat.2005.05.012
The surface stability and morphology evolution of a soft elastic film subjected to surface interactions such as van der Waals forces are investigated in the present paper. The three-dimensional analytical solution is obtained for the critical van der Waals force of bifurcation in terms of the surface energy, film thickness and elastic constants. The conditions of formation of different bifurcation modes (e.g., the two-dimensional periodic pattern and the three-dimensional doubly-periodic pattern) of films can be given from this solution by specifying the ratio of the wavenumbers in two directions. It is found that the wave length is proportional to the film thickness in both the two- and three-dimensional bifurcation modes when the surface energy is ignored, and that the surface energy of the film has a tendency to oppose the occurrence of inhomogeneous deformation. The three-dimensional, doubly-periodic morphology is more feasible energetically than the two-dimensional one. The obtained three-dimensional solution shows a good agreement with experimental results. In addition, we put forward both two- and three-dimensional finite element simulations of this instability problem. The numerical results are also in excellent consistency with our analytical results. (c) 2005 Elsevier Ltd. All rights reserved.
Fluid-structure interaction and computational aeroacoustics of the flow past a thin flexible structure
Acoustics '08 Paris
3755-3760
2008
10.1121/1.2934641
In the present work, the acoustic field resulting from the interaction of a thin flexible structure with a turbulent flow field is investigated by means of numerical simulation. Two different model configurations are considered: one is the flow over a flexible plate, in the second case the flexible plate is located in the wake of a square cylinder. The simulation is based on a partitioned approach employing two different simulation codes: a finite-volume flow solver of second order accuracy in space and time and a finite-element structural mechanics and acoustics solver. A code coupling interface is used for the exchange of data between the different discretizations. The numerical methodology allows for a decomposition of the acoustic field into one part generated by the structural vibrations and another part which is due to stream noise. Comparisons to experimental data available at our institute are provided.
Transonic flow of moist air around a thin airfoil with non-equilibrium and homogeneous condensation
Journal of Fluid Mechanics
403
173-199
2000
10.1017/S0022112099007053
A new small-disturbance model for a steady transonic flow of moist air with non-equilibrium and homogeneous condensation around a thin airfoil is presented. The model explores the nonlinear interactions among the near-sonic speed of the flow, the small thickness ratio and angle of attack of the airfoil, and the small amount of water vapour in the air. The condensation rate is calculated according to classical nucleation and droplet growth models. The asymptotic analysis gives the similarity parameters that govern the flow problem. Also, the flow field can be described by a non-homogeneous (extended) transonic small-disturbance (TSD) equation coupled with a set of four ordinary differential equations for the calculation of the condensate (or sublimate) mass fraction. An iterative numerical scheme which combines Murman & Cole's (1971) method for the solution of the TSD equation with Simpson's integration rule for the estimation of the condensate mass production is developed. The results show good agreement with available numerical simulations using the inviscid fluid flow equations. The model is used to study the effects of humidity and of energy supply from condensation on the aerodynamic performance of airfoils.
Beyond the Young-Laplace model for cluster growth during dewetting of thin films: Effective coarsening exponents and the role of long range dewetting interactions
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
88
1-29
2013
10.1103/PhysRevE.88.032113
Long range dewetting forces acting across thin films, such as the fundamental van der Waals interactions, may drive the formation of large clusters (tall multilayer islands) and pits, observed in thin films of diverse materials such as polymers, liquid crystals, and metals. In this study we further develop the methodology of the nonequilibrium statistical mechanics of thin films coarsening within continuum interface dynamics model incorporating long range dewetting interactions. The theoretical test bench model considered here is a generalization of the classical Mullins model for the dynamics of solid film surfaces. By analytic arguments and simulations of the model, we study the coarsening growth laws of clusters formed in thin films due to the dewetting interactions. The ultimate cluster growth scaling laws at long times are strongly universal: Short and long range dewetting interactions yield the same coarsening exponents. However, long range dewetting interactions, such as the van der Waals forces, introduce a distinct long lasting early time scaling behavior characterized by a slow growth of the cluster height/lateral size aspect ratio (i.e., a time-dependent Young angle) and by effective coarsening exponents that depend on cluster size. In this study, we develop a theory capable of analytically calculating these effective size-dependent coarsening exponents characterizing the cluster growth in the early time regime. Such a pronounced early time scaling behavior has been indeed seen in experiments; however, its physical origin has remained elusive to this date. Our theory attributes these observed phenomena to ubiquitous long range dewetting interactions acting across thin solid and liquid films. Our results are also applicable to cluster growth in initially very thin fluid films, formed by depositing a few monolayers or by a submonolayer deposition. Under this condition, the dominant coarsening mechanism is diffusive intercluster mass transport while the cluster coalescence plays a minor role, both in solid and in fluid films.
The effect of ply number, orientation angle and bonding type on residual stresses of woven steel fiber reinforced thermoplastic laminated composite plates subjected to transverse uniform load
Composites Science and Technology
64
7-8
1049-1056
2004
10.1016/j.compscitech.2003.09.014
This paper is concerned with the numerical results of the elasto-plastic stress analysis and residual stresses in woven steel fiber reinforced thermoplastic laminated composite plates for transverse uniform loads. The effects of ply number, orientation angle and bonding type on the residual stresses of laminated composite plates are investigated. Elasto-plastic stress analysis is carried out in the laminated plate by using the finite element technique. The finite element code ANSYS is used to perform the numerical analyses using an eight-node layered shell element. Yielding loads and residual stresses are obtained for symmetric and anti-symmetric laminated plates with simply supported boundary conditions. Different stacking sequences of laminated composites are used in analysis and the results are compared with each other. Three load steps are carried out for each analysis consecutively. In the first load step, the yielding transverse load is applied. Secondly, a series of load increments is added until the load reaches "Yielding Load+0.005 MPa". In the last step the external load is released to obtain the residual stress components. © 2003 Elsevier Ltd. All rights reserved.
A. Layered structures; B. Mechanical properties; B. Plastic deformation; C. Residual stress; Thermoplastic composite plate
The renaissance of continuum mechanics
Journal of Zhejiang University SCIENCE A
15
4
231-240
2014
10.1631/jzus.A1400079
Continuum mechanics, just as the name implies, deals with the mechanics problems of all continua, whose physical (or mechanical) properties are assumed to vary continuously in the spaces they occupy. Continuum mechanics may be seen as the symbol of modern mechanics, which differs greatly from current physics, the two often being mixed up by people and even scientists. In this short paper, I will first try to give an illustration on the differences between (modern) mechanics and physics, in my personal view, and then focus on some important current research activities in continuum mechanics, attempting to identify its path to the near future. We can see that continuum mechanics, while having a dominating impact on engineering design in the 20th century, also plays a pivotal role in modern science, and is much closer to physics, chemistry, biology, etc. than ever before.
10; 1631; a1400079; continuum mechanics; current research activities; doi; engineering; jzus; quantum mechanics; renaissance
Fractional Quantum Mechanics and Levy Path Integrals
Molecular Physics
37
145
8
1999
10.1016/S0375-9601(00)00201-2
The fractional quantum and statistical mechanics have been developed via new path integrals approach.
The mechanism of transition in the wake of a thin flat plate placed parallel to a uniform flow
Journal of Fluid Mechanics
11
03
321
1961
10.1017/S0022112061000561
A study was made of the laminar–turbulent transition of a wake behind a thin flat plate which was placed parallel to a uniform flow at subsonic speeds. Experimental results on the nature of the velocity fluctuations have made it possible to classify the transition region into three subregions: the linear region, the non-linear region and the three-dimensional region. In the linear region there is found a sinusoidal velocity fluctuation which is antisymmetrical with respect to the centre-line of the wake. The frequency of fluctuation is proportional to the $\frac{2}{3}$ power of the free-stream velocity, and the amplitude increases exponentially in the direction of flow. The behaviour of small disturbances in the linear region was investigated in detail by inducing velocity fluctuation with an external excitation — actually sound from a loudspeaker. Solutions of the equation of a small disturbance superposed on the laminar flow were obtained numerically and compared with the experimental results. The agreement between the two was satisfactory. When the amplitude of fluctuation exceeds a certain value, the growth rate deviates from being exponential due to non-linear effects. Although velocity fluctuations in the non-linear region are still sinusoidal and two-dimensional, the experimental results on the distributions of amplitude and phase indicate that the flow pattern may be described by the model of a double row of vortices. This configuration lasts until three-dimensional distortion takes place in the final subregion, the three-dimensional region, in which the fluctuation loses regularity and gradually develops into turbulence without being accompanied by abrupt breakdown or turbulent bursts.
Improving students' understanding of quantum mechanics
Physics Today
43-49
2006
10.1063/1.2349732
Richard Feynman once famously stated that nobody un- derstands quantum mechanics . He was, of course, referring to the many strange, unintuitive foundational aspects of quantum theory such as its inherent indeterminism and state reduction during measurement according to ...
Pre2015
Chalmers on Consciousness and Quantum Mechanics
Philosophy of Science
66
3
370
1999
10.1086/392693
In this book, The Conscious Mind, David Chalmers argues that his theory of consciousness can lend support to the Everett "no collapse" interpretation of quantum mechanics. We argue that Chalmers's argument fails, and that any Everett-style interpretation should be rejected.
Rock mechanics and rock engineering in China: developments and current state-of-the-art
International Journal of Rock Mechanics and Mining Sciences
37
3
447-465
2000
10.1016/S1365-1609(99)00072-6
This paper presents the development and state of the art of rock mechanics and rock engineering in China, looking back at the history of development of rock mechanics and the main achievements in rock engineering (Part I). Some large rock projects are introduced and aspects of near future progress and prospects are summarized (Part II).
OR Forum--Quantum Mechanics and Human Decision Making
Operations Research
61
1
1-16
2013
10.1287/opre.1120.1068
In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics, but the same could be explained by the newly discovered quantum theory. It resulted in a new mechanics called quantum mechanics that revolutionized scientific and technological developments. Again, at the beginning of the twenty-first century, it is being recognized that some experiments related to the human decision-making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision-making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quantum interference equation to illustrate the quantum approach. The explanation of disjunction effect experiments of Tversky and Shafir (Tversky A, Shafir E (1992) The disjunction effect in choice under uncertainty. Psych. Sci. 3(5):305--309) has been chosen to demonstrate the necessity of a quantum model. Further, to suggest the possibility of application of the quantum theory to the business-related decisions, some terms such as price operator, state of mind of the acquiring firm, etc., are introduced and discussed in context of the merger/acquisition of business firms. The possibility of the development in areas such as quantum finance, quantum management, application of quantum mechanics to the human dynamics related to healthcare management, etc., is also indicated. [ABSTRACT FROM AUTHOR]
BUSINESS; DECISION making; TECHNOLOGICAL innovations
Statistical mechanics of relativistic anyon-like systems
Nuclear Physics B
426
3
644-660
1994
10.1016/0550-3213(94)90024-8
To study the manifestation of the Aharonov-Bohm effect in many-body systems we consider the statistical mechanics of the Gross-Neveu model on a ring (1+1 dimensions) and on a cylinder (2+1 dimensions) with a thin solenoid coinciding with the axis. For such systems with a non-trivial magnetic flux ([theta]) many thermodynamical observables, such as the order parameter, induced current and virial coefficients, display a periodic but non-analytic dependence on [theta]. In the (2+1)-dimensional case we further find that there is an interval of (modulo integers) where parity is always spontaneously broken, independent of the circumference of the cylinder. We show that the mean-field character of the phase transitions is preserved to the leading order in 1/N, by veryfying the [theta]-independence of all the critical exponents. The precise nature of the quasi-particle, locally fermion-like and globally anyon-like, is illuminated through the calculation of the equal-time commutator and the decomposition of the propagator into a sum over paths classified by winding numbers.
Mechanics of edematous lungs.
Journal of applied physiology (Bethesda, Md. : 1985)
90
6
2088-2093
2001
Using the parenchymal marker technique, we measured pressure (P)-volume (P-V) curves of regions with volumes of approximately 1 cm3 in the dependent caudal lobes of oleic acid-injured dog lungs, during a very slow inflation from P = 0 to P = 30 cmH2O. The regional P-V curves are strongly sigmoidal. Regional volume, as a fraction of volume at total lung capacity, remains constant at 0.4-0.5 for airway P values from 0 to approximately 20 cmH2O and then increases rapidly, but continuously, to 1 at P = approximately 25 cmH2O. A model of parenchymal mechanics was modified to include the effects of elevated surface tension and fluid in the alveolar spaces. P-V curves calculated from the model are similar to the measured P-V curves. At lower lung volumes, P increases rapidly with lung volume as the air-fluid interface penetrates the mouth of the alveolus. At a value of P = approximately 20 cmH2O, the air-fluid interface is inside the alveolus and the lung is compliant, like an air-filled lung with constant surface tension. We conclude that the properties of the P-V curve of edematous lungs, particularly the knee in the P-V curve, are the result of the mechanics of parenchyma with constant surface tension and partially fluid-filled alveoli, not the result of abrupt opening of airways or atelectatic parenchyma.
Strain rate dependent analysis of a polymer matrix composite utilizing a micromechanics approach
Journal of composite materials
36
773-793
2002
10.1106/002199802024613
A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. The Ramaswamy–Stouffer viscoplastic constitutive equations for metals have been modified to model the strain rate dependent inelastic deformation of ductile polymers, including hydrostatic stress effects. These equations have been incorporated into a mechanics of materials based micromechanics model that was developed to analyze uniaxial composites at various fiber orientation angles. The Hashin failure criteria have been implemented into the micromechanics to predict ply failure strengths. The deformation response and ply failure strengths for the representative composite AS4/PEEK have been successfully predicted for a variety of fiber orientations and strain rates.
constitutive equations; impact.; micromechanics; polymer matrix composites; strength; viscoplasticity
Subsampling and homogenization to investigate variability of composite material mechanical properties
Computer Methods in Applied Mechanics and Engineering
241-244
238-245
2012
10.1016/j.cma.2012.06.003
This paper presents an innovative homogenization sampling technique applied to multiscale modelling of composite materials. The goal is to build efficiently statistical variability of mechanical properties at mesoscopic scale from the heterogeneous media analysis at microscopic scale. It is applied to the transverse elastic properties of a unidirectional Long Fibres Reinforced Composite (LFRC). A large representative part of the ply - the cell - is modelled from a micrography and studied at microscopic scale with the Finite Element Analysis (FEA) under 2D plane strain hypothesis. The study consists in estimating the effective elastic properties of subcells, subparts of the previous cell, thanks to a specifically developed numerical procedure.A unique calculation is computed on the entire ply reduced to three basic loading cases is applied to the cell. Subsamples taken into the simulation cell are homogenized at post-processing level of strain and stress fields. A standard mechanics approach was considered. Various subsampling schemes are performed with various size and spatial distribution to generate variability functions of effective elastic properties at mesoscopic scale. A statistical inference is highlighted: the variability parameters vary with the way of sampling. Dispersion functions are finally obtained and discussed. © 2012 Elsevier B.V.
Elastic properties; Finite Element Analysis (FEA); Multiscale modeling; Probabilistic methods; Structural composites
Kinematic variables bridging discrete and continuum granular mechanics
Mechanics Research Communications
33
5
651-666
2006
10.1016/j.mechrescom.2005.06.013
It is known that there is wide, and at present, unbridgeable, gap between discrete and continuum granular mechanics. In this contribution, first, microscopic kinematic variables neglected in classical continuum granular mechanics are investigated based on the kinematics of discs in contact. Then, a kinematic variable called the averaged pure rotation rate (APR) is proposed for an assembly of circular discs of different sizes, which is then used to produce another two kinematic tensors with one equal to the deformation rate tensor and the other unifying the spin tensor and the APR. As an example, the kinematic variables are incorporated into the unified double-slip plasticity model. Finally, these theoretical analyses are verified using a two-dimensional discrete element method. The study shows that these kinematic variables can be used to bridge discrete and continuum granular mechanics. © 2005 Elsevier Ltd. All rights reserved.
Continuum granular mechanics; Discrete element method; Discrete granular mechanics; Double-slip; Kinematic variables; Rotation rate model
Fracture Mechanics Ch07
Fracture Mechanics
171-187
2012
10.1016/B978-0-12-385001-0.00007-9
This chapter introduces various fracture criteria for predicting quasistatic crack growth in materials undergoing plastic deformations. In linear elastic fracture mechanics (LEFM), the near-tip stress and strain fields are always characterized by the inverse square-root singularity and the stress intensity factor is a fracture parameter for both crack initiation and propagation. In elastic-plastic fracture mechanics, it is much more difficult to find a similar parameter directly characterizing the intensity of the near-tip singular deformation field for both stationary and growing cracks under large-scale yielding (LSY) conditions. Elastic-plastic fracture criteria are thickness-dependent, that is, the critical value of the fracture parameter varies with specimen thickness.
crack growth resistance curve; crack tip opening angle criterion; crack tip opening displacement criterion; effective crack length; J-integral criterion; large scale yielding
What is Time in Quantum Mechanics?
Arxiv preprint
22 pages
2014
10.1142/S0219887814600196
Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic ``time of arrival operator" introduced by J. Kijowski and the EEQT method. It is suggested that for free particles the two methods may lead to the same result. On the other hand the EEQT method can be easily geometrized within the framework of Galilei-Newton general relativistic quantum mechanics developed by M. Modugno and collaborators, and that it can be applied to non--free evolutions. The way of geometrization of irreversible quantum dynamics based on dissipative Liouville equation is suggested.
1; 2010 msc; 37n20 81p15 81q35 81q65; general relativity; in schr; in standard quantum mechanics; introduction; quantum mechanics; time; time is a parameter; why
Constrained Finite Strip Method for Thin-Walled Members with General End Boundary Conditions
Journal of Engineering Mechanics
139
11
1566-1576
2013
10.1061/(ASCE)EM.1943-7889.0000591
The objective of this paper is to provide the theoretical background and illustrate the capabilities of the constrained finite strip method (cFSM) for thin-walled members with general end boundary conditions. Based on the conventional finite strip method (FSM), cFSM provides a mechanical methodology to separate the deformations of a thin-walled member into those consistent with global, distortional, local, and other (e.g., shear and transverse extension) modes. For elastic buckling analysis, this enables isolation of any given mode (modal decomposition) or quantitative measures of the interactions within a given general eigenmode (modal identification). Existing cFSM is only applicable to simply supported end boundary conditions. In this paper, FSM is first extended to general end boundary conditions, including simply- simply, clamped-clamped, simply-clamped, clamped-guided, and clamped-free. Next, with the conventional FSM for general end boundary conditions in place, the derivation of the constraint matrices for global, distortional, local, and other modes that play a central role in cFSM are summarized. Several bases (i.e., the constraint matrices) are presented for general end boundary conditions involving, in particular, different orthogonalization conditions. For modal identification, normalization schemes for the base vectors as well as the summation method employed for the modal participation calculation are also provided. Numerical examples of modal decomposition and identification are illustrated for a thin-walled member with general end boundary conditions. Recommendations on the choice of basis, orthogonalization, and normalization are provided. © 2013 American Society of Civil Engineers.
Constrained finite strip method; Modal decomposition; Modal identification; Thin-walled member
What the Wright Brothers Did and Did Not Understand About Flight Mechanics — In Modern Terms
AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
37
July
1-21
2001
When the Wright Brothers began their work at the end of the 19th century there were no theories of aerodynamics or of flight mechanics. Data were available for the lift and drag of certain kinds of airfoils, mostly thin and highly cambered imitations of birds' wings. The theory of airfoils began in 1902, but had no practical consequences until World War I, and was unknown to the Wrights and their contemporaries. Similarly, the first publication dealing with flight mechanics, appearing in 1903 was also not known by the Brothers; the subject was not developed usefully until 1911. Thus the Wrights developed their aircraft with repeated tests, keen observations; superb analysis and reasoning; and efficient design. They intuitively understood much of the flight mechanics they observed but there was much they could not understand or explain simply because the basis for understanding did not exist. The purpose of this paper is to trace the WrightS' research and development program and interpret in modern terms their observations and experiences with aerodynamics and flight mechanics.
Advances in Applied Mechanics Volume 27
Advances in Applied Mechanics
27
225-281
1989
10.1016/S0065-2156(08)70197-2
This chapter describes the convective and radiative heat transfer in porous media. Convective and radiative heat transfer and multiphase transport processes in porous media, both with or without phase change, have gained extensive attention. Several applications related to porous media require a detailed analysis of convective heat transfer in different geometrical shapes, orientations, and configurations. Based on the specific application, the flow in the porous medium may be internal or external. Forced convection over external boundaries in the presence of a porous medium constitutes a very important subject area. Analysis of convective heat transfer from this type of external boundary embedded in a porous medium has many important applications. It is shown that for the flow field the boundary effect is confined within a thin momentum boundary layer, which often plays an insignificant role in the overall flow consideration. The models developed for simultaneous heat and mass transfer processes in multiphase porous systems may have differences due to the various assumptions made in developing each model. The thermal radiation characteristics of porous beds are also elaborated.
Post natal development of articular cartilage mechanics
Comparative Biochemistry and Physiology - A Molecular and Integrative Physiology
153
2
S116
2009
Articular cartilage (AC) is the thin layer of soft tissue that covers the surfaces of bones in diarthrodial joints. Tissue composition and structure plays an important role in the mechanical functioning of AC. AC composition and structure, and therefore its mechanical properties, need to develop before puberty. Mechanical loads that AC needs to support in adult animals, are also the loads that govern (early) AC remodelling. We used sheep with ages between 0 and 78 weeks to assess the early development of AC, its influence on AC mechanics, vice versa.We measured collagen fibre orientation, collagen amounts, proteoglycan amounts and mechanical properties. AC mechanical properties are height dependent: they differ between articular surface and interface with the bone. A finite element model was used to predict tissue mechanics as a function of its (local) composition and structure. During development, AC thickness decreases. Collagen fibre orientation develops from a layered structure to an arcade structure. Collagen amounts increase, and increase most near the bone. Proteoglycan content also increases, and also most near the bone. Tissue stiffness increases, and the height dependent gradient in mechanical properties is amplified between birth and maturity. With the finite element model, we can predict height dependent mechanical properties that cannot be assessed experimentally. We use the model to investigate correlations between local AC mechanics and tissue remodelling.
adult animal; articular cartilage; bone; collagen; collagen fiber; height; maturity; mechanics; model; proteoglycan; puberty; rigidity; sheep; society; soft tissue; thickness; tissues
Device for testing thin specimens in pure bending
US Patent 8,544,340
2013
An improved test fixture to evaluate thin composite laminates commonly used in deployable space structures. The fixture is designed to impart a pure moment into the coupon, a necessary improvement to prior test methods where results are obtained by fitting material properties in a nonlinear structural analysis of the test. Fixture mechanics allow for direct calculation of the coupon flexural modulus and allowable flexural strain based on two key measurements, fixture displacement and applied load.
An integral method to derive thin- airfoil theory
Compte Rendus de LÁcadémie des Sciences, Serie II, Tome 322, nº 11, 3 Juin 2996. Fascicule b: MECHANICS CHEMISTRY • PHYSICS • ASTRONOMY
809-816
1996
A formal thin-airfoil theory is built that can apply to any order. The proposed method consists in asymptotically solving a system of singular and integral equations where the unknown quantities are distributions of sources and vortices to be spread over the exact boundary of the airfoil
Relativistic mechanics in a general setting
Int J Geom Methods Mod Phys
07
15
2010
10.1142/S0219887810004804
Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly considered.
A mechanistic model for fatigue damage evolution in composite laminates
Mechanics of Materials
29
June 1997
123-140
1998
10.1016/S0167-6636(98)00007-6
We propose a mechanistic model which is capable of describing the evolution of transverse cracking in cross ply laminates subjected to cyclic tension in the longitudinal direction. The key feature of the model is that it incorporates delamination associated with transverse cracks in a manner that induces further formation of transverse cracks as delamination grows in fatigue. A variational approach is taken to estimate the stresses in the region between transverse cracks, and these are found to be accurate away from the crack planes when comparison is made with finite element computations. The evolution of transverse crack density and the associated overall elastic moduli changes predicted by the model are in agreement with experimental results.
cross ply laminates; delamination; TRANSVERSE CRACKING; transverse cracks; VARIATIONAL APPROACH
Modeling of Cure-Induced Residual Stresses in 3D Woven Composites of Different Reinforcement Architectures
Key Engineering Materials
577-578
253-256
2013
10.4028/www.scientific.net/KEM.577-578.253
This paper presents finite element modeling effort to predict possible microcracking of the matrix in 3D woven composites during curing. Three different reinforcement architectures are considered: a ply-to-ply weave, a one-by-one and a two-by-two orthogonal through-thickness reinforcement. To realistically reproduce the as-woven geometry of the fabric, the data from the Digital Fabric Mechanics Analyzer software is used as input for finite element modeling. The curing processed is modeled in a simplified way as a uniform drop in temperature from the resin curing to room temperature. The simulations show that the amount of residual stress is strongly influenced by the presence of through-thickness reinforcement.
3d woven composite; curing; finite element analysis; matrix microcracking
Settling and deformation of a thin elastic shell on a thin fluid layer lying on a solid surface
J Colloid Interface Sci
245
1
187-197
2002
10.1006/jcis.2001.8008
placement of a soft contact lens onto the cornea, the upper eyelid deforms and settles the lens by squeezing fluid out of the post-lens tear film or POLTF (i.e., the tear fluid layer sandwiched between the lens and the cornea). This paper studies the physical mechanisms that control the dynamic state of the contact lens during blinking, i.e., its shape and its distance from the cornea, especially a long time after insertion. We model the lens as a deformable elastic shell and the cornea as a flat nondeformable body. The tear fluid is assumed to be Newtonian, and the lens is characterized by an elastic modulus and a Poisson ratio. Lubrication equations under creeping flow are used to solve the fluid problem, while the thin-shell approximation is applied to the solid lens. The solid and fluid mechanics problems are coupled by maintaining continuity of stress and velocity at the solid/liquid interface. Lid applied pressure causes the lens to approach the cornea by squeezing tear fluid out and also leads to the deformation of the lens. Subsequently, in the interblink period, since there is no applied force, the elastic energy stored in the lens due to its deformation is released causing it to move away from the cornea by imbibing tear fluid into the POLTF. If the POLTF thickness is large, the inward motion of the lens in the blink is more than the outward motion during interblink, and this causes the lens to settle closer to the cornea. Eventually, there may be a balance of the inward motion during the blink and the outward motion during the interblink. If so, the lens subsequently exhibits periodic steady-state motion. However, it is also possible that a balance of inward and outward motion is never achieved, and the lens continues to settle endlessly. If this happens, then the thinfilm interactions between the mucin-covered corneal surface and the lens material determine whether the lens actually touches the cornea and possibly adheres. Our elastohydrodynamic analysis serves as a useful tool to elucidate the effects of various lens parameters on the final settled state of the lens. In particular, we are concerned about eventual adherence and/or mechanical abrasion to the cornea, which is very important to the ocular health of soft contact lens wearers.
Trends in Computational Contact Mechanics
Lecture Notes in Applied and Computational Mechanics
58
121-134
2011
10.1007/978-3-642-22167-5
In alpine regions human settlements and infrastructure are at risk to be hit by landslides or other types of geological flows. This paper presents a new approach that can aid the design of protective constructions. An uncertainty analysis of the flow around a debris barrier is carried out using a chute flow laboratory model of the actual debris flow. A series of discrete element simulations thereby serves to assess barrier designs. In this study, the transformation method of fuzzy arithmetic is used to investigate the influence of epistemically uncertain model parameters. It turns out that parameter and modeling uncertainties can have a tremendous influence on the predicted efficiency of protective structures. © 2011 Springer-Verlag.
The Dirac Equation in Classical Statistical Mechanics
Quant-Ph/0206016
1-9
2002
10.1063/1.1524581
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic continuation, making the model `self-quantizing'. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum mechanics.
Stochastic mechanics according to E. Schrödinger
Physical Review A
33
3
1532-1548
1986
10.1103/PhysRevA.33.1532
In 1931 Schrödinger tried unsuccessfully to probabilistically derive his wave equation. We show that, after some improvements, his program yields two versions of stochastic mechanics. The first one coincides with Nelson stochastic mechanics, the second with the imaginary-time version of this theory, whose existence was unknown. The construction is founded on a variational approach inspired by Yasue.
Crack-morphological aspects in fracture mechanics
Engineering Fracture Mechanics
7
3
515-529
1975
10.1016/0013-7944(75)90052-1
Fracture mechanics can be regarded as a methodology to characterize the actual crack by using the parameters given by the analysis of a simple mathematical crack model. Therefore, the selection of these crack models has very significant meanings. In recent years, several precise crack models have been proposed.
Interaction of phase variation, host and pressure/gas composition: pneumococcal gene expression of PsaA, SpxB, Ply and LytA in simulated middle ear environments.
International journal of pediatric otorhinolaryngology
73
10
1417-22
2009
10.1016/j.ijporl.2009.07.007
OBJECTIVE: Streptococcus pneumoniae, a leading cause of otitis media (OM), undergoes spontaneous intra-strain variations in colony morphology. Transparent (T) variants are more efficient in colonizing the nasopharynx while opaque (O) variants exhibit greater virulence during systemic infections. This study was intended to delineate the underlying molecular mechanisms by which the predominant S. pneumoniae variant efficiently infects the middle ear (ME) mucosa.\n\nMETHODS: Human ME epithelial cells were preconditioned for 24h under one of the three gas/pressure conditions designed to simulate those for (1) normal ME (NME), (2) ME with Eustachian tube obstruction (ETO) and (3) ME with tympanostomy tube placement (TT), and then were incubated with ∼ 10(7)CFU/ml of either T or O variants of S. pneumoniae (6A) for 3h. Relative expression levels of genes encoding virulence factors, PsaA (surface adhesion), SpxB (pyruvate oxidase), Ply (pneumolysin), and LytA (autolysin) were assessed separately in epithelium-attached and supernatant bacteria 3h post infection using real-time PCR.\n\nRESULTS: Basal levels of the virulence molecules in inocula were comparable between two variants. However, relative expression levels of the gene transcripts were significantly induced in epithelium-attached T variants 3h after infection. Comparing with NME and TT conditions, ETO environment produced the largest effect on the differential expression of the virulence genes in the infected ME epithelial cells between T (induced) and O (suppressed) phenotypic pneumococci.\n\nCONCLUSIONS: T variant is a predominant phenotype responsible for the pathogenesis of pneumococcal OM.
Adhesins, Bacterial; Adhesins, Bacterial: genetics; Bacterial Proteins; Bacterial Proteins: genetics; Bacterial Proteins: metabolism; Cells, Cultured; Culture Media, Conditioned; Ear, Middle; Ear, Middle: cytology; Ear, Middle: microbiology; Epithelial Cells; Epithelial Cells: microbiology; Epithelial Cells: physiology; Gene Expression Regulation, Bacterial; Genes, Bacterial; Genes, Bacterial: genetics; Genes, Bacterial: physiology; Humans; Lipoproteins; Lipoproteins: genetics; Models, Biological; N-Acetylmuramoyl-L-alanine Amidase; N-Acetylmuramoyl-L-alanine Amidase: genetics; N-Acetylmuramoyl-L-alanine Amidase: metabolism; Otitis Media; Otitis Media: genetics; Otitis Media: microbiology; Phenotype; Pyruvate Oxidase; Pyruvate Oxidase: genetics; Sensitivity and Specificity; Streptococcus pneumoniae; Streptococcus pneumoniae: genetics; Streptococcus pneumoniae: metabolism; Streptolysins; Streptolysins: genetics; Streptolysins: metabolism; Virulence Factors; Virulence Factors: biosynthesis; Virulence Factors: genetics
Quasi static analysis of creasing and folding for three paperboards
Mechanics of Materials
69
1
11-34
2014
10.1016/j.mechmat.2013.09.016
The creasing and folding behavior of three paperboards have been studied both experimentally and numerically. Creasing and folding studies were performed on strips in both the machine direction and the cross machine direction. A finite element model that mimicked the experimental creasing and folding setup was developed, and the creasing and folding behavior could be well predicted for all three paperboards. An experimental characterization scheme consisting of three experiments was proposed, and was shown to be sufficient to predict the creasing and folding behavior. For the whole paperboard the shear strength profiles in the through thickness direction was determined with the notched shear test. Each ply was laid free by grinding, and density measurements and in-plane tension tests were performed on the bottom, middle and top plies of each paperboard. Instead of assuming uniform properties in each ply, the shear strength profiles were used to map the measured properties in the through thickness direction. Numerical simulations were performed when the ply and interface properties of the paperboards were altered to follow different shear strength profiles. This was done in order to mimic different production strategies. It was shown that the interface strengths mainly influenced the folding behavior. Whereas altered the ply properties affected the creasing force needed. © 2013 Elsevier Ltd. All rights reserved.
Creasing; Folding; Numerical modeling; Paperboard; Shear strength
A numerical study of thin film flow of a non-Newtonian fluid on a vertically moving belt using variational iteration approach
International Journal of Applied Mathematical Research
2
2
325-337
2013
10.14419/ijamr.v2i2.738
This paper provides an investigation regarding the modeling and analysis of a thin film flow of an Oldroyd 8-constant fluid on a vertically moving belt. The governing nonlinear problem is solved by using Variational Iteration Method (VIM). The results of the present method are then compared with those obtained by Adomian Decomposition Method (ADM) and an excellent agreement is observed. This comparison reveals that VIM may be considered as an efficient alternative method for solving nonlinear problems arising in non-Newtonian fluid mechanics. Expressions for some important physical quantities such as volume flux, average velocity, the belt speed for the lifting of the non-Newtonian fluid are also derived.
Supersymmetry in Classical Mechanics
New York
271
54
2001
We briefly review the universal supersymmetry present in classical hamiltonian systems and show its applications to field theories.
Influence of radial head prosthetic design on radiocapitellar joint contact mechanics
Journal of shoulder and elbow surgery / American Shoulder and Elbow Surgeons ...[et al.]
23
4
456-462
2014
10.1016/j.jse.2013.11.028; 10.1016/j.jse.2013.11.028
HYPOTHESIS: Our aim was to test whether anatomically designed metallic radial head implants could better reproduce native radiocapitellar contact pressure and areas than nonanatomic implants. METHODS: The distal humerus and proximal radius from 6 cadaveric upper extremities were serially tested in supination with 100 N of compression force at 4 angles of flexion (0 degrees , 30 degrees , 60 degrees , and 90 degrees ). By use of a thin flexible pressure transducer, contact pressures and areas were measured for the native radial head, an anatomic implant, a nonanatomic circular monopolar implant, and a bipolar nonanatomic implant. The data (mean contact pressure and mean contact area) were modeled using a 2-factor repeated-measures analysis of variance with P </= .05 considered to be significant. RESULTS: The mean contact areas for the prosthetic radial heads were significantly less than those seen with the intact radial heads at every angle tested (P < .01). The mean contact pressures increased significantly with all prosthetic radial head types as compared with the native head. The mean contact pressures increased by 29% with the anatomic prosthesis, 230% with the monopolar prosthesis, and 220% with the bipolar prosthesis. Peak pressures of more than 5 MPa were more commonly observed with both the monopolar and bipolar prostheses than with the anatomic or native radial heads. CONCLUSIONS: The geometry of radial head implants strongly influences their contact characteristics. In a direct radius-to-capitellum axial loading experiment, an anatomically designed radial head prosthesis had lower and more evenly distributed contact pressures than the nonanatomic implants that were tested.
anatomic radial head implant; circular radial head implant; contact area; Contact pressure; prosthesis; radial head
General relativistic statistical mechanics
arXiv
D87
84055
2013
10.1103/PhysRevD.87.084055
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = hbar d tau/ds, with k the Boltzmann constant, hbar the Planck constant, ds proper time and d tau the equilibrium thermal time.
Gravitomagnetism in quantum mechanics
Physical Review D
82
2
025004
2010
10.1103/PhysRevD.82.025004
We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field that is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form, which we then analyze in the nonrelativistic limit. We include a discussion of some rather general observable physical effects implied by the Schroedinger equation form, concentrating on gravitomagnet- ism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field
Impact fragmentation of high-velocity compact projectiles on thin plates: a physical and statistical characterization of fragment debris
International Journal of Impact Engineering
26
1-10
249-262
2001
10.1016/S0734-743X(01)00085-9
The high-velocity impact of a projectile onto a structure results in the creation and energetic expulsion of fragments of the interacting materials. The nature of this fragment debris is of concern in certain applications. Although more broadly applicable, the present study is motivated by a need to characterize the size and velocity distribution of fragments generated by orbital debris impacting external components of spacecraft structure, such as shielding and radiators. In this effort, statistical relations are developed to predict size, momentum and trajectory distributions of the debris. The underlying physics applied are those used in the fields of impact mechanics, thermodynamics of shocks, and statistical fragmentation. Equations from impact mechanics lead to predictions for mass, global momentum, and excess energy of the fragment debris. Relations from shock thermodynamics are developed to partition the initial kinetic energy into thermal and mechanical energies, and therefore to predict mass fractions of solid, liquid and vapor components and the subsequent dispersing motion of this fragment debris. Statistical methods of the energy-based Maxwell-Boltzmann type are pursued to characterize the inherently stochastic fragmentation event, emphasizing the extremes of fragment size and velocity. Computational simulations of impact events and data from impact fragmentation experiments are exploited in validating the underlying theoretical assumptions and the resulting impact fragmentation model.
Indentation Failure in Cross Ply Laminates, Comparison between Observations and 3D Field Solutions
Journal of Composite Materials
28
1803-1824
1994
10.1177/002199839402801804
Indentation damage in thick laminates is numerically and experimentally studied. Static indentation is performed for a spherical steel ball into thick laminates of two types; GFRP and CFRP. Numerical solutions reveal the correlation between the ratio of moduli and the mode of failure. A low value of E1/E2 results in failure initiation in the lower layer, while high value of E1/E2 results in crack initiation and onset on the upper layers. This is verified by the experimentally found divergence in terms of failure initiation between the laminates. The influence of cracks and delamination on the overall stress distribution is studied qualitatively by inserting cavities of appropriate size and shape into the finite element model.
The Possibility of Reconciling Quantum Mechanics with Classical Probability Theory
Theoretical and Mathematical Physics
149
3
14
2007
10.1007/s11232-006-0151-0
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability limits. We especially attend to the quantum state reduction problem.
algebra observables; probability theory; quantum; quantum measurement
Mixing and equilibration: protagonists in the scene of nonextensive statistical mechanics
Physica A: Statistical Mechanics and its Applications
305
1-2
1-18
2002
10.1016/S0378-4371(01)00633-1
After a brief review of the present status of nonextensive statistical mechanics, we present a conjectural scenario where mixing (characterized by the entropic index qmix[les]1) and equilibration (characterized by the entropic index qeq[ges]1) play central and inter-related roles, and appear to determine a priori the values of the relevant indices of the formalism. Boltzmann-Gibbs statistical mechanics is recovered as the qmix=qeq=1 particular case.
Computational analysis of magnetohydrodynamic natural convection in a square cavity with a thin fin
European Journal of Mechanics - B/Fluids
46
154-163
2014
10.1016/j.euromechflu.2014.03.002
A numerical study of laminar natural convection in a square cavity with a thin fin that is under the influence of a uniform magnetic field is presented. The side walls of the cavity are kept at different temperatures and the horizontal walls are thermally insulated. An Adaptive Network-based Fuzzy Inference System (ANFIS) approach and an Artificial Neural Network (ANN) approach are developed, trained and validated using the results of Computational Fluid Dynamics (CFD) analysis. The effects of pertinent parameters on fluid flow and heat transfer characteristics are studied. Among these parameters are the Rayleigh number (103≤Ra≤106), the Hartmann number (0≤Ha≤100), the position of the thin fin (0.1≤Yp≤0.9) and the length of the thin fin (0≤Lp≤0.8). The results show that ANFIS and ANN can successfully predict the fluid flow and heat transfer behaviour within the cavity in less time without compromising accuracy. In most cases, ANFIS can predict the results more accurately than ANN.
ANFIS; ANN; CFD; Magnetohydrodynamic; Natural convection; Square cavity
Damage Mechanics with Fabric Tensors
Mechanics of Advanced Materials and Structures
13
4
285-301
2006
10.1080/15376490600582784
A new formulation is presented to link continuum damage mechanics with the concept of fabric tensors within the framework of classical elasticity theory. A fourth-rank damage tensor is used and its exact relationship to the fabric tensors is illustrated. A model of damage mechanics for directional data is formulated using fabric tensors. The applications of the new formulation to micro-crack distributions are well illustrated in two solved examples. In the first example, a micro-crack distribution is considered with its data represented by a circular histogram. The values of the fabric tensors and damage tensor are calculated in this case. In the second example, two sets of parallel micro-crack distributions with two different orientations are investigated. In addition, a general hypothesis for damage mechanics is postulated. It is seen that the two available hypotheses of elastic strain equivalence and elastic energy equivalence may be obtained as special cases of the postulated general hypothesis. This general hypothesis is then used to derive the sought relationship between the damage tensor and fabric tensors. Finally, the evolution of the damage tensor is derived in a mathematically consistent manner based on sound thermodynamic principles.
Determination of the damage threshold in woven-ply thermoplastic laminates at T > Tg: Acoustic emission and microscopic damage analysis
Composites Part B: Engineering
64
138-146
2014
10.1016/j.compositesb.2014.04.026
An original in situ measurement of acoustic emission (AE) was applied to monitor damage progress in discrete steps during gradual load/unload tensile tests on [??45??]7 C/PPS laminates at temperatures T > Tg, when matrix ductility is enhanced. In order to understand the specific damage behavior of such materials under severe environmental conditions, AE analysis was accompanied by microscopic observations to detect the damage initiation threshold as well as the damage mechanisms within the composite material. Once the AE source mechanisms have been separated into classes thanks to the pattern recognition software Noesis, they have been identified to match physical phenomena. Earliest cracks events occur at the crimps where the rotation of warp/weft fibres takes place, followed by the intra-bundles splitting on free surface. It is observed that the onset of intralaminar cracking and debonding is affected by the presence of matrix-rich regions between the plies, because of an extensive plasticization of the PPS matrix. The study of the specific acoustic activity of neat PPS resin specimens confirms that the local plastic deformation in matrix-rich areas contributes to delay the initiation of damage, and subsequent AE signals. Finally, AE proved to be a relevant technique to investigate damage mechanisms and to determine accurately the damage threshold in TP-based composites to be used in aeronautical applications at T > Tg. ?? 2014 Elsevier Ltd. All rights reserved.
A. Thermoplastic resin; B. High-temperature properties; D. Acoustic emission; D. Fractography
mechanics
Nature
421
January
2003
The basic features of DNA were elucidated during the half- century following the discovery of the double helix. But it is only during the past decade that researchers have been able to manipulate single molecules of DNA to make direct measurements of its mechanical properties. These studies have illuminated the nature of interactions between DNA and proteins, the constraints within which the cellular machinery operates, and the forces created by DNA-dependent motors.
Crack and delamination risk evaluation of thin silicon based microelectronics devices 1
ICF11
2005
Enhancing miniaturization and system integration of microelectronics components demands growingly for novel solutions toward embedding active and passive components into substrates, clothes, protective sleeves of consumer goods smart, thin applications in general. As a result, the embedding of very thin silicon dies and metallic structures into highly flexible polymeric, paper like or textile materials causes several mechanical problems preventing those applications from being utilized. Various kinds of inhomogeneity, residual stresses from several steps of the manufacturing process contribute to interface delaminations, chip cracking and fatigue of solder interconnects. This paper intends to demonstrate and discuss advantages and needs of using fully parameterized modeling techniques for design optimizations of thin devices on the basis of nonlinear finite element simulations. These numerical investigations take into account the nonlinear, temperature and rate dependent behavior of the different materials used and the application of advanced fracture mechanics concepts (energy release rate, integral fracture approaches, mode-mixity examinations) with regards to the specific area of surface-near and interface-near micro scaled regions. For improving the utilized methodology, the evaluation of mixed mode interface delamination phenomena and fracture were combined with experimental investigations by means of SEM and AFM. 1
Confined capillary stresses during the initial growth of thin films on amorphous substrates
Journal of Applied Mechanics, Transactions ASME
69
4
425-432
2002
10.1115/1.1469001
Changes in substrate curvature indicating the existence of compressive stress in isolated crystallites are commonly observed during the initial stages of thin film deposition of metals on glass or ceramic substrates. Following the suggestion of Abermann et al. (R. Abermann et al., 1978, Thin Solid Films, 52, p. 215), we attribute the origin of this compressive stress to the action of capillary forces during film growth. As new atomic layers are deposited, the capillary forces acting on atoms near the surface are stored as transformation strains in the bulk of the crystallites. To test this concept, we propose three models for evaluating the capillary strains and their induced compressive stresses in a crystalline. A finite element analysis is performed to show that the model predictions agree well with experimental data.
Amorphous materials; Capillary stresses; Compressive stress; Computer simulation; Film growth; Finite element method; Mathematical models; Strain; Substrates; Thin films
Insertion sequence 1515 in the ply gene of a type 1 clinical isolate of Streptococcus pneumoniae abolishes pneumolysin expression.
Journal of clinical microbiology
45
7
2296-7
2007
10.1128/JCM.02168-06
A serotype 1 Streptococcus pneumoniae strain isolated by blood culture from a woman with pneumonia was found to harbor insertion sequence (IS) 1515 in the pneumolysin gene, abolishing pneumolysin expression. To our knowledge, this is the first report of an IS in the pneumolysin gene of S. pneumoniae.
Bacterial Proteins; Bacterial Proteins: genetics; DNA Transposable Elements; DNA Transposable Elements: genetics; Female; Gene Expression Regulation, Bacterial; Humans; Molecular Sequence Data; Mutagenesis, Insertional; Pneumonia, Pneumococcal; Pneumonia, Pneumococcal: microbiology; Streptococcus pneumoniae; Streptococcus pneumoniae: genetics; Streptolysins; Streptolysins: genetics
Statistical Mechanics of a Fluid Drop
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
380
1778
211-227
1982
10.1098/rspa.1982.0038
Proc. В. Soc. Lona. A 380, 211-227 (1982) Printed in Great Britain Statistical mechanics of a fluid drop BY JR HENDERSONf AND P. ScHOFIELDJ t Physical Chemistry Laboratory, South Parks Road, Oxford OXí 3QZ, UK % Materials Physics Division, AERE Harwell,
Statistical mechanics of neural networks
Physica A: Statistical Mechanics and its Applications
194
1-4
471-481
1993
10.1016/0378-4371(93)90378-H
We discuss several models of neural networks, including multilayer feed-forward nets as well as structured networks with attractor dynamics. Special emphasis is put on questions of storage capacity and invariant recognition, which can be analysed with statistical methods. We also briefly discuss a model of interacting synapses, which is motivated by experiment.
Chance in Boltzmannian Statistical Mechanics
Philosophy of Science
75
5
670-681
2008
10.1086/594513
In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statistical mechanics as chances in David Lewis’s (1994) sense. I first give a precise formulation of this proposal, then raise two fundamental objections, and finally conclude that these can be overcome only at the price of interpreting these probabilities epistemically.
Micro-mechanics of crack initiation
International Journal of Fracture
42
1
87-99
1990
10.1007/BF00018615
Abstract. Prior to the crack initiation , damage is most often localized at a scale below the size of the classical representative volume element of the continuum mechanics . This allows the stress and strain analyses in a component to neglect the strain-damage coupling at ... \n
Mechanics of the mitral valve
Biomechanics and modeling in mechanobiology
12
5
1053-1071
2013
10.1007/s10237-012-0462-z.Mechanics
Abstract Alterations in mitral valve mechanics are classical indicators of valvular heart disease, such as mitral valve prolapse, mitral regurgitation, and mitral stenosis. Computational modeling is a powerful technique to quantify these alterations, to explore ... \n
Effects of partial crack-face contact for the bending of thin shell structures
Theoretical and Applied Fracture Mechanics
49
1
128-150
2008
10.1016/j.tafmec.2007.10.003
The physical occurrence that crack surfaces are in contact at the compressive edges when a flat or a shell is subjected to a bending load has been recognized. This article presents a theoretical analysis of crack-face contact effect on the stress intensity factor of various shell structures such as spherical shell, cylindrical shell containing an axial crack, cylindrical shell containing a circumferential crack and shell with two non-zero curvatures, under a bending load. The formulation of the problem is based on the shear deformation theory, incorporating crack-face contact by introducing distributed force at the compressive edge. Material orthotropy is concerned in this analysis. Three-dimensional finite element analysis (FEA) is conduced to compare with the theoretical solution. It is found that due to curvature effect crack-face contact behavior in shells differs from that in flat plates, in that partial contact of crack surfaces may occur in shells, depending on the shell curvature and the nature of the bending load. Crack-face contact has significant influence on the stress intensity factor and it increases the membrane component but decreases the bending component. ?? 2007 Elsevier Ltd. All rights reserved.
Bending; Crack-face contact; Finite element analysis; Material orthotropy; Shell; Stress intensity factor
Generalized quantum mechanics
Communications in Mathematical Physics
37
3
221-256
1974
10.1007/BF01646346
A convex scheme of quantum theory is outlined where the states are not necessarily the density matrices in a Hilbert space. The physical interpretation of the scheme is given in terms of generalized ``impossibility principles''. The geometry of the convex set of all pure and mixed states (called a statistical figure) is conditioned by the dynamics of the system. This provides a method of constructing the statistical figures for non-linear variants of quantum mechanics where the superposition principle is no longer valid. Examples of that construction are given and its possible significance for the interrelation between quantum theory and general relativity is discussed.
Comment on ‘‘ Nonlocality , counterfactuals , and quantum mechanics ’’
Physical Review A
60
3
2595-2598
1999
10.1103/PhysRevA.59.126
Stapp {[Am.} J. Phys. 65, 300 (1997)] has recently argued from a version\nof the Hardy-type experiments that quantum mechanics must be nonlocal,\nindependent of any additional assumptions such as realism or hidden\nvariables. I argue either that his conclusions do not follow from\nhis assumptions or that his assumptions are not true of quantum mechanics\nand can be interpreted as assigning an unwarranted level of reality\nto the value of certain quantum attributes.
Nosé–Hoover nonequilibrium dynamics and statistical mechanics
Molecular Simulation
33
1-2
13-19
2007
10.1080/08927020601059869
<i>At</i> equilibrium Nose's 1984 revolutionary thermostat idea linked\nNewton's mechanics with Gibbs' statistical mechanics. His work expanded\nthe scope of isothermal and isobaric simulations. Nose-Hoover dynamics\nhas subsequently facilitated the simulation and detailed understanding\nof nonequilibrium problems. The fractal phase-space distributions,\nand their close link to the Lyapunov spectrum, provide a novel explanation\nof irreversibility and a rich field for exploration.
02; 05; 45; 70; -a; df; fractals; irreversibility; ln; molecular dynamics; ns; pacs numbers; thermostats
MECHANICS METHODOLOGY FOR TEXTILE PREFORM COMPOSITE MATERIALS
Composites
1
1996
NASA and its contractors have completed a program to develop a basic mechanics underpinning for textile composites. Three major deliverables were produced by the program: (1.) a set of test methods for measuring material properties and design allowables, (2.) mechanics models to predict the effects of the fiber preform architecture and constituent properties on engineering moduli, strength, damage resistance, and fatigue life, (3.) an electronic data base of coupon type test data. This report describes these three deliverables.
analysis; mechanical properties; test methods; textile composites
Hidden BRS invariance in classical mechanics
Physics Letters B
201
4
525-528
1988
10.1016/0370-2693(88)90611-9
We give in this paper a path integral formulation of classical mechanics. We do so by writing down the associated classical-generating functional. This functional exhibits an unexpected BRS-like and antiBRS-like invariance. This invariance allows for a simple expression, in term of superfields, of this generating functional. Associated to the BRS and antiBRS charges there is also a ghost charge whose conservation turns out to be nothing else than the wel-known Liouville theorem of classical mechanics.
Mechanics of strain gradient plasticity with particular reference to decomposition of the state variables into energetic and dissipative components
International Journal of Engineering Science
47
11-12
1405-1423
2009
10.1016/j.ijengsci.2009.05.013
The results of recent studies on strengthening and hardening mechanisms for micro/nano structured materials indicate that the use of only one type of energetic or dissipative description may be insufficient to accurately describe the size effects exhibited in metallic components. Therefore, it is important to incorporate more than one description of the thermodynamic processes into the modeling in order to have a better understanding of the hardening and strengthening mechanisms for micro/nano structured materials. The research presented here is based on this deficiency and the goal is to develop a strain gradient theory based on the decomposition of the state variables into energetic and dissipative components. This, in turn, endowed the constitutive equations to have both energetic and dissipative gradient length scales ???en and ???dis, respectively. The effect of the material microstructural interface between two materials is also incorporated into the proposed formulation. Hence four material length scales are introduced: two for the bulk and the other two for the interface. The resulting formulation exhibits the following important physical phenomena: (i) standard energetic hardening associated with plastic strain and nonlocal energetic hardening associated with plastic strain gradients; (ii) size dependent increase in yield strength which is characterized by the dissipative strengthening associated with plastic strain gradient rate; (iii) the effect of interfacial yield strength and hardening; (iv) description of the boundary layer; and (v) the effect of the different boundary conditions. The problem is solved analytically by using for example, a thin film on elastic substrate under uniaxial uniform tension or a single phase bicrystal under uniform tension where the interface represents the grain boundary. The interface model here describes the internal boundary of the plastic region and characterizes the physical understanding of the dislocation mechanics at the interface between two phases. The results of the analytical results indicate that the proposed theory qualitatively captures the overall physical behavior. However there is strong debate in the literature on the choice of accurate physical boundary conditions at the elastic plastic boundaries. Therefore, more elaborate studies are needed for better assessment of the boundary conditions of the higher-order strain gradient plasticity theories. ?? 2009 Elsevier Ltd. All rights reserved.
Dissipative; Energetic; Hardening; Micro; Nano; Strain gradient plasticity; Strengthening
Polymer Fluid Mechanics
Advances in Applied Mechanics
19
143-219
1979
10.1016/S0065-2156(08)70310-7
Polymeric liquids consists of high-molecular weight polymers or “macromolecules'’ in the form of polymer solutions or polymer melts. This chapter provides one of the most ubiquitous examples of the viscoelastic or non-Newtonian liquid and discusses certain developments in the mechanics of viscoelastic fluids, as typified by polymeric liquids. The term “mechanics” embodies both the underlying rheology, in the form of mechanical constitutive theories or models, and dynamics, as represented by the phenomena of fluid motion and the governing field equations of continuum mechanics. The chapter focuses on developments in the continuum and microstructural theory of polymer-fluid rheology and, to a lesser extent, in the fluid dynamics. The emphasis is on continuum mechanics, and, except insofar as they relate grossly to the characteristic departures from classical (Newtonian) fluid behavior, there is little said about the chemical structure and molecular physics of polymers. The objectives are to trace the progress in the selected avenues of research and to summarize and evaluate certain ideas and methods that appear to be in need of refinement or are most promising for further development. Several extensions of existing methods and some original results are presented.
Mechanics of reversible unzipping
Continuum Mechanics and Thermodynamics
21
251-268
2009
10.1007/s00161-009-0108-2
We study the mechanics of a reversible decohesion (unzipping) of an elastic layer subjected to quasi-static end-point loading. At the micro level the system is simulated by an elastic chain of particles interacting with a rigid foundation through breakable springs. Such system can be viewed as prototypical for the description of a wide range of phenomena from peeling of polymeric tapes, to rolling of cells, working of gecko's fibrillar structures and denaturation of DNA. We construct a rigorous continuum limit of the discrete model which captures both stable and metastable configurations and present a detailed parametric study of the interplay between elastic and cohesive interactions. We show that the model reproduces the experimentally observed abrupt transition from an incremental evolution of the adhesion front to a sudden complete decohesion of a macroscopic segment of the adhesion layer. As the microscopic parameters vary the macroscopic response changes from quasi-ductile to quasi-brittle, with corresponding decrease in the size of the adhesion hysteresis. At the micro-scale this corresponds to a transition from a `localized' to a `diffuse' structure of the decohesion front (domain wall). We obtain an explicit expression for the critical debonding threshold in the limit when the internal length scales are much smaller than the size of the system. The achieved parametric control of the microscopic mechanism can be used in the design of new biological inspired adhesion devices and machines.
Adhesion; Calculus of variations; ??-convergence; DNA; Gecko; Hysteresis; Peeling; Unzipping
Generalized statistical mechanics and fully developed turbulence
Physica A: Statistical Mechanics and its Applications
306
189-198
2002
10.1016/S0378-4371(02)00497-1
The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating friction forces, where Tsallis statistics can be proved rigorously. © 2002 Elsevier Science B.V. All rights reserved.
Fluctuating energy dissipation; Fully developed turbulence; Non-extensive statistical mechanics
Influence of frozen capillary waves on contact mechanics
Wear
264
746-749
2008
10.1016/j.wear.2006.10.028
Free surfaces of liquids exhibit thermally excited (capillary) surface waves. We show that the surface roughness which results from capillary waves when a glassy material is cooled below the glass transition temperature can have a large influence on the contact mechanics between the solids. The theory suggest a new explanation for puzzling experimental results [L. Bureau, T. Baumberger and C. Caroli, European Physical Journal E19, 163 (2006)] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. It also lend support for a recently developed contact mechanics theory. ?? 2007 Elsevier B.V. All rights reserved.
Contact mechanics; Frozen capillary waves; Glass transition temperature
Mechanics of the normal heart
Journal of Cardiac Surgery
21
6
615-620
2006
10.1111/j.1540-8191.2006.00314.x
Even though studies on isolated papillary muscles and cardiomyocytes can be applied to the mechanics of a beating heart, it is not always easy for physicians to relate these findings to clinical medicine. Thus, it is important to extend the studies to intact heart either in simulations or in animal models and even better to validate the results with human subjects. Advances in engineering and computer technology have allowed us to bridge the gap between physiology and mechanics. Cardiomyocyte stress/strain relates to muscle energy expenditure, which dictates oxygen and substrate utilization. Appreciation of this sequential relationship by clinicians will facilitate the logical development and assessment of therapies. Theory of finite element analysis (FEA) can predict cardiac mechanics under normal and pathologic conditions. Imaging studies provide an avenue to relate these predictions indirectly to experimental studies. In this fashion, we can understand the mechanical basis for the micro- and macroanatomical twisting motion of the beating heart. The purposes of this manuscript are: (1) to examine the terms that are traditionally used to describe mechanical stresses and strain within the ventricle, (2) to explore the three-dimensional organization of cardiomyocytes that influences global ventricular function, (3) to apply mechanical measures to both single cardiomyofibrils and the intact ventricle (4) to evaluate mathematical and computer models used to characterize cardiac mechanics, and (5) to outline the clinical methods available to measure ventricular function and relate findings from FEA to pathologic conditions.
Biomechanical Phenomena; Heart Ventricles; Heart Ventricles: cytology; Humans; Models, Theoretical; Muscle Cells; Muscle Cells: physiology; Myofibrils; Myofibrils: physiology; Terminology as Topic; Ventricular Function; Ventricular Function: physiology
Fluid mechanics
Course of Theoretical Physics
536
1959
The subject is treated as a branch of theoretical physics. There are 17 chapters including accounts of : theory of heat transfer; acoustics; theory of combustion; dynamics of superfluids; and relativistic fluid dynamics. The authors point out in the preface that it has not been possible to include any new results which have appeared since the last Russian edition. There has however been the addition of a further chapter on the general theory of fluctuations on fluid dynamics.
[a1960-00915]; fluids/ A4700 Fluid dynamics
BRACKET FORMULATION OF DISSIPATIVE FLUID MECHANICS EQUATIONS
Physics Letters
102
8
355-358
1984
10.1016/0375-9601(84)90297-4
The bracket formulation of the Euler fluid mechanics equations is extended to the fluid mechanics equations corre- sponding to the Navier-Stokes-Fourier and the Edelen constitutive relations.
Classical and Quantum Mechanics via Lie algebras
Arxiv preprint arXiv:0810.1019
376
2008
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
Quantum Physics
Constrained diffusional creep in thin copper films
Dislocations and Deformation Mechanics in Thin Films and Small Structures
673
Generic
2001
The mechanical properties of thin metal films have been investigated for many years. However, the underlying mechanisms are still not fully understood. In this paper we give an overview of our work on thermomechanical properties and microstructure evolution in pure Cu and dilute Cu-Al alloy films. Very clean films were produced by sputtering and annealing under ultra-high vacuum (UHV) conditions. We described stress-temperature curves of pure Cu films with a constrained diffusional creep model from the literature. In Cu-1at.%Al alloy films, Al surface segregation and oxidation led to a "self-passivating" effect. These films showed an increased high-temperature strength because of the suppression of constrained diffusional creep; however, under certain annealing conditions, these films deteriorated due to void growth at grain boundaries.
Annealing; Constrained diffusional creep; Copper; Creep; Diffusion in solids; Grain boundaries; High temperature properties; Metallic films; Metallographic microstructure; Microstructure evolution; Segregation (metallography); Self-passivating effect; Sputtering; Temperature; Thin films; Ultrahigh vacuum conditions; Void growth
Fully Lagrangian Modeling of Dynamics of MEMS With Thin Beams—Part II: Damped Vibrations
Journal of Applied Mechanics
76
5
051008
2009
10.1115/1.3086786
Micro-electro-mechanical systems (MEMS) often use beam or plate shaped conductors that are very thin with h/L approximate to O(10(-2) - 10(-3)) (in terms of the thickness h and length L of a beam or side of a square plate). A companion paper (Ghosh and Mukherjee, 2009, "Fully Lagrangian Modeling of Dynamics of MEMS With Thin Beams-Part I: Undamped Vibrations," ASME J. Appl. Mech., 76, p. 051007) addresses the coupled electromechanical problem of MEMS devices composed of thin beams. A new boundary element method (BEM) is coupled with the finite element method (FEM) by Ghosh and Mukherjee, and undamped vibrations are addressed there. The effect of damping due to the surrounding fluid modeled as Stokes flow is included in the present paper. Here, the elastic field modeled by the FEM is coupled with the applied electric field and the fluid field, both modeled by the BEM. As for the electric field, the BEM is adapted to efficiently handle narrow gaps between thin beams for the Stokes flow problem. The coupling of the various fields is carried out using a Newton scheme based on a Lagrangian description of the various domains. Numerical results are presented for damped vibrations of MEMS beams. [DOI: 10.1115/1.3086786]
aspect ratio; boundary element method; boundary integral equations; damping; micro-electro-mechanical systems; newton; singular integrals; stokes flow; thin beam
Combined asymptotic finite-element modeling of thin layers for scalar elliptic problems
Computer Methods in Applied Mechanics and Engineering
200
47-48
3255-3269
2011
10.1016/j.cma.2011.08.001
Thin layers with material properties which differ significantly from those of the adjacent media appear in a variety of applications, as in the form of fiber coatings in composite materials. Fully modeling of such thin layers by standard finite element (FE) analysis is often associated with difficult meshing and high computational cost. Asymptotic procedures which model such thin domains by an interface of no thickness on which appropriate interface conditions are devised have been known in the literature for some time. The present paper shows how the first-order asymptotic interface model proposed by B??vik in 1994, and later generalized by Benveniste, can be incorporated in a FE formulation, to yield an accurate and efficient computational scheme for problems involving thin layers. This is done here for linear scalar elliptic problems in two dimensions, prototyped by steady-state heat conduction. Moreover, it is shown that by somewhat modifying the formulation of the B??vik-Benveniste asymptotic model, the proposed formulation is made to preserve the self-adjointness of the original three-phase problem, thus leading to a symmetric FE stiffness matrix. Numerical examples are presented that demonstrate the performance of the method, and show that the proposed scheme is more cost-effective than the full standard FE modeling of the layer. ?? 2011 Elsevier B.V.
Asymptotic; Finite element; Interface; Interphase; Self-adjoint; Thin layer
X-ray Diffraction Studies of Multiple Orientation in Poly(9,9-bis(2-ethylhexyl)fluorene-2,7-diyl) Thin Films
The Journal of Physical Chemistry B
107
45
12425-12430
2003
10.1021/jp035259t
The structural investigation of poly(9,9-bis(2-ethylhexyl)fluorene-2,7-diyl) (PF2/6) in aligned thin films is presented. Formation of a thickness dependent triaxial texturing is identified in thermotropically aligned films. X-ray reflectivity measurements reveal good macroscopic quality, and polarized photoluminescence and dichroic ratios in absorption indicate clear axial alignment. Grazing-incidence X-ray diffraction shows axially aligned mesomorphic structure with a distinct arrangement of helices and large correlation lengths, indicating a high local lateral order. Theoretical models produced using molecular mechanics methods suggest 5/2-helicity. The polymer chains are parallel to the substrate in the c direction. In particular, the hexagonal-like cells are flattened in the direction of the surface normal and reveal two kinds of coexistent crystallites, a multiple orientation where the greater proportion of the crystallites have one crystal axis a perpendicular to the substrate surface, whereas a smaller proportion is aligned with the crystal axis a parallel to the surface. In thinner films the former class of orientation is usually dominant, while the proportion of the parallel orientation type increases with prolonged annealing.
Seams of different ply properties, Part 1 : Seam appearance
Journal of the Textile Institute
83
2
209-227
1992
10.1080/00405009308631244
This paper presents the results of experiments on seam sewn under constant sewing conditions when the mechanical properties of the plies are different. By using plies of the same fabric along different directions, the effects of the mean properties of the plies as well as their incompatability are studied, while the other two important factors, the fabric thickness and the compressive modulus, are kept unchanged. The extensibility and strength of such seams will be studied in the second part of this serries.
Seams
Mechanics of elastic networks.
Proceedings. Mathematical, physical, and engineering sciences / the Royal Society
470
2172
20140522
2014
10.1098/rspa.2014.0522
We consider a periodic lattice structure in d=2 or 3 dimensions with unit cell comprising Z thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the effective elasticity of such frameworks. The method yields the effective cubic elastic constants for three-dimensional space-filling lattices with Z=4, 6, 8, 12 and 14, the last being the 'stiffest' lattice proposed by Gurtner & Durand (Gurtner & Durand 2014 Proc. R. Soc. A 470, 20130611. (doi:10.1098/rspa.2013.0611)). The analytical expressions provide explicit formulae for the effective properties of pentamode materials, both isotropic and anisotropic, obtained from the general formulation in the stretch-dominated limit for Z=d+1.
Elasticity; Lattice; Pentamode
The role of flaw geometry in thin film delamination from two-dimensional interface flaws along free edges
Engineering Fracture Mechanics
70
13
1721-1736
2003
10.1016/S0013-7944(02)00170-4
Delamination from planar interface edge flaws between a thin film and a semi-infinite substrate is examined to determine the roles of flaw width and depth relative to the film thickness. The flaws have curved and straight sections, and the crack front intersects the free edge at a right angle. Three-dimensional finite element models are used to extract local energy release rates and mode-mixity angles along the entire crack front. This paper focuses the crack dimensions required to reach steady state, wherein energy release rates are independent of flaw dimensions along the entire crack front. Results indicate that moderate elastic mismatch, although affecting mode mixity, plays a small role in determining the crack aspect ratios required to reach steady state. For wide cracks, the energy release rate for crack advance into the film interior approaches the plane-strain steady-state value when the half-width of the crack is approximately four times its depth (for cracks whose depths is several times the film thickness). For narrow cracks, the energy release rate near the free edge is significantly greater than the plane-strain steady-state result, and reaches a steady state when the depth approximately 10 times its width (for widths several time the film thickness). The results imply that delamination from wide cracks is reasonably accurately predicted via plane-strain analyses. Conversely, two-dimensional models are incapable of accurately predicting delamination from narrow cracks, which have a tendency to widen into flaws with more balanced aspect ratios (i.e. without growth in the depth direction).
edge cracks; energy release rate; interface fracture mechanics; three dimensional
Liouville invariance in quantum and classical mechanics
Astronomy
1-14
2001
10.1023/A:1019657303471
The density-matrix and Heisenberg formulations of quantum mechanics follow--for unitary evolution--directy from the Schr"odinger equation. Nevertheless, the symmetries of the corresponding evolution operator, the Liouvillian L=i[.,H], need not be limited to those of the Hamiltonian H. This is due to L only involving eigenenergy_differences_, which can be degenerate even if the energies themselves are not. Remarkably, this possibility has rarely been mentioned in the literature, and never pursued more generally. We consider an example involving mesoscopic Josephson devices, but the analysis only assumes familiarity with basic quantum mechanics. Subsequently, such _L-symmetries_ are shown to occur more widely, in particular also in classical mechanics. The symmetry's relevance to dissipative systems and quantum-information processing is briefly discussed.
Exactly Solvable and Integrable Systems; Mathematical Physics; Quantum Physics
Quantum mechanics and consciousness: fact and fiction
arXiv
quant-ph
8
2001
This article was written in response to a request from an editor of American Vedantist. It is shown that the idea that consciousness is essential to understanding quantum mechanics arises from logical fallacies. This may be welcome news to those who share the author's annoyance at consciousness being dragged into discussions of physics, but beware: The same fallacies may underlie the reader's own way of making sense of quantum mechanics. The article ends up embracing a Vedantic world view, for two reasons. For one, such a world view seems to the author to be the most sensible alternative to a materialistic one. For another, quantum mechanics is inconsistent with a materialistic world view but makes perfect sense within a Vedantic framework of thought.
Basic Mechanics of the Metal Cutting Process
Jounral of Applied Mechanics
11
A168 - A175
1944
Mathematical analysis of geometry and mechanics of metal cutting process, covering two common types of geometry which occur in cutting; that of straight edged cutting tool moving relative to work piece in direction perpendicular to its cutting edge, termed "orthogonal cutting," and similar cutting tool so set that cutting edge is oblique to direction of relative motion of tool and work, termed "oblique cutting".
An experimental and numerical study on the interference-fit pin installation process for cross-ply glass fiber reinforced plastics (GFRP)
Composites Part B: Engineering
54
153-162
2013
10.1016/j.compositesb.2013.05.006
Interference-fit pin connections provide beneficial effects such as fatigue enhancement to the fiber reinforced composites. An interference-fit pin installation process simulation using three-dimensional (3-D) finite element analysis (FEA) was conducted considering the friction coefficient (0.1) and interference-fit percentages (0.4% and 1.0%). During the simulation, the stress and strain distributions of GFRP when installing interference-fit pin were investigated. The radial and the tangential strains in the vicinity of the hole acquired from the FEA were compared with strain gauge experimental measurements, showing fairly good agreement. With increasing interference fit percent, the strain magnitudes increased after pin installation. For 1% interference-fit, micro-scale fiber damage occurred in local regions around hole during the pin installation experiments, while minimal damage was observed for 0.4% interference-fit. ?? 2013 Elsevier Ltd. All rights reserved.
A. Glass fibers; B. Fatigue; B. Residual/internal stress; D. Mechanical testing Composite joints
Quantum mechanics without time: A model
Physical Review D
42
8
2638-2646
1990
10.1103/PhysRevD.42.2638
without time: A model. Carlo Rovelli Physics Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Sezione di Trieste, Istituto
On time-dependent behavior of cross-ply laminated strips with viscoelastic interfaces
Applied Mathematical Modelling
31
2
381-391
2007
10.1016/j.apm.2005.11.014
The two-dimensional problem of a simply supported laminated orthotropic strip with viscoelastic interfaces under static loading is studied. State-space formulations are developed based on the exact elasticity equations governing orthotropic media and the Kelvin-Voigt constitutive relation of interfaces. Since the response of the strip is time-dependent, the power series expansion technique is adopted to model the variations of elastic fields with time. Results show that the response of the laminated strip with viscoelastic interfaces changes remarkably with time, which is also significantly different from that of a plate with perfect interfaces or with viscous interfaces. Note that from the present analysis, the response for a laminated plate with spring-like interfaces or with viscous interfaces can be easily obtained because they are just two particular cases of the present Kelvin-Voigt model. ?? 2005 Elsevier Inc. All rights reserved.
Kelvin-Voigt model; Orthotropic laminate; State-space method; Viscoelastic interfaces
Similitude requirements and scaling laws for flutter prediction of angle-ply composite plates
Composites Part B: Engineering
42
1
51-56
2011
10.1016/j.compositesb.2010.09.010
This study describes the establishment of the necessary similarity conditions for dynamic aeroelastic stability of laminated composite plates. An analytical investigation based on the direct use of the governing equations of the systems is undertaken to derive the necessary scaling laws and similarity conditions. The method presented herein has already been shown to be effective in the design of scaled down models for buckling and vibration response of laminated composite shells and panels. In this study, the flutter speeds of the prototypes are predicted by projecting the flutter speed of the model using the derived scaling law. The results presented herein, indicate that, for flutter of composite plates, based on structural similitude, a set of scaling laws can be found, which are used to develop design rules for small scale models. Models with different material properties, thickness, fiber orientation, Mach number, aspect ratio, and number of plies than those of the prototype can predict the flutter behavior of the prototype with good accuracy. ?? 2010 Elsevier Ltd. All rights reserved.
A. Plate; A. Polymer-matrix composites (PMCs); Similitude
Entanglement Exchange and Bohmian Mechanics
Arxiv
15
2009
This paper analyses the phenomenon of entanglement exchange in Bohm's pilot wave interpretation of quantum mechanics. The interesting feature of the phenomenon is that systems become entangled without causal interaction; hence it is a useful situation for investigating the unique nature of interaction in Bohmian mechanics. The first two sections introduce, respectively, entanglement exchange in the standard interpretation of quantum mechanics, and the basic principles of Bohmian mechanics. The next section shows that the Bohmian interpretation makes the same experimental predictions about entanglement exchange as the standard one. The final section draws some conclusions about interactions and entanglement in Bohmian mechanics.
Quantum Physics
A criterion for crack nucleation at a notch in homogeneous materials
Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics
329
2
97-102
2001
10.1016/S1620-7742(01)01302-2
Experiments of Parvizi et al. on transverse fracture of cross-ply laminates showed that both energy (Griffith) and strength criteria are necessary conditions for fracture but neither one nor the other are sufficient. Thanks to the singularity at the tip of the notch, the incremental form of the Griffith criterion gives a lower bound of admissible crack lengths. On the contrary, the strength criterion leads to an upper bound. The consistency between these two conditions provides a general form of a criterion for crack nucleation.
Interpretations of Quantum Mechanics
Entanglement, Information, and the Interpretation of Quantum Mechanics
95-188
2009
10.1007/978-3-540-92128-8_3
Quantum mechanics was initially formulated in what appeared to be two fundamentally distinct ways, as Matrix mechanics with operator matrices satisfying $$[Q_i,P_j]=i\hbar\delta_{ij}$$ , and Wave mechanics with the function $$\psi$$ satisfying $$i\hbar(\partial\psi(\vec{q})/\partial t)=H(\vec{q},\vec{p})\psi(\vec{q})$$ , the former developed by Heisenberg, Born and Jordan [73, 74],, and the latter by Schrödinger [393]. Dirac, Jordan, Pauli, and Schrödinger subsequently provided arguments for the equivalence of these two approaches. However, the Dirac–Jordan equivalence proof made use of the Dirac $$\delta$$ ‘function,’ which is not well defined as a function because it takes an infinite value at a single point although it can be given a proper definition as distribution (or “improper function”). Von Neumann finally rigorously proved the equivalence and derived the hydrogen atom energy eigenvalue spectrum by making use of Hilbert space, a separable complete vector space with an inner product and a countable, potentially infinite basis (cf. [282] and [281], Appendix 4), capturing the theory’s mathematical essence [473 – 477]. Much later, exploring some ideas of Dirac involving the Lagrangian and action [139], Feynman also produced a third, mathematically equivalent formulation of the theory [168].
Steps toward the foundations of statistical mechanics: In and out of equilibrium
Condensed Matter Physics
9
2
219-236
2006
10.5488/CMP.9.2.219
The first part of the paper is devoted to the foundations, that is the mathematical and physical justification, of equilibrium statistical mechanics. It is a pedagogical attempt, mostly based on Khinchin's presentation, which purpose is to clarify some aspects of the development of statistical mechanics. In the second part, we discuss some recent developments that appeared out of equilibrium, such as fluctuation theorem and Jarzynski equality.
Fluctuation theorem; Foundations of statistical mechanics; Jarzynski equality
The influence of student understanding of classical physics when learning quantum mechanics
Research on teaching and learning quantum mechanics
1999
Understanding quantum mechanics is of growing importance, not just to future physicists, but to future engineers, chemists, and biologists. Fields in which understanding quantum mechanics is important include photonics, mesoscopic
Fracture Mechanics Ch06
Fracture Mechanics
123-169
2012
10.1016/B978-0-12-385001-0.00006-7
This chapter discusses the plasticity effects around a crack tip; for example, the stress and deformation fields, plastic zone size and shape, and crack tip opening displacement (CTOD). Knowledge of the plastic zone shape and size around a crack is useful to understand the plasticity effect on the fracture behavior of solids. Solutions of stresses in both elastic and plastic regions are required to determine the plastic zone shape. If the plastic zone around the crack tip is small compared to the region in which the crack tip K-fields apply, the singular elastic stress fields is used to estimate the plastic zone shape. The estimates thus obtained, however, are the first-order approximations because the stress redistribution caused by the small plastic zone is not considered. In elastic-plastic fracture mechanics, a parallel issue to the elastic crack tip K-field is the stress and deformation fields near a crack tip in an elastic-plastic material. The chapter also discusses energy release rate concept in elastic-plastic materials. Energy release rate plays a very important role in Griffith's theory of fracture. It is a common notion that a crack extends because of the surplus energy released to provide the energy needed in creating new surfaces during crack growth.
classical failure theory; elastic-plastic fracture mechanics; Griffith theory; history of fracture mechanics; linear elastic fracture mechanics
Against Pointillisme about mechanics
British Journal for the Philosophy of Science
57
4
709-753
2006
10.1093/bjps/axl026
This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. A companion paper argues against pointillisme about (chrono)-geometry, as proposed by Bricker. To avoid technicalities, I conduct the argument almost entirely in the context of ``Newtonian'' ideas about space and time, and the classical mechanics of point-particles, i.e. extensionless particles moving in a void. But both the debate and my arguments carry over to relativistic physics.
The Mechanics f Dynamic Fracture
Tenth U. S. National Congress of Applied Mechanics
49
1986
Some concepts available for interpreting dynamic fracture phenomena are reviewed. These include the mechanical characterization of crack edge fields, energy variations associated with crack growth, and experimental observations relevant to the points raised. More recently developed and still incomplete ideas on the influence of crack tip plasticity, material strain rate sensitivity and three dimensional effects are also outlined.
Fractal models in fracture mechanics
International Journal of Fracture
128
1
271-276
2004
10.1023/B:FRAC.0000040990.68602.e2
Application of fractal geometry to the problems of fracture mechanics is discussed. Fractal generalization of the energy balance equation to the case of non-square root singularities of the stress field is proposed. Analysis of the fracture at the sharp angular notch in a plate on the basis of the generalized energy balance equation is performed. Good corroboration between the suggested approach and experiments is observed.
Support Vectors and Statistical Mechanics
Advances in Large Margin Classifiers
359-368
2000
SVMs are analyzed using methods of statistical mechanics\nby representing the SVM solution as the limit of a family\nof Gibbs distributions. This way, one may derive rather\nprecise learning curves. The analysis in the paper shows\nthat for `favourable' input distributions, i.e.\ ones which\nallow a large margin, the expected generalization error\ndecays much more rapidly than predicted by\ndistribution-independent upper bounds of statistical\nlearning theory.
Emergent quantum mechanics of finances
Physica A: Statistical Mechanics and its Applications
403
1
148-154
2014
10.1016/j.physa.2014.02.037
This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed. ?? 2014 Elsevier B.V. All rights reserved.
Econophysics; Financial markets; Fractals; Schr??dinger equation; Statistical scaling
Mechanics of Hip Arthroscopy
Clinics in Sports Medicine
30
2
285-292
2011
10.1016/j.csm.2010.12.005
In this article, the concepts important for hip arthroscopy are reviewed. Room setup, necessary equipment, and the basics of patient positioning are detailed, and the benefits of lateral versus supine positions are evaluated. The placement of common arthroscopic portals and the authors' preferred position and technique for hip arthroscopy are discussed. Also, the potential complications encountered are discussed. ?? 2011 Elsevier Inc.
Hip arthroscopy; Positioning; Setup
Mechanics of glenohumeral instability
Clin Sports Med
10
4
783-788
1991
1138-5111
The glenohumeral joint is designed for mobility and is normally lax. It is stabilized in its midrange by its limited joint volume and concavity-compression. It is stabilized at the extremes of motion by its ligaments. An enhanced understanding of these stabilizing mechanisms helps us in the diagnosis and management of glenohumeral instability.
Humans; Joint Instability/ physiopathology; Ligaments, Articular/physiopathology; Shoulder Joint/ physiopathology
Three-dimensional modeling of ductile crack growth in thin sheet metals: Computational aspects and validation
Engineering Fracture Mechanics
63
4
347-374
1999
10.1016/S0013-7944(99)00034-X
This work describes the development of two types of three-dimensional (3D) finite element models to predict stable, Mode I crack growth in thin, ductile aluminum alloys. The two presented models extend the standard 2D form of the Crack Tip Opening Angle (CTOA) methodology, which determines crack extension based on obtaining a critical angle at the crack tip. The more general 3D model evaluates the CTOA at each node along the crack front which enables the development of tunneled profiles. The alternative, constant front approach, enforces uniform growth along the crack front, thereby growing the crack in a self-similar manner. For the constant front approach, evaluation of the CTOA occurs at a specified distance behind the crack front which decouples CTOA evaluation from mesh refinement. Both CTOA-based models include adaptive load control strategies to minimize the effects of discrete load increments on the growth response. Example analyses demonstrate that the more general 3D approach requires cube-shaped elements on the crack plane to eliminate a bias in growth directions. To evaluate the effectiveness of the constant front approach, this work also describes a validation study using load-crack extension data from 2.3 mm thick Al 2024-T3 specimens tested at NASA-Langley. The test matrix includes C(T) and M(T) specimens, with varying widths (50-600 mm), a/W ratios, and levels of mechanical restraint to suppress out-of-plane bending. Comparisons of load-crack extension curves from experiments and analyses of a 150 mm C(T) specimen, with out-of-plane bending prevented, provide a calibrated (critical) CTOA value of 5.1°. Analyses using the calibrated CTOA value and the constant front approach provide predictions of peak load for constrained and unconstrained specimens in good agreement with the experimental values. © 1999 Elsevier Science Ltd.
2024-T3 aluminum; 3D finite element analysis; Aluminum alloys; Bending (deformation); Crack propagation; Crack tip opening angle; CTOA; Ductility; Finite element method; Fracture mechanics; Mathematical models; Out-of-plane bending; Sheet metal; Stable crack growth
Aortic valve mechanics. Part II: a stress analysis of the porcine aortic valve leaflets in diastole.
Biomaterials, medical devices, and artificial organs
6
3
225-44
1978
10.3109/10731197809118703
The stress analysis of the porcine aortic valve leaflets in diastole at 80 mm Hg pressure in-vitro is presented. Incorporation of local geometrical asymmetry, material inhomogeneity, anistropy and non-linearity are applied. The stress theory used is a modified form of the thin membrane stress theory for a homogeneous linearly elastic and orthotropic lamina. Modifications are made so that the Hooke's law constitutive equations of stress may be applied to the inhomogeneous, non-lineary elastic and orthotropic thin (membrane) aortic valve leaflets. Stress calculations are made on the premise that the valve is in pre-transition (i.e. low elastic modulus) in the circumferential direction and post-transition (i.e. high elastic modulus) in the radial direction. It is shown that sigmaCIR less than 1 gm/mm2, and for most of the noncoronary leaflet, 0 less than sigmaRAD less than 30 gm/mm2. The areas of highest stress concentrations are in the areas of mutual leaflet coaptation near the Node of Arantii. A progressive increase of radial stresses from the sinus-annulus edge toward the node is observed.
Animals; Aortic Valve; Aortic Valve: physiology; Bioprosthesis; Diastole; Heart Valve Prosthesis; Mechanical; Myocardial Contraction; Stress; Swine
Statistical mechanics approach to dislocation cell patterning
Scripta Materialia
47
10
705-711
2002
10.1016/S1359-6462(02)00447-5
Based on the notion that dislocation patterning is a dissipative far-from-equilibrium process with intrinsic fluctuations acting on the evolution of the dislocation ensemble at the mesoscopic scale, a stochastic dislocation dynamics model is presented the analysis of which shows that fluctuations can induce patterning by dynamically stabilizing non-uniform dislocation distributions.
Co-rotating stationary states and vertical alignment of geostrophic vortices with thin cores
Journal of Fluid Mechanics
357
321-349
1998
10.1017/S0022112097008136
We investigate the evolution of nearby like-sign vortices whose centres are at different vertical levels in a stably stratified rotating fluid. We employ two differently singularized representations of the potential vorticity distribution in the quasi-geostrophic equations (QG), in order to elucidate the pair-interaction behaviour previously seen in non-singular QG numerical solutions. The first is an analytically tractable conservative (Hamiltonian) elliptical-moment model (EM) for thin-core vortices, which exhibits a regime of very strong horizontal elongation of a vortex in response to the strain induced by its partner. We interpret this as an early evolutionary stage towards the irreversible dissipative merger and alignment interactions. This interpretation is strengthened by weakly dissipative numerical solutions of a thin-core contour-dynamics model (CD), which exhibit even further progress towards the completion of these vortex interactions in the same regime. In the EM model we classify the co-rotating stationary states which exist always for vertically offset thin-core vortices. However, the mutual strain field among the vortices cannot be balanced by co-rotation in a weakly elongated stationary state for a certain class of neighbouring, but substantially non-aligned, vortex configurations, and our interpretive assumption is that such configurations will rapidly evolve in non-singular QG solutions towards a more aligned configuration through significantly non-conservative reorganizations of the potential vorticity field. Both the EM and CD models show qualitatively similar regime boundaries between evolutions with weakly and strongly deformed vortices. In particular, there is a fairly close correspondence between the occurrence of strong vortex elongation in the EM solutions and significant filamentation and splitting in the CD solutions.
Performance of piezoelectric fiber-reinforced composites for active structural-acoustic control of laminated composite plates.
IEEE transactions on ultrasonics, ferroelectrics, and frequency control
51
11
1477-90
2004
10.1109/TUFFC.2004.1367489
This paper deals with the active structural acoustic control of thin laminated composite plates using piezoelectric fiber-reinforced composite (PFRC) material for the constraining layer of active constrained layer damping (ACLD) treatment. A finite element model is developed for the laminated composite plates integrated with the patches of ACLD treatment to describe the coupled structural-acoustic behavior of the plates enclosing an acoustic cavity. The performance of the PFRC layers of the patches has been investigated for active control of sound radiated from thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite plates into the acoustic cavity. The significant effect of variation of piezoelectric fiber orientation in the PFRC layer on controlling the structure-borne sound radiated from thin laminated plates has been investigated to determine the fiber angle in the PFRC layer for which the structural-acoustic control authority of the patches becomes maximum.
Crop duster aviation mechanics: High risk for pesticide poisoning
Am J Public Health
80
10
1236-1239
1990
BIOSIS COPYRIGHT: BIOL ABS. A cross-sectional medical survey was conducted among 63 Nicaraguan aviation mechanics exposed to organophosphate and other toxic pesticides. Thirty-one (49 percent) reported having been acutely poisoned on the job. Also, seven of 14 novice mechanics, with less than one year on the job, reported that they had been poisoned. Thirty-eight (61 percent) had cholinesterase levels below the lower limit of normal, including three workers with levels less than 20 percent of the lower limit of normal. Risk factors for low cholinesterase included recent hire and recent poisoning. Workers did not use protective equipment, nor were there facilities for bathing on site. As a result of this survey, the government has prohibited the mixing and loading of pesticides at this airport and requires the washing of planes prior to maintenance work; coveralls and thin, pesticide impermeable gloves are to be issued to mechanics handling pesticide-contaminated parts. Closed system mixing and loa
Air pollution; Amino acids; Biochemistry; Biology; Environmental pollutants/poisoning; Enzymes/physiology; Herbicides; Hominidae; Legislation; Occupational diseases; Occupational health services; Organization and administration; Peptides; Pest control; Pesticides; Proteins; Soil pollutants; Therapeutics; Water pollution
On the rotation operators in quantum mechanics
Physica
42
4
572-580
1969
10.1016/0031-8914(69)90162-1
The confusion, existing about the exact form of the rotation operators in quantum mechanics, is cleared up by indicating some well hidden errors in the two standard books on angular momentum.
Continuum Mechanics in Physics Education
Physics Today
56
12
10
2003
10.1063/1.1650202
One of the oddities of contemporary physics education is the nearly complete absence of continuum mechanics in the typical undergraduate or graduate curriculum. Continuum mechanics refers to field descriptions of mechanical phenomena, which are usually modeled by partial differential equations. The Navier–Stokes equations for the velocity and pressure fields of Newtonian fluids provide an important example, but continuum modeling is of course also well developed for elastic and plastic solids, plasmas, complex fluids, and other systems.
Probability in Boltzmannian Statistical Mechanics
Time, Chance and Reduction: Philosophical Aspects of Statistical Mechanics
92-118
2010
In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statistical mechanics as Humean chances in David Lewis' (1994) sense. I first give a precise formulation of this proposal, then raise two fundamental objections, and finally conclude that these can be overcome only at the price of interpreting these probabilities epistemically.
Thermodynamics; Physics; Probability; Lewis; Laws
Statistical Mechanics and Quantum Mechanics
Nature
232
5311
449-450
1971
10.1038/232449a0
Part of the acceptance speech on the occasion of the award of the Lorentz Medal by the Royal Netherlands Academy of Sciences on June 27, 1970.
Quantum Mechanics, Volume 2
Advanced Quantum Mechanics
1978
Beginning students of quantum mechanics frequently have difficulty separatingessential underlying principles from the specific examples to which theseprinciples have historically been applied. This book is especially designed toeliminate that difficulty. Fourteen chapters, augmented by 14 "complementarysections," provide a clarity of organization, careful attention to pedagogicaldetails, and a wealth of topics and examples that allow physics professors totailor courses to meet students' specific needs. Each chapter starts with aclear exposition of the problem to be treated and then logically develops thephysical and mathematical concept. These chapters emphasize the underlyingprinciples of the material, undiluted by extensive references to applicationsand practical examples. (Such applications and practical examples arecontained in the complementary sections.) The book begins with a qualitativeintroduction to quantum mechanical ideas using simple optical analogies andcontinues with a systematic presentation of the mathematical tools andpostulates of quantum mechanics as well as a discussion of their physicalcontent. Applications follow, starting with the simplest ones (two-levelsystems, the harmonic oscillator, etc.), and becoming gradually morecomplicated (the hydrogen atom, approximation methods, etc.). Thecomplementary sections each expand this basic knowledge, supplying a widerange of applications and related topics which make use of the essentialskills. Here the authors include carefully written, detailed expositions of alarge number of special problems and more advanced topics-integrated as anessential portion of the text. These topics, however, are not interdependent;this allows professors to direct their quantum mechanics courses toward bothphysics and chemistry students.
Skeletal regulatory proteins enhance thin filament sliding speed and force by skeletal HMM
Journal of Muscle Research and Cell Motility
25
7
515-525
2004
10.1007/s10974-004-3787-0
At saturating calcium and nucleotide concentrations, troponin (Tn) and tropomyosin (Tm) enhance the in vitro motility speed of individual actin filaments, suggesting the roles of these thin filament proteins in regulating contraction may include a modulation of crossbridge kinetics. Using a homogeneous complement of fast rabbit skeletal proteins, we examined if Tn and Tm modify specific transitions in the crossbridge cycle by varying skeletal muscle crossbridge kinetics and measuring actin filament sliding speed and steady-state force using the in vitro motility and microneedle assays, respectively. Skeletal regulatory proteins increased the force and sliding speed of actin filaments sliding on skeletal HMM. Faster crossbridge cycling with increased temperature or with substitution of dATP as the contractile substrate resulted in both increased sliding speed and force of unregulated filaments, while the addition of regulatory proteins diminished or eliminated this increase. In contrast, regulatory proteins did not influence filament mechanics when crossbridge cycling was slowed with lowered ATP concentration. The results are most simply explained if addition of the Tn and Tm complex to actin enhances both the transition rate of the force-generating actomyosin isomerization (or the preceding transition) and the apparent crossbridge detachment rate, but that the relative influence of Tn and Tm is dependent on the external load.
Chapter 12 Quantum Mechanics
1960
Anyone who is not confused with quantum mechanics has not understood it
Comparative mammalian respiratory mechanics.
The American review of respiratory disease
19
485-510
1979
Respiratory mechanics can be studied in mammals of all sizes by the same methods used in man, although some definitions need to be modified and special attention given to small size and fast events. Mechanical properties vary with body size in regular ways. Operating pressures are invariant with size, volumes and compliances varying with body mass (M) approximately to the first power, and ventilation and conductance with M3/4. Thus, time constants vary with M1/4 and frequencies with M -1/4. Tracheal cross-section varies with M3/4 and appears to be constrained by expiratory flow-limitation mechanics. Smaller mammals have more compliant chest walls and lower relaxation volumes, so FRC is more likely to be influenced by reflex and dynamic mechanisms. Methods and procedures are not standardized; variability of observations is great and our ability to discriminate specialized characteristics is undeveloped. Recent fundamental challenges to conceptual foundations of scaling are unresolved. Thus, uncertainty and skepticism about existing views are appropriate.
Modeling slice-push cutting forces of a sheet stack based on fracture mechanics
Engineering Fracture Mechanics
124-125
234-247
2014
10.1016/j.engfracmech.2014.04.029
It is a well known phenomenon that cutting materials with a slicing motion is much easier than cutting by simply pushing the knife down into the material. Energy-based analyses proof that slice-push cutting reduces the overall cutting forces with an increasing slicing motion. In this investigation, a model describing the cutting of a thin and planar material with an asymmetrical knife is developed, using equilibrium of forces and basic concepts of fracture mechanics. Finite-element-simulations are performed to determine the relationship between cutting forces and the parameters describing crack propagation. Consequently, normal pressure on the crack surface caused by the flanks of the cutting edge of the blade is the main cause leading to a crack tip opening and thus propagation of the crack. Overall cutting forces are augmented by the friction forces caused by the relative motion between cutting knife and material. Thus, the slicing motion allows the advance force to be reduced. The presented model is experimentally verified by sideways cutting stacked paper sheets. ?? 2014 Elsevier Ltd.
Cutting; DENT; Fracture; Paper; Sheet; Stack
A Closed-Form Solution for Thermal Buckling of Cross-Ply Piezolaminated Plates
International Journal of Structural Stability and Dynamics
1450112
2015
10.1142/S0219455414501120
A thermal buckling analysis is presented for simply-supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and subjected to the combined action of thermal load and constant applied actuator voltage. The material properties of the composite and piezoelectric layers are assumed to be functions of temperature. Derivations of the equations are based on the classical laminated plate theory, using the von-Karman nonlinear kinematic relations. The Ritz method is adopted to obtain closed-form solutions for the critical buckling temperature. Numerical examples are presented to verify the proposed method. The effects of the applied actuator voltage, plate geometry and stacking sequence of laminates are investigated.
buckling; Laminated composite; piezoelectric; Ritz method; smart materials; temperature dependent properties; thermal load
Behaviour of antisymmetric angle-ply laminated plates using the affine transformation
Computers & Structures
61
2
375-383
1996
10.1016/0045-7949(96)00050-8
The bending, buckling and vibration behaviour of antisymmetrically laminated, angle-ply, thick, rectangular plates with simply-supported edges is investigated by the affine transformation. The general form for the equation of motions governing the behaviour of laminated plates is derived by introducing three new parameters of the generalized rigidity ratio (D∗), generalized Poisson's ratio (ϵ) and the principal rigidity ratio (α) in the affine transformation scheme. The results obtained by the proposed method are shown to be in a good agreement with those available in the literature. It is found that with increasing D∗ the deflection coefficients tend to decrease linearly while the buckling and frequency coefficients increase linearly. The effect of α shows an opposite tendency to D∗ while ϵ has negligible influence on the solution.
Stress analysis of axisymmetric shear deformable cross-ply laminated circular cylindrical shells
Journal of Engineering Mathematics
40
4
315-332
2001
10.1023/a:1017500411490
A generalized mixed theory for bending analysis of axisymmetric shear deformable laminated circular cylindrical shells is presented. The classical, first-order and higher-order shell theories have been used in the analysis. The Maupertuis-Lagrange (M-L) mixed variational formula is utilized to formulate the governing equations of circular cylindrical shells laminated by orthotropic layers. Analytical solutions are presented for symmetric and antisymmetric laminated circular cylindrical shells under sinusoidal loads and subjected to arbitrary boundary conditions. Numerical results of the higher-order theory for deflections and stresses of cross-ply laminated circular cylindrical shells are compared with those obtained by means of the classical and first-order shell theories. The effects, due to shear deformation, lamination schemes, loadings ratio, boundary conditions and orthotropy ratio on the deflections and stresses are investigated.
Effects of assembly and twisting nozzle pressures on the properties of two-ply air-jet spun yarns
Textile Research Journal
71
8
711-718
2001
10.1177/004051750107100810
The work described in this study focuses on determining the influence of various parameters such as assembly and twisting nozzle pressures, yarn count, and material type on the properties of two-ply air-jet spun yarns produced using a spin-assembly-winder concept on the PLYfiL system. The results show that the tenacity, irregularity, and hairiness of both untwisted and twisted yarns are influenced by changes in the nozzle pressure. Lower pressures in this range generally result in better tenacity values for twisted yarns. It is also likely that the properties of fibers and sliver are factors that affect yarn quality in air-jet spinning.
Jets; Nozzles; Pressure effects; Tenacity; Yarn
Effect of interlaminar bonding imperfections on the behavior of angle-ply laminated cylindrical panels
Composites Science and Technology
64
1753-1762
2004
10.1016/j.compscitech.2003.12.009
An elasticity method is developed to study the bending and free vibration of simply supported angle-ply laminated cylindrical panels in cylindrical bending. The bonding between any two adjacent layers is assumed to be either perfect or imperfect. For the imperfect bonding, a general spring-layer model is adopted. The present analysis is completely based on the state-space formulations, which is very effective for laminated structural analysis. Numerical results are finally presented and the effect of interfacial bonding imperfections on the statics and dynamics of the cylindrical panel is discussed. ?? 2004 Elsevier Ltd. All rights reserved.
A. Layered structures; B. Interface; C. Delamination; C. Laminates
Axisymmetric capillary waves on thin annular liquid sheets. II. Spatial development
Physics of Fluids
12
6
1440-1460
2000
10.1063/1.870394
The forced motion of semi-infinite axisymmetric thin inviscid annular liquid sheets, exiting from a nozzle or atomizer into a surrounding void under zero gravity but with constant gas-core pressure is analyzed by means of the reduced-dimension approach described in C. Mehring and W. A. Sirignano [Phys. Fluids 12, 1417 (2000)]. Linear analytical time-dependent ("limit-cycle") solutions to the pure boundary-value problem are presented as well as linear and nonlinear numerical (transient) solutions to the mixed boundary- and initial-value problem of initially undisturbed sheets harmonically forced at the orifice or nozzle exit. Group velocities for the six independent solutions to the linear boundary-value problem are used to determine the location of boundary conditions. Numerical simulations of the linear transient problem are employed to validate these predictions. Parameter studies on sheet breakup and collapse lengths as well as on breakup and collapse times are reported. The dependence on modulation frequency, modulated disturbance amplitude, Weber number, and annular radius is presented for various cases of the mixed problem, i.e., for linearly or nonlinearly stable and unstable, dilationally or sinusoidally forced sheets. Nonlinear effects often have significant effects on breakup times and lengths or on collapse times and lengths. Nonlinear wave forms can deviate substantially from linear predictions resulting in major impacts on the size of the rings and shells that will remain after breakup. (C) 2000 American Institute of Physics. [S1070-6631(00)00406-2]
AMPLITUDE; APQ Staff: Artur Tropmann; BOUNDARY; BOUNDARY-CONDITION; boundary conditions; BOUNDARY-CONDITIONS; BREAKUP; C; Ca; CAPILLARIES; CAPILLARY; COLLAPSE; CONSTANT; DEPENDENCE; DISTURBANCE; FLUID; FLUIDS; FORMS; FREQUENCIES; FREQUENCY; GRAVITY; IMPACT; INSTABILITIES; LENGTH; LIQUID; LIQUID SHEET; MECHANICS; MODULATION; MOTION; nozzle; NUMBER; numerical; numerical simulation; NUMERICAL-SIMULATION; NUMERICAL SIMULATIONS; PHYSICS; PREDICTION; PREDICTIONS; PRESSURE; PURE; SHEET; SHEETS; SHELLS; SIMULATION; SIMULATIONS; SIZE; Solutions; study; THIN; TIME; transient; VELOCITY; WAVE; WAVE-FORMS; WAVES; Weber number; WELL; WILL
Vibration and Buckling of Cross-Ply Composite Beams using Refined Shear Deformation Theory
International Journal of Mechanical Sciences
62
1
67-76
2012
Vibration and buckling analysis of cross-ply composite beams using refined shear deformation theory is presented. The theory accounts for the parabolical variation of shear strains through the depth of beam. Three governing equations of motion are derived from the Hamiltons principle. The resulting coupling is referred to as triply coupled vibration and buckling. A two-noded C1 beam element with five degree-of-freedom per node is developed to solve the problem. Numerical results are obtained for composite beams to investigate modulus ratio on the natural frequencies, critical buckling loads and load-frequency interaction curves.
acoustics; aerospace engineering; buckling; composite beams; controls; dynamics; engineering; mechanical engineering; refined shear deformation theory; triply coupled vibration
3D finite element analysis of multiple transverse cracking in hybrid cross-ply composite laminates
Journal of Reinforced Plastics and Composites
18
9
776-797
1999
10.1177/073168449901800901
This paper presents the analysis of multiple transverse cracking in hybrid composite laminates subjected to uniaxial loading. The 3D finite element method has been used for evaluating the strain energy release rates and stiffness reductions in different glass/epoxy and graphite/epoxy hybrid cross-ply composite laminates as the transverse crack extends in the width direction. The procedure is based on the computation of strain energy in the laminates with a simulated crack and its extension for incremental applied strains. Results are presented for various combinations of crack lengths and crack densities.
Algebraic quantum mechanics and pregeometry
AIP Conference Proceedings
810
314-324
2006
10.1063/1.2158735
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.
Non-commutative geometry; Non-locality; Quantum pre-space
Mechanics of an Adhesive Anchor System Subjected to a Pullout Load. I: Elastic Analysis
Journal of Structural Engineering
140
2
04013052
2014
10.1061/(ASCE)ST.1943-541X.0000826
An elastic solution is developed for an anchor embedded in a concrete hole and bonded to the concrete through an adhesive layer that is not necessarily thin. Both bonded and debonded conditions are considered for the embedded end of the anchor. Aweak-form stress boundary condition yields an approximate solution for the elastic fields in both the anchor core and the adhesive layer, which compares favorably with an axisymmetric finite-element solution. The explicit elastic solution is useful as a more complete design basis for such anchors but also provides a platform for the analysis of the long term response of bonded anchors when time-dependent effects are observed. Paper II pursues that analysis.
Adhesive anchor; Analysis and computation; Axisymmetric elastic analysis; Boundary value problem; Concrete; Embedment; Finite-element method
On complexified mechanics and coquaternions
Journal of Physics A: Mathematical and Theoretical
44
7
072001
2011
10.1088/1751-8113/44/7/072001
While real Hamiltonian mechanics and Hermitian quantum mechanics can\nboth be cast in the framework of complex canonical equations, their\ncomplex generalizations have hitherto remained tangential. In this\ncommunication, quaternionic and coquaternionic (split-signature\nanalogue of quaternions) extensions of Hamiltonian mechanics are\nintroduced and are shown to offer a unifying framework for complexified\nclassical and quantum mechanics. In particular, quantum theories\ncharacterized by complex Hamiltonians invariant under spacetime\nreflection are shown to be equivalent to certain coquaternionic\nextensions of Hermitian quantum theories. One of the interesting\nconsequences is that the spacetime dimension of these systems is six,\nnot four, on account of the structures of coquaternionic quantum\nmechanics.
Numerical simulation of rarefied gas flow through a thin orifice
Journal of Fluid Mechanics
518
35-60
2004
10.1017/s0022112004000710
Rarefied gas flow through a thin orifice is studied on the basis of the direct simulation Monte Carlo method. The mass flow rate and the flow field are calculated over the whole range of the Knudsen number for various values of the pressure ratio. It is found that at all values of the pressure ratio a significant variation of the flow rate occurs in the transition regime between the free-molecular and hydrodynamic regimes. In the hydrodynamic regime the flow rate tends to a constant value. In the case of finite pressure ratio the flow field qualitatively differs from that for outflow into vacuum, namely vortices appear in the downflow container on approaching the hydrodynamic regime. Then, in the hydrodynamic regime the gas flow forms a strong jet. A comparison of the numerical results with experimental data available in the open literature has been performed.
boundary; circular orifice; coefficients; high knudsen numbers; lampis scattering kernel; raman-spectroscopy; slit; tubes; vacuum
Forming of thin-walled tubes into toroidal shells
Journal of Materials Processing Technology
210
689-695
2010
10.1016/j.jmatprotec.2009.12.007
The purpose of this paper is to introduce a new forming process that is capable of shaping thin-walled industrial tubes into toroidal shells in a single-stage operation. The methodology draws from the existing know-how on conventional end forming of tubes to aspects of deformation mechanics that are necessary to identify the typical modes of deformation and to establish the formability limits in terms of the major process variables. The approach is illustrated and enriched with selected test cases obtained from finite element modelling and experimentation and the overall presentation is expected to effectively contribute to transferable of original technological knowledge. The new proposed process is a fast and low-cost manufacturing alternative to existing solutions for producing toroidal shells that are based on incremental forming and hydroforming. However, it is shown that the overall feasibility of the process is limited to toroidal shells having slenderness ratios within a compact range in order to avoid superposition of material along the equatorial plane and to prevent fracture during forming. © 2009 Elsevier B.V. All rights reserved.
Experimentation; Finite element method; Forming of tubes; Toroidal shells
Statistical mechanics of a discrete nonlinear system
Physical review letters
84
17
3740-3
2000
10.1103/PhysRevLett.84.3740
Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.
The logic of quantum mechanics-Take II
arXiv preprint
23
2012
We put forward a new take on the logic of quantum mechanics, following Schroedinger's point of view that it is composition which makes quantum theory what it is, rather than its particular propositional structure due to the existence of superpositions, as proposed by Birkhoff and von Neumann. This gives rise to an intrinsically quantitative kind of logic, which truly deserves the name `logic' in that it also models meaning in natural language, the latter being the origin of logic, that it supports automation, the most prominent practical use of logic, and that it supports probabilistic inference.
Continuum modeling of charged vacancy migration in elastic dielectric solids, with application to perovskite thin films
Mechanics Research Communications
35
1-2
57-64
2008
10.1016/j.mechrescom.2007.08.002
A continuum theory describing the behavior of dielectric materials containing mobile, electrically charged vacancies is formulated. The theory is implemented to simulate diffusion, at the nanometer scale, of oxygen vacancies in acceptor-doped barium strontium titanate (BST) thin films in the paraelectric state. In the simulations, charged vacancies coalesce into boundary layers of large concentration at potential-free interfaces, with increases in the local electric field intensity emerging near such boundaries. Upon relating this increase to a reduction in the energy barrier for charge transmission from film to electrode at the interface, and accepting an inverse relationship between the concentrations of doping elements and mobile oxygen vacancies, the model shows agreement with observed trends of decreasing current losses with increased doping.
dielectric; diffusion; electromechanics; thin films; vacancies
Response of flexure-torsion coupled composite thin-walled beams with closed cross-sections to random loads
Mechanics Research Communications
32
1
25-41
2005
10.1016/j.mechrescom.2004.03.012
A study of the flexure-torsion coupled random response of the composite beams with solid or thin-walled closed-sections subjected to various types of concentrated and distributed random excitations is dealt with in this paper. The effects of flexure-torsion coupling, shear deformation and rotary inertia are included in the present formulations. The random excitations are assumed to be stationary, ergodic and Gaussian. Analytical expressions for the displacement response of the composite beams are obtained by using normal mode superposition method combined with frequency response function method. The present method can produce the effective solutions for the composite Timoshenko beams with circumferentially antisymmetric (CAS) configuration and more general beam assemblages of connected beams. The influences of flexure-torsion coupling, shear deformation and rotary inertia on the random response of an appropriately chosen composite beam from the literature are demonstrated and discussed. ?? 2004 Elsevier Ltd. All rights reserved.
Composite beams; Coupled flexural-torsional vibrations; Normal mode method; Random response; Shear deformation and rotary inertia; Thin-walled closed beams
Quantum Mechanics and Closed Timelike Curves
Quantum Biosystems
8
2007
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.
02; 03; 04; 10; 20; 30; ab; chronology protection conjecture; cv; generalizations of quantum; impossibility of time travel; mechanics; p; pacs
Fracture Mechanics Determinations
Fracture Mechanics of Ceramics
1
17-48
1974
Techniques for the evaluation of fracture mechanics parameters are described. The selection of techniques for various ceramic applications is discussed, emphasizing the particular problems encountered with these measurements in ceramic systems. Finally, the application of fracture mechanics parameters to problems in both materials development and failure prediction in ceramic systems is described.
Mechanics of Tether Formation in Liposomes
Journal of Biomechanical Engineering
124
5
576
2002
10.1115/1.1500341
It is well-known that a "tether" may be drawn out from a pressurized liposome by means of a suitably applied radial-outward force applied locally to the lipid bilayer. The tether is a narrow, uniform cylindrical tube, which joins the main vesicle in a short "transition region." A first-order energy analysis establishes the broad relationship between the force F needed to draw the tether, the radius R0 of the tether, the bending-stiffness constant B for the lipid bilayer and the membrane tension T in the pressurized liposome. The aim of the present paper is to study in detail the "transition region" between the tether and the main vesicle, by means of a careful application of the engineering theory of axisymmetric shell structures. It turns out that the well-known textbook "thin-shell" theory is inadequate for this purpose, because the tether is evidently an example of a thick-walled shell; and a novel ingredient of the present study is the introduction of elastic constitutive relations that are appropriate to the thick-shell situation. The governing equations are set up in dimensionless form, and are solved by means of a "shooting" technique, starting with a single disposable parameter at a point on the meridian in the tether, which can be adjusted until the boundary conditions at the far "equator" of the main vessel are satisfied. It turns out that the "transition region" between the tether and the main vessel is well characterized by only a few parameters, while the tether and main vessel themselves are described by very simple equations. Introduction of the thick-shell constitutive relation makes little difference to the conformation of and stress-resultants in, the main vessel; but it makes a great deal of difference in the tether itself Indeed, a kind of phase-change appears to take place in the "transition region" between these two zones of the liposome.
Dynamical scenario for nonextensive statistical mechanics
Physica A: Statistical Mechanics and its Applications
340
1-3
12
2003
10.1016/j.physa.2004.03.072
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions, mixing and ergodicity in Gibbs Gamma-space. What are the corresponding hypothesis for nonextensive statistical mechanics? A scenario for answering such question is advanced, which naturally includes the it a priori determination of the entropic index q, as well as its cause and manifestations, for say many-body Hamiltonian systems, in (i) sensitivity to the initial conditions in Gibbs Gamma-space, (ii) relaxation of macroscopic quantities towards their values in anomalous stationary states that differ from the usual thermal equilibrium (e.g., in some classes of metastable or quasi-stationary states), and (iii) energy distribution in the Gamma-space for the same anomalous stationary states.
metastable states; mixing; nonextensive statistical mechanics; nonlinear dynamics; weak chaos
Helical flow of a power-law fluid in a thin annulus with permeable walls
International Journal of Non-Linear Mechanics
41
6-7
761-765
2006
DOI 10.1016/j.ijnonlinmec.2006.03.001
Helical flow of a power-law fluid in a thin annulus is investigated with a view to modeling biofluid flow around the commonly occurring non-planar bend. The inner cylinder is rotating with angular velocity omega and the outer cylinder is permeable. The velocity distribution and the fractional increase in volume flow rate are obtained. When the permeability parameter sigma --> infinity, the results agree with those of Bird et al. [Dynamics of polymer liquids, vol. 1, Fluid Mechanics, 1977, Wiley, New York]. Numerical methods are used to find the velocity components and the volume flow rate for the helical flow of a physiological fluid (power-law fluid). Possible advantages of the observed helical flow characteristics with permeability effects are discussed. (C) 2006 Elsevier Ltd. All rights reserved.
helical flow; permeable walls; power-law fluid; symmetric pipe
Contact with stick zone between an indenter and a thin incompressible layer
European Journal of Mechanics, A/Solids
30
6
884-892
2011
10.1016/j.euromechsol.2011.04.010
The dominant asymptotic term for the indentation of a thin elastic incompressible layer by an axisymmetric rigid indenter is considered. Complete adhesion is supposed everywhere in the contact area or else in a given inner region surrounded by an annular frictionless zone. Both the problems are formulated in the form of systems of coupled dual integral equations. Using operators transforming kernels of the Hankel transform into kernels of the Weber-Orr transform, the dual integral equations are reduced to systems of Fredholm integral equations of the second kind whose structures permit deriving asymptotic solutions. Simple expressions for the contact stresses, the penetration depth, and the contact radius in the case of an unknown contact area are obtained. Explicit formulae, derived for the flat and power law indenter profiles, allow us to analyze how stick and frictionless zones affect mechanical characteristics. Results manifest that the punch penetration exhibits strong sensitivity to contact conditions inspite of the fact that the radial traction is small. A conical indenter is less sensitive than flat-ended and spherical indenters. ?? 2011 Elsevier Masson SAS. All rights reserved.
Adhesion; Contact mechanics; Incompressible layer
Random walk in a discrete and continuous system with a thin membrane
Physica A: Statistical Mechanics and its Applications
298
285-296
2015
10.1016/S0378-4371(01)00262-X
Random walk in a one-dimensional system with a thin membrane (which is treated as a partially permeable wall with its internal structure being not explicitly involved into our considerations) is discussed for the discrete and continuous time and space variables. The Green's functions of the membrane system for the discrete space variable are obtained using the method of generating function. The Green's functions for the continuous system are obtained from the discrete ones by taking the continuum limit. It is shown that the boundary condition at the membrane, which is commonly used in stationary system (where the flux flowing through the membrane is proportional to the difference of the concentration of the diffusing particle between the membrane surfaces) is appropriate also for the non-stationary system. ?? 2001 Elsevier Science B.V. All rights reserved.
Diffusion; Green's functions; Random walk
Quantum states of neutrons in magnetic thin films
Physical Review B
71
21
1-6
2005
10.1103/PhysRevB.71.214423
We have studied experimentally and theoretically the interaction of polarized neutrons with magnetic thin films and magnetic multilayers. In particular, we have analyzed the behavior of the critical edges for total external reflection in both cases. For a single film we have observed experimentally and theoretically a simple behavior: the critical edges remain fixed and the intensity varies according to the angle between the polarization axis and the magnetization vector inside the film. For the multilayer case we find that the critical edges for spin-up and spin-down polarized neutrons move toward each other as a function of the angle between the magnetization vectors in adjacent ferromagnetic films. Although the results for multilayers and single thick layers appear to be different, in fact, the same spinor method explains both results. An interpretation of the critical edges behavior for the multilyers as a superposition of ferromagnetic and antifferomagnetic states is given.
neutron; neutron reflectivity; polarised neutrons; quantum mechanics
Low Velocity Impact Studies on a 4-Ply Knitted Kevlar Fabric Reinforced Epoxy Composite
Journal of Reinforced Plastics and Composites
21
2
121-138
2002
10.1177/0731684402021002289
Four-ply knitted Kevlar fabric reinforced epoxy composites with three different stacking sequences were subjected to normal impact of up to 10 J using a hemispherical steel impactor. Similar modes of damage were observed from impacts on all three different stacking sequences where damage progressed from matrix cracking and fibre/matrix debonding at low impact energies to fibre breakage and eventual through-thickness cracks at higher impact energies. A critical mode of damage occurred at about 4.5 J where there was a sudden deterioration of impact resistance due to fibre breakage at the top and bottom plys. The only significant difference among composites of different stacking sequences subjected to low velocity impacts of similar magnitude was the propagation of through-thickness cracks at impact energy larger than 5 J.
Microcracking in cross-ply laminates due to biaxial mechanical and thermal loading
AIAA Journal
44
12
2949-2957
2006
10.2514/1.20798
This paper presents a methodology to predict microcracking and microcrack density in both surface and internal plies of a symmetric cross-ply laminate under biaxial mechanical and thermal loading conditions. The thermoelastic properties of the microcracked laminates at different crack densities were determined by finite element analysis of the unit cells bounded by the microcracks. Analytical expressions for the stiffness and coefficients of thermal expansion as functions of crack densities were obtained in the form of response surface approximations. These analytical expressions were then used to predict the formation of a new set of microcracks by equating the change in strain energy in the unit cell before and after the formation of the microcracks to the critical fracture energy required for their formation. Analytical expressions obtained as response surface approximations were also used to predict progressive microcracking. Both displacement and load control cases were considered along with thermal loading. Results from the current methodology agree very well with published data.
Design of shear-deformable antisymmetric angle-ply laminates to maximize the fundamental frequency and frequency separation
Composite Structures
2
4
349-369
1984
10.1016/0263-8223(84)90005-9
An antisymmetrically laminated angle-ply plate is optimized with the objectives of maximizing the fundamental eigenfrequency and the distance between two consecutive natural frequencies. The formulation includes the contribution of the shear deformation, but neglects the in-plane and rotary inertias. The design variables are the fiber orientations and the thicknesses of individual layers. The design problems are cast into a mathematical programming format and solved by using a quasi-Newton function maximization algorithm. A penalty function method is employed to maximize the fundamental frequency, subject to lower bound constraints on higher-order frequencies. Numerical results are presented for laminates constructed of high-modulus fiber-reinforced materials, and the effects of various problem parameters on the efficiency of the designs are investigated. It is shown that the design variables may not be determined optimally if the effect of shear deformation is neglected. Moreover, it was observed that the classical plate theory leads to erroneous results in optimal material selection problems.
Quantum Mechanics and the Nature of Reality
Science and Religion in Dialogue
97-104
2010
10.1002/9781444317350.ch6
This chapter contains sections titled:\n\n* Introduction\n* The Wave Function\n* Possible Christian Responses to Quantum Mechanics\n* Notes
central mysteries of quantum mechanics - beam of p; Copenhagen interpretation and many-worlds interpre; Copenhagen interpretation of quantum mechanics, “o; elements of quantum mechanics - compatible with Ch; many-worlds theory and hidden-variable theories, l; possible Christian responses to quantum mechanics; quantum mechanical explanation for behavior - wave; quantum mechanics and nature of reality; Quantum mechanics, a nonlocal theory; wave function, complex-valued number, physically i
Simply supported empty and filled thin-square-tubular beams under central wedge loading
Thin-Walled Structures
34
4
261-278
1999
10.1016/S0263-8231(99)00014-2
Experiments were performed whereby thin-walled square tubes of different span lengths were simply supported and laterally loaded by a wedge indenter in an Instron machine and under the impact of a drop hammer. The tubes were empty as well as filled with polyurethane foam or wood. The span length seems to greatly influence the mode of deformation. Typical histories of deformation and load-compression curves of empty and filled tubes are presented and the effect of infill material and the rate of loading on energy absorbing characteristics of the tubes is discussed. Based on the mechanics of deformation observed experimentally, an analysis is presented to compute the collapse load as well as the post collapse load-compression curve for the simply supported tubes. The analysis considers the formation of stationary and rolling plastic hinges. The results thus obtained compare well with the experiments.
collapse; filled; foam; impact; lateral; square tubes; wood
Free vibrations of laminated composite plates using second-order shear deformation theory
Computers & Structures
71
6
617-626
1999
10.1016/S0045-7949(98)00301-0
A complete set of linear equations of the second-order theory of laminated composite plates are obtained. A generalized Levy type solution in conjunction with the state space concept is used to analyze the free vibration behavior of cross-ply and antisymmetric angle-ply laminated plates. Exact fundamental frequencies of cross-ply plate strips are obtained for arbitrary boundary conditions. The exact analytical solutions are obtained for thick and moderately thick plates as well as for thin plates and plate strips. It is shown that the results of the second-order theory are very close to the results of the first-order and third-order theories reported in the literature, and different from those of the classical Kirchhoff’s theory for thick laminates.
Composite plates; Deformation theory; Free vibration
Fractals and quantum mechanics
Chaos
10
4
780-790
2000
10.1063/1.1050284
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics. (c) 2000 American Institute of Physics.
Parametric Investigation of Gas Permeability in Cross-Ply Laminates Using Finite Elements
AIAA Journal
45
4
934-941
2007
10.2514/1.26602
Three-dimensional finite element models are used to study the influence of various parameters on the gas permeability of cross-ply composite laminate. It is shown that the intersection area, which is formed between two adjacent plies due to crack opening, is the most crucial factor in determining the permeability. It is found that the intersection areas obtained by superposing crack opening displacements of two-dimensional models are not accurate.Afull three-dimensional model is required to obtain a detailed andprecise prediction.Theintersection area is found to be related not only to the resultant forces and thermal loads but also to the delamination shape and the delamination length. Laminates with different stacking sequence are studied, and it is found that for the same number of plies the laminate with dispersed plies shows lower permeability. Effect of temperature-dependent material properties is investigated as well.
Nonlinear curvature-based model and resonant finite-amplitude vibrations of symmetric cross-ply laminates
Journal of Sound and Vibration
331
12
2836-2855
2012
http://dx.doi.org/10.1016/j.jsv.2012.01.030
Moving from a general plate theory, a modified general classical laminated plate theory (MGCLPT) exhibiting nonlinear curvatures but still allowing for some worth features of linear curvature models (von Karman) is formulated. Starting from MGCLPT partial differential equations, a minimal discretized model suitable for the analysis of resonant finite-amplitude vibrations of symmetric cross-ply laminates, with immovable or movable supports, is obtained via the Galerkin procedure. Periodic responses of a single-mode model and of a 3:1 internally resonant two-mode model excited at primary resonance are obtained via the multiple time scale method. The influence of various system parameters (thickness ratio, plate aspect, number of laminae, kind of material, mode number) is addressed, and the comparison of nonlinear vibration results as obtained with the MGCLPT and the von Karman models for different boundary conditions shows some interesting differences.
A study on the effects of clearance and interference fits in a pin-loaded cross-ply FGRP laminate
Journal of Composite Materials
32
8
783-802
1998
10.1177/002199839803200805
The elastic behavior of a cross-ply fiber glass-reinforced epoxy laminate loaded in tension through a pin fitted with clearance and interference is examined. A nonlinear contact analysis using the Finite Element Method and an experimental study by Speckle Interferometry are performed, showing fairly good correlation. An interesting comparison is performed between FEM results and Hertzian contact theory. Major conclusions are: (1) clearance causes high compressive stress in the bearing area, and does not influence the peak tensile stress; (2) interference has beneficial effects on the joint, as (a) it lowers the peak circumferential stress, and (b) it decreases the change of stress due to the application of the load. This last conclusion suggests that interference can improve the fatigue life of the joint.
Gravity-driven thin film flow of an ellis fluid
Journal of Non-Newtonian Fluid Mechanics
202
88-98
2013
10.1016/j.jnnfm.2013.09.010
The thin film lubrication approximation has been studied extensively for moving contact lines of Newtonian fluids. However, many industrial and biological applications of the thin film equation involve shear-thinning fluids, which often also exhibit a Newtonian plateau at low shear. This study presents new numerical simulations of the three-dimensional (i.e. two-dimensional spreading), constant-volume, gravity-driven, free surface flow of an Ellis fluid. The numerical solution was validated with a new similarity solution, compared to previous experiments, and then used in a parametric study. The parametric study centered around rheological data for an example biological application of thin film flow: topical drug delivery of anti-HIV microbicide formulations, e.g. hydroxyethylcellulose (HEC) polymer solutions. The parametric study evaluated how spreading length and front velocity saturation depend on Ellis parameters. A lower concentration polymer solution with smaller zero shear viscosity (??0), ??1/2, and ?? values spread further. However, when comparing any two fluids with any possible combinations of Ellis parameters, the impact of changing one parameter on spreading length depends on the direction and magnitude of changes in the other two parameters. In addition, the isolated effect of the shear-thinning parameter, ??, on the front velocity saturation depended on ??1/2. This study highlighted the relative effects of the individual Ellis parameters, and showed that the shear rates in this flow were in both the shear-thinning and plateau regions of rheological behavior, emphasizing the importance of characterizing the full range of shear-rates in rheological measurements. The validated numerical model and parametric study provides a useful tool for future steps to optimize flow of a fluid with rheological behavior well-described by the Ellis constitutive model, in a range of industrial and biological applications. ?? 2013 Elsevier B.V.
Ellis fluid; Lubrication approximation; Microbicide; Shear-thinning; Thin film
On the Structure of Classical Mechanics
British J. Philos. Sci.
2014
10.1093/bjps/axu005
Jill North (North, 2009) has recently argued that Hamiltonian mechanics ascribes less structure to the world than Lagrangian mechanics does. I will argue that North's argument is not sound. In doing so, I will present some obstacles that must be navigated by anyone interested in comparing the amounts of structure that different physical theories ascribe to the world.
Bohmian mechanics and consistent histories
Physics Letters A
261
5-6
10
1995
10.1016/S0375-9601(99)00542-3
The interpretations of a particular quantum gedanken experiment provided by Bohmian mechanics and consistent histories are shown to contradict each other, both in the absence and in the presence of a measuring device. The consistent history result seems closer to standard quantum mechanics, and shows no evidence of the mysterious nonlocal influences present in the Bohmian description.
Cohesive modeling of low-velocity impact damage in layered functionally graded beams
Mechanics Research Communications
35
1-2
104-114
2008
10.1016/j.mechrescom.2007.09.005
Numerical analysis of the low-velocity impact damage of a layered composite beam with a functionally graded core is performed using the multiple-isoparametric cohesive volume finite element (MCVFE) scheme. A mixed-mode intrinsic cohesive zone model is used to simulate the spontaneous damage initiation and growth in this work. The inhomogeneous Young's modulus variation is assumed to be symmetric about the neutral plane. Our parametric simulations showed that the energetics of damage is altered by the presence of a functionally graded core. The effect of including a functionally graded core is to advance the time of fracture initiation compared to a cross-ply (90??) core. The assumed symmetry and linear inhomogeneity leads to the energetics for the graded core to be similar to those observed for a 45?? core ply-orientation. ?? 2007 Elsevier Ltd. All rights reserved.
Cohesive zone model; Functionally graded materials; Low-velocity impact damage; Multiple-isoparametric cohesive volume finite elem; Multiscale modeling
Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces
arXiv
29
1999
10.1007/978-94-011-4303-5
This contribution to the proceedings of the 1999 NATO ASI on Quantum Geometry at Akureyri, Iceland, is based on notes of lectures given by A. Strominger. Topics include N-particle conformal quantum mechanics, extended superconformal quantum mechanics and multi-black hole moduli spaces.
Relativity, Quantum Mechanics and EPR
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
Volume One: Contributed Papers
114-128
1992
The Einstein-Podolsky-Rosen argument for the incompleteness of quantum mechanics involves two assumptions: one about locality and the other about when it is legitimate to infer the existence of an element-of-reality. Using one simple thought experiment, we argue that quantum predictions and the relativity of simultaneity require that both these assumptions fail, whether or not quantum mechanics is complete.
Quantum Mechanics
Temporal Ordering in Quantum Mechanics
Journal of Physics A
135
35
7641-7652
2002
10.1088/0305-4470/35/35/308
We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one particle (in higher dimensions). In quantum mechanics, we find that diffraction effects introduce a minimum inaccuracy to which the temporal order-of-arrival can be determined unambiguously. The minimum inaccuracy of the measurement is given by dt=1/E where E is the total kinetic energy of the two particles. Similar restrictions apply to the case of coincidence measurements. We show that these limitations are much weaker than limitations on measuring the time-of-arrival of a particle to a fixed location.
Teaching classical mechanics using smartphones
The Physics Teacher
51
6
376
2013
10.1119/1.4818381
Using a personal computer and a smartphone, iMecaProf is a software that\nprovides a complete teaching environment for practicals associated to a\nClassical Mechanics course. iMecaProf proposes a visual, real time and\ninteractive representation of data transmitted by a smartphone using the\nformalism of Classical Mechanics. Using smartphones is more than using a set of\nsensors. iMecaProf shows students that important concepts of physics they here\nlearn, are necessary to control daily life smartphone operations. This is\npractical introduction to mechanical microsensors that are nowadays a key\ntechnology in advanced trajectory control. First version of iMecaProf can be\nfreely downloaded. It will be tested this academic year in Universit\'e Joseph\nFourier (Grenoble, France)
Quantum Mechanics of Black Holes
Science
337
6094
538-540
2012
10.1126/science.1221693
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Assumed Natural Strain NURBS-based solid-shell element for the analysis of large deformation elasto-plastic thin-shell structures
Computer Methods in Applied Mechanics and Engineering
284
861-880
2015
10.1016/j.cma.2014.10.037
In this work, a recently proposed quadratic NURBS-based solid-shell element based on the Assumed Natural Strain (ANS) method is applied in the analysis of shell-like structures in the geometrical nonlinear regime, together with small strain plasticity. The proposed formulation is based on the additive split of the Green–Lagrange strain tensor, leading to a straightforward implementation of the nonlinear kinematics and to the introduction of a corotational coordinate system, used to integrate the constitutive law, ensuring incremental objectivity. Since the proposed approach is based on Updated Lagrangian formulation combined with a corotational coordinate system, the extension of the ANS methodology is straightforward. Well-known benchmark tests are employed to assess the performance of the proposed formulation and to establish a detailed comparison with the formulations available in the literature. The results indicate that the proposed solid-shell approach based on the NURBS ANS methodology presents good predictability characteristics in the analysis of elasto-plastic thin-shell structures subjected to large deformations.
assumed natural strain; geometric nonlinearity; isogeometric analysis; nurbs; small strains; solid-shell
Stress-strain state of an anisotropic plate with an elliptic hole and thin rigid inclusions
Journal of Applied Mechanics and Technical Physics
48
4
614-620
2007
10.1007/s10808-007-0077-9
The stress-strain state of an anisotropic plate containing an elliptic hole and thin, absolutely rigid, curvilinear inclusions is studied. General integral representations of the solution of the problem are constructed that satisfy automatically the boundary conditions on the elliptic-hole contour and at infinity. The unknown density functions appearing in the potential representations of the solution are determined from the boundary conditions at the rigid inclusion contours. The problem is reduced to a system of singular integral equations which is solved by a numerical method. The effects of the material anisotropy, the degree of ellipticity of the elliptic hole, and the geometry of the rigid inclusions on the stress concentration in the plate are studied. The numerical results obtained are compared with existing analytical solutions. © Springer Science+Business Media, Inc. 2007.
Anisotropic plate; Anisotropy; Atress concentrations; Boundary conditions; Computational mechanics; Ellipticity; Integral equation; Probability density function; Stress concentration; Stress intensity factor; Stress intensity factors; Stress-strain curves; Thin rigid inclusions
Flow stabilities during the squeeze flow of multiaxial laminates
Journal of Composite Materials
31
21
2146-2160
1997
0803973233
This paper examines the effect that ply arrangement has on the processing characteristics of aligned long fiber reinforced composite laminates. Mon specifically, this study focuses on the difference between the consolidation squeeze flow behavior of unidirectional and multiaxial ply laminates. A commercially produced material tape composed of aligned carbon fibers in a thermoplastic PEEK matrix (APC-2) was used to construct the laminates. Using specially designed hot platens, constant platen closure rate squeeze flow experiments were performed on 70 ply unidirectional [0 degrees] laminates. Flow visualization techniques were then used to measure the velocity profile of the material during flow. Similar squeeze flow experiments were also carried out on macro-ply [0(14),90(14),0(7)](s) and cross-ply [0 degrees,90 degrees](18s) laminates. Comparisons are made between the generated squeeze forces and macroscopic flow deformation of the three laminate configurations.
fibers; fluids; parallel disks; thin
Observer Mechanics: A Formal Theory of Perception.
PsycCRITIQUES
36
5
1-2
1991
10.1037/029771
A central thesis of "Observer Mechanics" is that every perceptual capacity (e.g., stereovision, auditory localization, sentence parsing, haptic recognition) can be described as an instance of a single formal structure: viz., an "observer." The first two chapters of "Observer Mechanics" develop this structure, resulting in a formal definition of an observer. The third chapter considers the relationship between observers and Turing machines. The fourth chapter discusses the semantics of observers. Chapters 5-7 present a formal framework in which to describe an observer and its objects of perception, and then develop on this framework a perceptual dynamics. Using this dynamics, Chapter 8 defines conditions in which an observer may be said to perceive truly. Chapter 9 discusses how stabilities in perceptual dynamics might permit the genesis of higher level observers. Chapter 10 comments on the relationship between the formalisms of quantum mechanics and observer mechanics. Finally, the epilogue discusses the philosophical context and implications of observer mechanics.
Energy density mechanics applied to coating blistering problems
Theoretical and Applied Fracture Mechanics
56
2
89-94
2011
10.1016/j.tafmec.2011.10.004
The use of fracture mechanics outside the area of mechanics, including materials science, is evidence that the concept is capable of handling failures involving almost any types of crack propagations. This paper outlines the simple method on how to use fracture mechanics concepts in coating study by using a concrete example that is easy to follow. The example presented here is the use of fracture mechanics to develop equation governing the blister propagation using the concept pioneered by Sih, the SED concept. Despite being simple, the method gives excellently good agreement with those available solutions derived by other methods. ?? 2011 Elsevier Ltd.
Blister; Coating; Fracture mechanics; Strain energy density
The extended range of reaction-layer fatigue susceptibility of polycrystalline silicon thin films
International Journal of Fracture
135
1-4
1-18
2005
10.1007/s10704-005-3469-y
A linear elastic fracture mechanics analysis of a silicon dioxide-polycrystalline silicon (SiO(2)-Si) bimaterial system was performed to assess the vulnerability of micron-scale silicon structures, such as microelectromechanical systems, to fatigue in ambient air. Previous research has shown that fatigue of silicon films is due to a "reaction-layer fatigue" process where silicon structural films fail due to the sequential, mechanically induced thickening and environmentally assisted cracking of the silicon dioxide reaction layer which forms on the surface upon exposure to air. This work specifically considered the stability of a crack reaching the SiO(2)-Si interface. This analysis revealed a significant overestimate in the oxide thicknesses susceptible to reaction-layer fatigue reported in our previous studies. Instead, a surface oxide layer as thin as 15 nm may activate this fatigue mechanism for a polycrystalline silicon thin film whose fracture strength exceeds 5 GPa.
behavior; failure; fracture-toughness; high-cycle fatigue; interface; mechanics; mems; polysilicon mems structures; reaction-layer fatigue; silicon; single-crystal silicon; strength; stress-corrosion cracking
The fracture problem in the framework of generalized statistical mechanics
ICF XI - 11th International Conference on Fracture
2005
In order to study the relation between the ohmic resistance measured in a thin conducting ribbon and the length of a transversal cut, we employ a one-parameter deformed exponential and logarithm that were recently introduced in the framework of a generalized statistical mechanics. The analytical results have been compared with the data that was experimentally obtained and numerically computed with the boundary element method. Remarkably, the new deformed functions that interpolate between the standard functions and the power law functions, allow the best fit of the experimental data to be obtained for a wide range of the cut length. 1
Time of arrival in Classical and Quantum Mechanics
Arxiv preprint
2000
The time of arrival at an arbitrary position in configuration space can be given as a function of the phase space variables for the Liouville integrable systems of classical mechanics, but only for them. We review the Jacobi-Lie transformation that explicitly implements this function of positions and momenta. We then discuss the recently developed quantum formalism for the time of arrival. We first analyze the case of free particles in one and three space dimensions. Then, we apply the quantum version of the Jacobi-Lie transformation to work out the time of arrival operator in the presence of interactions. We discuss the formalism and its interpretation. We finish by disclosing the presence (absence) of "instantaneous" tunneling for thin (thick) barriers.
Quantum Physics
Mechanics of shear rupture applied to earthquake zones
Fracture Mechanics of Rock
351-428
1986
The mechanics of shear slippage and rupture in rock masses are reviewed. The essential ideas in fracture mechanics are summarized emphasizing the interpretation and relation among the fracture parameters in shear cracks. The slip-weakening model is described. The general formulation of the problem of nonuniform slip distribution in a continuum is covered.
A microdebonding study of the high-temperature oxidation embrittlement of a cross-ply glass-ceramic/SiC composite
Composites Science and Technology
56
12
1453-1459
1996
A constant cross-section specimen with adhesively bonded tabs has been used for an investigation of the high-temperature tensile behavior of a cross-plied glass-ceramic-matrix composite consisting of GAS-II reinforced with Nicalon SiC fiber. Oxidation of the exposed interfaces along matrix cracks in 0 degrees plies lowers the composite failure strain at 800 degrees C to the 0 degrees ply matrix-cracking strain. Scanning electron microscopy and microdebonding analysis of the fracture surfaces indicate that the embrittlement process is the result of oxidation of the carbon-rich interphase as the matrix crack encounters 0 degrees ply fibers, the interphase subsequently fuses with a higher bond strength and the crack grows through the fibers. Planar cracks grow inwards from the surface, covering the entire fracture surface given enough time (or sufficient strain). Degradation of the fibers does not appear to contribute to the embrittlement. Transverse plies crack at a lower strain than does the matrix in the 0 degrees plies. However, it appears that oxygen does not enter 90 degrees ply cracks in sufficient quantity to produce oxidation embrittlement, at least up to the 0 degrees matrix-cracking strain. The strain to crack the 90 degrees plies does not decrease significantly at high temperatures despite the fact that the cracks are primarily in the fiber/matrix interphase as they grow across the 90 degrees plies. (C) 1997 Elsevier Science Limited.
brittle-matrix composites; calcium aluminosilicate; ceramic-matrix composites; fiber; high-temperature properties; interface; interfaces; kinetics; mechanisms; oxidation; silicon carbide fiber; strength
Coupled bend and torsion analysis of the spatial thin-walled beam using timoshenko theory
Gongcheng Lixue/Engineering Mechanics
25
5
2008
Thin-walled beams with constant sections, whose geometrical centers and shear ones do not coincide, are mainly concerned. Based on the theory of Timoshenko beams and thin-walled members, rotation displacements and warp angles of sections are independently interpolated in order that traverse shear deformation and warp engendered by transverse shear and second-order shear stress be included. Through the equation of virtual work, element stiffness matrix is deduced. Some examples given in the context verify the accuracy of the suggested model and its availability in the engineering and confirm the indispensability of considering the influence of coupled bend and torsion when there is at least one asymmetric axis in the sections.
Beam theory of Timoshenko; Coupling of bending and twisting; Finite element; Spatial beam element; Thin-walled structure
High-precision analysis method for elastic thin plate based on trigonometric wavelet
Jisuan Lixue Xuebao/Chinese Journal of Computational Mechanics
29
5
710-715
2012
Taking trigonometric Hermite wavelet that has both good approximation characteristics of trigonometric function and multi-resolution, local characteristics of wavelet as trial function, the bending, vibration and stability of rectangle elastic thin plate under different boundary conditions are solved based on the principle of minimum potential energy. Furthermore, two approaches, hierarchical and multi-resolution approach, are presented to improve accuracy of calculation. Numerical examples show that trigonometric wavelet method can process kinds of boundary conditions conveniently and performs well in solving the bending, vibration and stability of rectangle elastic thin plate, especially for natural vibration feature analysis, and hierarchical and multi-resolution approaches can improve the analysis precision effectively.
Hierarchical; Multi-resolution; Thin plate; Trigonometric wavelet; Uniform formulation
On distortion of symmetric and periodic open-section thin-walled members
Thin-Walled Structures
94
314-324
2015
10.1016/j.tws.2015.04.018
This paper discusses aspects related to the mechanics underlying the distortion of thin-walled members with symmetric and periodic open cross-section, such as those commonly employed in cold-formed steel construction. The Generalised Beam Theory (GBT) framework is employed to determine the cross-section distortional deformation modes and obtain insight into the problem under consideration. Besides reviewing the well known case of reflectional symmetry, the implications of rotational symmetry and periodicity through translation or glide reflection are examined. For each case, computationally efficient procedures to obtain the distortional modes are provided. Several examples are presented throughout the paper, in order to enable a better grasp of the concepts and procedures addressed.
Cross-section distortion; Generalised Beam Theory (GBT); Periodicity; Reflectional symmetry; Rotational symmetry; Thin-walled members
Free vibrations of laminated composite plates using second-order shear deformation theory
Computers and Structures
71
6
617-626
1999
A complete set of linear equations of the second-order theory of laminated\ncomposite plates are obtained. A generalized Levy type solution in\nconjunction with the state space concept is used to analyze the free\nvibration behavior of cross-ply and antisymmetric angle-ply laminated\nplates. Exact fundamental frequencies of cross-ply plate strips are\nobtained for arbitrary boundary conditions. The exact analytical\nsolutions are obtained for thick and moderately thick plates as well\nas for thin plates and plate strips. It is shown that the results\nof the second-order theory are very close to the results of the first-order\nand third-order theories reported in the literature, and different\nfrom those of the classical Kirchhoff's theory for thick laminates.
Time, Quantum Mechanics, and Tense
Synthese
107
1
19-53
1996
10.1007/BF00413901
The relational approach to tense holds that {\textquotedblleft}the\nnow{\textquotedblright}, {\textquotedblleft}passage{\textquotedblright},\nand {\textquotedblleft}becoming{\textquotedblright} are to be understood\nin terms of relations between events. The debate over the adequacy\nof this framework is illustrated by a comparative study of the sense\nin which physical theories, (in)deterministic and (non)relativistic,\ncan lend expression to the metaphysics at issue. The objective is\nnot to settle the matter, but to clarify the nature of this metaphysics\nand to establish that the same issues are at stake in the relational\napproach to value-definiteness and probability in quantum mechanics.\nThey concern the existence of a unique present, respectively actuality,\nand a notion of identity over time that cannot be paraphrased in\nterms of relations.
On micro-meso relations homogenizing electrical properties of transversely cracked laminated composites
Composite Structures
105
66-74
2013
10.1016/j.compstruct.2013.05.001
A practical way to track the development of transverse cracking in a laminated composite is to monitor the change of its electrical resistance. Yet, the relations between transverse cracking and the global modification of resistivity is still unclear that makes difficult to interpret these non-destructive-testing results. Here, we introduce the homogenization process that defines at the meso scale an equivalent homogeneous ply that is energetically equivalent to the cracked one. It is shown that this equivalent ply mainly depends on the cracking level while it can be considered independent on the rest of the laminated structure. The direct consequence is that the meso scale is a pertinent one to perform the homogenization. Then, non-destructive electrical measurements can be considered as a reliable technique to access meso scale damage indicators. ?? 2013 Elsevier Ltd.
A. Laminates; B. Electrical properties; B. Transverse cracking; C. Damage mechanics
Educational Software for Stress Analysis of Idealized Thin Walled Open Sections
Applied Mechanics and Materials
315
339-343
2013
10.4028/www.scientific.net/AMM.315.339
An educational software which can aid students in stress analysis of idealized thin-walled open sections has been developed. The software enables students to select different cross-sections which may be subjected to bending, shear or torsional loads and evaluate the stresses on it. Results obtained through this software have been validated. The software has been developed using MATLAB with graphical user interface (GUI). The software is expected to be a useful tool for effective teaching learning process of courses on thin-walled structures and aircraft structures. © (2013) Trans Tech Publications, Switzerland.
Aircraft structures; Educational software; Idealized thin-walled sections; Stress analysis
Trends in 20th Century Celestial Mechanics
Publications of the National Astronomical Observatory of Japan
9
55-112
2007
We review some of the major achievements of celestial mechanics in the twentieth century, and discuss some unsolved problems that are left to the twenty-1rst century. The four major research fields in celestial mechanics are treated: dynamical systems, three-body problems, solar system dynamics, and numerical methods. Over the past decades, celestial mechanics has become extremely specialized and categorized along many trajectories, from purely mathematical to quite practical points of view, as well as in what has involved digital computer innovation. These various ends of celestial mechanics sometimes exist in isolation, losing their connections with each other. The purpose of this manuscript is to ¯nd clues for rediscovering connections between each of these fields by listing some of major achievements in hoping to find new paths for celestial mechanics in the new century.
celestial mechanics; dynamical system; numerical method; planetary dynamics; three-body problem
Performance evaluation of multilayer thin film coatings under mixed rolling–sliding dry contact conditions
Wear
268
1-2
269-276
2010
10.1016/j.wear.2009.08.001
This paper focuses on the application of advanced finite element analysis to simulate the response of complex multilayer coatings when subjected to mixed rolling-sliding dry contact conditions, typical of those experienced by heavily loaded gear tooth flanks. In this study, a versatile model is developed to investigate the response of a variety of complex coatings. Through the investigation of three advanced surface coatings the developed model is shown to offer detailed subsurface stress and strain information, quantifying the benefits provided by the application of each coating. A number of rolling contact fatigue tests were also conducted to complement the computational simulations. An adapted twin disc testing machine was used to investigate the progressive wear rates of the three advanced surface coatings when subjected to mixed rolling-sliding contact at high load and in dry conditions. The result is a clear indication that advanced surface coating techniques can provide significant improvements in wear resistance and surface durability. From the rolling contact fatigue experiments conducted in this study, a multilayer tungsten carbide/carbon coating was shown to provide the most significant increase in surface durability with a 16-fold reduction in measured weight loss compared to the uncoated substrate over the 145,000 cycle test duration investigated. © 2009 Elsevier B.V. All rights reserved.
Abaqus; Coating simulation; Contact mechanics; FEA; Gears; Motorsport
Covariant statistical mechanics
Il Nuovo Cimento B (1965-1970)
58
1
295-307
1968
10.1007/BF02711798
Summary A covariant formulation of thermodynamics is derived from statistical mechanics.
Mechanics of Accounting (Book)
Accounting Review
5
3
271
1930
Reviews the book "Mechanics of Accounting," by Leo A. Schmidt.
ACCOUNTING; BOOKS -- Reviews; MECHANICS of Accounting (Book); NONFICTION; SCHMIDT, Leo; SCHMIDT, Leo A.
A primer on quantum mechanics and its interpretations
Quantum
36
2010
All the concepts and principles necessary to understand quantum mechanics on an initial level are given in a form suitable for the non-expert. The concepts explained include visualizing the wave function, wave-particle duality, the implications of Schrodinger's cat, probability, the uncertainty principle, collapse of the wave function, and others. However, because of the peculiar, non-intuitive nature of quantum mechanics, one must understand the potential interpretations of its mathematics before one can properly understand these concepts. Thus the paper is organized aorund interpretations, conceptual pictures that explain the peculiar properties of the theory. The only interpretation that currently satisfies all the constraints imposed by experiments and the theory itself makes use of a perceiving Mind which is outside the laws of quantum mechanics.
Stress distributions in cracked thin cylindrical shells: Series expansion
Theoretical and Applied Fracture Mechanics
13
1
39-51
1990
10.1016/0167-8442(90)90014-Q
This work deals with the approximate solutions to thin cylindrical shells with cracks under a single and mixed mode crack extension. Series expansions for the stress and displacement functions are employed. The convergence of the series near the crack tip region is investigated. The results are compared with those found from a finite element analysis which involved laborious calculations as the crack tip is approached. Improvement in the numerical solution can be more easily obtained by taking higher order terms in the series expansion. Strain energy density distributions have also been evaluated by the caustics method and compared to those obtained by finite element and series expansion.
Calculation of the characteristics of thin elastic rods with a periodic structure
Journal of Applied Mathematics and Mechanics
55
3
358-365
1991
10.1016/0021-8928(91)90039-W
A transfer is made from the three-dimensional theory of elasticity in a thin rod to the problem of the theory of beams. The transfer differs from the problems of plates discussed in /1, 2/ (see also the references in /3/), in that the dimensions are reduced, during the passage to the limit, by two, i.e. from three (the dimensions of the initial problem in the theory of elasticity) to one (the dimensions of the limit problem in the theory of beams). In /1, 2/ the dimensions change from three to two. This leads to differences in the form of the asymptotic expansion, in the methods for studying it and in the appearance of new types of cellular problems. © 1992.
On the large amplitude oscillations of a thin elastic beam
International Journal of Non-Linear Mechanics
1
4
217-238
1966
10.1016/0020-7462(66)90006-0
This paper is concerned with the finite amplitude, free, planar oscillations of a thin elastic beam. By assuming the motion to be inextensional but at the same time recognizing the existence of a resultant normal force acting on each cross-section of the beam a system of governing equations is derived which is manageable but still meaningful. For the case of the simply-supported beam a finite difference, Galerkin, and (regular) perturbation solutions are explicitly obtained. The results are compared and discussed. In the course of obtaining the various solutions it is found that an additional simplification in the form of the governing equations is possible. This simplification turns out to be quite important from a general point of view of obtaining approximate analytical solutions.
Incompressible viscous fluid flows in a thin spherical shell
Journal of Mathematical Fluid Mechanics
11
1
28
2006
10.1007/s00021-007-0248-8
Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional Navier-Stokes equations on a sphere. The stationary flow on the sphere has two singularities (a sink and a source) at the North and South poles of the sphere. We prove analytically for the linearized Navier-Stokes equations that the stationary flow is asymptotically stable. When the spherical layer is truncated between two symmetrical rings, we study eigenvalues of the linearized equations numerically by using power series solutions and show that the stationary flow remains asymptotically stable for all Reynolds numbers.
associated legendre equation; asymptotic; navier; numerical approximation eigenvalues; sphere; stability stationary flow; stokes equations a
Mechanics of Natural Solids
Mechanics of Natural Solids
239-254
2009
10.1007/978-3-642-03578-4
In many reservoir engineering and tectonic problems, the ability to predict the occurrence and extent of inelastic deformation\n and strain localization hinges upon a fundamental understanding of the phenomenology and micromechanics of compaction in reservoir\n rock. This paper reviews recent research advances on inelastic compaction and strain localization in porous sandstone, with\n focus on the synthesis of laboratory data, quantitative characterization of damage, fracture mechanics modeling and discrete\n element simulation. Specific topics reviewed here include: phenomenology of inelastic compaction and failure, micromechanics\n of grain crushing and pore collapse, bifurcation analysis and discrete element modeling of compaction bands, and stress conditions\n for the propagation of compaction bands.
Initiation and growth criteria for transverse matrix cracks in composite laminates
Composites Science and Technology
60
2
185-195
2000
10.1016/S0266-3538(99)00114-1
Cecchin and Monti [Cecchin E, Monti A. Experimental techniques for analysis of matrix crack evolution in composite laminates. Masters thesis, Department of Solid Mechanics, Royal Institute of Technology (KTH), Stockholm, Sweden, 1998.] have presented experimental results using off-axis loaded tensile specimens that made it possible to introduce transverse matrix cracks which started from one edge of a specimen and arrested before reaching the other edge. Matrix crack positions and lengths were registered as functions of the applied load through optical images which were captured at regular external load intervals. In the present paper, the experimental data from Cecchin and Monti are analysed. Since several transverse matrix cracks appeared in each specimen and crack growth can be observed at different load levels, a single macroscopic specimen generates lots of data for crack initiation and propagation. Glass/epoxy cross-ply laminates with two different transverse ply thicknesses are investigated. The results strongly indicate that the energy release rate is a relevant measure for prediction of crack growth whereas the local strain controls matrix crack initiation.
a; b; c; damage mechanics; fracture toughness; matrix composites; matrix cracking; mechanical properties; pmcs; polymer
Fluid Mechanics
Most
411-438
2005
10.1007/b138775
This chapter presents some exact and approximate solutions of the Navier-Stokes equations for simple geometries and situations, retaining the viscous terms everywhere in the flow and applying the no-slip boundary condition at solid surfaces. Viscous flows generically fall into two categories, laminar and turbulent, but the boundary between them is imperfectly defined. Similarity solutions to partial differential equations are possible when a variable transformation exists that allows the partial differential equation to be rewritten as an ordinary differential equation. Several simple and physically revealing unsteady flow problems are presented and solved in the chapter. The first is the flow due to impulsive motion of a flat plate parallel to itself, commonly known as Stokes' first problem. A similarity solution is one of several ways to solve Stokes' first problem. The flow discussed in this chapter is an unsteady viscous flow that includes an imposed time scale. Many physical problems can be described by the behavior of a system when a certain parameter is either very small or very large. Analytical methods in fluid flow problems are useful in understanding the physics of fluid flows and in making generalizations.
Thin-film modelling of poroviscous free surface flows
European Journal of Applied Mathematics
16
519-553
2005
10.1017/S095679250500584X
Thin-film models for the flow of a low reduced-Reynolds-number poroviscous droplet over a planar substrate are developed. One of the formulations is used to develop a minimal model for active animal cell motion in which the microscopic mechanisms of polymerisation and depolymerisation near the outer cell periphery are modelled by specifying the rate of mass transfer between the phases at the contact-line in terms of the velocity of the latter. An asymptotic analysis in the limit corresponding to strong cell-substrate adhesion is shown to lead to a novel class of multi-valued contact-line laws, a qualitative analysis of which leads in two dimensions to some intriguing behaviour, including (i) periodic contraction and expansion (pulsation), (ii) steady propagation at a contant speed, (iii) an unsteady combination of pulsation and propagation, and (iv) a bistable regime in which both non-motile and motile solutions are admissible, each of them being stable to sufficiently small perturbations, but with sufficiently large perturbations being able to 'prod' a stationary cell into motion or halt a moving one; these qualitative predictions are where possible compared with experiment. The contact-line behaviour is likely to be highly sensitive to environmental signals; the formulation may, therefore, provide a useful 'minimal' modelling framework for investigation of chemotactic effects at the cell scale. The corresponding extensional flow formulations are also noted.
Cell Motion; Cytoplasm; Driven; Droplet; Dynamics; Mechanics; Motility; Reactive Flow; Tumor
Average warping in the torsion of thin-walled open-section beams
Journal of the Mechanics and Physics of Solids
3
4
267-274
1955
10.1016/0022-5096(55)90037-5
It is suggested that in the theory of non-uniform torsion of thin-walled beams of open cross-section it is strictly relevant to define average longitudinal warping as the mean value taken over the whole cross-sectional area, and not as the mean value taken over the centre-line of the wall, as suggested by Timosbenko (1945). This alternative concept was used earlier by Wagner (1029) ; it seems desirable at this stage to re-define the warping stiffness in the general case in terms of this alternative value of average warping. © 1955.
The propagation of elastic waves in thin cylindrical shells
Journal of the Mechanics and Physics of Solids
14
3
121-130
1966
10.1016/0022-5096(66)90032-9
The propagation of longitudinal elastic waves along cylindrical shells can be treated in terms of the exact three-dimensional elastic theory. When the thickness of the shell is very small compared with its radius r, the shell might be expected to behave like a flat plate for wavelengths small compared with r. In this paper it is shown theoretically and verified experimentally that this is so, and that both symmetrical and antisymmetrical plate waves can be propagated. The experimental part of the paper is concerned with the signal velocity of a mechanical pulse travelling in a thin-walled steel tube, and it is found that those Fourier components which travel with the symmetrical plate wave velocity appear at the head of the pulse as it propagates down the tube.
Semiclassical quantum mechanics
Communications in Mathematical Physics
71
1
77-93
1980
10.1007/BF01230088
Abstract. We consider the h-~0 limit of the dynamics generated by the Hamiltonian H(h)= -(hZ/2m)A + V. We prove that the evolution of certain Gaussian states is determined asymptotically as h~0 by classical . For
A computational mechanics model for the brim forming process in paperboard container manufacturing
Journal of Manufacturing Science and Engineering-Transactions of the Asme
125
3
476-483
2003
10.1115/1.1580527
The manufacturing process of brim forming in paperboard containers consists of taking a thin paperboard shell and forming a brim to provide additional stiffness to the structure. A paper cup is an example of such a structure manufactured at rates exceeding 300 units per minute. A realistic model for the manufacturing process is not available and the effects of process and material parameters are not well understood. In this study, a finite element model of this highly nonlinear problem is presented. The model takes into account the material orthotropy and nonlinear elastic-plastic behavior die paperboard contact interaction during loading and unloading, and friction between the metal die and paperboard, die geometry, and environmental conditions. Model predictions of the force-displacement curve agree well with the experimentally observed results.
Elastic-plastic solution to stamping thin strip on elastic foundation
Transactions of Nonferrous Metals Society of China
16
2
339-345
2006
10.1016/S1003-6326(06)60058-7
An analytical method was proposed to solve the mechanical problems of stamping a thin strip on an elastic foundation. The thin strip was divided into four parts according to its deformation and contact with the punch and the elastic foundation, especially an elastic-plastic part was considered in the deflection of the thin strip. Analytical solutions were derived individually for each part and two models were established with the help of elastic and plastic large deflection theories. Compatibility conditions between the neighboring parts of the thin strip constructed the non-linear equation group. Solutions were carried out by programming with a software. The deformation shape, the membrane force, and the moment and shear force of the deformed thin strip were obtained. The results of the two models were compared. The study shows that the method is effective.
beam bending; contact mechanics; elastic-plastic solution; thin strip stamping
Stationary nonequilibrium statistical mechanics
arXiv
1-17
2005
A brief review on the dynamical systems approach to nonequilibrium statistical mechanics and chaotic dynamics
Statistical Mechanics
Relativistic Quantum Mechanics
New York
300
1964
In this text the authors develop a propagator theory of Dirac particles, photons, and Klein-Gordon mesons and per-form a series of calculations designed to illustrate varioususeful techniques and concepts in electromagnetic, weak, andstrong interactions. these include defining and implementingthe renormalization program and evaluating effects of radia-tive corrections, such as the Lamb shift, in low-ordercalculations. The necessary background for the book is pro-vided by a course in nonrelativistic quantum mechanics atthe general level of Schiff's text, QUANTUM MECHANICS.
The mechanics of splashing
Journal of Colloid and Interface Science
124
1
309-316
1988
10.1016/0021-9797(88)90352-9
A new but very simple experimental technique is presented for the determination of the distribution of the velocity and direction for splashed droplets. It is shown that the distribution of ejection angles depends upon the depth of the liquid surface from which the droplets originate, and that there is a wide range of splash droplet emission velocities.
Integral equation and sensitivity analyses of creep behavior for PVDF thin films
Mechanics of Materials
40
7
594-601
2008
10.1016/j.mechmat.2008.02.001
This paper presents an analytic study of a linear viscoelasticity\nconstitutive equation involving stress, strain and creep compliance\nwhile simultaneously correcting a previously reported investigation\n[Vinogradov, A.M., Schmidt, V.H., Tuthill, G.F., Bohannan, G.W.,\n(2004). Damping and electromechanical energy losses in the piezoelectric\npolymer PVDF. Mechanics of Materials 36, 1007-1016]. The constitutive\nequation is presented as a linear, weakly-singular Volterra integral\nequation of the second kind in the stress variable. An analytic solution\nis developed, using the Laplace transform technique, for acquiring\nthe stress history based on a specified creep compliance function\nand input strain. The time-dependent stress solution is expressed\nin terms of an infinite series involving the provided strain history.\nAn example is studied involving constant strain input. This example\npermits an aposteriori error estimate for the stress based on the\ntruncated series. Finally, a novel first-order sensitivity analysis\nis presented to assist in developing experiments for estimating the\nparameters associated with the compliance function. Using the proposed\nfirst-order sensitivity analysis, it is possible to investigate how\nthe uncertainty associated with these parameters propagate into the\nstress history.
The Representation of Time and Change in Mechanics
Philosophy of Physics
133-228
2007
10.1016/B978-044451560-5/50005-1
xiii \nxiii \nIntroduction \nJeremy Butterfield and John Earman \nxxiii \nList of Contributors \nPart A \n1 \nOn Symplectic Reduction in Classical Mechanics \nJeremy Butterfield \n133 \nThe Representation of Time and Change in Mechanics \nGordon Belot \n229 \nClassical Relativity Theory \n275 \nMichael Dickson \n417 \nBetween Classical and Quantum \nN. P. Landsman \n555 \nQuantum Information and Computing \nJeffrey Bub \n661 \nThe Conceptual Basis of Quantum Field Theory \nGerard `t Hooft \n731 \nAlgebraic Quantum Field Theory \nHans Halvorson (with an Appendix by Michael M¨ \nuger) \nIndex to Part A and Part B \nDavid B. Malamet \nNon-Relativistic Quantum Mechanics \nI-1David B. Malamet \nNon-Relativistic Quantum Mechanics
Time; Physics
Yielding and Strain Hardening in Metallic Thin Films on Substrates: an Edge Dislocation Climb Model
Mathematics and Mechanics of Solids
14
1-2
207-219
2009
10.1177/1081286508092612
Yielding and strain hardening in metallic thin films on substrates are studied using a simple edge dislocation climb model, modified to mimic dislocation processes in passivated, single crystal FCC metal films with a (111) texture. The aim of the modeling is to produce closed-form solutions for the yield strength and rate of strain hardening that can be compared with experiment. The models give a good account of the dependence of the yield strength of passivated gold films on silicon substrates on the film thickness and they are in broad agreement with the experimental observation that plastic flow in passivated metal films is characterized by very high rates of strain hardening. However, these simple models fail to predict the observed decrease in the rate of strain hardening with increasing film thickness, a result that requires more computationally intensive discrete dislocation modeling.
Experimental-numerical hybrid stress analysis for a curving crack in a thin glass plate under thermal load
Engineering Fracture Mechanics
131
514-524
2014
10.1016/j.engfracmech.2014.09.007
The stress fields around an oscillating crack tip in a thin plate are studied using an experimental-numerical hybrid method. Instantaneous phase-stepping photoelasticity using a CCD camera equipped with a pixelated microretarder array is used for measuring the stress fields around a propagating crack tip. Not only the principal direction but also the principal stress difference around a growing crack is obtained. Then, the stress distributions around a crack are evaluated by the experimental-numerical hybrid method. Results show that the proposed hybrid method is effective for the study of crack growth behavior in the glass plate. The results obtained in this study show that the compressive stresses exist around the tensile stress region at the crack tip. It can be considered that the existence of the compressive stress distribution surrounding the tensile stress field at the crack tip leads to both the high value of the stress intensity factor and the crack oscillation. © 2014 Elsevier Ltd.
Influence of crack fractal geometry on elastic–plastic fracture mechanics
Physica A: Statistical Mechanics and its Applications
295
1-2
144-148
2001
10.1016/S0378-4371(01)00067-X
Fractal geometry is introduced into elastic–plastic fracture mechanics characterizing the morphology of crack surface. It is shown that the rising of the J–R curve is correlated to the ruggedness dimension (Hurst's exponent) of the crack surface. Experimental results are fitted. Our propositions differ from other currently used in the literature compromising the results therein presented.
Life prediction of cross-ply metal matrix composites undergoing thermomechanical fatigue
Fatigue and Fracture of Engineering Materials and Structures
21
4
493-508
1998
10.1046/j.1460-2695.1998.00061.x
A life prediction model that was originally developed for the axial loading of unidirectional metal matrix composites (MMCs) undergoing combined thermal and mechanical loading is extended to the axial loading of cross-ply MMCs by adding an internally initiated matrix fatigue damage term. This new term accounts for the growth of cracks that initiate at the location where fibre-matrix separation occurs in the transversely-oriented plies. A comparison of the model predictions to experimental data on SCS-6/Timetal 21S shows that the model reasonably accounts for the dependence of applied stress, temperature and environment, as well as cyclic frequency. The dominant damage accumulation process for cross-ply MMCs with weak fibre-matrix bonds is described by this internally initiated matrix fatigue damage process for most stress-temperature cycle combinations. However, the fibre-dominated damage accumulation process operates under in-phase TMF when both stress and temperature are high. Environment-enhanced matrix fatigue is the dominant damage accumulation process under isothermal fatigue when stress is low and temperature is high.
Crack propagation; Elasticity; Environmental testing; Fatigue of materials; Fiber reinforced materials; Laminates; Metallic matrix composites; Shear stress; Stress analysis; Thermal effects
Cure monitoring of cross-ply composite laminates with an encapsulated fibre Bragg grating
5th International Conference on Emerging Technologies in Non-Destructive Testing, NDT
175-176
2012
A very important aspect of a composite manufacturing process is the appearance of residual strains and stresses during the curing cycle. The formation of thermal residual strains arise mainly from the difference in thermal expansion between the reinforcement fibres and the matrix material. In this paper, Fibre Bragg grating sensors are used to monitor the internal strain state of a cross-ply laminate [02, 902]2s during its curing cycle. In a first experiment, it is shown that transverse strain fields can influence the residual strain measurements. Therefore, one should try to isolate the sensor from these transversal strain fields. In the second experiment, this is done by integrating the sensors in a capillary. As such we were able to quantify the longitudinal residual strains of a cross-ply laminate. © 2012 Taylor & Francis Group, London.
Composite laminate; Composite manufacturing proces
An Iteration Method for the Large-Amplitude Flexural Vibration of Antisymmetric Cross-Ply Rectangular-Plates
Composite Structures
18
3
263-282
1991
Doi 10.1016/0263-8223(91)90036-X
An analytical solution to the large amplitude free-vibration problem of antisymmetric cross-ply rectangular composite plates, having an additional quadratic nonlinear term in the modal equation of equilibrium is contained herein. It is shown that the classical two-term perturbation solution and further extension of the same for five-term fail to yield any meaningful results when the coefficients of nonlinear terms in the modal equation are large. Hence, an iteration method, used to solve the Duffing's equation for isotropic plates, has been extended to solve the present modal equation of equilibrium corresponding to the anti-symmetric cross-ply rectangular plates with simply supported edges. It is observed that the Duffing's assumption of considering the first Fourier coefficient as amplitude results in erroneous estimation of nonlinear free-vibration behaviour of such plates. The nonlinear frequencies obtained from second iteration of the proposed iteration method compare well with those obtained from the direct numerical integration method which is found to yield accurate results. It is seen that the presence of an additional quadratic term in the modal equation results in different amplitudes in the positive and negative half cycles of vibration.
VIBRATIONS OF A CROSS-PLY CERAMIC MATRIX COMPOSITE BEAM WITH MATRIX CRACKS
ICF10, Honolulu, Hawaii - 2001
2001
The paper illustrates the effect of matrix cracks in longitudinal and transverse layers of a cross-ply ceramic matrix beam (CMC) on its stiffness and vibration frequencies. Even if vibration amplitudes are small, the physical nonlinearity is introduced by the interfacial fiber-matrix friction in the vicinity of matrix cracks in the longitudinal layers. A closed-form solution for mechanical properties of a cross-ply beam with matrix cracks is developed in the paper. The frequency of free vibrations of a simply supported beam is derived as a function of the amplitude, accounting for the effect of matrix cracks. The conclusions that follow from the numerical analysis enable us to suggest a simple and accurate design formula for the fundamental frequency
bimodular material; ceramic matrix composites; matrix cracks; physical nonlinearity; vibrations
Optimization of laminated composite plates based on the last-ply failure criterion
Wuhan Ligong Daxue Xuebao (Jiaotong Kexue Yu Gongcheng Ban)/Journal of Wuhan University of Technology (Transportation Science and Engineering)
30
1
140-142+149
2006
In this paper, a last-ply failure (LPF) analysis method for laminated composite plates is incorporated in the finite element code-ANSYS. A optimum design method is presented. The composite structure is analyzed considering both in-plane and out-plane loads. For each lamina, two major failure modes-matrix failure and fiber breakage are considered. After lamina has failed, the laminate stiffness is modified to reflect the damage, and stresses in the structure are re-analyzed. This procedure is repeatedly performed until the whole structure fails and thus the. ultimate strength is determined. Given the fiber orientation and the lamina thickness as the design variables and the LPF load as the objective, a structural optimization problem is solved.
Composite; Last-ply failure; Optimum design
Flexural analysis of cross-ply laminated plates subjected to nonlinear thermal and mechanical loadings
Acta Mechanica
224
3
675-690
2012
10.1007/s00707-012-0774-1
The objective of this paper is to present an equivalent single-layer shear deformation theory for eval- uation of displacements and stresses of cross-ply laminated plates subjected to uniformly distributed nonlinear thermo-mechanical load. A trigonometric shear deformation theory is used. The in-plane displacement field uses a sinusoidal function in terms of the thickness coordinate to include the shear deformation effect. The the- ory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of a shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to uniformly distributed nonlinear thermo-mechanical load are obtained. Numerical results of the present theory for displacement and thermal stresses are compared with those of classical, first-order and higher-order shear deformation plate theories.
Statistical Mechanics of Wormholes
arXiv:1109.6577
2011
The statistical mechanics of a gas of Einstein-Kalb-Ramond wormholes is studied in this paper. The wormholes studied are the result of sewing together two Reissner-Nordstrom-type black hole metrics at their horizons. By requiring the stress-energy tensor associated with this geometry to be that of a Kalb-Ramond field, we obtain the mass and Kalb-Ramond `charge` of the wormholes in terms of the parameters describing the mass density, tension and pressure. We investigate the statistical mechanics of this system of wormholes within the context of the statistical bootstrap model. A gas of such wormholes is found to obey the bootstrap condition only for an extreme, non-thermodynamic, energy and `charge` distribution among the particles. We comment briefly on the scattering of quantum wormholes.
Fluid mechanics: Mist opportunities
Nature
482
7386
476
2012
10.1038/482476a
From the fixative properties of hairsprays to the stickiness of filaments on beetles' feet, the wetting of flexible fibres with droplets of liquid is a universal phenomenon—but one we know surprisingly little about. On page 510 of this issue, Duprat et al. formulate rules to describe ... \n
Ultimate strength of a composite cylinder subjected to three-point bending: correlation of beam theory with experiment
Composite Structures
63
3-4
439-445
2004
10.1016/S0263-8223(03)00192-2
This paper investigates the ultimate bending response of a solid composite cylinder reinforced with uniaxially aligned continuous fibers. Experiments exhibited remarkable nonlinear load–deflections up to failure, indicating that a progressive failure process must have occurred in the cylinder. Thus, the failure of the outmost filament initially subjected to the maximum bending stress does not correspond to the ultimate failure, and additional loads should be still applicable to the cylinder. To reveal this progressive failure process, the cylinder is discretized into a number of parallel layers of different widths. Each layer is considered as a unidirectional lamina, whose overall load component is determined within the framework of classical beam theory. However, the lamina non- linearity has been incorporated in the analysis using an instantaneous stiffness element defined by the micromechanics bridging model. The benefit of this model is in that only the constituent fiber and matrix properties are required in the analysis. As neither the first ply nor the last ply failure corresponds to the ultimate failure, in addition to the stress failure criterion used to detect the failure of an individual ply another deformation related parameter must be also employed to govern the ultimate failure and then to determine the ultimate strength. In the present case when a 16 layers discretization has been employed, the predicted fourth ply failure strength has been found to work for the ultimate strength and to correlate reasonably well with the experimental coun- terpart.
beam theory; bending response; composite cylinder; ultimate strength
Quantum Mechanics: Incomplete and Non Local Theory
arXiv preprint arXiv:1103.0420
1-15
2011
We will show for undergraduate and graduate students of physics that Quantum Mechanics is an incomplete and non-local theory. The problem of non-locality is discussed by analyzing the Bell's theorem where are considered correlations between measurements results performed on physical systems that are far apart, but that interacted in the past. The experimental violations of Bell's theorem show a very general result thatquantum phenomena are nonlocal and that, inevitably, Quantum Mechanics is non-local.
bell theorem; incomplete and non; local theory; quantum mechanics
Thin Oxidation Study with Various Thermodynamic Parameters
ECS Transactions
18
1
575-580
2009
10.1149/1.3096504
The structure analysis of extremely thin thermally grown SiO2 (< 25 Aå) indicates that most silicon atoms share two of the four tetrahedrally-coordinated oxygen atoms with the adjacent silicon atoms. Molecular mechanics simulation of the single chain of SiO2 tetrahedrons is presented. The extremely thin oxide film is composed of the close-packed short chains of the tetrahedrons perpendicular to Si substrate. Diffusion experiment of an acid vapor through non-oxide polyhydroxystyrene films de-convolutes four prototropic states of fluoresceinamine monolayer to resemble the change of the intermediate states of Si atoms during the thermal oxygen diffusion processes at Si/SiO2 interface.
Passivation Effects in Copper Thin Films
AIP Conference Proceedings
817
185-191
2006
10.1063/1.2173548
We studied the influence of a 10 nm AlxOy passivation on the stress-temperature behavior of 100 nm and 1 μm thick Cu films. At low temperatures, the passivation induces a large tensile stress increase in the 100 nm film; however, its effect on the 1 μm film is negligible. At high temperatures, the opposite behavior is observed; while the passivation does not change the 100 nm film behavior, it strengthens the 1 μm film by driving it deeper into compression. These observations are explained in light of a combination of constrained diffusional creep and dislocation dynamics unique to ultra-thin films. © 2006 American Institute of Physics.
Passivation; Thermomechanical behavior; Thin films mechanics
Statistical mechanics of two-dimensional vortices
Journal of statistical physics
17
5
323-355
1977
10.1007/BF01014402
The formation of large-scale vortices is an intriguing phenomenon in two-dimensional turbulence. Such organization is observed in large-scale oceanic or atmospheric flows, and can be reproduced in laboratory experiments and numerical simulations. A general explanation of this organization was first proposed by Onsager (1949) by considering the statistical mechanics for a set of point vortices in two-dimensional hydrodynamics. Similarly, the structure and the organization of stellar systems (globular clusters, elliptical galaxies,...) in astrophysics can be understood by developing a statistical mechanics for a system of particles in gravitational interaction as initiated by Chandrasekhar (1942). These statistical mechanics turn out to be relatively similar and present the same difficulties due to the unshielded long-range nature of the interaction. This analogy concerns not only the equilibrium states, i.e. the formation of large-scale structures, but also the relaxation towards equilibrium and the statistics of fluctuations. We will discuss these analogies in detail and also point out the specificities of each system.
Physlets for quantum mechanics
Computing in Science and Engineering
2003
10.1109/MCISE.2003.1166558
Page 1. significant educational gain. 1 In addition, students often approach typical end-of-chapter textbook prob- lems by finding
Thermophones by quantum mechanics
2010 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, ITherm 2010
2
5
2010
10.1109/ITHERM.2010.5501315
Thermophones are thought to produce sound from vibrations by converting current at audio frequencies to rapid temperature changes. However, thermophones recently fabricated from nanoscale sheets of carbon nanotubes (CNTs) produce higher sound pressure levels (SPL) without vibration. Classical heat transfer cannot explain CNT thermophones, and instead quantum mechanics (QM) as embodied in the theory of QED induced EM radiation is proposed. QED stands for quantum electrodynamics and EM for electromagnetic. Atoms in CNT films having thickness <; 0.2 microns are under EM confinement at levels beyond the ultraviolet (UV) that by QM have vanishing specific heat, and therefore Joule heat cannot be conserved by an increase in temperature. Conservation proceeds by the QED induced up-conversion of low frequency Joule heat to the UV confinement frequency of the film. Sound is produced from the pressure changes that accompany the absorption of UV emission by the surrounding air.
Quantum mechanics; Thermophones
Relativistic viscoelastic fluid mechanics
Physical Review E
84
2
026316
2011
10.1103/PhysRevE.84.026316
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski spacetime become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Mechanics of Materials 2
Mechanics of Materials 2
443-508
1997
10.1016/B978-075063266-9/50012-3
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
Fluid Mechanics
Fluid Mechanics
779-852
2012
10.1016/B978-0-12-382100-3.10016-2
This chapter introduces biofluid mechanics. The human body is a complex system that requires materials such as air, water, minerals, and nutrients for survival and function. The associated bio transport and distribution processes involve interactions with membranes, cells, tissues, and organs comprising the body. The primary functions of the cardiovascular system are: to pick up oxygen and nutrients from the lungs and the intestine, respectively, and deliver them to tissues (cells) of the body, to remove waste and carbon dioxide from the body for excretion through the kidneys and the lungs, respectively, and to regulate body temperature by advecting the heat generated and transferring it to the environment outside the skin. The motive mechanism for blood flow is the prevailing pressure gradient. The circulations associated with the cardiovascular system may be considered three subsystems. These are: systemic circulation, pulmonary circulation, and coronory circulation.
Topological factors derived from Bohmian mechanics
Annales Henri Poincare
7
791-807
2006
10.1007/s00023-006-0269-5
We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental group of Q. We employ wave functions on the universal covering space of Q. As a byproduct of our analysis, we obtain an explanation, within the framework of Bohmian mechanics, of the fact that the wave function of a system of identical particles is either symmetric or anti-symmetric.
03; 2000; 65; 81p99; 81q70; 81s99; bohmian mechanics; dedicated to rafael sorkin; his 60th birthday; msc; multiply-connected configuration spaces; on the occasion of; pacs; ta; topological phases; universal covering space; vf
7 Winning Examples of Game Mechanics in Action
Mashable.com
2011
Gamification is the use of game mechanics to engage audiences and improve a business. These seven gamified innovations should inspire you to strategize via game analysis.
Surface Transport in Continuum Mechanics
Mathematics and Mechanics of Solids
14
6
587-598
2008
10.1177/1081286507087316
A moving surface is considered as a 3-dimensional submanifold in the 4-dimensional space-time setting. Elementary differential geometry is used to identify parameter-time and parameter independent normal-time derivatives, and their differences. A few elementary observations are made concerning surface transport theorems.
4d representation; normal-time derivative; parameter-time derivative; surface gradient; surface transport
Comparison of Various Shear Deformation Theories for Bending, Buckling, and Vibration of Rectangular Symmetric Cross-ply Plate with Simply Supported Edges
Journal of Composite Materials
40
23
2143-2155
2006
10.1177/0021998306062313
In the present study, unified shear deformation theory which was proposed by Soldatos, K.P. and Timarci, T. (1993). A Unified Formulation of Laminated Composite, Shear Deformable Five-degrees-of-freedom Cylindrical Shells on the Basis of a Unified Shear Deformable Shell Theory, Compos. Struct., 25(1-4): 165-171 is used to analyze simply supported symmetric cross-ply rectangular plates for deflections, stresses, natural frequencies, and buckling loads. This theory enables the selection of different in-plane displacement components to represent shear deformation. Exponential shear deformation theory, which is proposed by Karama et al., 40(6) (2003). Mechanical Behavior of Laminated Composite Beam by New Multi-layered Laminated Composite Structures Model with Transverse Shear Stress Continuity, Int J Solids Struct., 40: 1525-1546, is used for the first time to analyze the problem considered. Results which are found by exponential theory are compared with those obtained by using the parabolic shear deformation theory of Reddy, J.N., 51(4) (1984). A Simple Higher-order Theory for Laminated Composite Plates, J Appl Mech., 51: 745-752, the trigonometric shear deformation theory of Touratier, M., 29(8) (1991). An Efficient Standard Plate Theory, Int. Jnl. Engng. Sci., 29(8): 901-916, the hyperbolic shear deformation theory of Soldatos, K.P., 94(3-4) (1992). A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates, Acta Mech., 94: 1995-220 and with the available three-dimensional elasticity solutions. The study shows that while the transverse displacement and the stresses are best predicted by the exponential shear deformation theory, the parabolic shear deformation and the hyperbolic shear deformation theories yield more accurate predictions for the natural frequencies and the buckling loads. © 2006 SAGE Publications.
Uncertainty propagation in inverse reliability-based design of composite structures
International Journal of Mechanics and Materials in Design
6
1
89-102
2010
10.1007/s10999-010-9123-5
An approach for the analysis of uncertainty\r\npropagation in reliability-based design optimization of\r\ncomposite laminate structures is presented. Using the\r\nUniform Design Method (UDM), a set of design points\r\nis generated over a domain centered on the mean\r\nreference values of the random variables. A method-\r\nology based on inverse optimal design of composite\r\nstructures to achieve a specified reliability level is\r\nproposed, and the corresponding maximum load is\r\noutlined as a function of ply angle. Using the generated\r\nUDM design points as input/output patterns, an\r\nArtificial Neural Network (ANN) is developed based\r\non an evolutionary learning process. Then, a Monte\r\nCarlo simulation using ANN development is per-\r\nformed to simulate the behavior of the critical Tsai\r\nnumber, structural reliability index, and their relative\r\nsensitivities as a function of the ply angle of laminates.\r\nThe results are generated for uniformly distributed\r\nrandom variables on a domain centered on mean\r\nvalues. The statistical analysis of the results enables the\r\nstudy of the variability of the reliability index and its\r\nsensitivity relative to the ply angle. Numerical\r\nexamples showing the utility of the approach for robust\r\ndesign of angle-ply laminates are presented.
Artificial Neural Network; Composite structures; Inverse RBDO; Monte Carlo simulation; Relative sensitivities; Reliability index variability; Uncertainty propagation; Uniform Design Method
Use of one-ply composite tissues in an automated optical assay for recovery of Listeria from food contact surfaces and poultry-processing environments.
Journal of food protection
70
5
1263-6
2007
A novel one-ply composite tissue (CT) method using the Soleris (formerly BioSys) optical analysis system was compared with the conventional U.S. Department of Agriculture (USDA) environmental sponge enrichment method for recovery of Listeria from food contact surfaces and poultry-processing environments. Stainless steel and high-density polyethylene plates were inoculated to contain a six-strain L. monocytogenes cocktail at 10(4), 10(2), and 10 CFU per plate, whereas samples from naturally contaminated surfaces and floor drains from a poultry-processing facility were collected with CTs and environmental sponges. CT samples were transferred into Soleris system vials, and presumptive-positive samples were further confirmed. Sponge samples were processed for Listeria using the USDA culture method. L. monocytogenes recovery rates from inoculated stainless steel and polyethylene surfaces were then compared for the two methods in terms of sensitivity, specificity, and positive and negative predictive values. No significant differences (P > 0.05) were found between the two methods for recovery of L. monocytogenes from any of the inoculated stainless steel and polyethylene surfaces or environmental samples. Sensitivity, specificity, and overall accuracy of the CT-Soleris for recovery of Listeria from environmental samples were 83, 97, and 95%, respectively. Listeria was detected 2 to 3 days sooner with the CT-Soleris method than with the USDA culture method, thus supporting the increased efficacy of this new protocol for environmental sampling.
Animals; Bacterial Adhesion; Colony Count; Consumer Product Safety; Environmental Microbiology; Equipment Contamination; Food Contamination; Food Contamination: analysis; Food Microbiology; Food-Processing Industry; Humans; Listeria monocytogenes; Listeria monocytogenes: isolation & purification; Listeria monocytogenes: physiology; Microbial; Microbial: methods; Polyethylene; Poultry; Poultry: microbiology; Predictive Value of Tests; Reproducibility of Results; Sensitivity and Specificity; Stainless Steel
Analogy between mechanics and electricity
European Journal of Physics1
6
16-21
1985
10.1238/Physica.Regular.065a00300
The dissipativetransport of energy is described in the momentum current picture. This picture provides a local-causes approach t o mechanics whereby forces are considered as momentum currents. In this approach, friction, i.e. mechanical heat production, appears when a momentum current flows between two bodies of different velocities. The treatment o the f transport and dissipation of energy follows the same rules in mechanics as in electricity. An ‘Ohm’s Law of momentum currents’ is introduced in analogy to Ohm’s Law in electricity. Newton’s Third Law reduces to a simple statement about momentum conservation.
Numerical simulation of damage processes of laminated composites subjected to quasi-static indentation
Fuhe Cailiao Xuebao/Acta Materiae Compositae Sinica
30
1
252-256
2013
Starting from the indentation damage mechanics, a numerical model of laminated composites subjected to quasi-static indentation was established on the basis of progressive damage mechanics. The different kinds of composite damages and their progressive processes were quantitatively analyzed. Furthermore, under the condition of same laminates thickness, the effect of single ply thickness on the indentation damage was discussed. The results show that the increase of single ply thickness can enlarge the matrix damage and the delamination degree, whereas it can restrain the development of fiber fracture.
Composite; Composite damage; Composite materials; Computer simulation; Damage; Damage process; Fiber fracture; Indentation damage; Laminated composites; Laminates; Numerical simulation; Progressive damage; Quasi-static indentation; Single ply
Thermodynamics in solid mechanics: a commentary.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
363
1836
2465-77
2005
10.1098/rsta.2005.1669
This commentary on thermodynamics in solid mechanics aims to provide an overview of the main concepts of thermodynamic processes as they apply to, and may be exploited for, studies in nonlinear solid mechanics. We give a descriptive commentary on the (physical) interpretation of these concepts, and relate these where appropriate to behaviour of solids under thermo-mechanical conditions. The motivation is firstly that students of solid mechanics have often had less exposure to thermodynamics than those in other branches of science and engineering, yet there is great value in analytical formulations of material behaviour derived from the principles of thermodynamics. It also sets the contributions in this Theme Issue in context. Along with the deliberately descriptive treatment of thermodynamics, we do outline the main mathematical statements that define the subject, knowing that full details are provided by the authors in their corresponding contributions to this issue. The commentary ends on a lighter note. In order to aid understanding and to stimulate discussion of thermodynamics in solid mechanics, we have invented a number of very basic and completely fictitious materials. These have strange and extreme behaviours that describe certain thermodynamics concepts, such as entropy, in isolation from the complexities of real material behaviour.
Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 2. Liquid dynamics
Journal of Fluid Mechanics
758
508-521
2014
10.1017/jfm.2012.233
The agitation of the liquid phase has been investigated experimentally in a homogeneous swarm of bubbles rising at high Reynolds number within a thin gap. Owing to the wall friction, the bubble wakes are strongly attenuated. Consequently, liquid fluctuations result from disturbances localized near the bubbles and direct interactions between them. The signature of the average wake rapidly fades and the probability density function of the fluctuations becomes Gaussian as the gas volume fraction α increases. The energy of the fluctuations scales differently with α depending on the direction, indicating that hydrodynamic interactions are different in the horizontal and vertical directions. The spatial spectrum shows that the length scales of the fluctuations are independent of α and exhibits a k−3 subrange, which results from localized random flow disturbances of various sizes. Comparisons with the dynamics of the gas phase show that liquid and bubble agitations are driven by the same mechanism in the vertical direction, whereas they turn out to be almost uncoupled in the horizontal direction. Comparisons with unconfined flows show that the generation of liquid fluctuations is very different. However, the cause of the k−3 spectral subrange is the same for confined flows as for the spatial fluctuation of unconfined flows.
drops and bubbles; gas/liquid flow; multiphase and particle-laden flows
A numerical investigation into the response of free end tubular composite poles subjected to axial and lateral loads
Thin-Walled Structures
48
8
650-659
2010
10.1016/j.tws.2010.04.002
This paper presents a numerical investigation of cantilevered glass fiber-reinforced polymer (GFRP) tubular poles subjected to lateral and axial loads. A 3D finite element analysis was conducted to establish the lateral loaddeflection responses under different axial loads and the axial loadbending moment interaction curves at ultimate. The model accounts for geometric nonlinearities and the composite laminate structure. Failure modes were established based on either material failure according to the Tsai-Wu failure criterion, or stability failure. The model was validated by using experimental results. A parametric study was then carried out on poles with various angle-ply and cross-ply laminates as well as different diameter-to-thickness (D/t) and length-to-diameter (L/D) ratios. The study showed that the reduction in axial strength as (L/D) ratio increases becomes more severe as (D/t) ratio is reduced. The GFRP laminate structure has a considerable effect on axial and flexural strengths of the poles for certain (D/t) ratios. It was also shown that axial loadmoment interaction curves are generally linear. Increasing the fraction of longitudinal fibers in cross-ply laminates or reducing the fiber angle with the longitudinal direction in angle-ply laminates results in a larger interaction curve. A simplified design approach for the poles has been proposed. ?? 2010 Elsevier Ltd. All rights resvered.
Axial load; Cantilevered pole; Flexure; FRP; Lateral load; Numerical
Quantum Mechanics: To Condense or Not to Condense
Science
298
5594
760-761
2002
10.1126/science.1078819
... 298 no. 5594 pp. 760-761 DOI: 10.1126/science.1078819. Perspective. QUANTUM MECHANICS To Condense or Not to Condense . ... The author is at the Institut für Theoretische Physik, ETH Zürich, 8093 Zürich, Switzerland. E-mail: rice {at}itp.phys.ethz.ch. ...
Thin liquid layers supported by steady air-flow surface traction
Journal of Fluid Mechanics
251
-1
709
2006
10.1017/S0022112093003581
Upward flow of air can support a thin layer of liquid on a plane wall\nagainst gravity. Such apparently stationary layers are for example\nsometimes seen on the windscreen of a car travelling at high speed\nin rain. We solve here the two-dimensional case of a layer whose\nlength is finite, but significantly greater than the meniscus length.\nThe flow is steady, with a fixed layer boundary, inside which there\nis a steadily circulating viscous liquid, and outside which the air\nexerts a traction which is assumed to have a known (small) constant\ndrag coefficient CD. The air also exerts a non-uniform pressure on\nthe liquid layer, of a magnitude determined by the shape of the layer,\nand the relationship between these two quantities can be obtained\nby thin-airfoil theory. In the lubrication approximation, the problem\ncan be reduced to a nonlinear singular integro-differential equation\nto determine the unknown shape of the layer boundary. This equation\nis solved numerically for various (small) wall angles, for cases\nwhere the effect of surface tension is confined to a small meniscus\nregion near the layer's leading edge. The numerical results indicate\nthat solutions exist only for walls whose inclination is less than\n0.70 C�D, and, for a range of inclinations below that maximum value,\nthat two distinct steady solutions can exist at each inclination.
Cumulative streams during the impact collapse of cavities in thin liquid layers
Journal of Applied Mechanics and Technical Physics
11
2
332-335
1972
10.1007/BF00908117
High-speed motion-picture photography has been used to study the dynamics of the impactr induced collapse of air-filled bubbles in thin layers of various liquids. The circular surface of the bubble is disruptive in an arbitrary manner during the collapse, and high-velocity cumulative streams arise. The stream parameters have been measured as functions of the initial experimental conditions. © 1972 Consultants Bureau.
Dynamics of a diverging liquid meniscus in a capillary, taking into account the specific properties of thin films
Journal of Applied Mechanics and Technical Physics
17
3
355-362
1977
10.1007/BF00853569
The theory of the diverging meniscus of a Newtonian liquid for capillary flow conditions at low meniscus velocities, in which the thermodynamic and Theological features of thin wetting films appear, is set forth. Two cases are considered: thermodynamically stable wetting film with high viscosity in the boundary layer on a completely wetted solid surface and a thermodynamically unstable film on a conditionally wetted solid surface exhibiting a liquid slip effect. © 1977 Plenum Publishing Corporation.
Molecular Mechanics
Accurate Molecular Structures Their Determination and Importance
117
1-10
1982
10.1007/978-90-481-3862-3
We present an extension of the generalized amber force field to allow the modeling of azobenzenes by means of classical molecular mechanics. TD-DFT calculations were employed to derive different interaction models for 4-hydroxy-4'-methyl-azobenzene, including the ground (S(0)) and S(1) excited state. For both states, partial charges and the -N=N- torsion potentials were characterized. On this basis, we pave the way to large-scale model simulations involving azobenzene molecular switches. Using the example of an isolated molecule, the mechanics of cyclic switching processes are demonstrated by classical molecular dynamics simulations.
Numerical methods in rock mechanics
International Journal of Rock Mechanics and Mining Sciences
39
4
409-427
2002
10.1016/S1365-1609(02)00065-5
The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures built on and in rock masses, and hence for supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating couplings between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized. Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference list, `significant' references are asterisked and `very significant' references are doubly asterisked.
coupled processes; design; numerical modelling; outstanding issues; review; rock mechanics
Thermo-mechanical fatigue behavior of an angle-ply SCS-6/Ti-15-3 metal matrix composite
Composites Science and Technology
52
1
47-59
1994
10.1016/0266-3538(94)90007-8
The response of the continuous-fiber-reinforced metal-matrix composite SCS-6/Ti-15-3 with orientation [±45]2s was investigated under fatigue conditions. Three temperature and load profiles were used to characterize the metal-matrix composite, namely: isothermal fatigue (IF) at 427°C, in-phase thermo-mechanical fatigue (IP-TMF) from 149°C to 427°C, and out-of-phase thermo-mechanical fatigue (OP-TMF) from 149°C to 427°C. At high stress levels (above 400 MPa) the [±45]2s laminate displayed in-phase, out-of-phase, and isothermal fatigue lives which were all within 1000 cycles. At these high stress levels the laminate exhibited the most detrimental fatigue response when subjected to the in-phase TMF profile. The IP-TMF and IF curves displayed equivalent fatigue lives at stress levels below 400 MPa. At these lower stress levels (below 400 MPa) the OP-TMF lives were approximately a factor of two lower than the IP-TMF and IF lives. Mechanical strain measurements, Young's modulus calculations, micromechanical analysis, acetate edge replication, metallography, and fractography were all employed to explain the damage mechanisms and their effects on the fatigue life of the laminate. The initial mode of damage for all specimens tested at all load-temperature profiles was fiber-matrix interfacial failures. Matrix plasticity, matrix cracking, fiber rotation, and fiber failures were evident at all applied stress levels in IP-TMF, OP-TMF, and IF. The degree of each of these mechanisms was dependent on both the applied stress level and the temperature profile.
fatigue; metal-matrix composites; silicon carbide fibers; thermo-mechanical fatigue; titanium matrix
Laminated anisotropic thin plate with an elliptic inhomogeneity
Mechanics of Materials
36
7
647-657
2004
10.1016/S0167-6636(03)00081-4
This work is concerned with a through-thickness elliptic elastic inhomogeneity in a laminated anisotropic elastic thin plate within the context of the Kirchhoff theory. By means of the octet formalism recently established by the authors, an exact closed-form solution is obtained, for the first time, for coupled stretching and bending deformations of the plate subjected to remote uniform membrane stress resultants and bending moments. The stress resultants inside the elastic elliptic inhomogeneity are uniform, which is consistent with the uniformity property of the Eshelby inclusion solution in three-dimensional elasticity. In two special limit cases where the elliptic inhomogeneity becomes an elliptic rigid inclusion or hole, the corresponding solutions are also obtained. A relation between the rotational moment and the rotation is given for the elliptic rigid inclusion problem. The concentration factors of hoop membrane stress resultants and hoop bending moments are given for the elliptic hole problem. The intensity factors of membrane stress resultants and moments are obtained for a Griffith crack. Displacements, slopes, membrane stress resultants and bending moments along the elliptic boundary for the elliptic inhomogeneity, rigid inclusion and hole problems are all presented in a real form. © 2003 Elsevier Ltd. All rights reserved.
Anisotropy; Approximation theory; Bending (deformation); Boundary conditions; Coupled stretching and bending; Crack; Elasticity; Hole; Inclusion; Inclusions; Inhomogeneity; Laminated plate; Laminated plates; Laminates; Octet formalism; Problem solving; Stress analysis; Stroh formalism
Micromechanical analysis of grid-reinforced thin composite generally orthotropic shells
Composites Part B: Engineering
39
627-644
2008
10.1016/j.compositesb.2007.06.005
This paper develops a comprehensive micromechanical model for the analysis of periodic thin composite shells with an embedded grid of generally orthotropic reinforcements. The use of generally orthotropic constituents renders the analysis more complicated than with simply isotropic reinforcements, but significantly enhances the applicability of the model. The model is derived on the basis of asymptotic homogenization and allows the determination of the effective elastic stiffnesses (coefficients) of the composite shells. These effective coefficients are only dependent on the structural make-up of the pertinent periodicity unit (referred to as unit cell) of the composite shell, and are completely independent of the global formulation of the problem. As such, they are universal in nature and can be used to study a wide variety of boundary-value problems. In the limiting case in which the shell reduces to a thin flat plate with periodicity in the two in-plane orthogonal directions, the derived model converges to that of previously obtained models. The model is illustrated by means of several examples of practical importance including cylindrical-reinforced shells, multi-layer shells, grid-reinforced plates and single-walled carbon nanotubes. ?? 2007 Elsevier Ltd. All rights reserved.
B. Anisotropy; C. Analytical modeling; C. Micro-mechanics; Composite shell (nominated)
The constitutive modeling of thin films with random material wrinkles
19th AIAA Applied Aerodynamics Conference
13471
2001
10.2514/6.2001-1347
Material wrinkles drastically alter the structural constitutive properties of thin films. Normally linear elastic materials, when wrinkled, become highly nonlinear and initially inelastic. Stiffness' reduced by 99% and negative Poisson's ratios are typically observed. This paper presents an effective continuum constitutive model for the elastic effects of material wrinkles in thin films. The model considers general two-dimensional stress and strain states (simultaneous bi-axial and shear stress/strain) and neglects out of plane bending. The constitutive model is derived from a traditional mechanics analysis of an idealized physical model of random material wrinkles. Model parameters are the directly measurable wrinkle characteristics of amplitude and wavelength. For these reasons, the equations are mechanistic and deterministic. The model is compared with bi-axial tensile test data for wrinkled Kapton® HN and is shown to deterministically predict strain as a function of stress with an average RMS error of 22%. On average, fitting the model to test data yields an RMS error of 1.2%
Inferring Mechanics of Web Censorship Around the World
Free and Open Communications on the Internet
2012
While mechanics ofWeb censorship in China are well studied, those of other countries are less understood. Through a combination of personal contacts and Planet-Lab nodes, we conduct experiments to explore the mechanics of Web censorship in 11 countries around the world, including China. Our work provides insights into the diversity of modus operandi of censors around the world and can guide future work on censorship evasion.
47 Gamification elements, mechanics and ideas - Gamified UK Blog
Gamified UK
2015
To go alone with the recent update to my User Types pages, I thought it would be nice to give you a list of mechanics, elements and ideas that can be used to support each type. These are by no means all there are, but these are the ones that I chose to include with my Gamification Inspiration Cards.
game elements; game mechanics; game thinking; mechanics; people; player types; user types
Homogenization and 2-Scale Convergence for a Stokes-Flow in a Thin Elastic Porous-Medium
Comptes Rendus De L Academie Des Sciences Serie Ii Fascicule B-Mecanique Physique Chimie Astronomie
321
6
211-216
1995
In the general framework of the homogenization method, we study the behaviour of a thin elastic periodic structure immersed in a viscous fluid. First we prove the convergence of the homogenization process by using the two-scale convergence method; it is possible to take the limit as delta --> 0, the small parameter which characterizes the thickness of the solid part. We obtain a viscoelastic medium with fading memory.
mechanics
A boundary integral equation formulation for large amplitude nonlinear vibration of thin elastic plates
Computer Methods in Applied Mechanics and Engineering
86
1
73-86
1991
http://dx.doi.org/10.1016/0045-7825(91)90139-W
An integral equation formulation for large amplitude free vibration of thin plates is presented. The Von Karman nonlinear plate bending theory is adopted. By using the harmonic balance method and discretizing both on the boundary and in the domain, the amplitude dependent eigenvalue equations are obtained. An appropriate iterative procedure is proposed to solve the nonlinear free vibration problems. A number of numerical examples are given to demonstrate its feasibility and efficiency.
On the calculation of gate tunneling currents in ultra-thin metal–insulator–semiconductor capacitors
Microelectronics Reliability
41
1
31-35
2001
10.1016/S0026-2714(00)00205-5
The calculation of gate tunneling currents in metal–insulator–semiconductor structures with ultra-thin gate stacks directly relies on quantum mechanical principles. In this paper, it is illustrated that well-known techniques based on elementary quantum physics and statistical mechanics can successfully be applied to solve some conceptual problems encountered on calculating the gate current and the charge distribution.
Computation of Thin-Plate Splines
SIAM Journal on Scientific and Statistical Computing
12
6
1304-1313
1991
10.1137/0912070
Thin-plate splines are an attractive method for interpolating and smoothing arbitrarily spaced points in the plane. A major problem in the application of thin-plate splines is that their computation involves the solution of a linear system that is illconditioned for large data sets. A technique for preconditioning the system is proposed that greatly extends the usefulness of thin-plate splines.
65D07; 65U05; bivariate splines; Dirichlet tessellation; ill-conditioned matrices; nonparametric regression; preconditioning; spatial regression; thin-plate splines
A continuum model for the flow of thin liquid films over intermittently chemically patterned surfaces
European Physical Journal-Special Topics
166
159-163
2009
10.1140/epjst/e2009-00899-5
It is known from both experiments and molecular dynamics simulations that chemically patterning a solid surface has an effect on the flow of an adjacent liquid. This fact is in stark contrast with predictions of classical fluid mechanics where the no-slip boundary condition is insensitive to the chemistry of the solid substrate. It has been shown that the influence on the flow caused by a steep change in the wettability of the solid substrate can be described in the framework of continuum mechanics using the interface formation theory. The present work extends this study to the case of intermittent patterning. Results show that variations in wettability of the substrate can significantly affect the flow, especially of thin films, which may have applications to the design of microfluidic devices.
Fracture Mechanics Ch01
Fracture Mechanics
1-10
2012
10.1016/B978-0-12-385001-0.00001-8
This chapter provides an overview on fracture mechanic concepts and discusses various fundamentals like failure of solids. Failure of solids and structures can take various forms. A structure may fail without breaking the material, such as in elastic buckling. However, failure of the material in a structure leads to failure of the structure. Fracture mechanics is a subject of engineering science that deals with failure of solids caused by crack initiation and propagation. There are two basic approaches to establish fracture criteria, or crack propagation criteria: crack tip stress field (local) and energy balance (global) approaches. In the crack tip field approach, the crack tip stress and displacement states are first analyzed and parameters governing the near tip stress and displacement fields are identified. A fundamental concept of fracture mechanics is to accept the theoretical stress singularity at the crack tip but not use the stress directly to determine failure/crack extension. This is based on the fact that the tip stress is limited by the yield stress or the cohesive stress between atoms and singular stresses are the results of linear elasticity. It is also recognized that the singular stress field is a convenient representation of the actual finite stress field if the discrepancy between the two lies in a small region near the crack tip. This notion is referred to as small-scale yielding.
classical failure theory; elastic-plastic fracture mechanics; Griffith theory; history of fracture mechanics; linear elastic fracture mechanics
Initial and progressive failure analysis of laminated composite structures under dynamic loading
Composite Structures
27
4
439-456
1994
10.1016/0263-8223(94)90270-4
The problem of theoretical prediction of the initial failure and ply-by-ply failure processes in laminated composite structures under dynamic loading is under consideration. A history of deformation can be predicted at any point of a structure using the proposed analytical techniques. The phenometological. second-order tensor-polynomial and maximum stress failure criteria are used to calculate the lower bound of an applied dynamic load. This lower bound corresponds to a start of failure in a structural part. A ply-by-ply failure model is then developed. Using the model, some higher bound for a critical dynamic load impulse value, corresponding to the total exhaustion of a load-bearing capacity by all of the layers in a laminated structure can be predicted. The analysis is applied to thin-walled imperfect laminated graphite/epoxy cylindrical shells, loaded with a short-time impulse of axial compression or external pressure. A general approach to the 3D dynamic deformation analysis of a brick-type mosaic plate and its interaction with a rigid impactor is proposed The approach allows one to model both the initial and damage induced inhomogeneities in a composite structure under dynamic impulsive or impact loading cases.
Mechanics of Materials
Studies in health technology and informatics
152
910-911
2008
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
Biocompatible Materials; Biocompatible Materials: chemistry; Biological; Biomechanics; Biomedical Engineering; Chemical; Models; Physics
Presentation of Newtonian Mechanics
American Journal of Physics
29
9
617
1961
10.1119/1.1937860
Classical mechanics is sketched in elementary terms, from a sophisticated point of view. It is stressed that no formulation of the laws of motion constitutes a complete theory, susceptible of being compared with experiment. Instead, what these laws do is to show how to formulatetheories of particular motions, by the introduction of (additional) laws of force. Because the basic force laws are simple in a suitable coordinate system, the over-all theory is simple, and useful, and is believed. The presentation given is designed for pedagogic use.
Fracture mechanics model for slip surface propagation in soil and rock masses
Second Annual ASCE Engineering Mechanics Specialty Conference
1
23-25
1977
Landslides on slopes of overconsolidated clay or clay shale seem typically to occur by the development of a narrow slip surface, possibly initiated by a stress concentration from cutting or erosion at the base of a slope, which then propagates upwards through the soil until the landslide instability occurs. Often the time scale of such "progressive failures" extends over several years and the problem of modelling them includes the identification of the physical origin of this time dependence. See the reviews by Skempton [1] and Bjerrum [2] for background. The shear crack mode of failure, dictated by the unstably falling stress vs. deformation diagrams for such materials, invalidates conventional Ulimiting equilibrium" approaches since the peak strength 'cannot generally be mobilized simultaneously over all the failure surface. A different approach was proposed by Palmer and Rice [3] based on tensile crack models with cohesive zones. In their model spatially continuous. deformation is assumed to give way, at peak strength, to localized shearing in a thin slip surface for which. the strength is some monotonically decreasing function. r(O), of the relative slip 6. Here r( o ) = T ,the peak strength, wheras T(O) approaches Tr , the residual strength, at sufficiently large 0 ; the function r(O) is dependent additionally on the "effective" compressive stress acting normal to the slip surface.
Clay shales; erosion; Failures; Landslides; peak ground acceleration; Rock mass; Rock mechanics
Pedestrian notes on quantum mechanics
Arxiv preprint grqc9411035
1994
I present an elementary essay on some issues related to nonrelativistic quantum mechanics, which is written in the spirit of extreme simplicity, making it an easy-to-read paper. Moreover, one can find a useful collection of ideas and opinions expressed by many well-known authors in this vast research field
Effect of residual stress on the indentation-induced interface delamination mechanism for a hard thin films on an ductile substrates
Gongcheng Lixue/Engineering Mechanics
30
1
69-75
2013
Hard thin films are often subjected to high loadings in the engineering applications. The shear and normal delaminations formed in the system including hard thin films and ductile substrates under the contact loading affect the reliability of the materials. The great residual stress in the hard thin films influences the interface between the films and the substrates, even resulting in the failure of the interface. In this paper, the effect of residual stress on the interface delamination of the hard thin films on ductile substrates is simulated by the cohesive model and finite element method. The critical indentation depth and critical load are obtained under alterable residual stress when the shear or normal delamination occurs, indicating the delamination mechanism induced by indentation. The failure mechanism map for the interface between the hard thin films and the ductile substrates is indicated when the residual stress is considered. This provides guidelines for engineering applications of thin films and the measurement of bonding behavior at the interface by using indentation.
Bonding behavior; Cohesive model; Computer simulation; Contact loading; Critical load; Delamination; Delamination mechanisms; Ductile substrate; Engineering applications; Failure (mechanical); Failure mechanism; Finite element method; Hard thin films; High loadings; Indentation; Indentation depth; Interface delamination; Loading; Residual stress; Residual stresses; Substrates
Factors affecting the interlaminar fracture energy of graphite/epoxy laminates
Proceedings of the 4th International Conference on Composite Materials, ICCM-IV
279-286
1982
The delamination fracture energy of graphite/epoxy composites has been examined utilizing a fracture mechanics approach. The material of primary interest was Hercules AS1/3501-6 with comparison testing on HMS/3501-6 and GY70/5208. The principal variables were moisture content, temperature and ply orientation. Both mode I opening and mode II shear stress fields were applied to specimens containing teflon strip notches.
Composite materials; Cracking (fracturing); Crack propagation; Epoxy laminates; Fracture mechanics; Fractures (materials); Fracture toughness; Graphite; Moisture
Stability and acoustic scattering in a cylindrical thin shell containing compressible mean flow
Journal of Fluid Mechanics
602
403-426
2008
Doi 10.1017/S0022112008001031
We consider the stability of small perturbations to a uniform inviscid compressible flow within a cylindrical linear-elastic thin shell. The thin shell is modelled using Flugge's equations, and is forced from the inside by the fluid, and from the outside by damping and spring forces. In addition to acoustic waves within the fluid, the system supports surface waves, which are strongly coupled to the thin shell. Stability is analysed using the Briggs-Bers criterion, and the system is found to be either stable or absolutely unstable, with absolute instability occurring for sufficiently small shell thicknesses. This is significantly different from the stability of a thin shell containing incompressible fluid, even for parameters for which the fluid would otherwise be expected to behave incompressibly (for example, water within a steel thin shell). Asymptotic expressions are derived for the shell thickness separating stable and unstable behaviour. We then consider the scattering of waves by a sudden change in the duct boundary from rigid to thin shell, using the Wiener-Hopf technique. For the scattering of an inbound acoustic wave in the rigid-wall section, the surface waves are found to play an important role close to the sudden boundary change. The solution is given analytically as a sum of duct modes. The results in this paper add to the understanding of the stability of surface waves in models of acoustic linings in aeroengine ducts. The oft-used mass-spring-damper model is regularized by the shell bending terms, and even when these terms are very small, the stability and scattering results are quite different from what has been claimed for the mass-spring damper model. The scattering results derived here are exact, unique and causal, without the need to apply a Kutta-like condition or to include an instability wave. A movie is available with the online version of the paper.
classification; duct; instability; layer; modes; radiation; sound; vortex sheet
Three-dimensional variational analysis of Pagano's problems for laminated composite plates
Composites Science and Technology
60
2407-2425
2000
10.1016/S0266-3538(00)00035-X
A brief survey of more than 50 previously published papers on numerical simulation of Pagano's 3-D (bidirectional bending) and 2-D (cylindrical bending) closed-form solutions for cross-ply and angle-ply composite plates is presented in the Introduction. Previous 3-D analysis approaches and numerical results obtained with the use of piece-wise polynomial splines and Bernstein polynomials are then reviewed. The major part of this work is devoted to the application of a novel 3-D displacement-assumed variational-analysis approach, which utilizes Bernstein basis functions in the three coordinate directions. Four classical transverse bending problems of laminated composite plates solved by Pagano are considered: (i) bidirectional transverse bending of simply supported cross-ply rectangular plates, (ii) cylindrical bending of simply supported cross-ply unsymmetric plates, (iii) cylindrical bending of single-layer monoclinic plates with different off-axis reinforcement angles, and (iv) cylindrical bending of simply supported angle-ply symmetric and unsymmetric plates. The problems (ii)-(iv) are 2-D (plane strain) in nature, and this feature has been utilized in Pagano's solutions. Nevertheless, the 3-D boundary value problem formulation used in the present work allows one to accurately simulate the cylindrical bending case and obtain numerical results that are nearly identical to the benchmark data for all of the examples solved. Overall, numerical results obtained in this work for all of the cases, (i)-(iv), are the closest to the benchmark data among up-to-date published results and can be used for future reference. (C) 2000 Elsevier Science Ltd. All rights reserved.
3-D elasticity; Analytical modeling; Computational modeling; Laminate mechanics; Layered structures; Plates; Stress analysis
Determination of the Intrinsic Stress-Strain Equation of Thin Polymer-Films from Stretching Experiments under Plane-Strain Tension
Polymer
34
13
2740-2749
1993
10.1016/0032-3861(93)90116-R
Thin films of amorphous poly(ethylene terephthalate) were stretched under plane-strain tension at temperatures from 20-degrees-C to 100-degrees-C and at various elongation-rates. It was observed that under such a deformation regime a neck is likely to form perpendicular to the tensile axis and to propagate steadily towards the gripped ends of the sample. The kinetics of the neck propagation was recorded carefully during the course of the tests by means of a photographic technique and the profile of the neck was analysed by quantitative microscopy during the propagation stage. It is shown that, under simple assumptions, the plastic constitutive equation of the material can be determined from this procedure in terms of the local effective stress versus the local effective strain and effective strain-rate at each of the temperatures investigated. It is demonstrated that the method employed is generally applicable to most ductile polymers.
films; necking; Neck propagation; plane-strain tension; Poly(ethylene terephthalate); solid polymers
Glancing angle deposition on a roll: Towards high-throughput nanostructured thin films
Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films
31
3
031507
2013
10.1116/1.4798947
Increasing the throughput of the powerful single-step glancing angle deposition (GLAD) method using a prototype simplified roll-to-roll (R2R) system has been explored. While the conventional GLAD technique is popular for fabricating nanostructured devices in a single deposition step, it is not a high-output process. To evaluate the feasibility of large area GLAD deposition, the authors examined the geometrical considerations required to eventually achieve GLAD in a roll-to-roll manufacturing system. Nominal deposition and rotation angles were mathematically translated to their effective R2R counterparts, allowing for deposition recipes of the archetype GLAD nanostructures (slanted posts, vertical posts, and square spirals) and the mechanics of the phi-sweep technique to be converted to this space. Representative structures were then deposited, and the phi-sweep technique successfully applied, in a prototype single barrel roller R2R experimental system. This prototype system provides a foundation for moving GLAD from the laboratory to mass production. (C) 2013 American Vacuum Society.
TAPE; TO-ROLL
Bohmian mechanics to high-order harmonic generation
Chin.phys.B
19
2
1-5
2010
10.1088/1674-1056/19/2/020302
This paper introduces Bohmian mechanics (BM) into the intense laser-atom physics to study high-order\nharmonic generation. In BM, the trajectories of atomic electron in an intense laser field can be\nobtained with the Bohm–Newton equation. The power spectrum with the trajectory of an atomic electron
bohmian mechanics; high-order harmonic generation
A critical survey of the 9-node degenerated shell element with special emphasis on thin shell application and reduced integration
Computer Methods in Applied Mechanics and Engineering
20
3
323-350
1979
10.1016/0045-7825(79)90007-0
Since the publication of Ahmad's degenerated thick shell element in 1970, a large number of authors have studied this simple type of element and made their proposals for improving its behaviour. Special emphasis was placed on thin plate and shell applications. The present paper discusses special aspects of the 9-node Lagrangian element. Interesting facts are presented-in particular, a mathematical explanation of why reduced shear integration leads to improved results. Another topic deals with thin plate and shell applications. A modification of the stiffness is proposed which allows the application of the element like a Kirchhoff-type model to any plate problem. In the final section a case study of a variety of proposed element models is presented, and the accuracy is shown for various plate and shell problems.
An evaluation of higher-order single crystal strength models for constrained thin films subjected to simple shear
Journal of the Mechanics and Physics of Solids
61
9
1935–1954
2013
10.1016/j.jmps.2013.04.007
Abstract An evaluation of different dislocation density-based strength models for a theory of micropolar single crystal plasticity is presented through detailed comparison with discrete dislocation dynamics simulations of a constrained thin film subjected to simple shear. The principal component of the evaluation is determining the most appropriate way to incorporate scale-dependent strengthening due to geometrically necessary dislocations (GNDs) within the model. We find that some models give results consistent with the discrete dislocation simulations, yet it is shown that models based on a generalized Taylor relation do not. Additionally, we briefly discuss the differences between models derived from unified (single) and independent (multiple) flow criteria, and demonstrate that single criterion models provide comparable predictive capability while introducing fewer nonlocal constitutive parameters.
Crystal plasticity; Discrete dislocation dynamics; Geometrically necessary dislocations; Micropolar; Strain gradient; <!– Tag Not Handled –><keyword id=#key0010#>Strain; Thin films
ON THE FINITE EXTENSION OF A VISCOELASTIC TWO-PLY FILAMENT YARN
Textile Research Journal
48
2
61-67
1978
The finite creep deformation of a two-ply filament yarn subjected to axial forces and twisting moments at both ends has been investigated. Each filament in the yarn is treated as a linearly viscoelastic slender curved rod. Analysis is based on the theory of finite deformation of slender curved rods. The extensional relaxation modulus of the filament is derived from a model of a three-element solid. Poisson's ratio is regarded as constant. Geometrical nonlinearity is introduced by reductions in the helical angle and cross section of the filament. Two problems have been considered - namely, the extension of a yarn with fixed ends, and the extension of a yarn with free ends. Effects of initial helical angle and of the superposition of a twisting moment on the axial extension of the yarn have also been included in the study.
MATHEMATICAL TECHNIQUES; VISCOELASTICITY; YARN
Compression Failure Mechanisms of Single-Ply, Unidirectional, Carbon-Fiber Composites
Sampe Quarterly-Society for the Advancement of Material and Process Engineering
23
3
29-36
1992
A single-ply composite compression test was used to study compression failure mechanisms as a function of fiber type, matrix type, and interfacial strength. Composites made with low- and intermediate-modulus fibers (Hercules AS4 and IM7) in either an epoxy (Hercules 3501-6) or a thermoplastic (ULTEM and LARC-TPI) matrix failed by kink banding and out-of-plane slip. The failures proceeded by rapid and catastrophic damage propagation across the specimen width. Composites made with high-modulus fibers (Hercules HMS4/3501-6) had a much lower compression strength. Their failures were characterized by kink banding and longitudinal splitting. The damage propagated slowly across the specimen width. Composites made with fibers treated to give low interfacial strength had low compression strength. These composites typically failed near the specimen ends and had long kink bands.
epoxy; kinking; superposed hydrostatic-pressure
A model of composite laminated Reddy plate based on new modified couple stress theory
Composite Structures
94
7
2143-2156
2012
10.1016/j.compstruct.2012.02.009
Based on new modified couple stress theory a model for composite laminated Reddy plate is developed in first time. In this theory a new curvature tensor is defined for establishing the constitutive relations of laminated plate. The characterization of anisotropy is incorporated into higher-order laminated plate theories based on the modified couple stress theory by Yang et al. in 2002. The form of new curvature tensor is asymmetric, however it can result in same as the symmetric curvature tensor in the isotropic elasticity. The present model of thick plate can be viewed as a simplified couple stress theory in engineering mechanics. Moreover, a more simplified model for cross-ply composite laminated Reddy plate of couple stress theory with one material’s length constant is used to demonstrate the scale effects. Numerical results show that the present plate model can capture the scale effects of microstructure. Additionally, the present model of thick plate model can be degenerated to the model of composite cross-ply laminated Kirchhoff plate and Mindlin plate of couple stress theory.
composite laminated reddy plate; material length parameter; modified couple stress
Quantum Chaos and Semiclassical Mechanics
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
1992
50-65
1992
This paper discusses the problem of finding and defining chaos in quantum mechanics. While chaotic time evolution appears to be ubiquitous in classical mechanics, it is apparently absent in quantum mechanics in part because for a bound, isolated quantum system, the evolution of its state is multiply periodic. This has led a number of investigators to search for semiclassical signatures of chaos. Here I am concerned with the status of semiclassical mechanics as a distinct third theory of the asymptotic domain between classical and quantum mechanics. I discuss in some detail the meaning of such crucial locutions as the "classical counterpart to a quantum system" and a quantum system's "underlying classical motion". A proper elucidation of these concepts requires a semiclassical association between phase space surfaces and wave-functions. This significance of this association is discussed in some detail., Volume Two: Symposia and Invited Papers
The Probabilistic Argument for a Non-Classical Logic of Quantum Mechanics
Philosophy of Science
33
1
14-21
1966
10.1086/288067
The aim of this paper is to state the single most powerful argument for use of a non-classical logic in quantum mechanics. In outline the argument is the following. The working logic of a science is the logic of the events and propositions to which probabilities are assigned. A probability should be assigned to every element of the algebra of events. In the case of quantum mechanics probabilities may be assigned to events but not, without restriction, to the conjunction of two events. The conclusion is that the working logic of quantum mechanics is not classical. The nature of the logic that is appropriate for quantum mechanics is examined.
Growth patterns and bending mechanics of branches
Trees - Structure and Function
5
4
232-238
1991
10.1007/BF00227530
P Castera/Inra/CNRS/Rheol Bois Bordeaux Lab/Domaine Hermitage/BP 10/F-33610 Gazinet Cestas, France
Bohmian mechanics without wave function ontology
Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
44
4
365-378
2013
10.1016/j.shpsb.2013.07.004
In this paper, I critically assess different interpretations of Bohmian mechanics that are not committed to an ontology based on the wave function being an actual physical object that inhabits configuration space. More specifically, my aim is to explore the connection between the denial of configuration space realism and another interpretive debate that is specific to Bohmian mechanics: the quantum potential versus guidance approaches. Whereas defenders of the quantum potential approach to the theory claim that Bohmian mechanics is better formulated as quasi-Newtonian, via the postulation of forces proportional to acceleration; advocates of the guidance approach defend the notion that the theory is essentially first-order and incorporates some concepts akin to those of Aristotelian physics. Here I analyze whether the desideratum of an interpretation of Bohmian mechanics that is both explanatorily adequate and not committed to configuration space realism favors one of these two approaches to the theory over the other. Contrary to some recent claims in the literature, I argue that the quasi-Newtonian approach based on the idea of a quantum potential does not come out the winner. © 2013 Elsevier Ltd.
Bohmian mechanics; Causation; Explanation; Quantum mechanics; Quantum potential; Wave function
Application of fracture mechanics to railway components
Materialprufung
46
7-8
354-362
2004
The paper gives an overview on the most relevant fracture mechanics issues for railway components with the main focus on highly safety relevant structures such as axles, wheels and rails. Several patterns of damage observed in practical application are briefly addressed with respect to their potential integration in fracture mechanics based design and maintenance concepts.
Static and vibration analysis of axi-symmetric angle-ply laminated cylindrical shell using state space differential quadrature method
International Journal of Pressure Vessels and Piping
86
11
738-747
2009
10.1016/j.ijpvp.2009.07.002
In this study, static and free vibration characteristics of anisotropic laminated cylindrical shell with various end conditions are considered by making the use of differential quadrature method (DQM). Equations of motion are derived based on three-dimensional theory of elasticity. Applying the state space in conjunction with DQM to the governing differential equations and to the edges boundary conditions in term of displacements, new state equations at discrete points are derived. By solving the obtained state equations, static and frequency behavior of laminated shell are evaluated. To ensure the accuracy of the present approach, comparisons are made with those for the shell with simply supported edges which can be solved analytically. Finally, the effect of edges condition on the static and vibration behaviour of shell is investigated. ?? 2009 Elsevier Ltd. All rights reserved.
Differential quadrature; Laminated shell; State space; Static; Vibration
Quantum Mechanics in a Rotating Frame
Physics
1-8
2003
The rotating frame is considered in quantum mechanics on the basis of the\nposition dependent boost relating this frame to the non rotating inertial\nframe. We derive the Sagnac phase shift and the spin coupling with the rotation\nin the non relativistic limit by a simple treatment. By taking the low energy\nlimit of the Dirac equation with a spin connection, we obtain the Hamiltonian\nfor the rotating frame, which gives rise to all the phase shifts discussed\nbefore. Furthermore, we obtain a new phase shift due to the spin-orbit\ncoupling.
Quantum Physics
Contact mechanics
getcited.org
468
1987
... Post a Comment. CONTRIBUTORS: Author: Johnson , KL (b. 1925, d. ----. PUBLISHER: ... VOLUME/EDITION: PAGES (INTRO/BODY): xi, 452 p. SUBJECT(S): Mechanics, Applied; Surfaces (Technology); Rolling contact; Contact mechanics . DISCIPLINE: No discipline assigned. ...
Thin melanoma.
Archives of pathology & laboratory medicine
135
3
342-346
2011
10.1043/2009-0479-RA.1
The incidence of malignant melanoma is increasing and a preponderance of the melanomas diagnosed today are "thin in terms of Breslow criteria. Although thin melanomas, as a group, are associated with a very good prognosis, a subset of these tumors may metastasize and cause death. These cases can be identified by using prognostic models, including the "standard" American Joint Committee on Cancer criteria, and other attributes identified in follow-up studies.
Multi-directional stiffness degradation induced by matrix cracking in composite laminates
International Journal of Fatigue
24
2-4
119-125
2002
10.1016/S0142-1123(01)00066-4
A model was developed for predicting the stiffness degradation of fiber reinforced plastics (FRP), with ply configuration [0m/±θn]S, induced by matrix cracking under in-plane tension. The model assumes that the cracks in off-axis plies are uniformly distributed and a damage variable D is defined. Based on the theory of fracture mechanics, the elastic moduli of cracked matrix are obtained and indicated by the damage variable D, then the reduction of elastic moduli of laminates caused by the matrix cracks was studied. Comparison with experimental values for the glass/epoxy [903/0]S, [0/90]S and [0/±45]S laminates shows good agreement with the theoretical prediction given by the presented model.
Fatigue damage; Matrix crack; Matrix crack saturation state; Stiffness degradation
MECHANICS OF SELF-REPRODUCTION
Annals of Human Genetics
23
59-72
1958
10.1111/j.1469-1809.1958.tb01442.x
The construction of various types of machines which can be automatically self-reproducing, in a sense derived from von Neumann, has been outlined. The features, which any such machine must possess, have been discussed and their possible significance in the understanding of DNA replication has been indicated.I am much indebted to Dr C. A. B. Smith for his valuable suggestions in the interest of making this paper comprehensible, and to Mr A. J. Lee for his admirable drawings.
A simple atomic force microscopy calibration method for direct measurement of surface energy on nanostructured surfaces covered with molecularly thin liquid films.
The Review of scientific instruments
80
5
055109
2009
10.1063/1.3136908
A simple calibration method is described for the determination of surface energy by atomic force microscopy (AFM) pull-off force measurements on nanostructured surfaces covered with molecularly thin liquid films. The method is based on correlating pull-off forces measured in arbitrary units on a nanostructured surface with pull-off forces measured on macroscopically smooth dip-coated gauge surfaces with known surface energy. The method avoids the need for complex calibration of the AFM cantilever stiffness and the determination of the radius of curvature of the AFM tip. Both of the latter measurements are associated with indirect and less accurate measurements of surface energy based on various contact mechanics adhesion models.
Atomic Force; Atomic Force: methods; Atomic Force: standards; Calibration; Lubricants; Microscopy; Nanostructures; Nanostructures: chemistry; Surface Properties
Dynamic properties of density graded thin-walled metal hollow sphere arrays
Mechanics of Advanced Materials …
2012
10.1080/15376494.2011.627642
In order to improve the dynamic properties of uniform cellular materials, a 2D density graded metal hollow sphere (MHS) array is investigated by explicit FEM simulation of in-plane crushing of sphere systems. The grading is established by changing sphere wall thickness ... \n
Remarks on gravity and quantum mechanics
Quantum
7
2010
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Quantum Statistical Mechanics. III. Equilibrium Probability
arXiv
22
2014
Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.
Macroscopic Fracture Mechanics of Advanced Composite Materials
Journal of Composite Materials
5
446-454
1971
10.1177/002199837100500402
The application of classical fracture mechanics to laminated com posites is discussed. A convenient method is presented for predicting the static strength of a flawed specimen. Theoretical predictions are compared with experimental data for specimens containing two types of flaws.
Conformal and superconformal mechanics revisited
Nuclear Physics B
677
485-500
2004
10.1016/j.nuclphysb.2003.10.015
We find, at the Lagrangian off-shell level, the explicit equivalence transformation which relates the conformal mechanics of De Alfaro, Fubini and Furlan to the conformal mechanics describing the radial motion of the charged massive particle in the Bertotti-Robinson AdS2×S2 background. Thus we demonstrate the classical equivalence of these two systems which are usually regarded as essentially different "old" and "new" conformal mechanics models. We also construct a similar transformation for N=2, SU(1,1 1) superconformal mechanics in N=2 superfield formulation. Performing this transformation in the action of the N=2 superconformal mechanics, we find an off-shell superfield action of N=2 superextension of Bertotti-Robinson particle. Such an action has not been given before. We show its on-shell equivalence to the AdS2 superparticle action derived from the spontaneous partial breaking of SU(1,1 1) superconformal symmetry treated as the N=2 AdS2 supersymmetry. © 2003 Elsevier B.V. All rights reserved.
AdS/CFT; Conformal mechanics; Superparticle
Interpreting Quantum Mechanics according to a Pragmatist Approach
Foundations of Physics
38
9
843-868
2008
10.1007/s10701-008-9240-2
The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in micro-physics, and third, in showing that quantum mechanics is the only theorywhich fulfils exactly these functions.
instrumentalism; interpretation; pragmatism; quantum mechanics
Probabilistic fracture mechanics application to highway bridges
Engineering Fracture Mechanics
37
5
969-985
1990
10.1016/0013-7944(90)90021-8
A probabilistic fracture mechanics model was developed for determining the risk of fatigue failure of steel highway bridges. A deterministic fracture mechanics calculation of crack growth with stochastic inputs for crack growth rate, fracture toughness, initial crack size and load history was used. Stress intensity expressions were compiled from literature for typical AASHTO category bridge details. Statistical distributions for input variables were derived from data reported in literature. The model was found to predict well the short service life of the Yellow Mill Pond Bridge in Connecticut.
The algebraic entropy of classical mechanics
Journal of Mathematical Physics
44
7
23
2002
10.1063/1.1576904
We describe the `Lie algebra of classical mechanics', modelled on the Lie algebra generated by kinetic and potential energy of a simple mechanical system with respect to the canonical Poisson bracket. It is a polynomially graded Lie algebra, a class we introduce. We describe these Lie algebras, give an algorithm to calculate the dimensions cn of the homogeneous subspaces of the Lie algebra of classical mechanics, and determine the value of its entropy limntoinfty cn 1/n. It is $1.82542377420108..., a fundamental constant associated to classical mechanics.
Fundamentals of Mechanics of Robotic Manipulation
Meccanica
41
2
233-236
2006
10.1007/s11012-005-2920-5
"Manipulation" refers to a variety of physical changes made to the world around us. Mechanics of Robotic Manipulation addresses one form of robotic manipulation, moving objects, and the various processes involvedgrasping, carrying, pushing, dropping, throwing, and so on. Unlike most books on the subject, it focuses on manipulation rather than manipulators. This attention to processes rather than devices allows a more fundamental approach, leading to results that apply to a broad range of devices, not just robotic arms.The book draws both on classical mechanics and on classical planning, which introduces the element of imperfect information. The book does not propose a specific solution to the problem of manipulation, but rather outlines a path of inquiry.
Point Transformations in Quantum Mechanics
Physical Review
85
4
653-661
1952
10.1103/PhysRev.85.653
An isomorphism is shown to exist between the group of point transformations in classical mechanics and a certain subgroup of the group of all unitary transformations in quantum mechanics. This isomorphism is used to indicate that the quantum analogs of physically significant classical expressions can be constructed uniquely in any coordinate system. There is no ambiguity in the ordering of noncommuting quantum operators, and the method of constructing the quantum analogs is covariant under general coordinate transformations. The method is actually only applicable to systems having Lagrangians which are at most quadratic in the velocities, but this includes all systems which are presently of interest in physics. The method is applied to two intrinsically nonlinear examples, one of which is the gravitational field. The correct Hamiltonian operator for a quantized version of Einstein's gravitational theory is constructed.
Statistical mechanics of combinatorial search
Proceedings Workshop on Physics and Computation. PhysComp '94
1994
The statistical mechanics of combinatorial search problems is\ndescribed using the example of the well-known NP-complete graph coloring\nproblem. A simple parameter describing the problem structure predicts\nthe difficulty of solving the problem, on average. However, because of\nthe large variance associated with this prediction, it is of limited\ndirect use for individual instances. Additional parameters, describing\nthe problem structure as well as the heuristic effectiveness, are\nintroduced to address this issue. This also highlights the distinction\nbetween the statistical mechanics of combinatorial search problems, with\ntheir exponentially large search spaces, and physical systems, whose\ninteractions are often governed by a simple Euclidean metric
Matrix elasticity perturbation and Lamin-A/C expression in stem cells modulate their mechanics and lineage specification
American Physical Society, APS March Meeting 2012
2012
Commitment of stem cells to different lineages is regulated by many cues in their local microenvironment. They are particularly sensitive to the mechanical properties of their extracellular matrix. Nuclear lamins are fibrous proteins providing structural function and transcriptional regulation in the cell nucleus. In particular Lamin A/C levels could influence cellular mechanical sensitivity. Here we show that perturbation of the extracellular matrix and nucleus mechanics can direct stem cells lineage specification. We studied the behavior of human mensechymal stem cells (hMSC) cultured on thin highly ordered collagen nanofilms. To tune the mechanical properties of the nanofilms we used the enzyme transglutaminase as a crosslinking agent. AFM imaging and manipulation is used to examine the nano topography and mechanical properties of the films and cells. Film stiffening affects cells morphology, cytoskeleton organization and their elastic response. hMSCs cultured for two weeks on collagen nanofilms initially tune their stiffness with matrix elasticity but later continuously change it with time. We observed upregulation of osteogenic markers on cross-linked films and increased lamin A/C expression. We show that manipulating Lamin-A/C expression in stem cells also directs cell lineage with knockdown favoring adipogenesis and over expression favoring osteogenesis. We found positive correlation between matrix and nucleus mechanics and that they have a synergistic effect on hMSCs differentiation potential.
Geophysical Aspects of Non-Newtonian Fluid Mechanics
Geomorphological Fluid Mechanics
34-51
2001
doi: 10.1007/3-540-45670-8_2
Non-Newtonian fluid mechanics is a vast subject that has several journals partly, or primarily, dedicated to its investigation (Journal of Non-Newtonian Fluid Mechanics, Rheologica Acta, Journal of Fluid Mechanics, Journal of Rheology, amongst others). It is an area of active research, both for industrial fluid problems and for applications elsewhere, notably geophysically motivated issues such as the flow of lava and ice, mud slides, snow avalanches and debris flows. The main motivation for this research activity is that, apart from some annoyingly common fluids such as air and water, virtually no fluid is actually Newtonian (that is, havinga simple linear relation between stress and strain-rate characterized by a constant viscosity). Several textbooks are useful sources of information; for example, [1],[2],[3] are standard texts giving mathematical and engineering perspectives upon the subject. In these lecture notes, Ancey's chapter on rheology (Chap. 3) gives further introduction.
Mechanics of failure mechanisms in structures
Solid Mechanics and its Applications
191
1-106
2013
10.1007/978-94-007-4930-6_1
This bookexamines the mechanisms and underlying mechanics of failure in materials including metals, ceramics, polymers, composites and bio-materials.Covers fracture, fatigue, buckling, bio-material failure in prosthetic heart valves and hip joints and more." Failures in Chap. 1 of metals include time independent and time dependent tensile and compressive loading for both static and dynamic cases. Both theoretical and experimental results are presented. Chapter 2 includes a consideration of the basic elements of fracture mechanics, the effects of toughness gradients, and the effects creep induced brittleness. The statistical, bimodal character ofmulti-site fatigue cracking in the small crack regime is discussed in Chap. 3. The use of the range of the stress intensity factor in computing the rate of fatigue crack growth rate in the long crack regime, the effects of variable amplitude loading including tensile and compressive overloading, and environment effects are also discussed. Failure mechanisms in ceramic composites, polymeric composites and metallic composites are discussed in Chaps. 4, 5 and 6. Failures in biomaterials are discussed in Chap. 7. Failure mechanisms in systems with multiple structural elements are discussed in Chap. 8.
Statistical mechanics based on Renyi entropy
Physica A
280
3-4
337-345
2000
10.1016/S0378-4371(00)00007-8
In this work we show that it is possible to obtain a generalized statistical mechanics (thermostatistics) based on Renyi entropy, to be maximized with adequate constraints. The equilibrium probability distribution thus obtained has a very interesting property. Indeed, it reminds us the statistical distribution proposed by Tsallis, known to conveniently describe a variety of phenomena in nonextensive systems. Moreover, some examples are worked out in order to illustrate the main features of the herein introduced formalism. (C) 2000 Elsevier Science B.V. All rights reserved
1; 150; 2000; ANOMALOUS DIFFUSION; BACKGROUND-RADIATION; constraint; distribution; Distributions; entropy; Equilibria; Equilibrium; formalism; FORM INVARIANCE; generalized; in; main; mechanic; mechanics; NONEXTENSIVE STATISTICS; order; out; probability; property; Renyi entropy; statistical; statistical mechanics; Statistical-Mechanics; system; Systems; THERMODYNAMIC STABILITY CONDITIONS; thermostatistics; TSALLIS STATISTICS; UNIVERSE; work
Mechanics-based kinematic modeling of a continuum manipulator
2013 IEEE/RSJ International Conference on Intelligent Robots and Systems
5052-5058
2013
10.1109/IROS.2013.6697087
A continuum manipulator with triangular notches is proposed for the potential medical applications, which is driven in the plane by wires embedded in bilateral symmetry channels. The focus of this present research is a mechanics-based kinematic model of the proposed continuum manipulator using the Timoshenko beam theory to map the driven load to the manipulator shape. In the proposed model, the continuum manipulator is divided into several V-shape units, each of which consists of two 2-node Timoshenko beam elements. Compared with previous approaches, our proposed model discards the constant curvature approximation, in which the distributed force caused by the interface contact between the wire and the V-shape unit is also considered simultaneously. The proposed mechanics model is validated experimentally on a segment of Nitinol flexible manipulator, which illustrates the effectiveness of our model to describe the continuum manipulator shaping.
2-node Timoshenko beam elements; bilateral symmetry channels; constant curvature approximation; continuum manipulator shaping; continuum mechanics; distributed force; flexible manipulators; Force; interface contact; Kinematics; manipulator kinematics; Manipulators; mechanics-based kinematic modeling; medical applications; Nitinol flexible manipulator; Robot kinematics; Timoshenko beam theory; triangular notches; Vectors; V-shape units; wires; Wires
The classical and quantum mechanics of a particle on a knot
Annals of Physics
359
20-30
2015
10.1016/j.aop.2015.04.004
A free particle is constrained to move on a knot obtained by winding around a putative torus. The classical equations of motion for this system are solved in a closed form. The exact energy eigenspectrum, in the thin torus limit, is obtained by mapping the time-independent Schrodinger equation to the Mathieu equation. In the general case, the eigenvalue problem is described by the Hill equation. Finite-thickness corrections are incorporated perturbatively by truncating the Hill equation. Comparisons and contrasts between this problem and the well-studied problem of a particle on a circle (planar rigid rotor) are performed throughout.
Statistical mechanics of magnetic bubble arrays. {I. Topology} and thermalization
Phys. Rev. B
46
9
5142--
1992
Bubble domains in thin magnetic garnet films are an experimentally\naccessible two-dimensional system with well-characterized properties.\nBubble arrays can be directly viewed with polarized light using optical\nmicroscopy, digital imaging, and computer-video techniques. The structure\nand dynamics of topological defects can be studied in detail. We\npresent observations of the interactions and dynamics of defects\nin magnetic bubble arrays. Quasithermal Brownian motion of bubbles\nin an applied ac magnetic field arises from microscopic substrate\nroughness. Experimental measurements of diffusive bubble motion are\nused to estimate the effective temperature, and the effective pinning\nenergy and length scales for microscopic roughness in the garnet\nfilm.
RF magnetron sputtered crystalline TiNiCu shape memory alloy thin Film
Smart Structures and Materials 2001: Active Materials: Behavior and Mechanics
4333
207-213
2001
10.1117/12.432758
Shape memory alloys (SMAs) offer a unique combination of novel properties, such as shape memory effect, super-elasticity, biocompatibility and high damping capacity, and thin film SMAs have the potential to become a primary actuating mechanism for micro-actuators. In this study, TiNiCu films were successfully prepared by mix sputtering of a Ti55Ni45 target with a separated Cu target. Crystalline structure, residual stress and phase transformation properties of the TiNiCu films were investigated using X-ray diffraction (XRD), differential scanning calorimeter (DSC), and curvature measurement methods. Effects of the processing parameters on the film composition, phase transformation and shape-memory effects were analyzed. Results showed that films prepared at high Ar gas pressure exhibited a columnar structure, while films deposited at a low Ar gas pressure showed smooth and featureless structure. Chemical composition of TiNiCu thin films was dependent on the DC power of copper target. DSC, XRD and curvature measurement revealed clearly the martensitic transformation of the deposited TiNiCu films. When the freestanding film was heated and cooled, a "two-way" shape memory effect can be clearly observed.
deposition; martensite; shape memory alloys; sputter-deposition; Ti-Ni-Cu thin film; transformation
Asymmetric Cold Rolling of Thin Strip with Roll Edge Kiss
Industrial Electronics and Applications, 2007. ICIEA 2007. 2nd IEEE Conference on
2781-2786
2007
Asymmetric rolling can reduce the thickness of rolled strip and rolling load significantly. In this paper, the asymmetric cold rolling of thin strip with roll edge kiss was analysed theoretically and the rolling pressure, intermediate force between the work roll and backup roll, the work roll edge kiss force, the strip profile after rolling are obtained for this special asymmetric rolling. The rolling pressure, intermediate force, roll edge kiss force and the strip profile are compared for various roll speed ratios, reduction and friction coefficients. Simulation result shows that the roll speed ratio and reduction have a significant influence on the profile of rolled strip, and the calculated rolling forces are consistent with the measured values. The effect of friction in the roll bite on mechanics of the asymmetric cold rolling of thin strip with roll edge kiss is also discussed.
asymmetric cold rolling; cold rolling; friction; friction coefficients; roll edge kiss; strip profile; strips; thin strip
Axial Impact Performance of Aluminium Thin Cylindrical Tube
Applied Mechanics and Materials
315
1-5
2013
10.4028/www.scientific.net/AMM.315.1
One of the important objectives in this research is investigating the behavior on the cylindrical tube structure via computer simulations. When a thin cylindrical structure is experienced an impact loading, the crushing process on impact can only be observed by a high speed camera. Recording the stress and strain data is also not possible experimentally. A numerical approach implementing finite element method with a dynamic-explicit code is an effective solution to observe the crushing process. A thin cylindrical structure found in aluminium can is modeled. A finite element impact simulation is then performed to observe the crushing process sequence and the stress and strain development history on axial impact employing IMPACT application program. An experimental of thin cylindrical structure on axial impact is conducted. The final crushing pattern after the impact is then compared with that from simulation. The result shows that final crushing pattern is in a good agreement with that shown in experiment. The stress and strain histories can be observed from the simulation. © (2013) Trans Tech Publications, Switzerland.
Finite element method; Impact; Simulation; Vertical impact tester
Dynamic characteristics of cylindrical hybrid panels containing viscoelastic layer based on layerwise mechanics
Composites Part B: Engineering
38
159-171
2007
10.1016/j.compositesb.2006.07.002
The viscoelastic damping model of the cylindrical hybrid panels with co-cured, free and constrained layers has been developed and investigated by using the refined finite element method based on the layerwise shell theory. The transverse shear and normal strains and the curved geometry are exactly taken into account in the present layerwise shell model, which can depict the zig-zag in-plane and out-of-plane displacements. The damped natural frequencies, modal loss factors and frequency response functions of cylindrical viscoelastic hybrid panels are compared with those of the base composite panel without a viscoelastic layer. The difference in the free vibration and damping of the thin and thick composite laminates and the viscoelastic sandwiched beam between full and partial layerwise theories is verified by comparison with the published results. Various damping characteristics of cylindrical hybrid panels with free viscoelastic layer, constrained layer damping, and co-cured sandwich laminates are investigated. Present results show that the full layerwise damping model accurately predicted the vibration and damping of the cylindrical hybrid panels with viscoelastic layers. ?? 2006.
A. Hybrid; B. Vibration; C. Finite element analysis
Fluid mechanics of the atmosphere
Journal of Atmospheric and Terrestrial Physics
58
1191
1996
10.1016/S0021-9169(96)90062-8
Fluid Mechanics of the Atmosphere presents the fundamental equations which govern most of the flow problems studied by atmospheric scientists. The equations are derived in a systematic way that is intended to facilitate critical evaluation. The goal of this text is twofold. First the book supplies the student a background familiarity in the underlying physics behind the mathematics. Second it explores some systematic methods of relating these physics to atmospheric problems, including rotating frames of reference effects, vorticity dynamics, and turbulence effects on closure.Key Features* Stresses vorticity, principles of scaling, and turbulence* Extensively illustrated* Includes end-of-chapter summaries and problem sets* Classroom tested for five years
Microsystems and mechanics
Procedia IUTAM
10
138-160
2013
10.1016/j.piutam.2014.01.015
Study, design and industrial production of microsystems implies complex processes in which many disciplines like physics, chemistry, material science, electronics and mechanics play a central role. This paper contains an overview of important mechanical aspects in design and reliability of microsystems. Starting from the past nine years experience of the research group with reference to real devices, some key mechanical issues are discussed which concern dissipative phenomena inducing damping in vibrating devices, mechanical characterization of materials at the scale of micron, consequences of impacts due to accidental drop and spontaneous adhesion or stiction phenomena. ?? 2013 Published by Elsevier Ltd.
Accidental drop; Damping; Mechanical reliability; MEMS; Microsystems; Resonators; Stiction
Classical Mechanics and Entropy
Foundations of Physics
6
4
327-337
1993
10.1007/BF00665652
This note addresses a problem of nineteenth century applied mathematics-- is it possible in the context of Hamiltonian mechanics to define a function S of the generalized coordinates and momenta which is monotonieally increasing along orbits? The question is of interest, because, for a sytem not in thermodynamic equilibrium, entropy should increase strictly monotonically along an orbit, and a negative answer implies that mechanical principles different from those of Haxniltonian mechanics must be introduced to explain thermodynamics. This note answers the question rigorously for Hamiltonian systems confined to an invariant region of finite volume in phase space; it is not possible to define a eontinuous function which increases monotonically along orbits. An appendix gives a translation of an 1889 paper of Poincaré addressing the same issue
constant of the motion; entropy; hamiltonian mechanics; nonequilibrium thermodynamics; poincaré; poincaré recurrence theorem; the science of thermodynamics
Formulation of turbulence mechanics
Physical Review E
69
5
056317
2004
10.1103/PhysRevE.69.056317
This paper presents a setup of turbulence mechanics for averaged description of turbulence, founded on laws of momentum, moment of momentum, and energy, complemented by common rheological principles for formulating constitutive relations between generalized forces and generalized velocities of the description. A kinematical-geometrical principle is adopted to determine internal rotating degrees of freedom of turbulent media generated by the eddy structure of turbulent flow fields. The connection between the formulated mechanics and some models (as K-ε model), widely used in practical engineering flow calculations, is established. As an example, the formulated mechanics is applied to describe some classical flow patterns.
Geometrical description of quantum mechanics—transformations and dynamics
Physica Scripta
82
3
038117
2010
10.1088/0031-8949/82/03/038117
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the study of separability and entanglement for states of composite quantum systems.
Quantum Mechanics interpreted in Quantum Real Numbers
Quantum
26
2002
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms of quantum mechanics are re-interpreted. Our aim is to show that, when formulated in the language of quantum real numbers, the laws of quantum mechanics appear more natural, less counterintuitive than when they are presented in terms of standard numbers.
Canonical Ensemble in Non-extensive Statistical Mechanics
arXiv:1503.03778
5
1-15
2015
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. However, the non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. This procedure can leave physical principles unclear. In this article we investigate the canonical ensemble in the non-extensive statistical mechanics using a more traditional way, by considering a small system interacting with a large reservoir via short-range forces. The reservoir is characterized by generalized entropy instead of the Boltzmann-Gibbs entropy. Assuming equal probabilities for all available microstates we derive the equations of the non-extensive statistical mechanics. Such a procedure can provide deeper insight into applicability of the non-extensive statistics.
Liquid Thin Film Hydrodynamics: Dewetting and Pattern Formation
Mechanics over Micro and Nano Scales
193-215
2011
Doi 10.1007/978-1-4419-9601-5_6
Ultra-thin polymer films become unstable due to various types of interaction forces like van der Waals interaction, steric forces, molecular level recoiling, sudden release of residual stresses or due to the presence of defects on substrate or the film, resulting in disintegration and rupture of the film, which is also associated with morphological evolution and formation of mesoscale surface features. In this chapter we introduce the concept of dewetting first, followed by a brief theoretical discussion on the conditions under which a thin liquid film can spontaneously become unstable, based on a linear stability analysis. We subsequently discuss the morphological evolution sequence under true experimental conditions. The instability-mediated structures are inherently random and isotropic, thereby having limited practical utility. We discuss how dewetting on a topographically patterned substrate might be useful in imposing long-range order to the dewetted structures. Finally, we discuss some recent developments on suppressing dewetting in unstable film by incorporation of nanoparticles or nanofillers in extremely low amount to the polymer matrix. This approach of stabilizing ultra-thin films will be extremely useful from the standpoint of coatings, which should not degrade and disintegrate with time.
behavior; cross-linking; dynamics; instability; morphology; polymer-films; polystyrene films; rupture; silsesquioxane; solid-surfaces
Scaling, percolation and coarsening in epitaxial thin film growth
Physica A: Statistical Mechanics and its Applications
266
173-185
1999
10.1016/S0378-4371(98)00589-5
The results of recent theoretical and simulational studies of submonolayer and multilayer homoepitaxial growth is discussed. In the submonolayer regime, the results provide a quantitative explanation for the variation of the island density, critical island size island morphology and size distribution and island coalescence and percolation as a function of temperature and deposition rate. In multilayer growth, a realistic model for homoepitaxial growth on fcc and bcc lattices is presented which takes into account the correct crystal structure. The effects of instabilities which lead to mound formation and coarsening are discussed. An accurate prediction of the observed mound angle for Fe/Fe(1 0 0) deposition is obtained analytically and by kinetic Monte Carlo simulations. The general dependence of the mound angle, and mound coarsening behavior on temperature, deposition rate, and strength of the step barrier in bcc(1 0 0) and fcc(1 0 0) growth is also presented and compared with recent experiments.
a brilliant scientist; alexander; and a kind and; coarsening; dedicate this paper to; especially his; genuine friend; he made signiÿcant contributions; his papers on surface; including the subject of; in physics; i would like to; morphology; mound formation; of topics; percolation; physics; the memory of shlomo; this paper; to a wide range
Rhetoric's Mechanics: the Retooling of Equipment Writing Production
College Composition and Communication
60
2
366-387
2008
10.2307/20457063
Teaching rhetorical production in a digital age calls for us to rethink our discipline's current distaste for writing mechanics. Yet, the digital mechanics of writing are much broader than grammatical concerns. They include production tools that allow for the invention and circulation of audio, visual, and multigenre writing.
Introduction to Quantum Mechanics
Quantum
1
468
2005
This book first teaches learners how todoquantum mechanics, and then provides them with a more insightful discussion of what itmeans.Fundamental principles are covered, quantum theory presented, and special techniques developed for attacking realistic problems.The book's two-part coverage organizes topics under basic theory, and assembles an arsenal of approximation schemes with illustrative applications.For physicists and engineers.
Fracture mechanics characterization of an anisotropic geomaterial
Engineering Fracture Mechanics
84
111-122
2012
10.1016/j.engfracmech.2012.01.010
Argillites are considered worldwide as potential host rock for high level radioactive waste given the low permeability and strong adsorption potential. However, the excavation of the galleries of a repository would produce a disturbed zone around the boundaries rich of new fractures which may enhance the conductivity of the rock along the gallery axis.Several mine-by experiments have been performed in underground rock labs to investigate the features of the disturbed zone. In Mont Terri URL (Kanton Jura, Switzerland) the EZ-B experiment was specifically conceived for the measurement of excavation induced fractures around a small chamber. The host rock of the URL is a particularly compact and resistant argillite, known as the Opalinus Clay (OPA) excavated and OPA samples were subjected to fracture mechanics tests at the rock mechanics lab of IGAG-CNR in Torino, Italy. The tests aimed at the understanding aspects of the fracturing process occurring in OPA of Mont Terri, which may be considered a transversely isotropic geomaterial, whose planes of isotropy coincide with the bedding. ?? 2012 Elsevier Ltd.
Apparent fracture toughness; Argillites; Cohesive crack; Fictitious crack model; Fracture energy; Non-linear fracture mechanics; Semi-circular specimen under three-point bending (; Size effect; Transversal isotropy
On crack initiation angle of mixed mode ductile fracture with continuum damage mechanics
Engineering Fracture Mechanics
32
4
601-612
1989
This paper presents the development and examination of two fracture criteria proposed for predicting the crack initiation angle in mixed mode ductile fracture based on the theory of continuum damage mechanics. The criteria are deduced respectively from the postulates that 1. (1) a crack propagates at the direction where the ratio of the effective damage equivalent stress and the effective plastic equivalent stress reaches its maximum or Max [C([theta])] for which , 2. (2) a crack propagates at the direction of maximum effective damage equivalent stress . The criteria are used to predict the angles of crack initiation in mixed mode specimens made of aluminium alloy 2024-T3. The thin aluminium plates embedded with an isolated crack of inclined angle [beta] = 30, 45, 60 and 75° are manufactured to simulate mixed mode fracture. In order to investigate the effects of material anisotropy, the mixed mode specimens are produced both parallel to and, transverse from the rolling direction. A finite element analysis based on the anisotropic model of continuum damage mechanics theory proposed earlier by the authors is performed and the angles of crack initiation of the five mixed mode specimens predicted using the proposed fracture criteria and the strain energy density criterion based on the conventional fracture mechanics. The angles of predicted crack initiation based on the proposed fracture criteria not only agree satisfactorily with those determined experimentally but also offer overall better accuracy as compared with those predicted using the conventional fracture mechanics approach. In addition, there is a definite, although not significant, effect of the material anisotropy on the measured crack initiation angles.
APPLICABILITY OF FRACTURE MECHANICS PARAMETERS TO CRACK PROPAGATION UNDER CREEP CONDITION
Journal of Engineering Materials and Technology, Transactions of the ASME
99 Ser H
4
298-305
1977
A critical examination is made of the applicability of fracture mechanics parameters to crack propagation under creep condition with 304 stainless steels for a variety of specimen geometrics at relatively high stress levels. The creep crack propagation rate could not be described in terms of elastic stress intensity factor but it could be in terms of net section stress for all dimensions of thin plate specimen. The net section stress, however, could not explain the difference between crack propagation rates of thin plate specimens and those of notched round bar specimens. This difference could be ascribed to the plastic constraint around the crack tip. Applicability of the modified J-integral to creep crack propagation was also examined and the results showed that this parameter was better for predicting the creep crack propagation rate at a high stress level. In the case of specimens of similar geometries, the net section stress could be used in place of the modified J-integral provided that crack propagation rate was divided by the characteristic length of the specimen.
FRACTURE MECHANICS; J INTEGRAL; STAINLESS STEEL - Crack Propagation; STEEL - Creep
Cellular Mechanics of Acute Leukemia and Chemotherapy
Cellular and Biomolecular Mechanics and Mechanobiology
4
523-558
2011
10.1007/8415_2010_27
Cellular mechanics plays a major role in the pathophysiology of hematologic diseases, in which the alterations of biophysical properties of circulating blood cells influence vascular flow and contribute to vascular complications. In particular, the cellular mechanical alterations that occur in acute leukemia, cancer of blood cell precursors, may lead to life-threatening complications that result in microvascular compromise of vital organs such as the brain and lung. As such, pharmacological agents that modulate the cellular mechanics of leukemia cells have the potential to both improve and worsen the symptoms and outcome of these complications. Recent technological advances have provided the necessary tools to study leukemia, cancer of blood cell precursors, cellular mechanics and have vastly improved our understanding of the biophysical aspects of leukemia pathophysiology. In this chapter, we review studies from our laboratory and other researchers that focus on the interactions between cellular mechanics, pharmacological agents, and leukemia biology, and we also highlight the novel tools and techniques developed to conduct those experiments. These studies clearly stress the important role the nascent field of cellular mechanics will have in clinical medicine in the near future.
Experimental studies on thin-walled grooved tubes under axial compression
Experimental Mechanics
44
1
101-108
2004
We study experimentally the axial crushing behavior and crashworthiness characteristics of thin-walled steel tubes containing annular grooves. The grooves determine the positions of the folds and control the buckling mode of deformation. In the present work we aim to improve the uniformity of the load-displacement behavior and to predict the energy absorption capacity of the tubes. Grooves are cut circumferentially and alternately inside and outside the tubes at predetermined intervals. Quasi-static axial crushing tests are performed with different groove distances. Photographs are taken during axial buckling and the specimens after crushing are sectioned axially to carry out the measurements. The deformation modes and load-displacement curves are described and energy absorption and mean post-buckling load are determined. The convolutions are achieved by folding in an axisymmetric concertina mode about the circumferential grooves. The results show that the load-displacement curve and energy absorbed by the axial crushing of tubes can be controlled by the introduction of grooves with different distances. © 2004 Society for Experimental Mechanics.
Axial crushing; Buckling; Buckling behavior; Compaction; Crashworthiness; Crushing; cylinder; Deformation; Energy absorption; Grooved tubes; Load uniformity; Steel; Steel tubes; Thin-walled grooved tubes; Thin-walled structures; Tubes (components)
On a Non-Linear Theory of Thin Jets. Part 2. A Linear Theory for Small Injection Angles
Journal of Fluid Mechanics
33
02
261-272
1968
A non-linear potential problem which describes the injection of a high speed jet into a uniform flow of lower total head is linearized when the jet injection angle is small. The resulting linear problem is solved using the Wiener–Hopf technique. Numerical results for the position of the streamline separating the jet from the free stream and the pressure coefficient along the upstream wall are obtained for various injection angles.
Not printed
Physicalism Versus Quantum Mechanics
Mind, Matter and Quantum Mechanics
245-260
2009
10.1007/978-3-540-89654-8_13
The widely held philosophical position called “physicalism” has been described and defended in a recent book by Jaegwon Kim. The physicalist position claims that the world is basically purely physical. However, “physical” is interpreted in a way predicated, in effect, upon certain properties of classical physics that are contradicted by the precepts of orthodox quantum physics. Kim’s arguments reveal two horns of a dilemma that the physicalist is forced to face as a consequence of accepting this classical notion of “physical”. Kim admits that neither of the two options, “epiphenomenalism” or “reduction”, is very palatable, but he finds a compromise that he deems acceptable.
A Gravitational Explanation for Quantum Mechanics
arXiv preprint quant-ph/9609021
10
1996
10.1063/1.2737003
It is shown that certain structures in classical General Relativity can give rise to non-classical logic, normally associated with Quantum Mechanics. A 4-geon model of an elementary particle is proposed which is asymptotically flat, particle-like and has a non-trivial causal structure. The usual Cauchy data are no longer sufficient to determine a unique evolution. The measurement apparatus itself can impose non-redundant boundary conditions. Measurements of such an object would fail to satisfy the distributive law of classical physics. This model reconciles General Relativity and Quantum Mechanics without the need for Quantum Gravity. The equations of Quantum Mechanics are unmodified but it is not universal; classical particles and waves could exist and there is no graviton.
Is quantum mechanics based on an invariance principle?
Journal of Physics A: Mathematical and General
40
17
4567
2007
10.1088/1751-8113/40/17/012
<P>Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position–momentum inequality. These transformations are induced by isotropic space dilations. This invariance imposes a change in the laws of classical mechanics that exactly corresponds to the transition-to-quantum mechanics. The Schrödinger equation appears jointly with a second nonlinear equation describing non-unitary processes. Unitary and non-unitary evolutions are exclusive and appear sequentially in time. The non-unitary equation admits solutions that seem to correspond to the collapse of the wavefunction.</P>
Fundamentals of Surface Mechanics
Springer Science
2002
10.1007/978-0-387-21776-5
Introduction to Contact Mechanics, Second Edition is a gentle introduction to the mechanics of solid bodies in contact for graduate students, post doctoral individuals, and the beginning researcher. This second edition maintains the introductory character of the first with a focus on materials science as distinct from straight solid mechanics theory. Every chapter has been updated to make the book easier to read and more informative. A new chapter on depth sensing indentation has been added, and the contents of the other chapters have been completely overhauled with added figures, formulae and explanations. The author begins with an introduction to the mechanical properties of materials, general fracture mechanics and the fracture of brittle solids. This is followed by a detailed description of indentation stress fields for both elastic and elastic-plastic contact. The discussion then turns to the formation of Hertzian cone cracks in brittle materials, subsurface damage in ductile materials, and the meaning of hardness. The author concludes with an overview of practical methods of indentation.
Two-Time Correlation Functions: Stochastic and Conventional Quantum Mechanics
European Physical Journal B
48
2
233-242
2002
10.1140/epjb/e2005-00399-4
An investigation of two-time correlation functions is reported within the framework of (i) Stochastic Quantum Mechanics and (ii) conventional Heisenberg-Schr"odinger Quantum Mechanics. The spectral functions associated with the two-time electric dipole correlation functions are worked out in detail for the case of the hydrogen atom. While the single time averages are identical for stochastic and conventional quantum mechanics, differences arise in the two approaches for multiple time correlation functions.
A combined modeling–experimental study of the crack opening displacement fracture criterion for characterization of stable crack growth under mixed mode I/II loading in thin sheet materials
Engineering Fracture Mechanics
66
171-185
2000
10.1016/S0013-7944(00)00011-4
Recent experimental studies have shown that a critical Crack Opening Displacement (COD) has the potential to be a viable parameter for predicting the onset of crack growth in thin sheet 2024-T3 aluminum under combined tension (mode I) and in-plane shear (mode II) loading conditions. To assess the viability of using a critical COD criterion for prediction of crack growth in components experiencing mixed mode loading, the enclosed work presents a complete set of simulation studies and experimental measurements for crack growth under nominally mode I/II conditions. For the first time, finite element crack growth simulations under mixed mode I/II conditions have been performed for the Arcan test specimen using recently measured crack growth path information and the load-crack extension data for the mode I/II experiments. Simulation results indicate that the predicted COD is in excellent agreement with measurements. Specifically, simulation results indicate that (a) the magnitude of COD during simulated crack growth is nearly constant for Delta a > 5 mm; (b) for Phi less than or equal to 60 degrees, the predicted COD is primarily perpendicular to the crack path (i.e., mode I in nature); (c) for Phi > 60 degrees, the predicted COD is primarily parallel to the crack path (i.e., mode II in nature); (d) near the transitional angle between mode I and mode II fracture, the COD components are more unstable during the crack growth process and (e) simulation predictions for the strain fields are in quantitative agreement with measurement. Taken together, the results from the combined simulation-experimentation program provides strong justification for the use of a COD-based fracture criterion to predict crack growth in thin-sheet materials. (C) 2000 Elsevier Science Ltd. All rights reserved.
arcan test specimen experiments; ii; mixed mode i; numerical simulations; stable crack growth; thin sheet aluminum
POVMs: a small but important step beyond standard quantum mechanics
ProcLeiden061
1
1
1-11
2006
10.1142/9789812771186_0005
It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical observable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a peripheral issue, allegedly to be understood in terms of a trivial nonideality of practical measurement procedures, but that this generalization touches the very core of quantum mechanics, viz. complementarity and violation of the Bell inequalities.
bell inequalities; complementarity; positive operator-valued measure
Course 10 Two lectures on iterative coding and statistical mechanics
Les Houches Summer School Proceedings
83
C
467-487
2006
10.1016/S0924-8099(06)80047-8
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects, such as, iterative belief propagation decoding. Relations with statistical mechanics, inference and random combinatorial optimization are stressed, as well as some general mathematical ideas and open problems.
The Principle of the Identity of Indiscernibles and Quantum Mechanics*
Philosophy of Science
77
1
117-136
2010
10.1086/650211
It is argued that recent discussion of the principle of the identity of indiscernibles (PII) and quantum mechanics has lost sight of the broader philosophical motivation and significance of PII and that the `received view' of the status of PII in the light of quantum mechanics survives recent criticisms of it by Muller, Saunders, and Seevinck.
Elastic–Plastic Contact Mechanics of Indentations Accounting for Phase Transformations
Experimental Mechanics
43
3
303-308
2003
10.1177/0014485103036023
A contact mechanics model is developed which takes into account possible phase transformations in materials induced by hydrostatic and shear stresses associated with indentation. The proposed model allows prediction of the average thickness and approximate shape of the phase transformation zone in semiconductors and ceramics under various types of diamond indenters. The results of theoretical calculation are in good agreement with the available experimental data.
Higher-order electromechanical response of thin films by contact resonance piezoresponse force microscopy.
IEEE transactions on ultrasonics, ferroelectrics, and frequency control
53
12
2309-22
2006
10.1109/TUFFC.2006.179
Piezoresponse scanning force microscopy (PFM) has turned into an established technique for imaging ferroelectric domains in ferroelectric thin films. At least for soft cantilevers, the piezoresponse signal is not only dependent on the elastic properties of the material under investigation but also on the elastic properties of the cantilever. Due to this dependency, the cantilever response and, therefore, the measured properties depend on the frequency of the small alternating current (AC) testing voltage. At the contact resonance, the cantilever response is maximum, and this increased sensitivity can be used to detect very small signals or to decrease the voltage applied to the sample. We have shown that by using the hysteretic ferroelectric switching, it is possible to separate the signal into its components (viz. electromechanical and electrostatic contributions). Additionally, the measurement frequency can be tuned such that the second and third harmonics of the electromechanical response can be detected at the cantilever resonance, providing information about the higher-order electromechanical coefficients. We assume that this nonlinear behavior seen in local and macroscopic measurements is rooted in the nonlinearity of the dielectric permittivity. Our results are of crucial importance for the study of ferroelectric and electromechanical properties of nanostructures.
Computer Simulation; Elasticity; Electric Impedance; Electrochemistry; Electrochemistry: instrumentation; Electrochemistry: methods; Electromagnetic Fields; Mechanics; Membranes, Artificial; Microscopy, Atomic Force; Microscopy, Atomic Force: methods; Models, Chemical; Nanostructures; Nanostructures: chemistry; Nanostructures: radiation effects; Nanostructures: ultrastructure; Particle Size; Stress, Mechanical
Characterization of microscopic deformation in polymeric thin films using particle image velocimetry
Third International Conference on Experimental Mechanics and Third Conference of the Asian-Committee-on-Experimental-Mechanics, Pts 1and 2
5852
608-613
2005
Doi 10.1117/12.621738
The effectiveness of a technique based on particle image velocimetry (PIV) for measuring the instantaneous deformation field in planar polymeric films is investigated. Detailed deformation of polymeric films under complex stretching conditions will be very useful in characterization as well as optimization of mechanical properties. PIV is a method for measuring velocity fields in many fluid mechanics applications. In this technique, light scattering from glass micro-particles is used for estimating flow fields. In this work, the particles are spread on the surface of a polymeric film. The film is kept in a laser sheet while the deformation takes place. Two consecutive images of areas as large as 100 cm(2) are taken, separated by small time interval At. Displacement of seed particles over this time interval is estimated using cross-correlation. The polymer film was stretched uniaxially at constant rates. The deformation fields in the thin films over the time of stretching were evaluated. Films with introduced defects were also investigated for the measurement of the planar deformation fields. It is shown that the technique has potential to quantify the instantaneous deformation rate and strain fields for a large area in the plane of a film.
particle image velocimetry; seed particles; stretching rate; thin films
Bending of single crystal thin films modeled with micropolar crystal plasticity
International Journal of Engineering Science
49
12
1357-1366
2011
10.1016/j.ijengsci.2011.05.018
The scale-dependent mechanical response of single crystal thin films subjected to pure bending is investigated using a dislocation-based model of micropolar single crystal plasticity via finite element simulations. Due to the presence of couple stresses, the driving force for plastic slip in a micropolar crystal contains an intrinsic back stress component that is related to gradients in lattice torsion-curvature. Strain gradient-dependent back stresses are a common feature of various types of generalized crystal plasticity theories; however, it is often introduced either in a phenomenological manner without additional kinematics or by designating the plastic slips as generalized degrees-of-freedom. The treatment of lattice rotations as fundamental degrees-of-freedom instead of plastic slips greatly reduces the complexity (computational expense) of the single crystal model, and leads to the incorporation of additional elastoplastic kinematics since the lattice torsion-curvature is taken as a work-conjugate continuum deformation measure. A recently proposed single criterion micropolar framework is employed in which the evolution of both the plastic strains and torsion-curvatures are coupled through the use of a unified flow rule. The deformation behavior is characterized by the moment-rotation response and the dislocation substructure evolution for various slip configurations and specimen thicknesses. The results are compared to analogous simulations carried out using a model of discrete dislocation dynamics as well as a statistical-mechanics inspired, flux-based model of nonlocal crystal plasticity. The micropolar model demonstrates good qualitative and quantitative agreement with the previous results up to certain inherent limitations of the current formulation.
Influence of strain on space-charge distribution at ferroelectric thin-film free surfaces
Acta Materialia
60
19
6457-6463
2012
10.1016/j.actamat.2012.07.050
Ferroelectric perovskites are wide-bandgap semiconductors and therefore are often modeled as perfect dielectrics. However, space charges can play an important role in regions with large electric fields, such as at domain walls, free surfaces, near electrodes, etc. In this paper, we apply a mesoscale model to examine the space-charge distribution at free-surface closure domain patterns in a ferroelectric thin film. The model uses a conventional electromechanical phase-field approach for ferroelectric domain patterns in combination with drift-diffusion based equations to model space-charge distribution. We additionally apply a boundary element method to compute the stray electric fields outside the ferroelectric free surface. We probe the influence of mechanical strain, such as would be applied through a substrate, on the distribution of space charge. We find an indirect, but strong, coupling between mechanics and space-charge distribution. The physical mechanism of this coupling is as follows: the mechanical strain induces changes in the domain patterns and polarization distribution; this in turn changes the local electric fields sufficiently that space charges are redistributed on the free surface rather than moving towards the bottom electrode. We note two interesting features of this coupling: first, the coupling mechanism is operative only at free surfaces due to the complex domain patterns in these regions, and would not occur in the bulk; second, although domain patterns are visually only marginally changed by the presence of space charges, the changes in electric field due to these seemingly small changes is significant and this provides the coupling with space charge. ?? 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Closure domains; Ferroelectrics; Free surface; Space charge
Analysis of multiple cracks in thin coating on orthotropic substrate under mechanical and residual stresses
Engineering Fracture Mechanics
77
2
229-248
2010
10.1016/j.engfracmech.2009.07.010
The analysis addresses a typical failure development pattern in thin films consisting of a system of multiple surface cracks leading to and branching along or near the interface between the film and the base material. The process is driven by thermal residual stresses and/or mechanical loading. Due to the high temperature gradients during the fabrication process, usually a net of surface cracks develops, which gives the appearance of a granular structure of the surface. A periodic array of parallel surface cracks is assumed. A "unit cell" or single cracked segment attached to the substrate is analyzed instead by assuming the channel cracks are spaced more or less uniformly and perfectly aligned in parallel in the transverse direction of the coating. The analysis is specialized to orthotropic and transversally isotropic materials. The problem is solved using FEM combined with the reciprocal theorem. Matched asymptotic procedure [Leguillon D, Sanchez-Palencia E. Computation of singular solutions in elliptic problems and elasticity. Paris: Masson; 1987; Vu-Quoc L, Tran VX. Singularity analysis and fracture energy-release rate for composites: piecewise homogenous-anisotropic materials. Comput Methods Appl Mech Engng 2006;195:5162-97] is used to derive the change of potential energy. Higher-order terms in the asymptotics are considered. The competition between penetration and debond for periodically distributed edge cracks especially near the critical value of the ratio of fracture spacing to the layer thickness is examined. © 2009 Elsevier Ltd. All rights reserved.
Interface; Matched asymptotic expansions; Multiple cracks; Reciprocal theorem; Surface layer; Thermal stresses
Statistical mechanics of optimization problems
Physica A: Statistical Mechanics and its Applications
365
1
1-6
2006
10.1016/j.physa.2006.01.033
Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the presentation I will describe in details the problems related to the coloring of a random graph. © 2006 Elsevier B.V. All rights reserved.
Coloring; Random systems; Satisfiable
First-Person Plural Quantum Mechanics
Arxiv Preprints
1-41
2014
Doing justice to quantum mechanics calls for a deeper examination of the relations between our experience, its objects, and its subjects than either third-person interpretations or the first-person singular interpretation of the QBist permit. The metaphysical space opened by Bohr’s employment of the “Kantian wedge” between the objective world, about which we can communicate, and the world “in itself” al- lows quantum mechanics to unfold its metaphysical potential. This in turn makes it possible to go a long way towards bridging the episte- mological gap between the empirical and transcendental conceptions of reality.
S-Matrix Formulation of Statistical Mechanics
Physical Review
187
1
345
1969
10.1103/PhysRev.187.345
We have formulated the statistical mechanics in terms of the S matrix, which describes the scattering processes taking place in the thermodynamical system of interest. Such a formulation is necessary for studying the systems whose microscopic constituents behave according to the laws of relativistic quantum mechanics. Our result is a simple prescription for calculating the grand canonical potential of any gaseous system given the free-particle energies and S-matrix elements. When applied to a nonrelativistic gas, it gives a simple prescription for calculating all virial coefficients. Simplified relativistic gas models are considered as examples of application. A general form of the Levinson's Theorem for any number of particles follows immediately from our formalism. Its applications in statistical mechanics are briefly discussed.
Mechanics of hierarchical materials
International Journal of Fracture
150
1-2
221-226
2008
10.1007/s10704-008-9219-1
In this paper the simplest mathematical model to design bio-inpired hierarchical materials is propossed. Simple formulas describing the dependence of strenght,toughness and stiffness on the considere size scale are derived, taking into account the toughening biomechanism.
Bio; Fracture; Hierarchical; Materials; Nano; Strength
Statistical mechanics of economics i
Physics Letters, Section A: General, Atomic and Solid State Physics
375
6
966-973
2011
10.1016/j.physleta.2011.01.003
We show that statistical mechanics is useful in the description of financial crisis and economics. Taking a large amount of instant snapshots of a market over an interval of time we construct their ensembles and study their statistical interference. This results in a probability description of the market and gives capital, money, income, wealth and debt distributions, which in the most cases takes the form of the Bose-Einstein distribution. In addition, statistical mechanics provides the main market equations and laws which govern the correlations between the amount of money, debt, product, prices and number of retailers. We applied the found relations to a study of the evolution of the economics in USA between the years 1996 to 2008 and observe that over that time the income of a major population is well described by the Bose-Einstein distribution which parameters are different for each year. Each financial crisis corresponds to a peak in the absolute activity coefficient. The analysis correctly indicates the past crises and predicts the future one. ?? 2011 Elsevier B.V.
Econometrics; Financial crisis; Income; Market; Money; Statistical mechanics
Quantum mechanics: No more fields
Nature Physics
11
3
211-212
2015
10.1038/nphys3226
A self-accelerating electronic wave packet can acquire a phase akin to the Aharonov–Bohm effect, but in the absence of a magnetic field.
Distribution functions in classical and quantum mechanics
Progr. Theor. Phys. Suppl
1989
The correspondence between classical and quantum mechanics is an important subject for the better understandings of “quantum chaos”. In particular, it is very important to investigate the correspondence between distribution functions in classical mechanics and in phase space representation of quantum mechanics. This is the review of our recent progresses in the study of distribution functions in classical and quantum mechanics, namely distribution functions in classical mechanics and in coarse-grained classical mechanics as well as the Wigner function and the Husimi function. Topics dealt with include formulations of the Wigner representation, the Husimi representation and coarse-grained classical mechanics, and their applications to the analyses of the eigenstates and time developments of the distribution functions.
Three-dimensional effect in the prediction of flange delamination in composite skin-stringer pull-off specimens
Journal of composites technology & research
24
3
180-187
2000
Three-dimensional finite element modeling was used to analyze the delamination between the stiffener flange and the skin of a typical pull-off specimen representing a section of a stiffened skin panel. The finite element analysis results were used to calculate the total strain energy release rate and its Mode I, Mode II, and Mode III components along the delamination front through the width of the pull-off specimen. Three-dimensional modeling makes it possible to represent ply-by-ply lamina properties in the model. However, the ply-by-ply approach should not be used for highly angle ply laminates because of the strong transverse effect from adjacent plies. A smeared properties approach is more robust for the strain energy release rate analysis of delamination between ±45-degree angle ply laminates. The three-dimensional analysis indicates that delamination failure between the stiffener flange and the skin is dominated by Mode I and Mode II delamination modes. The three-dimensional analysis predicts delamination growth from the interior of the pull-off specimen width, and higher pull-off load is required to grow the delamination close to the free edges. The delamination initiation load along the interior of the pull-off specimen width does not change with the change of the width of the pull-off specimen. However, the wider specimen has stronger free edge effects than the narrower specimen. The lay-up of the skin and the flange can have significant effect on the delamination initiation load. Stiffening the skin and maintaining the compliant flange will increase the delamination initiation load.
Aile; Ala; Assemblage; Carbon fiber; Composite material; Damaging; Delaminación; Délaminage; Delamination; Deterioración; Endommagement; Energía deformación; Energie déformation; Ensamble; Epóxido resina; Epoxyde résine; Epoxy resin; Essai détachement; Estratificado; Estudio teórico; Etude théorique; Fiber reinforced material; Fibra carbón; Fibre carbone; Finite element method; Fracture mechanics; Joining; Laminate; Material compuesto; Material reforzado fibra; Matériau composite; Matériau renforcé fibre; Mecánica ruptura; Mécanique rupture; Méthode élément fini; Método elemento finito; Modèle 3 dimensions; Modeling; Modélisation; Modelización; Modelo 3 dimensiones; Sección variable; Section variable; Strain energy; Stratifié; Theoretical study; Three dimensional model; Variable section; Vitesse libération énergie; Wing
Development of an anisotropic, multilayered, shear-deformable rectangular plate element
Computers & Structures
21
4
789-796
1985
10.1016/0045-7949(85)90155-5
A multilayered anisotropic flat plate element which includes the effects of the transverse shear deformation is developed by making use of the displacement formulation. The discrete element is a rectangle with 32 degrees of freedom which include extension, bending, and transverse shear deformation states. The formulation is based on an improved bi-dimensional transverse shear deformation plate theory which accounts for piecewise linear distribution across the thickness of the inplane displacements u and v, and allows the contact conditions at the interfaces between the layers to be satisfied. In order to demonstrate the accuracy and efficiency of the developed finite element, the solutions for two sample problems are given. Problems, for which analytical solutions are available, were selected so that a comparison between the analytical and numerical solutions could be made. The first example is the well-established cylindrical bending problem of cross-ply and angle-ply laminates; the second one is the bending of a symmetric cross-ply square plate simply-supported on all edges. The tests carried out show that the element is very efficient in predicting the responses of thick and thin laminated plates. Also predicting, at very low span-to-thickness ratios and models, the warpage of the cross-section, which has been found to be unfeasible by other conventional finite-element displacement approaches.
A Chaotic, Deterministic Model for Quantum Mechanics
Arxiv Preprints
1-28
2014
With the decline of the Copenhagen interpretation of quantum mechanics and the recent exper- iments indicating that quantum mechanics does actually embody ’objective reality’, one might ask if a ’mechanical’, conceptual model for quantum mechanics could be found. We propose such a model.
PROCESSING OF THERMOPLASTIC MATRIX COMPOSITES
Review of Progress in Quantitative Nondestructive Evaluation
1257-1265
1987
The mechanisms governing intimate contact and bond formation at the ply interfaces of a thermoplastic composite during processing have been identified. The theory of autohesion is used toe xplain interfacial bond strength development during processing. A viscoelastic mechanics model simulating the compression of resin impregnaed tows was developed to explain the phenomenon by which the prepreg ply interfaces achieve intimate contact. Based on the resultst of this investiation it is clear that further work is needed to obtain a better understanding og the influence of fiber reinforcement on the resin viscosity. Also, the effect of the fiber reinforcement on the interfacial bond formation needs to be examined.
Incomplete statistics: nonextensive generalizations of statistical mechanics
Chaos, Solitons and Fractals
12
8
1431-1437
2001
10.1016/S0960-0779(00)00113-2
Statistical mechanics is generalized on the basis of incomplete information theory for inexact or incomplete probability distribution. An incomplete normalization ∑i=1w piq=1 with positive real q is proposed and, thanks to the q-deformed logarithmic function used as information measureleads to a nonextensive entropy:The resulting incomplete statistical mechanics is proved to have the same theoretical characteristics as the Tsallis one for complete probability distributions.
Computational analysis of thin coating layer failure using a cohesive model and gradient plasticity
Engineering Fracture Mechanics
70
14
1929-1942
2003
10.1016/S0013-7944(03)00132-2
Thermal barrier coatings (TBC) are widely used to prevent transient high temperature attack and allow components high durability. Due to strong inhomogeneous material properties the TBC failure often initiates near the interface between the brittle oxide layer and the ductile substrate. A reliable prediction of the TBC failure requires detailed information about the crack tip field and the consequent fracture criteria. In the present paper both cohesive model and gradient plasticity are used to simulate the failure process and to study interdependence of the interface stress distribution with the specific fracture energies. Computations confirm that combination of the two models is able to simulate different failure mechanisms in the TBC system. The computational model has the potential to give a realistic prediction of the crack propagation process.
cohesive model; finite element; gradient plasticity; interfacial cracks; internal material length; thermal barrier coating
The Ontology of Bohmian Mechanics
The British Journal for the Philosophy of Science
1-24
2013
10.1093/bjps/axt019
The paper points out that the modern formulation of Bohm's quantum theory known as Bohmian mechanics is committed only to particles' positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm's theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general.
bohmian mechanics; dispositionalism; humeanism; law of motion; non-locality; primitive ontology; wave-function
Reversible mechanics and time’s arrow
Physical Review A
37
1
252-257
1988
10.1103/PhysRevA.37.252
The microscopic mechanics discovered by {N}ose, of which {G}auss's isokinetic mechanics is a special case, makes is possible to simulate macroscopic irreversible nonequilibrium flows with purely reversible equations of motion. The {G}auss-{N}ose and {N}ose-{H}oover equations of motion explicitly include time-reversible momentum and energy reservoirs. Computer simulations of nonequilibrium steady-state systems described by {G}auss-{N}ose mechanics invariably evolve in such a way as to increase entropy. The corresponding phase-space distribution functions, which include reservoir degrees of freedom, collapse onto stable strange attractors. Hypothetical time-reversed motions, which would violate the second law of thermodynamics, cannot be observed for two reasons: First, such reversed motions would occupy zero volume in the phase space; second, they would be dynamically unstable. Thus, {N}ose's reversible mechanics is fully consisten with irrversible thermodynamics, in the way forecast by {P}rigogine. That is, the consistency follows from the formulation of new microscopic equations of motion.
Entropy in Nonequilibrium Statistical Mechanics
Matrix
75
11
20
2006
10.1143/JPSJ.76.067001
Entropy in nonequilibrium statistical mechanics is investigated theoretically so as to extend the well-established equilibrium framework to open nonequilibrium systems. We first derive a microscopic expression of nonequilibrium entropy for an assembly of identical bosons/fermions interacting via a two-body potential. This is performed by starting from the Dyson equation on the Keldysh contour and following closely the procedure of Ivanov, Knoll and Voskresensky Nucl. Phys. A bf 672 (2000) 313. The obtained expression is identical in form with an exact expression of equilibrium entropy and obeys an equation of motion which satisfies the H-theorem in a limiting case. Thus, entropy can be defined unambiguously in nonequilibrium systems so as to embrace equilibrium statistical mechanics. This expression, however, differs from the one obtained by Ivanov em et al., and we show explicitly that their ``memory corrections'' are not necessary. Based on our expression of nonequilibrium entropy, we then propose the following principle of maximum entropy for nonequilibrium steady states: ``The state which is realized most probably among possible steady states without time evolution is the one that makes entropy maximum as a function of mechanical variables, such as the total particle number, energy, momentum, energy flux, etc.'' During the course of the study, we also develop a compact real-time perturbation expansion in terms of the matrix Keldysh Green's function.
Hybrid laminated-glass plate: Design and assessment
Composite Structures
106
250-263
2013
10.1016/j.compstruct.2013.05.041
This paper is focused on laminated glass plate designed with the “sacrificial ply” concept: The glass layer that collects the live loads is considered as broken (i.e., it is not considered), independently of whether or not it is fractured. Accordingly, the load-bearing system is composed of: Heath-strengthened (or annealed) glass layer, plus interlayer, plus toughened (tempered, or chemically-strengthened) glass layer. Hence, the laminated glass plate is hybrid. The first part of the paper derives the constitutive law of the interlayer materials that belong to the latest generation. Then, the behavior of the laminated glass plate is predicted by using this new constitutive law in lieu of the constitutive law of traditional interlayer materials, and the results are analyzed. The second part discusses the results of a theoretical analysis conducted on products available on the architectural marketplace that encompass glass structural applications. These results prove that the ultimate load is dictated by the toughened glass only if the stiffness of the interlayer surpasses a critical value; otherwise, it is dictated by the less resistant glass. However, the critical value is very high. Moreover, the results prove that assessment cannot use practical or simplified expressions (e.g., effective thickness), since these expressions provide the maximum stress in the plate but not in each layer.
Hybrid laminate; Laminated glass; Laminatedplate; Laminate mechanics; Sacrificial ply; Three-layered plate
An analysis of fracture and delamination in thin coatings subjected to contact loading
Wear
198
1-2
15-32
1996
10.1016/0043-1648(95)06885-6
Hard coatings, which are used to protect surfaces that are subjected to contact loading, may fracture or delaminate from their substrates. A simple model of this process is presented. The coating is idealized as a brittle elastic layer of uniform thickness, which is bonded to the surface of a half-space. The coating, substrate, and interface are assumed to contain microcracks. The solids is loaded by an elastic cylindrical indenter, which slides over the surface of the coating. The influence of residual stress in the coating is also taken into account. A simple method is described for calculating the contact stress fields in a layered elastic solid. Methods of linear elastic fracture mechanics are then used to calculate the loads required to initiate fracture in the coating, or to cause the coating to delaminate from its substrate. The results suggest that fracture is more likely to initiate from flaws in the coating than from flaws in the interface between layer and substrate. The pattern of fracture which occurs under the indenter is also analyzed in detail. It is shown that both the fracture loads and the fracture pattern are strongly influenced by the mismatch in elastic properties between the layer and its substrate. Variations in coating properties and coating thickness may change the fracture loads by up to a factor of 10.
Strata Mechanics
Developments in Geotechnical Engineering
32
260-263
1981
10.1016/B978-0-444-42086-2.50050-8
SUMMARY\n: The time sequence of a sudden collapse of room and pillar workings confirms the hypothesis that the cause of the pillar failure is the uncontrolled energy release by the strong strata in the higher roof.
Quantum Mechanics from Classical Logic
Journal of Physics: Conference Series
361
012024
2012
10.1088/1742-6596/361/1/012024
Although quantum mechanics is generally considered to be fundamentally incompatible with classical logic, it is argued here that the gap is not as great as it seems. Any classical, discrete, time reversible system can be naturally described using a quantum Hilbert space, operators, and a Schr¨ odinger equation. The quantum states generated this way resemble the ones in the real world so much that one wonders why this could not be used to interpret all of quantum mechanics this way. Indeed, such an interpretation leads to the most natural explanation as to why a wave function appears to “collapse” when a measurement is made, and why probabilities obey the Born rule. Because it is real quantum mechanics that we generate, Bell’s inequalities should not be an obstacle.
Applied Quantum Mechanics 2nd Edition
- Libri_QUANTUM
2006
Electrical and mechanical engineers, materials scientists and applied physicists will find Levi's uniquely practical 2006 explanation of quantum mechanics invaluable. This updated and expanded edition of the bestselling original text covers quantization of angular momentum and quantum communication, and problems and additional references are included. Using real-world engineering examples to engage the reader, the author makes quantum mechanics accessible and relevant to the engineering student. Numerous illustrations, exercises, worked examples and problems are included; Matlab source codes to support the text are available from www.cambridge.org//9780521183994
applied quantum mechanics; blank; electrical and mechanical engineers; levi; materials scientists and applied; of quantum mechanics invaluable; physicists will find; second edition; s page intentionally left; s uniquely practical explanation; this updated
Is Quantum Mechanics needed to explain consciousness?
NeuroQuantology
6
1
43-45
2008
10.14704/nq.2008.6.1.155
In this short comment to a recent contribution by E. Manousakis it is argued that the reported agreement between the measured time evolution of conscious states during binocular rivalry and predictions derived from quantum mechanical formalisms does not require any direct effect of quantum mechanics. The recursive consumption analysis process in the Ouroboros Model can yield the same behavior
Statistical Mechanics of Periodic Frustrated Ising Systems
Statistical Mechanics of Periodic Frustrated Ising …
251
April
1986
10.1007/3-540-16473-1
The present book reviews the thoery of phase transitions in Ising systems with competing interactions. Because of this competition no configuration of Ising spins (s_i = /pm 1) can minimize the energy of all interactions simultaneously. Even in the groundstate (T=0) some interactions are 'broken', i.e. remain in the energetically unfavorable configuration.
Experimental study of low-velocity impacts on glass-epoxy laminated composite plates
Mechanics of Materials
291-300
2008
10.1007/s10999-008-9071-5
In this investigation, glass-epoxy lami- nated plates were subjected to crush experimental tests in a SHIMATSU universal traction machine and low- velocity crash impact tests in a drop test IMATEK machine. The results are shown and the dimensions of the damage are evaluated. The characterization of the damage is done in relation to the type of test, the ply stacking sequence, the plate dimensions and the maximum force achieved in the impact. In order to verify if low-velocity impacts can be modelled by crush tests on laminated composites, the results are compared and several relevant ideas are developed.
delamination; impact behaviour; laminates behavior; quasi-static
Corner transfer matrices in statistical mechanics
Journal of Physics A: Mathematical and Theoretical
40
42
12577-12588
2007
10.1088/1751-8113/40/42/S05
Corner transfer matrices are a useful tool in the statistical mechanics of simple two-dimensinal models. They can be very effective way of obtaining series expansions of unsolved models, and of calculating the order parameters of solved ones. Here we review these features and discuss the reason why the method fails to give the order parameter of the chiral Potts model.
Statistical Mechanics
The strength of fibre reinforced polymer under a complex loading
Journal of Composite Materials
47
20-21
2525-2552
2013
10.1177/0021998313476328
This article presents a model, known as generalized Daniels’ model, describing the process of micro-damage accumulation, deformation and failure of multilayered fibre reinforced composite structures under complex internal states of stress responding to external plane-stress loading. The model considers three independent kinds of ply micro-damage: longitudinal, transverse and shear. Non-linear analysis, taking into account scissoring effects, is used to make theoretical predictions for all the 13 test cases involved in the third world-wide failure exercise. The cases cover the biaxial failure behaviour of a unidirectional and multi-directional laminates, failure of thick and thin cross ply and quasi-isotropic laminates under tension, damage due to thermal loading, bending of a general laminate, loading and re-loading and the predictions of the tensile and compressive strength values of test specimens with an open hole. For the prediction of notched strength of laminates with hole, the model is used with a non-local approach based on the specific size of ply microstructure and Neuber’s hyperbola of specific deformation energy. The results are presented for all the 13 test cases.
Attenuation of the depolarizing field in a thin film model relaxor
Physica A: Statistical Mechanics and its Applications
390
21-22
3955-3961
2011
10.1016/j.physa.2011.06.039
The behavior of the polarization in a microscopic statistical model for a thin film relaxor placed between two metallic electrodes is studied by numerical simulations. Depolarization fields different from zero, due to a non-perfect compensation of surface charges at the metallic electrodes, are taken into account. Different thicknesses and different values of the compositional charge disorder density for the relaxor are considered. Depolarization field is found to be extremely attenuated for large values of the number density of charge carriers in the relaxor. In such a case, field attenuation allows for the existence of a homogeneous ferroelectric ground state.
Depolarization field; Relaxors; Thin films
Thermodynamics Confronts Quantum Mechanics
Physics
7
35
2014
10.1103/Physics.7.35
Heat flow carried by electrons in a thermoelectric device requires a surprisingly wide “pipe”—a rare case where quantum effects have macroscopic consequences.
3.8 continuum damage mechanics
Handbook of Materials Modeling
Cdm
1183-1192
2005
Continuum Damage Mechanics (CDM) can be thought of as a subset of ISV theory as described earlier. It was introduced by Kachanov\n[1] and modi- fied somewhat by Rabotnov [2] has now reached a stage that practical engineering problems can be solved. In\ncontrast to fracture mechanics which considers the process of initiation and growth of microcracks as a discontinuous phenomenon,\ncontinuum damage mechanics uses a continuous variable, Φ, which is related to the density of these defects, to describe the deterioration of the material before the initiation of\nmacrocracks.\n\nBased on the damage variable Φ, constitutive equations of evolution are developed to predict the initiation of macrocracks for different types of phenomena.\nLemaitre [3] and Chaboche [4] used it to solve different types of fatigue problems.Leckie and Hayhurst [5], Hult [6], and\nLemaitre and Chaboche [7] used it to solve creep and creep-fatigue interaction problems. Also, it was used by Lemaitre for\nductile plastic fracture [8–10] and for a number of other applications [11].
Mechanics of Coatings, Proceedings of the 16th Leeds-Lyon Symposium on Tribology held at The lnstitut National des Sciences Appliquées
Tribology Series
17
409-415
1990
10.1016/S0167-8922(08)70280-3
The tribological behavior of TiN-coated Inconel 625 rings in dry sliding contact with carbon graphite was investigated with the aid of ring-on-ring sliding tests, computer-assisted profilometry, optical microscopy and scanning electron microscopy. Residual stresses and preferred orientations in TiN coatings were determined by X-ray diffractometry methods. Both hardness and Young's modulus of the TiN coatings were measured by nanoindentation hardness testing. Friction, wear, and spalling results were related to the hardness, residual stress, preferred crystallographic orientation, and thickness of the coating. To better understand the effects of coating and substrate properties on coating performance, thermal and thermoelastic models of the sliding contact were developed. Finite element methods were used to study the thermomechanical behavior of the thin TiN coatings.
Rock Mechanics
Rock Mechanics Felsmechanik Mecanique des Roches
3
179-180
1971
10.1007/BF01238443
Although Rock Mechanics addresses many of the rock mechanics issues which arise in underground mining engineering, it is not a text exclusively for mining applications. It consists of five categories of topics on the science and practice of rock engineering: basic engineering principles relevant to rock mechanics; mechanical properties of rock and rock masses; design of underground excavations in various rock mass conditions; mining methods and their implementation; and guidelines on rock mechanics practice. Throughout the text, and particularly in those sections concerned with excavation design and design of mining layouts, reference is made to computational methods of analysis of stress and displacement in a rock mass. The principles of various computational schemes, such as boundary element, finite element and distinct element methods, are considered. This new edition has been completely revised to reflect the notable innovations in mining engineering and the remarkable developments in the science of rock mechanics and the practice of rock engineering that have taken place over the last two decades. Based on extensive professional, research and teaching experience, this book will provide an authoritative and comprehensive text for final year undergraduates and commencing postgraduate students. For professional practitioners, not only will it be of interest to mining and geological engineers but also to civil engineers, structural and mining geologists and geophysicists as a standard work for professional reference purposes. B.H.G. Brady is Emeritus Professor and former Dean of the Faculty of Engineering, Computing and Mathematics at The University of Western Australia, and a consulting rock mechanics engineer. E.T. Brown is Senior Consultant, Golder Associates Pty Ltd, Brisbane, Australia and formerly Senior Deputy Vice-Chancellor of The University of Queensland, Australia.
Analysis of surface cracks in multi-crystalline thin silicon wafers
Engineering Fracture Mechanics
124-125
310-321
2014
10.1016/j.engfracmech.2014.04.012
Surface cracks are the most common defects in solar silicon wafers. The stress intensity factors (SIFs) calculated by the semi-analytical equation derived by Newman and Raju have been compared with results of 3D finite element analysis for a wide range of semi-elliptical surface crack configurations in thin silicon wafer subjected to bending. It has been shown that the geometrical nonlinearity of silicon wafers significantly influences the SIF values. The discrepancy between nonlinear and linear models is 19% for a surface crack with 20μm depth and 1mm length, while it is 74% for a surface crack with 160μm depth and 100mm length. Furthermore, the results show that for long surface cracks (a/c⩽0.01) finite element models should be used to calculate the SIF and the existing semi-analytical solution is not reliable.
Fracture mechanics; Geometrical nonlinearity; Silicon wafer; Stress intensity factor; Surface crack
Nonequilibrium statistical mechanics of a two-temperature Ising ring with conserved dynamics
Physical Review E
90
6
062113
2014
10.1103/PhysRevE.90.062113
The statistical mechanics of a one-dimensional Ising model in thermal equilibrium is well-established, textbook material. Yet, when driven far from equilibrium by coupling two sectors to two baths at different temperatures, it exhibits remarkable phenomena, including an unexpected 'freezing by heating.' These phenomena are explored through systematic numerical simulations. Our study reveals complicated relaxation processes as well as a crossover between two very different steady-state regimes.
Influence of liquid and gas compressibility on the growth of waves in thin liquid sheets
Fluid Dynamics Research
42
3
035508
2010
10.1088/0169-5983/42/3/035508
The growth of waves along the direction of motion of viscous compressible liquid sheets in inviscid compressible gas streams was investigated. Gas streams were considered to move at different velocities relative to the liquid sheet. A dispersion relation was derived for the spatial growth of longitudinal waves in the presence of lateral wave modes. The solution of the dispersion relation showed that the incorporation of gas compressibility increases the growth of paraantisymmetric waves. Compressibility in liquid, such as obtained by the dispersion of gas bubbles, has a much lower influence on the growth of paraantisymmetric waves. The presence of lateral wave modes did not influence longitudinal wave growth when the compressibility of liquid and gas was considered in the model. © 2010 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.
Crack patterns in thin layers under temperature loading. Part II: Cyclic loading
Engineering Fracture Mechanics
73
7
939-952
2006
10.1016/j.engfracmech.2005.10.013
The paper presents an analysis of cracking and delamination of an elastic plate bonded to a rigid substrate. The plate is subjected to a cyclic temperature loading. The bond between the plate and the substrate is simulated using rigid-frictional and rigid-cohesive-frictional interface models. The states of adaptation or incremental failure are distinguished in the case of the softening interfacial law. The proposed modelling is validated to predict fragmentation of a concrete pavement subjected to temperature loading. The obtained results can serve as reference solutions for numerical calculations of more complex cases. © 2005 Elsevier Ltd. All rights reserved.
Cohesive zone modelling; Cyclic loading; Delamination; Segmentation cracking; Temperature loading
EMERGENT QUANTUM MECHANICS AS A CLASSICAL, IRREVERSIBLE THERMODYNAMICS
International Journal of Geometric Methods in Modern Physics
10
04
1350007
2013
10.1142/S0219887813500072
Quantum mechanics emerges à la Verlinde from a foliation of ℝ3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantized in units of Boltzmann's constant kB. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on ℝ3. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant ℏ from Boltzmann's constant kB.
COHESIVE MODEL FOR THIN FILM / SUBSTRATE INTERFACIAL CLEAVAGE FRACTURE
ICF10, Honolulu, Hawaii - 2001
2001
Film/substrate structure is a basic structure widely used in microelectronic and materials science and technology. A modified three-parameter (Γ0,σ/σy,t) cohesive model was used to investigate the cleavage fracture under plastic atmosphere. The model was also used to discuss the whole process of the initialization and extension of interface crack between uniform and functional graded metal thin film and ceramic substrate under residual stresses. This model was also used to analyze the interfacial crack extension between enhanced functional graded thin film and substrate. The characteristic of the interfacial crack in graded film/substrate was emphasized.
Molecular mechanics modeling of azobenzene-based photoswitches
Journal of Molecular Modeling
18
2479-2482
2012
10.1007/s00894-011-1270-6
We present an extension of the generalized amber force field to allow the modeling of azobenzenes by means of classical molecular mechanics. TD-DFT calculations were employed to derive different interaction models for 4-hydroxy-4'-methyl-azobenzene, including the ground (S(0)) and S(1) excited state. For both states, partial charges and the -N = N- torsion potentials were characterized. On this basis, we pave the way to large-scale model simulations involving azobenzene molecular switches. Using the example of an isolated molecule, the mechanics of cyclic switching processes are demonstrated by classical molecular dynamics simulations.
Azobenzene; Force-field; Molecular switch; TD-DFT
Thin-film flow of a viscoelastic fluid on an axisymmetric substrate of arbitrary shape
Journal of Fluid Mechanics
552
37-71
2006
DOI 10.1017/S0022112005008475
The interplay between inertia and elasticity is examined in this study for the transient axisymmetric flow of a thin film. The fluid is assumed to emerge from an annulus, as it is driven by axial pressure gradient and/or gravity. The substrate is assumed to be stationary and of arbitrary shape. The boundary-layer equations are generalized for a viscoelastic film obeying the Oldroyd-B constitutive model. These equations are solved by expanding the flow field in terms of orthonormal shape functions in the radial direction and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction. It is found that the viscosity ratio and fluid elasticity can have a significant effect on steady state as well as transient behaviour. It is also found that low-inertia and/or highly elastic fluids tend to accumulate near the annulus, exhibiting a standing wave that grows with time. This behaviour clearly illustrates the difficulty associated with coating viscoelastic high-viscosity fluids. A criterion for film rupture is also established, which is based on the steepening of flow and stress gradients. The topography of the substrate has a drastic effect on the flow as well.
Simulation of non-uniform wafer geometry and thin film residual stress on overlay errors
Metrology, Inspection, and Process Control for Microlithography XXV
7971
79711U (6 pp.)
2011
10.1117/12.879493
The deposition of residually stressed films in semiconductor manufacturing processes introduces elastic distortions in the wafer that can contribute to overlay errors in lithographic patterning. The distortion induced by film deposition causes out-of-plane distortion (i.e. wafer shape) that can be measured with commercial metrology tools as well as in-plane distortion that leads to overlay errors. In the present work, overlay errors and out-of-plane distortion of wafers resulting from residual stresses that are non-uniform over the area of wafer are examined using computational mechanics modeling. The results of these simulations are used to examine the correlations between wafer shape features and overlay errors. Specifically, connections between overlay errors and metrics based on the slope of the wafer shape are assessed.
coating techniques; internal stresses; nanolithography; nanopatterning; semiconductor device manufacture; semiconductor device models; thin films; wafer-scale integration
A Stack of YBCO Annuli, Thin Plate and Bulk, for Micro-NMR Spectroscopy
IEEE Transactions on Applied Superconductivity
22
3
4302204
2012
http://dx.doi.org/10.1109/TASC.2011.2178969
A new annulus magnet, the latest in a series of compact magnets being developed for NMR spectroscopy applications at the MIT Francis Bitter Magnet Laboratory, was built and tested in a bath of liquid nitrogen at 77 K. The magnet, YP2800, a stack of 2800 thin YBCO plate annuli, each either 40- or 46-mm square and 0.08-mm thick with a 26-mm bore, is an upgraded version of the two earlier plate annulus magnets, YP750 (750 plates) and YP1070 (1070). This paper presents construction details and test results of YP2800. Its spatial field homogeneity and temporal stability were measured, analyzed, and compared with those of YP750 and YP1070. Also, four YBCO bulk annuli, each 26-mm i.d., 46-mm o.d., and 5.2-mm thick, were added to YP2800 and their impacts on field strength and homogeneity were investigated experimentally.
12: Superconductivity (CD); 22: Electronic Components and Materials (EA); 70: Superconductors (General) (SO); 9E: Superconductors (WC); Ceramic Abstracts/World Ceramics Abstracts; Solid; Physics--Mechanics; Yes: (AN)
The effects of marcel defects on composite structural properties
Composite Structures: Theory and Practice
1383
158-187
2001
Doi 10.1520/Stp14509s
This paper describes a method for predicting key structural properties of carbon fiber reinforced composite materials containing ply waviness several times the nominal ply thickness. These so-called marcelled regions have been observed in a number of highly loaded thick structural components. The origins of these defects are not fully understood, although several contributing factors have been identified. The goal of this work is to develop an analysis based disposition criterion for components where fabrication process changes cannot be readily implemented to eliminate marcel defects. Work to date has focused on developing a micro-mechanics-based procedure for modeling the strength and stiffness properties of a marcelled region given basic properties of the material and simple geometric parameters of the marcel that can be measured nondestructively. The result is a general constitutive model that can be used in global structural analysis packages to assess the effects marcel defects have on component performance. Analyses of test coupons containing marcelled regions have been carried out to illustrate the method and establish the validity of the modeling approach. Results indicate that the degree to which marcel defects affect structural properties depends not only on the maximum fiber misalignment angle, but also on the location and size of the marcelled region and nominal applied strain field.
accept/reject criteria; constitutive model; marcel defect; ply waviness; test data; waviness
Screw dislocation interacting with an interfacial crack in two anisotropic thin films with finite thickness
Mechanics of Materials
33
97-103
2001
10.1016/S0167-6636(00)00061-2
Two bonded dissimilar anisotropic thin films of equal thickness h with an interfacial crack under an anti-plane singularity such as a screw dislocation or an anti-plane line force is analyzed by conformal mapping technique. The image forces on the screw dislocation, the energy release rate, and stress intensity factor are explicitly derived in terms of complex potentials. The interaction problems in two bonded orthotropic films are exemplified and the results for various particular cases of the present study are compared with the known solutions, demonstrating the versatility of this study.
A new method for determination of bending rigidities of thin anisotropic plates
Journal of Applied Mechanics-Transactions of the ASME
57
4
964-968
1990
The paper presents a new method to determine the six elastic bending rigidities of thin anisotropic plates. The experimental procedure only requires one plate specimen submitted to several bending tests performed on the same testing device. The data processing is based on the principle of virtual work and it is shown that simple linear relationships between the bending rigidities, applied loads, and plate curvature can be derived using particular virtual displacement fields. The unknown plate rigidities are the solution of a set of linear equations. The numerical simulations of various relevant bending configurations of anisotropic laminated plates point out the efficiency of this new approach.
The induction of electric currents in non-uniform thin sheets and shells
The Quarterly Journal of Mechanics and Applied Mathematics
2
3
283-310
1949
10.1093/qjmam/2.3.283
General equations are obtained for the induction of electric currents\nin any thin-sheet distribution of conducting material by periodic\nor aperiodic fields. Methods of solving the equations for non-uniform\nplane sheets and spherical shells are considered. Numerical calculations\nfor a special case of the plane sheet are made to illustrate some\nimportent features. The case of the spherical shell is considered\nin some detail, with a view to geomagnetic applications. Methods\nof approximating to the solution when the conductivity is given as\nan empiric function are described.
A Grand Isostress Ensemble Monte-Carlo Study of Thin-Films under Shear
Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics
98
3
454-457
1994
Thin films of monatomic fluid constrained between two plane-parallel structured solid walls have been simulated by Monte Carlo under conditions (fixed temperature, chemical potential and normal stress or load) prevailing in high-precision measurements of surface forces. Several phases of the film (corresponding to different numbers of layers of fluid parallel with the walls) are generally consistent with these conditions, but only one is thermodynamically stable; the others are metastable. When the walls are properly aligned, epitaxial solidlike phases are stable. These melt under shear, eventually becoming metastable, whereupon a drainage (or imbibition) transition occurs, leading to a stable phase with fewer (or more) layers.
computer experiments; interfaces; liquid-films; phase transitions; statistical mechanics; thermodynamics
The plastic loss of stability of a thin-walled tube under axial compression
Journal of Applied Mathematics and Mechanics
76
3
358-366
2012
10.1016/j.jappmathmech.2012.07.013
A theoretical model of the plastic shaping of ring folds in the axial\ncompression of a thin-walled tube with smooth plates after local\nloss of stability is presented. The initial stage of the shaping\nis calculated using membrane theory of a rigid-plastic envelope under\nthe von Mises plasticity condition, taking into account the deformation\nstrengthening and the change in the wall thickness. The final stage\nis calculated using moment theory with the finite curvature of the\ncurvilinear parts of the folds. The calculated forms of the folds\nand the force-displacement dependences when there is loss of stability\nagree satisfactorily with experimental data.
Electromechanical control of the dynamics of a thin elasticplate: Analytical method and finite differences simulation
Mechanics Research Communications
61
19-26
2014
10.1016/j.mechrescom.2014.06.005
The electromechanical control of the dynamics of thin elastic plate is analysed using both the modal approach and the direct numerical simulation of partial differential equation. The electromechanical controller is constituted of a RL circuit with some stings connected through a magnet to the plate. The direct numerical simulation reveals the existence of different vibration modes. The boundary limits of the control parameters leading to the reduction of vibration amplitude, snap through instability and Melnikov chaos are determined and plotted in terms of the system parameters. It is seen that electromechanical control can eliminate the chaotic domain leading to periodic oscillations.
Control of vibrations; Dissipative chaos; Melnikov chaos; Plate dynamics; Snap through instability
A new approach to an analysis of large deflections of thin elastic plates
International Journal of Non-Linear Mechanics
16
1
47-52
1981
10.1016/0020-7462(81)90031-7
-For thin plates undergoing large deflections a modified energy expression has been suggested and a new set of differential equations has been obtained in a decoupled form Accuracy of the equations has been tested for a circular and a square plate x~ lth immovable as well as mo~ able edge conditions under a uniform static load Results obtained are m excellent agreement with other known results These new equations are more advantageous than Berger s decoupled equations which fall to give meaningful results for movable edge conditions
On the factors affecting the propagation of long fatigue cracks in thin-sheet wrought aluminium alloys
International Journal of Fatigue
25
9-11
885-889
2003
10.1016/S0142-1123(03)00158-0
The paper deals with the propagation of long fatigue cracks in commercial heat-treatable thin-sheet wrought aluminium alloys with focus on the mid-region of the cyclic stress intensity factor. The experimental observations support the distinction of two groups of alloy conditions according to the degree of coherency of the strength-controlling precipitates. A model explaining the observations for the first group, which is characterized by predominantly incoherent precipitates, is proposed. These precipitates cannot be cut by dislocations and both a homogeneous slip distribution and a continuum-mechanics dominated crack path are favoured. The reasons why the alloys with a high degree of coherency of the strength-controlling precipitates deviate from the fatigue crack growth behaviour common of the representatives of the first group are analysed.
aluminium alloys; fatigue crack growth
Weinberg's non-linear quantum mechanics and supraluminal communications
Physics Letters A
143
1-2
1-2
1990
10.1016/0375-9601(90)90786-N
We show with an example that Weinberg's general framework for introducing non-linear corrections into quantum mechanics allows for arbitrarily fast communications.
PREDICTIONS OF TRANSVERSE DEFLECTIONS A N D IN- PLANE STRAINS IN IMPULSIVELY LOADED THIN PLATES
Africa
29
6
435-442
1987
DOI: 10.1016/0020-7403(87)90004-X
This paper is an extension of earlier work [Nurick et al., Inelastic\nBehaviour of Plates and Shells. Springer Verlag, Berlin (1986)] in\nwhich experimental and theoretical studies of thin circular, square\nand rectangular plates subject to transverse impulsive loading were\npresented. Major interest in the experimental study was the range\nwhere the permanent displacement is large, up to 12 times the thickness\nof the plate. The theoretical model was based on a rigid-plastic\nmembrane theory, using the concept of the instantaneous mode approximation\ntechnique. Predicted transverse displacements agreed well with experimental\ndata. However, it was assumed that points on the plate surface move\nonly in the direction normal to the initial plane of the plate: as\na consequence of that, in-plane membrane strains are incorrectly\npredicted. In this paper the mode approximation is modified by assuming\nthat points on the plate surface move in a direction which is instantaneously\nnormal to the current plate surface. The modified theory continues\nto give good predictions of the transverse displacement, and gives\nquite good estimates of in-plane strains.
A new approach for handling and transferring of thin semiconductor materials
Microsystem Technologies
9
3
204-209
2003
10.1007/s00542-002-0226-2
Abstract Based on the fracture mechanics analysis of crack propagation, the phenomenon of subcritical crack growth was utilized for a controlled debonding of directly wafer-bonded interfaces. The approach allowed the well-defined separation of bonded wafers although the bond strength was high due to thermal annealing. The achieved splitting velocity depended on the wafer material, the wafer thickness ratio, the bonding process parameters, and the environmental conditions during cleaving. In combination with wafer bonding, the method can be used for a temporary stiffening and handling of thin and brittle wafers during fabrication, even if the wafers are exposed to high process temperatures. The approach can also be applied to fabricate micromechanical systems (MEMS).
Fully non-linear magnetoelastic interactions of a circular cylindrical thin shell subject to electromagnetic fields
International Journal of Non-Linear Mechanics
46
2
425-435
2011
http://dx.doi.org/10.1016/j.ijnonlinmec.2010.11.002
By using the mixed Lagrangian–Eulerian description and adopting the von Kármán's strain approximation, the non-linear magnetoelastic interactions of a circular cylindrical thin shell experiencing moderately large deflections are fully explored. The shell is assumed to be perfectly electroconductive and immersed in an applied magnetic field and carrying electric current. The magnetoelastic loads acting on the shell associated with the Lorentz forces and Maxwell's stress jumps are explicitly represented and the approximated governing systems for the induced magnetic fields outside the shell in total Lagrangian description are obtained. Case study on a shell's cross section model is conducted and pertinent conclusions are drawn.
Circular cylindrical shell; Geometrically non-linear; Magnetoelastic interactions; Mixed Lagrangian–Eulerian description
Fatigue damage evaluation of thin-walled short elbow under seismic loadings
The 14th International Conference on Structural Mechanics in Reactor Technology
229-236
1997
A fatigue damage evaluation method was developed for thin-walled short elbow under seismic loadings, which uses detailed numerical analysis along with the classic LCF evaluation. The applicability of the method was validated by comparison with dynamic failure tests a short elbows. The usage factors of fatigue damage obtained by the method could predict the occurence of through-wall-crack failure in the test with errors less than 25%. It was shown that the fully numerical approach is feasible for the LCF evaluation of piping systems under seismic loadings.
fatigue damage; seismic loading; shor elbow
The vibrations of a thin elastic orthotropic circular cylindrical shell with free and hinged edges
Journal of Applied Mathematics and Mechanics
72
3
312-322
2008
http://dx.doi.org/10.1016/j.jappmathmech.2008.07.009
The problem of the existence of natural oscillations of a thin elastic\northotropic circular closed cylindrical shell with free and hinge-mounted\nends and of an open cylindrical shell with free and hinge-mounted\nedges, when the two boundary generatrices are hinge-mounted is investigated.\nDispersion equations and asymptotic formulae for finding the natural\nfrequencies of possible vibration modes are obtained using the system\nof equations corresponding to the classical theory of orthotropic\ncylindrical shells. A mechanism is proposed by means of which the\nvibrations can be separated into possible types. Approximate values\nof the dimensionless characteristic of the natural frequency and\nthe attenuation characteristic of the corresponding vibration modes\nare obtained using the examples of closed and open orthotropic cylindrical\nshells of different lengths.
Correlation experiments in nonlinear quantum mechanics
Physics Letters A
301
August
139-152
2002
10.1016/S0375-9601(02)00959-3
We show how one can compute multiple-time multi-particle correlation functions in nonlinear quantum mechanics in a way which guarantees locality of the formalism.
Classical and Quantum Mechanics via Lie Algebras
arXiv
2011
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
$PT$-symmetric quantum mechanics is a Hermitian quantum mechanics
arXiv:1312.7738 [math-ph, physics:quant-ph]
2013
The author discusses a different kind of Hermitian quantum mechanics, called $J$-Hermitian quantum mechanics. He shows that $PT$-symmetric quantum mechanics is indeed $J$-Hermitian quantum mechanics, and that time evolution (in the Krein space of states) is unitary if and only if Hamiltonian is $J$-Hermitian (or equivalently $PT$-symmetric). An issue with unitarity comes up when time evolution is considered in the Hilbert space of states rather than in the Krein space of states. The author offers possible scenarios with this issue.
Electroelasticity relations and fracture mechanics of piezoelectric structures
Applied Mechanics Reviews
60
1-6
21-36
2007
Doi 10.1115/1.2375142
Three-dimensional (3D) constitutive equations of piezoelectric (PZ) plates and shells are considered for inverse linear and electrostrictive (quadratic) piezoeffects. Prestressed multilayer PZ shells reinforced with metal including the case of uneven thickness polarization are studied. Asymptotic and variational methods to solve the governing differential equations of PZ shells are considered. Concentrations of electrical and mechanical fields near structure imperfections and external local loading are investigated. The electrothermoviscoelastic heating of PZ shells is considered at harmonic excitation. From numerical analysis and the experimental data of energy dissipation and the temperature behavior of PZ shell the conditions of optimal transformation of electric energy into mechanical deformations are defined. Thus, the geometrical parameters and working frequencies are determined with due account of dielectric relaxation processes. The following nonlinear phenomena are studied: acoustoelectronic wave amplification; electron injection into metalized polar dielectric; resonance growth by 5-20 times of internal electrical field strength in the PZ shells and plates; and autothermostabilization of ferroelectric resonators. For a better understanding of R.D. Mindlins gradient theory of polarization in view of electron processes in thin metal-dielectric-metal structures, use was made of solid state physics interpretations as well as experimental data. High concentration of mechanical stresses and temperature and electrical fields near structure defects (first of all, near boundary between various materials) defines the main properties of polar dielectrics. An unknown domain of electrode rough surface influence was estimated, and as result an uneven polarization distribution was found. A theory of nonlinear autowave systems with energy dissipation was used in a physical model of the electrothermal fracture of dielectrics (contacting with metal electrodes), and as a result a nondestructive testing method to study the microstructure defect formation has been suggested.
cylindrical-shells; dielectric-metal mdm; electro-elastic plates; electromechanical fatigue; ferroelectric ceramics; semiconductor-devices; shape control; shell theory; space-charge; stationary distribution
Mechanics of complex hydraulic fractures in the Earth's crust
ProQuest Dissertations and Theses
350-350 p.
2004
Hydraulic fracturing is an important and abundant process in both industrial applications and natural environments. The current work is the first systematic quantitative study of the effect of interaction in and between complex hydraulic fractures at different spatial scales. A mathematical model, based on the boundary collocation method, has been developed. The model has been employed for a typical field case, a highly segmented vein. This vein is well-mapped, and therefore, represents a well constrained example. The computed apertures are compared to the measured apertures. By using the simplest constitutive model, based on an ideal elastic material, and including the effect of interaction between the segments, it was possible to obtain an excellent match at all considered scales. It was also shown that the concept of effective fracture, as currently accepted in the literature, is not always applicable and may lead to unbounded inaccuracy. Unfortunately, in most cases, very little (if any) directly measured data on fracture and material properties is available. An important example of such a weakly constrained case, involving hydraulic fracturing, is diking beneath the seafloor at mid-oceanic ridges. In this study, it is shown that the commonly accepted scenario of a dike propagating from the center of the pressurized magma chamber to the ocean floor is not consistent with conventional fracture mechanics due to the fact that the chamber has the shape of a thin lens. Even at such a large scale (i.e., a kilometer or more), the mechanical principles of elastic interaction appear to be applicable. Since diking is likely to generate a region of high permeability near its margin, in addition to heat, the ongoing hydrothermal activity becomes localized. Our modeling suggests the probable positions of the propagating dikes. Consequently, comparing the observed locations of hydrothermal sites with respect to that of the magma chamber could be useful for constraining the mechanisms of magma lens evolution.
0373:Geophysics; 0388:Hydrology; 0543:Civil engineering; Applied sciences; Civil engineering; Crust; Earth sciences; Geophysics; Hydraulic fractures; Hydrology; Magma
Fatigue life methodology for tapered composite flexbeam laminates
Journal of the American Helicopter Society
43
2
146-155
1998
The viability of a method for determining the fatigue life of composite rotor hub flexbeam laminates using delamination fatigue characterization data and a geometric non-linear finite element (FE) analysis was studied. Combined tension and bending loading was applied to non-linear tapered flexbeam laminates with internal ply drops. These laminates, consisting of coupon specimens cut from a full-size S2/E7T1 glass-epoxy flexbeam were tested in a hydraulic load frame under combined axial-tension and transverse cyclic bending loads. The magnitude of the axial load remained constant and the direction of the load rotated with the specimen as the cyclic bending load was applied. The first delamination damage observed in the specimens occurred at the area around the tip of the outermost ply-drop group. Subsequently, unstable delamination occurred by complete delamination along the length of the specimen. Continued cycling resulted in multiple delaminations. A 2D finite element model of the flexbeam was developed and a geometrically non-linear analysis was performed. The global responses of the model and test specimens agreed very well in terms of the transverse flexbeam tip-displacement and Happing angle. The FE model was used to calculate strain energy release rates (G) for delaminations initiating at the tip of the outer ply-drop area and growing toward the thick or thin regions of the flexbeam, as was observed in the specimens. The delamination growth toward the thick region was primarily mode II (shear), whereas delamination growth toward the thin region was almost completely mode I (opening). Material characterization data from cyclic double-cantilevered beam tests was used with the peak calculated G values to generate a curve predicting fatigue failure by unstable delamination as a function of the number of loading cycles. The calculated fatigue lives compared well with the test data.
Trebuchet Mechanics
The Algorithmic Beauty of the Trebuchet
1-58
2001
The trebuchet, a medieval catapult driven by a falling, hinged counterweight, has been simulated to progressively more accurate approximations by successively more realistic physical models. The first of these, a "black box" model in which the mechanism for the transfer of the potential energy of the counter-weight to the kinetic energy of the released projectile is left unspecified, led to a definition of a "Range Efficiency," Reff, equal to the measured range of the projectile divided by the range of the black box model, given by twice the ratio of the CW to projectile masses times the distance that the CW falls. This range efficiency can be used to compare actual trebuchets to simulated ones, design "back of the envelope" trebuchets, and is useful in understanding the results of more sophisticated simulations. The method used to arrive at the most accurate simulations is to use the Mathematica programming language to derive the three coupled differential equations from the Lagrangian for the system. This method allows the sliding constraint equations to be readily derived and translated into a form useful for other, faster, computer languages. The equations, while consisting of many terms, are amenable to solution by Mathematica's differential equation solver, as well as by a fourth-order Runge-Kutta method. The solution has been verified by various methods, including one that involves using the solution to calculate the total energy of the system at every instant and showing that it is a constant. The physics of the release mechanism is also described in some detail, and the dependence of the range on the finger angle and the coefficients of friction is given in approximate terms. The benefits of propping the counterweight, as opposed to letting it hang freely from the end of the beam is also discussed. A major result is the design of an efficient trebuchet, by exploring the design space by doing thousands of simulations. The result indicates that one in which the beam is initially at a 45 angle, the sling is equal in length to the length of the long arm of the beam, and the long arm of the beam is four times as long as the short arm, is a reasonably efficient one, and is therefore recommended as a "nominal" design.
Fluid mechanics in terms of eigenparameters Part II: Exemplary applications
Chemical Engineering Science
55
6
1179-1188
2000
10.1016/S0009-2509(99)00159-1
In chemical engineering, fluid mechanics is a tool for the successful design of processes, which involve heat and mass transfer as well as chemical reactions. In order to exemplify this particular role of fluid mechanics, the implications of fluid mechanics on the heat transfer are demonstrated exemplarily. (C) 1999 Elsevier Science Ltd. All rights reserved.
Recent development in the mechanics of superplasticity and its applications
Journal of Materials Processing Technology
151
196-202
2004
10.1016/j.matprotec.2004.04.039
This paper reviewsthe recent developments in the mechanics of superplasticity and its applications in industrial practice. After introducing the phenomena of superplasticity, the basic experiments for determining material deformation behavior and related parameters, and constructing superplastic constitutive equations, are reviewed. Finite element related formulations and techniques for simulating superplastic forming are discussed, together with some practical applications.
constitutive equation; finite element method; microstructure variation; superplastic experiment; superplastic forming; superplastic mechanics
Relativistic Celestial Mechanics of the Solar System
Relativistic Celestial Mechanics of the Solar System
2011
10.1002/9783527634569
his authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping.
Analysis of mechanics properties on FRP-concrete-steel double-skin tubular short columns
Xi'an Jianzhu Keji Daxue Xuebao/Journal of Xi'an University of Architecture and Technology
45
5
2013
Using the twin shear unified limit solutions of thin-walled cylinder, the formula of axial bearing capacity for FRP-concrete-steel double-skin tubular short columns was presented by considering the influence of intermediate principal stress and the internal thin-walled steel tube effect. Nonlinear element analysis models of composite columns under axial load were developed by using ANSYS program. Then, the ultimate bearing capacities and the stress-strain relationship curves for members were carried out. The finite element results agree well with the calculated results obtained in the paper and test results from the references. Based on the results achieved influences of loads on the stress distribution and the thickness to diameter ratio for steel tube and the concrete strength on bearing capacities for members were studied.
FPR-concrete-steel double-skin tubular; Mechanics properties; Nonlinear finite element analysis; The twin shear unified strength theory; Thin-walled cylinder
A study of stable crack growth in thin sec specimens of 304 stainless steel by computer vision
Engineering Fracture Mechanics
52
3
525-555
1995
10.1016/0013-7944(94)00295-S
Computer vision methods were used to study crack growth and crack blunting in thin, 304 stainless steel single edge cracked (SEC) specimens with various a/w ratios. The in-plane displacement and strain distributions in the vicinity of the crack tip before and after crack growth were obtained and compared with theoretical predictions. Results for a growing crack indicate that for small amounts of crack growth, a critical value for the [omega] factor is a predictor of the presence of HRR-type fields. Specifically, with [Delta]a < 0.08a0 and [omega] > 10, where a0 is the initial crack length, the crack tip deformation fields have the same form as observed for stationary cracks; the HRR dominant zones exist for V and [epsilon]yy but the field variables U, [epsilon]xx and [epsilon]xy have either non-existent or much smaller HRR zones. For a limited range of crack growth (0.08a0 < [Delta]a < 0.20a0), trends in the crack tip deformation fields in a segment of the crack tip region are reasonably predicted by the plane strain, quasi-static growing crack tip fields. For larger amounts of crack growth ([Delta]a > 0.20 � a0), available theories were unable to predict the observed deformations. The J-integral, crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) were investigated to determine if they can be used as fracture parameters for thin specimens. Results indicate that the CTOD-[Delta]a and CTOA-[Delta]a curves were reasonably independent of a/w ratios for all [Delta]a, with CTOA having the admirable quality of being constant during crack growth for [Delta]a > t. The Javg- [Delta]a (J[tau]) trends were independent of a/w ratio only for [Delta]a < t, where t is the specimen thickness, with a substantial increase in scatter for larger [Delta]a. In addition, it was determined that the general form of the CTOA-[Delta]a data appears to be due to crack tunneling within the thin specimen for [Delta]a < t, with the initial large values of CTOA occuring during the tunneling phase of crack extension. Finally, the elastic unloading phenomenon for a growing crack was investigated and found to be in reasonable agreement with analytical predictions.
Finite element modeling of tensile test of thin-film specimens
SEM Annual Conference and Exposition on Experimental and Applied Mechanics 2006
1
339-344
2006
Finite element models of thin film samples strained on a tensile test apparatus have been presented. Test samples made up of thin film coatings on conforming polyamide substrates have been studied. Validity of the testing technique with sample on compliant substrate has been investigated using a parametric study. Results indicate that a 5% difference in Poisson's ratio between the substrate and the thin film coating results in a maximum strain variation of around 2%. The loading scheme and model has been developed so as to characterize closely the experimental setup comprising of a hybrid linear actuator, high precision load cell and LVDT. The models were run using FEA software and the results were compared with experimental data. Errors in results due to misalignment of samples have been estimated. Possible techniques for improving values for micromechanical properties and the experimental setup of the samples have been suggested based on an iterative analysis scheme for the models.
Actuators; Computer software; Finite element method; Hybrid linear actuators; Parametric study; Poisson ratio; Polyamides; Strain; Tensile testing; Thin film coatings; Thin films
Reviving the Mission of Rock Mechanics Teaching in Mining and Civil Engineering
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts
31
2
135-142
1994
Doi 10.1016/0148-9062(94)92803-7
The subject of teaching rock mechanics is nearly completely absent from rock mechanics journals as well as from national and international symposia. At all ISRM Congresses, since 1964, there has never been a theme or even a session devoted to the teaching of rock mechanics. In the halls of academia, mining and civil engineering professors very seldom discuss the pedagogic issues associated with their main mission: education. The subjects prevailing in professional discussions are research, writing papers and attending meetings. The author performed a study involving mining and civil engineering undergraduate programs in the U.S.A. and Europe, and concluded that rock mechanics teaching is out of date with the educational issues of today, that the material taught is infrequently updated, that the teaching techniques have hardly changed, that little attention is paid to engineering design in rock mechanics while sophisticated computer analyses and laboratory testing predominate. Rock mechanics is seldom a required course at the undergraduate level and is mostly taught at a graduate level as an elective. It is thus not surprising that industry is not convinced of the value of rock mechanics in practice. Recommendations are made about what steps should be taken urgently to salvage the subject we care about so much and to bring renewed devotion to the teaching of rock mechanics.
education
Contribution of Powder Coal Ply ASH to Concrete Properties
Studies in Environmental Science
Volume 48
385-398
1991
10.1016/S0166-1116(08)70428-X
Summary The mechanisms through which powder coal fly ash contributes to cementitious binder systems are discussed. Special attention is given to the so-called pozzolanity of fly ash and the ability to densify the transition zone between the cementitious matrix and aggregate grains. These various phenomena can lead to an improvement of the features of concrete of which part of the portland cement has been replaced in comparison with reference composites without cement replacement. The nature of these phenomena is discussed. It is shown that the fly ash performance in concrete not only depends on the features of the fly ash but also on other parameters, notably cement type and composition, water cement ratio and temperature. A model for fly ash reaction in concrete is presented, explaining the various effects of fly ash on concrete properties.
Design of a handling device for composite ply lay-up automation
Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments
790-795 vol.1
1991
10.1109/ICAR.1991.240578
Discusses the development of an essential core element of a technically viable automated propeller preform lay-up cell, an effective gripper device. The success of the gripper development programme has hinged upon the application of a structured design approach encompassing: an analysis of the existing manual lay-up process, as well as both front and back end operations; an adaptation of the existing lay-up process to make it easier to automate; an analysis of the handling properties of plies to be laid-up; a comprehensive conceptual design investigation; and the manufacture and operational trial of a half scale prototype gripper unit. The full scale gripper unit, which has evolved from the structured design programme, offers complete operational capability and long term flexibility, combined with low mass and minimal control requirements.<>
Boosted Statistical Mechanics
International Journal of Theoretical Physics
2015
10.1007/s10773-014-2506-x
Starting with the basic principles of Relativistic Quantum Mechanics, we give a rigorous, but completely elementary proof of the relation between fundamental observables of a statistical system, when measured within two inertial reference frames, related by a Lorentz transformation.
Lorentz transformations; Relativistic quantum mechanics; Statistical mechanics
Structural Mechanics E1.1
Engineering Fracture Mechanics
11
3
607
2006
This second edition of Structural Mechanics has been extended to cover the major part of the structural mechanics/analysis syllabuses of most civil engineering courses up to the end of second year level.
Buckling of multiwalled carbon nanotubes under axial compression and bending via a molecular mechanics model
Physical Review B
72
6
2005
Artn 064101\rDoi 10.1103/Physrevb.72.064101
Based on a molecular mechanics model, analytical solutions are obtained for the critical buckling strain of multiwalled carbon nanotubes (MWNT's) under axial compression and bending. We show that only part of the outer layers buckles first while the remaining inner part remains stable in a very thick MWNT, which is quite different from the initial buckling mode of a relatively thin MWNT in which all individual tubes buckle simultaneously. Such a difference in the initial buckling modes results in quite different size effects on the critical buckling strain of thin and thick MWNT's. For instance, inserting more inner individual tubes may increase the critical buckling strain of a thin MWNT, but cannot increase the critical buckling strain of a thick tube. The effects of tube size on the initial buckling wavelength are also examined, and it is shown that the initial buckling wavelength is weakly dependent on the thickness of the MWNT.
deformation; elastic medium; large-strain; resonances; single; stiffness; wall
Mechanics of bilayer membranes
Journal of Colloid and Interface Science
51
2
266-271
1975
10.1016/0021-9797(75)90112-5
The general mechanics of elastic deformations in bilayer membranes is developed, resulting in three elastic constants characterizing a bilayer surface. The theoretical analysis is applied to bilayer systems containing organic solvents (referred to as "solvent bilayers") and to planar bilayer membranes free of solvent (referred to as "nonsolvent bilayers"). The relationship between a normal surface traction (e.g. electrocompression resulting from transmembrane potential difference) and change in membrane thickness is investigated for the two types of bilayers.
Minimum energy configurations in the N-body problem and the celestial mechanics of granular systems
Celestial Mechanics and Dynamical Astronomy
113
291-320
2012
10.1007/s10569-012-9416-0
Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a granular mechanics extension of usual celestial mechanics questions such as relative equilibria and stability. This paper specifically studies and finds all relative equilibria and minimum energy configurations for N=1,2,3 and develops hypotheses on the relative equilibria and minimum energy configurations for N=4 bodies.
Surfactant effects on the dynamics of a thin liquid sheet
Journal of Fluid Mechanics
300
-1
71
2006
10.1017/S0022112095003612
The dynamics of a free-surface slender two-dimensional stream (liquid sheet) issuing from a nozzle in the gravitational field in still air, under the effect of surface-active agents, are analysed experimentally. The particular test section geometry (the liquid is forced to assume a bidimensional form between two vertical guides and a horizontal plate placed at a certain variable distance from the nozzle exit section) employed in this study gives rise to various flow regimes depending on the governing parameters : liquid flow rate, sheet height, surface pressure, gravity. Two basic phenomena are observed : thinning of the sheet (with recirculating motion inside it) and sheet-threadlines transition. For a certain surfactant (bulk) concentration, there exists a minimum critical flow rate value for which the sheet is seen to thin starting at both of the sheet bottom corners. A ridge, usually referred to as a Reynolds ridge in the literature, separates the sheet from the thin-film regions. The thin films exhibit recirculating flows (caused by the onset of surfactant-induced surface-pressure-driven convection in the gravitational field) and extend to the entire rectangular interface as the flow rate is reduced. At zero flow rate the thinned sheet resembles a plane vertical soap film showing a recirculating cellular structure. These phenomena are linked to the presence of surface-active material adsorbed at the liquid-air interface and occur when the sheet height exceeds a critical value. Otherwise, at a critical flow rate value the liquid sheet breaks up into an array of (more or less regularly distributed) discrete threadlines (vertical jets), whose spacing depends on the surface tension of the test liquid.
Breakage mechanics — Part I : Theory
Mechanics and Physics of solidechanics and Physics of solid
55
1274-1297
2007
10.1016/j.jmps.2006.11.003
Different measures have been suggested for quantifying the amount of fragmentation in randomly compacted crushable aggregates. A most effective and popular measure is to adopt variants of Hardin’s [1985. Crushing of soil particles. J. Geotech. Eng. ASCE 111(10), 1177–1192] definition of relative breakage ‘Br’. In this paper we further develop the concept of breakage to formulate a new continuum mechanics theory for crushable granular materials based on statistical and thermo- mechanical principles. Analogous to the damage internal variable ‘D’ which is used in continuum damage mechanics (CDM), here the breakage internal variable ‘B’ is adopted. This internal variable represents a particular form of the relative breakage ‘Br’ and measures the relative distance of the current grain size distribution from the initial and ultimate distributions. Similar to ‘D’, ‘B’ varies from zero to one and describes processes of micro-fractures and the growth of surface area. However, unlike damage that is most suitable to tensioned solid-like materials, the breakage is aimed towards compressed granular matter. While damage effectively represents the opening of micro-cavities and cracks, breakage represents comminution of particles. We term the new theory continuum breakage mechanics (CBM), reflecting the analogy with CDM. A focus is given to developing fundamental concepts and postulates, and identifying the physical meaning of the various variables. In this part of the paper we limit the study to describe an ideal dissipative process that includes breakage without plasticity. Plastic strains are essential, however, in representing aspects that relate to frictional dissipation, and this is covered in Part II of this paper together with model examples
0022-5096; 61 2 935 12113; 61 2 935 13343; all rights reserved; ã tel; au; breakage; civil; comminution; continuum mechanics; edu; einav; e-mail address; fax; grain size distribution; granular materials; i; r 2006 elsevier ltd; - see front matter; usyd
Plasticity in passive cell mechanics
International Journal of Non-Linear Mechanics
56
56-60
2013
10.1016/j.ijnonlinmec.2013.04.007
A sufficiently large load applied to a living cell for a sufficiently long time produces a deformation which is not entirely recoverable by passive mechanisms. This kind of plastic behavior is well documented by experiments but it is still seldom investigated in terms of mechanical theories. Here we discuss a finite visco-elasto-plastic model where the rest elongation of the cell evolves in time as a function of the dissipated energy at a microstructural level. The theoretical predictions of the proposed model reproduce, also in quantitative terms, the passive mechanics of optically stretched cells. ?? 2013 Elsevier Ltd. All rights reserved.
Cell mechanics; Living cell; Plastic hardening; Visco-elasto-plasticity
The Absolute Instability of Thin Wakes in an Incompressible/Compressible Fluid
Theoretical and Computational Fluid Dynamics
13
2
91-114
1999
http://dx.doi.org/10.1007/s001620050006
The absolute/convective instability of two-dimensional wakes forming behind a flat plate and near the trailing-edge of a thin wedge-shaped aerofoil in an incompressible/compressible fluid is investigated. The mean velocity profiles are obtained by solving numerically the classical compressible boundary-layer equations with a negative pressure gradient for the flat plate case, and the incompressible triple-deck equations for a thin wedge-shaped trailing-edge. In addition for a Joukowski aerofoil the incompressible mean boundary-layer flow in the vicinity of the trailing-edge is also calculated by solving the interactive boundary-layer equations. A linear stability analysis of the boundary-layer profiles shows that a pocket of absolute instability occurs downstream of the trailing-edge with the extent of the instability region increasing with more adverse pressure gradients. The region of absolute instability persists along the near-wake axis, while the majority of the wake is convectively unstable. For a thin wedge-shaped trailing-edge in an incompressible fluid, a similar stability analysis of the velocity profiles obtained via a composite expansion, also shows the occurrence of absolute instability behind the trailing-edge for a wedge angle greater than a critical value. For increasing values of the wedge angle and for thicker aerofoils, separation takes place near the trailing-edge and the extent of absolute instability increases. Calculations also show that for insulated plates compressibility has a stabilizing effect but cooling the wall destabilizes the flow unlike wall heating.
Physics--Mechanics
Aspects of the mechanics of lobed liposomes.
Journal of Biomechanical Engineering
118
4
482-488
1996
Hotani has studied, by means of dark-field light microscopy, morphological transformations which unilamellar liposomes undergo when their interior volume decreases steadily with time as a consequence of osmosis. In a previous paper, we made a theoretical study of the initial buckling of an originally spherical vesicle into the observed oblate spheroidal shape; and we argued that some in-plane shear elastic stiffness is required-in addition to the well-known flexural stiffness of the lipid bilayer-in order to explain the observed phenomena. In the present paper, we consider a later stage in the chain of morphological transitions observed by Hotani, when a series of cudgel-shaped lobes have sprung out of a previously axisymmetric, biconcave-shaped vesicle. Specifically, we compare the observed shapes of such lobes with half of a series of "peanut"-shaped vesicles that are an equilibrium conformation of an initially spherical liposome under reduced internal volume. We find that the shapes do not match well. On the other hand, the observed lobe forms do match satisfactorily portions of "undulating tube" shapes which evolve from a hypothetical cylindrical vesicle, according to some simple calculations. In view of this agreement, we are led to propose that the formation of cudgel-shaped lobes requires some sliding of one lipid monolayer over another. This conflicts, of course, with the Love-Kirchhoff hypothesis which is normally invoked at the outset of analyses of lipid vesicles by means of classical thin-shell theory; but it is in accord with previous suggestions in the context of more obviously severe distortion of the lipid bilayer.
Exactly Solvable Quantum Mechanics
arXiv
48
2014
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.
closure relations; exact solvability; factorised hamiltonian; flectionless potentials; heisenberg operator solutions; intertwining relations; new orthogonal polynomials; re-; shape in-; variance
Representative Ensembles in Statistical Mechanics
arXiv
18
2007
The notion of representative statistical ensembles, correctly representing statistical systems, is strictly formulated. This notion allows for a proper description of statistical systems, avoiding inconsistencies in theory. As an illustration, a Bose-condensed system is considered. It is shown that a self-consistent treatment of the latter, using a representative ensemble, always yields a conserving and gapless theory.
Statistical Mechanics
Statistical mechanics of multipartite entanglement
Journal of Physics A: Mathematical and Theoretical
42
5
055304
2009
10.1088/1751-8113/42/5/055304
We consider a system of n qubits and characterize its multipartite entanglement in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those maximally multipartite entangled states whose average purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.
Electrofracture mechanics of dielectric aging
Journal of Applied Physics
56
2
455-459
1984
10.1063/1.333931
We introduce a fracture mechanics concept of aging in solid dielectrics. The key element is that growth of a damage structure is only possible if the release of electrostatic energy due to growth exceeds the formation energy of the damage structure. Both the electrostatic energy release and the formation energy are calculated for simple examples.
Physically based damage models for laminated composites
Proceedings of the I MECH E Part L Journal of Materials:Design and Applications
217
L3
163-199
2003
10.1243/146442003322256187
The computing power that is available for engineering calculation continues to grow at a dramatic pace. Engineers in industry want to have seamless models that can be used to design across the scale range from atoms to structures, including simulation of the manufacturing process. A limited aspect of this wish is the requirement to deal effectively with the progressive growth of microstructural damage in composites and its effect on both property degradation and the catastrophic failure event. This paper reviews progress that is being made at the National Physical Laboratory (NPL) with the development and validation of physically based damage growth models for laminated composites. The review includes: (a) prediction of undamaged ply properties determined from the properties of the fibre and the matrix, with emphasis on comparison of analytical models with each other, and with finite and boundary element solutions; (b) discussion of various stress transfer models, and their validation, that have been developed for application to the prediction of the properties of composite laminates having ply crack damage; (c) prediction of ply cracking in multiple-ply cross-ply laminates subject to triaxial loading (without shear) and bending; (d) prediction of ply cracking in general symmetric laminates subject to combined triaxial loading and in-plane shear loading; (e) consideration in a damage mechanics context of progressive ply crack formation in general symmetric laminates subject to thermal residual stresses and general in-plane loading, where an important new methodology is described that results from attempting to develop a continuum damage model from a physically based discrete ply cracking model based on energy concepts; (f) discussion of how the models might be integrated into finite element analysis (FEA) systems to enable strain softening in structures to be adequately modelled. The paper also includes statements concerning the status of the various models in relation to alternative approaches, and to model validation.
cte
Probability interpretation of quantum mechanics
American Journal of Physics
48
12
1029
1980
10.1119/1.12299
The paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the ’’paradoxical’’ aspects of quantum mechanics lose their counterintuitive character.
Identification of multiple directional damages in a thin cylindrical shell
International Journal of Solids and Structures
43
9
2723-2743
2006
10.1016/j.ijsolstr.2005.03.077
In this paper, a structural damage identification method (SDIM) is developed to identify the line crack-like directional damages generated within a cylindrical shell. First, the equations of motion for a damaged cylindrical shell are derived. Based on a theory of continuum damage mechanics, a small material volume containing a directional damage is represented by the effective orthotropic elastic stiffness, which is dependent of the size and the orientation of the damage with respect to the global coordinates. The present SDIM is then derived from the frequency response function (FRF) directly solved from the equations of motion of a damaged shell. In contrast with most existing SDIMs which require the modal parameters measured in both intact and damaged states, the present SDIM may require only the FRF-data measured at damaged state. By virtue of utilizing FRF-data, one may choose as many sets of excitation frequency and FRF measurement point as needed to acquire a sufficient number of equations for damage identification analysis. The numerically simulated damage identification tests are conducted to study the feasibility of the present SDIM.
Continuum damage model; Cylindrical shell; Damage identification; Frequency response function; Orthotropic damage; Structural damage
Integration, electrical and electromechanical properties of PZT and PMN-PT thin films for MEMS applications
Smart Structures and Materials 2002: Active Materials: Behavior and Mechanics
4699
114-123
2002
10.1117/12.474966
Piezoelectric and electrostrictive thin films are potential candidates for actuator functions in micro-electro-mechanical systems (MEMS) offering displacements and forces which outperform standard solutions, e.g. in micro mirrors and micro relays. Within this context the paper reports on the preparation and the integration processes of chemical solution deposited (CSD) Pb(Zr-x Til-x)O-3 (PZT) and (PbMg1/3Nb2/3)(l-z)-(PbTiO3)(z) (PMN-PT) thin films in combination with silicon bulk micro machining technique. The operativeness of the processes is demonstrated by the development of an integrated micro actuator for a micro switch application, Furthermore, the work deals also with the characterization of the integrated materials. For fabrication control and electrical characterizations microscopy, SEM, hysteresis- and CV-, and degradation measurements were performed. Laser interferometry and resonance frequency measurements were used to characterize the electromechanical performance of both materials in comparison to the behavior of the developed micro actuator.
displacements; Interferometer; mems; Nb doping; pb(zr,ti)o-3; PMN-PT; PZT; sol-gel method
Experimental study of a potential weakening effect in spheres with thin hard coatings
Wear
296
1-2
590-597
2012
10.1016/j.wear.2012.08.018
A potential weakening effect caused by very thin hard coatings on spherical substrates is investigated experimentally. This weakening effect reduces the resistance of the coated system to onset of plasticity. Half-coated spheres are prepared using an ion beam assisted deposition system. The coated and uncoated portions of these half-coated spheres are loaded by a rigid flat into their elastic-plastic regime of deformation and then unloaded. The resulting maximum interference after loading and residual interference at the completion of unloading are measured and used in an elastic-plastic loading index model to evaluate the plasticity levels of both the uncoated and coated portions on each sphere. The experimental results validate qualitatively the potential weakening effect, which was predicted theoretically in previous publications. ?? 2012 Elsevier B.V.
Contact mechanics; Thin hard coatings; Weakening effect
Stochastic numerical treatment for thin film flow of third grade fluid using unsupervised neural networks
Journal of the Taiwan Institute of Chemical Engineers
48
26-39
2015
10.1016/j.jtice.2014.10.018
In the present study, novel soft computing techniques are developed for numerical treatment of non-linear thin film flow (TFF) problem of third grade fluids using artificial neural networks (ANNs), particle swarm optimization (PSO), sequential quadratic programming (SQP), and their hybrid combinations. The strength of universal function approximation capabilities of ANNs is exploited in formulation of mathematical model of the problem based on an unsupervised error. The training of the design parameter of the networks is performed with PSO, SQP, and hybrid approach PSO–SQP. The proposed schemes are evaluated on four variants of the two cases of TFF problems by taking different values of material parameter and Stokes number. The reliability and effectiveness of the proposed approaches are validated through the results of statistical analyses based on sufficient large number of independent runs.
Artificial neural networks; Computational fluid mechanics; Hybrid computing techniques; Particle swarm optimization; Sequential quadratic programming; Thin film flow problems
Unsteady flows in a capillary lined with a thin porous surface layer by method of fundamental solutions
International Journal of Theoretical and Applied Multiscale Mechanics
1
1
86-106
2009
10.1504/IJTAMM.2009.022473
This paper studies unsteady viscous flows in a capillary using the method of fundamental solutions. The effect on fluid velocity of a thin porous surface layer on the wall of the tube is modelled using a slip boundary condition. Laplace transform is used to handle the time variables in the problem. Fundamental solutions of point force in the transformed domain and in the time domain are derived. This study extends our previous work by developing a sophisticated boundary singularity scheme based on the Method of Fundamental Solution {(MFS).}
2009; and; boundary singularity method; capillary lined with a; follows; h; liu; method of fundamental solution; p; porous layer; reference to this paper; should be made as; slip boundary condition; stokes flow; thin porous; unsteady flows in a; w; wang; wen; y
Large free vibration of thin plates: Hierarchic finite Element Method and asymptotic linearization
European Journal of Mechanics, A/Solids
28
1
155-165
2009
10.1016/j.euromechsol.2008.04.002
The aim of this work is to study the free dynamic response of thin plates characterized by geometrical nonlinearities. To achieve this task, the equation of motion of the plate is first carried out through modeling by hierarchical finite element method whose interpolating shape functions are sinusoidal. Then, the study of the nonlinear vibrations was carried out by the development of asymptotic linearization and equivalent linearization methods in modal space. The nonlinear angular frequencies are successively deduced by exciting the corresponding vibrating mode of the structure. The confrontation of these results to those obtained by the iterative method in the physical space and to those found in the literature, showed a very good agreement between the various methods. From the elementary nonlinear frequencies we showed that there exists an equivalent linear dynamical system characterized by only one equivalent linear stiffness matrix. Numerical experiments were carried out on beams and thin plates of various dimensions ratios and boundary conditions. These numerical test simulations, whether in time space or frequency space, have showed that the nonlinear elastic energy is restored by the equivalent linear dynamical system. Nevertheless, we have to say that the dynamic effects of modes above the excited one are neglected. ?? 2008 Elsevier Masson SAS. All rights reserved.
Asymptotic linearization; Equivalent linear dynamical system; Equivalent linearization; HFEM; Nonlinear dynamics
Transient Stress Concentration in Diffusional Creep of a Thin Foil with Heterogeneous Grain Boundary Diffusivity
Mathematics And Mechanics Of Solids
14
1-2
179-191
2009
10.1177/1081286508092610
Coble creep in thin films with heterogeneous grain boundary (GB) diffusivity and non-uniform grain size is investigated in the model problem of a thin foil with a high diffusivity GB joined with a low diffusivity GB of unequal length and subjected to a far field uniaxial tensile stress. It is found that a transient stress peak emerges near the GB junction on the characteristic time scale of the high diffusivity boundary and then disappears when the system reaches steady-state on the characteristic time scale of the low diffusivity boundary. We show that for a given GB size ratio, this stress depends logarithmically on the GB diffusivity ratio. Based on the GB diffusivity and size ratios, we present a diagram demarcating the regime in which peak stress is determined by the steady state solution and that determined by the transient stress solution.
A closed-form solution for elastic buckling of thin-walled unstiffened circular cylinders in pure flexure
Thin-Walled Structures
80
120-129
2014
10.1016/j.tws.2014.03.002
To date, despite the significant development in the field of structural mechanics, there still remains a paradox in the solutions available for a classical shell buckling problem. The difference in strength between a cylindrical shell under uniform axial compression and that under pure bending is not quite well investigated. This lack of research is reflected in the wide variations in the elastic bending strength and the slenderness limits given in current international design standards. The discrepancies in the available classical solutions and hence the design rules have initiated the current research. The main aim of this paper is to present a closed-form solution for the elastic buckling strength of unstiffened circular cylinders under pure bending using a new simplified energy approach employing the well-known Ritz method. Two types of analyses are presented for cylinders with large (D/t>200) and medium (100<D/t<200) diameter-to-thickness ratios. A unique testing rig was used to experimentally verify the new theory using a Moir?? fringe film. The theoretical results are compared against the available and present test results and the existing classical solutions. The current design rules for thin-cylinders in international steel specifications are also compared, and the newly derived design curve is proposed which was found in a good agreement with the available test results. ?? 2014 Elsevier Ltd.
Bending; Buckling; Closed-form; Cylinder; Elastic
The effects of shear deformation and curvature on buckling and vibrations of cross-ply laminated composite shells
Journal of Sound and Vibration
150
3
405-433
1991
10.1016/0022-460X(91)90895-Q
On the basis of Flügge's approximations and with account taken of the transverse shear deformation (SDT) and all rotatory inertias, the equations of in-plane buckling and free vibrations of multi-layered, anisotropic, doubly curved shells are presented. As a particular case, the equations relative to Love's approximations and Donnell's approximations and as well as of the corresponding classical theories (CLT) are derived. Analytical exact solutions are presented for buckling under axial compression and free vibrations of cross-ply laminated, simply supported, circular cylindrical and spherical composite shells. Depending on geometric parameters of the shell (length to radius ratio aR, length to thickness ratio ah and radius to thickness ratio Rh), numerical results (in tables and figures) are quoted to compare the different theories, and some trends are singled out about the effects of both transverse shear deformations and curvatures of the shell. Particular attention is given to the application of Flügge's approximations in which are presented solutions of the equilibrium equations containing terms of the same order in hR. Finally, the effects of coupled out-of-plane stiffnesses on the theories is investigated.
Free Vibration Analysis of Two Layered Cross-Ply Laminated Beams Using Layer-Wise Trigonometric Shear Deformation Theory
Journal of Reinforced Plastics and Composites
21
16
1477-1492
2002
10.1177/0731684402021016472
In this paper, variationally consistent layer-wise trigonometric shear deformation theory (LTSDT) has been extended to deal with free vibration of two-layered laminated cross-ply beams. In this displacement based theory, constitutive relations between shear-stresses and shear-strains are satisfied in both the layers, and, therefore, shear correction factor is not required. In-plane displacement is such that the resultant of normal stress acting over the cross section is zero. Compatibility at the layer interface in respect of in-plane displacement is also satisfied. Present theory contains even less number of unknown variables than those of the first order shear deformation theory (FSDT). In the present formulation, effects of rotary inertia and other inertias are also included. The efficacy of the present theory is demonstrated through the illustrative example.
Scale Effect and Buckling Analysis of Multilayered Graphene Sheets Based on Nonlocal Continuum Mechanics
Journal of Computational and Theoretical Nanoscience
7
10
1948-1954
2010
10.1166/jctn.2010.1565
In the present work, stability analysis of multilayered graphene sheets embedded in polymer matrix has been carried out employing continuum mechanics. Graphene sheets have been considered as continuum thin orthotropic plate. Nonlocal theory has been employed to capture the effect of structural discreteness of graphene sheets. Governing equations have been derived using the principle of virtual work. The developed governing equations have been solved for buckling loads using Navier's approach for simply supported boundary condition. Parametric study has been performed to investigate the dependence of small scale effect on various parameters. It has been shown that nonlocal effect is quite significant for some situations whereas insignificant for some situations.
Monte Carlo Eigenvalue Methods in Quantum Mechanics and Statistical Mechanics
ArXiv
41
1998
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the underlying mathematics is quite similar in that they are stochastic implementations of the power method. In all cases, optimized trial states can be used to reduce the errors of Monte Carlo estimates.
Condensed Matter
Boundary conditions for quantum mechanics on cones and fields around cosmic strings
Communications in Mathematical Physics
139
July 2015
103-139
1991
10.1007/BF02102731
We study the options for boundary conditions at the conical singularity for quantum mechanics on a two-dimensional cone with deficit angle lE 2pgr and for classical and quantum scalar fields propagating with a translationally invariant dynamics in the 1+3 dimensional spacetime around an idealized straight infinitely long, infinitesimally thin cosmic string. The key to our analysis is the observation that minus-the-Laplacian on a cone possesses a one-parameter family of selfadjoint extensions. These may be labeled by a parameterR with the dimensions of length—taking values in [0, infin). ForR=0, the extension is positive. WhenRne0 there is a bound state. Each of our problems has a range of possible dynamical evolutions corresponding to a range of allowedR-values. They correspond to either finite, forR=0, or logarithmically divergent, forRne0, boundary conditions at zero radius. Non-zeroR-values are a satisfactory replacement for the (mathematically ill-defined) notion of delta-function potentials at the cone's apex. We discuss the relevance of the various idealized dynamics to quantum mechanics on a cone with a rounded-off centre and field theory around a ldquotruerdquo string of finite thickness. Provided one is interested in effects at sufficiently large length scales, the ldquotruerdquo dynamics will depend on the details of the interaction of the wave function with the cone's centre (/field with the string etc.) only through a single parameterR (its ldquoscattering lengthrdquo) and will be well-approximated by the dynamics for the corresponding idealized problem with the sameR-value. This turns out to be zero if the interaction with the centre is purely gravitational and minimally coupled, but non-zero values can be important to model nongravitational (or non-minimally coupled) interactions. Especially, we point out the relevance of non-zeroR-values to electromagnetic waves around superconducting strings. We also briefly speculate on the relevance of theR-parameter in the application of quantum mechanics on cones to 1+2 dimensional quantum gravity with massive scalars.
the Response of Unsymmetric Laminates To Simple Applied Forces
Mechanics of Advanced Materials and Structures
3
1
65-80
1996
10.1080/10759419608945854
The snap-through behaviour from one cylindrical configuration to another of an unsymmetric (02/902)T cross-ply laminate is modelled using a simple Rayleigh-Ritz approach. Snap-through is caused by two opposing moments which are produced by opposing forces acting through known moment arms. The snap-through force is predicted, and the predictions are compared with experimental measurements. Correlation is good. The experimental set-up used to measure the force is described, as are the details of the Rayleigh-Ritz approach.
Uncertainty relations in stochastic mechanics
Journal of Mathematical Physics
26
11
2781-2783
1985
doi:10.1063/1.526700
Position–momentum uncertainty in Nelson’s stochastic mechanics [Phys. Rev. 150, 1079 (1966)] has previously been investigated by de la Peña‐Auerbach and Cetto [Phys. Lett. A 39, 65 (1972)]. In this paper their result is generalized, and full equivalence between the uncertainty relations in stochastic mechanics and conventional quantum mechanics is established. Force–momentum uncertainty is also considered.
Probability interpretation of quantum mechanics
American Journal of Physics
48
12
1029
1980
The paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the ’’paradoxical’’ aspects of quantum mechanics lose their counterintuitive character
MIXED STATE; PROBABILITY; QUANTUM MECHANICS
A Stroh-type formalism for anisotropic thin plates with bending-extension coupling
Archive of Applied Mechanics (Ingenieur Archiv)
73
9-10
690-710
2004
10.1007/s00419-004-0322-0
In the present paper, a complete Stroh-type formalism for the problems of anisotropic thin plates with bending-extension coupling is developed. The formalism includes two forms, the hybrid formalism and the displacement formalism, which are related to each other. Both the hybrid and the displacement formalisms with their respective structures of eigenrelations and general solutions are perfectly alike to the Stroh formalism for plane strain problems. Therefore, most of the identities and mathematical techniques developed for the Stroh formalism can be conveniently transferred and applied to the two formalisms. The hybrid Stroh-type formalism is suitable for mixed boundary value problems, while the displacement Stroh-type formalism is suitable for displacement- or stress-only boundary value problems. As applications of the Stroh-type formalism, several problems are solved. One is the derivation of singular solutions for an anisotropic thin plate with bending-extension coupling. The other is the analysis of an anisotropic plate with a hole solved by the displacement formalism.
anisotropic plate; composite; crack; elliptic hole; laminate; singular solution; stroh-type formalism
Resistance of grain boundary array to cleavage cracking in free-standing thin film
Mechanics of Materials
41
2
131-138
2009
10.1016/j.mechmat.2008.10.006
In a previous experimental study on free-standing silicon thin film, it was observed that cleavage front transmission across a through-thickness grain boundary could be considerably constrained by film surfaces. As a result, the boundary toughness was much lower than its bulk counterpart. In this study, inspired by the observation of crack front behaviors at triple grain boundary junctions, we perform a theoretical analysis on the fracture resistance of a regular grain boundary array in a thin film. The result indicates that as the cleavage front breaks down into a number of sections by the grain boundaries, the overall fracture resistance can be increased by nearly 60%. However, if the grain size is too small, the fracture resistance may decrease. The optimum grain size is around 1/5 to 1/4 of the film thickness. This finding provides a scientific basis for further experimental investigation on advanced processing techniques. ?? 2008 Elsevier Ltd. All rights reserved.
A Microbeam Bending Method for Studying Stress- Strain Relations for Metal Thin Films on Silicon Substrates
Journal of the Mechanics and Physics of solids
53
1-31
2004
10.1016/j.jmps.2004.08.007
We have developed a microbeam bending technique for determining elastic-plastic, stress-strain relations for thin metal films on silicon substrates. The method is similar to previous microbeam bending techniques, except that triangular silicon microbeams are used in place of rectangular beams. The triangular beam has the advantage that the entire film on the top surface of the beam is subjected to a uniform state of plane strain as the beam is deflected, unlike the standard rectangular geometry where the bending is concentrated at the support. We present a method of analysis for determining two Ramberg-Osgood parameters for describing the stress-strain relation for the film. These parameters are obtained by fitting the elastic-plastic model to the measured loaddisplacement data, and utilizing the known elastic properties of both film and substrate. As a part of the analysis we compute the position of the neutral plane for bending, which changes as the film deforms plastically. This knowledge, in turn, allows average stressstrain relations to be determined accurately without forcing the film to closely follow the Ramberg-Osgood law. The method we have developed can be used to determine the elastic-plastic properties of thin metal films on silicon substrates up to strains of about 1%.
Fractional quantum mechanics
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
62
3 Pt A
3135-45
2000
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Levy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schrodinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.
Non-commutative Supersymmetric Quantum Mechanics
Physics Letters B
670
4-5
407-415
2008
10.1016/j.physletb.2008.11.011
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible applications in physical systems with potentials involving spin and non-local interactions.
Realism, Operationalism, and Quantum Mechanics
Foundations of Physics
13
8
813-841
1983
10.1007/BF01906271
A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.
Supersymmetric Fluid Mechanics
Physical Review D
62
8
12
2000
10.1103/PhysRevD.62.085019
When anticommuting Grassmann variables are introduced into a fluid dynamical model with irrotational velocity and no vorticity, the velocity acquires a nonvanishing curl and the resultant vorticity is described by Gaussian potentials formed from the Grassmann variables. Upon adding a further specific interaction with the Grassmann degrees of freedom, the model becomes supersymmetric.
Statistical mechanics of optimization problems
Physica A: Statistical Mechanics and its Applications
365
1
10
2006
10.1016/j.physa.2006.01.033
Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the presentation I will describe in details the problems related to the coloring of a random graph.
coloring; random systems; satisfiable
Maximally realistic causal quantum mechanics
Physics Letters A
255
4-6
201-208
1999
10.1016/S0375-9601(99)00186-3
We present a causal Hamiltonian quantum mechanics in 2n-dimensional phase space which is more realistic than de Broglie–Bohm mechanics. The positive definite phase space density reproduces as marginals the correct quantum probability densities of n+1 different complete commuting sets of observables e.g. positions, momenta and n−1 other sets.
03.65.Bz
A probabilistic mechanics theory for random dynamics
1002.4026
2010
This is the general review of an extension of the Newtonian mechanics theory to the systems undergoing random motion, i.e., a probabilistic formalism of mechanics. This work is somewhat inspired by the paradoxical relationship between classical mechanics and thermodynamics. The outcome of our work is that the experimental verification of Newton law of motion in a random dynamics implies a stochastic extension of the virtual work principle and the least action principle which become respectively <dW>=0 and <dA>=0 averaged over all the random paths instead of dW=0 and dA=0 for single path in the regular dynamics. A probabilistic mechanics can be formulated from these extended principles. This mechanics theory can be applied to thermodynamic system to reproduce, justify or revisit a number of results, rules and principles can be reviewed and modified. In particular, we have reproduced the entropy increase of certain nonequilibrium process such as free expansion of gas and heat conduction without considering local equilibrium state, and reached a modified Liouville theorem which relates the entropy production to the work performed by random forces.
Formation and characterization of three-ply structured multiferroic Sm0.88Nd0.12Fe1.93–Pb(Zr0.53Ti0.47)O3 ceramic composites via a solid solution process
Journal of the European Ceramic Society
31
9
1753-1761
2011
10.1016/j.jeurceramsoc.2011.03.032
A new three-ply structured multiferroic Sm0.88Nd0.12Fe1.93–Pb(Zr0.53Ti0.47)O3 (MS-PZT) ceramic composite has been developed successfully by cofiring at 900°C under argon atmosphere via a solid solution process. The magnetic and polarization hysteresis loops prove the coexistence of the ferromagnetic and ferroelectric phases in the composites. TEM images show the alloy particles were dispersed uniformly and mainly located at the PZT grain boundaries. The DC resistivity as high as 109–1010Ω.cm was obtained and only varies slightly with the volume fraction of the conductive phase Sm0.88Nd0.12Fe1.93. The composites can be poled under a high electric field strength at a temperature of 150–180°C. The dielectric, piezoelectric, and magnetic properties of the composites can be tailored according to the desirable requirement to meet designated application by a simple, flexible, and reproducible route, providing a promising potential approach to a new class of electric circuit and significant miniaturization of devices.
Composites; Electrical properties; Piezoelectric properties; Powders-solid state reaction; Three-ply-structure
Effects of defect geometry on fatigue crack growth behavior of cross-ply Ti–6Al–4V/SCS-6 metal matrix composites
Acta Materialia
52
9
2691-2700
2004
10.1016/j.actamat.2004.02.017
The present study describes the fatigue crack growth behavior of [0/90]2s and [90/0]2s laminates of Ti–6Al–4V/SCS-6 composite containing either part-through thickness or through thickness defects under a constant load range at room temperature in air. This study also compares the effect of composite architecture on the fatigue crack growth resistance of these laminates. Acoustic emission was used to detect the number and the location of in situ fiber failures. It was found that the specimens containing part-through thickness defects showed lower crack arrest/catastrophic failure (CA/CF) transitions compared to the specimens where cracks were grown from through thickness defects. Additionally, the higher CA/CF transition of [90/0]2s laminate compared to [0/90]2s laminate irrespective of defect geometry could be attributed to the composite architecture or lay up sequences in these laminates.
Defect geometry effect; Fatigue; Metal matrix composites; Microstructure; Titanium
Non-Hermitian Multiconfiguration Molecular Mechanics
Journal of Chemical Theory and Computation
5
6
1454-1461
2009
doi:10.1021/ct900077g
We present a new version of the multiconfiguration molecular mechanics (MCMM) algorithm for fitting potential energy surfaces of complex reactive systems. The main improvement consists in allowing the valence bond configuration interaction matrix to be non-Hermitian, which broadens the range of geometries over which the potential energy surface can be fit accurately. A second improvement is that the new algorithm has simpler gradients and Hessians and executes faster. The performance of the new algorithm is evaluated using the example of two model reactions.
XXXX
Errors and paradoxes in quantum mechanics
Compendium of Quantum Physics
8
2007
10.1007/978-3-540-70626-7_68
Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosopy.
Bohr; thought experiments
Remarks on Osmosis, Quantum Mechanics, and Gravity
Journal of Physics: Conference Series
361
012010
2012
10.1088/1742-6596/361/1/012010
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Quantum mechanics as an approximation of statistical mechanics for classical fields
Reports on Mathematical Physics
60
453-484
2007
10.1016/S0034-4877(07)80345-4
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the term of the second order. To escape technical difficulties related to the infinite dimension of phase space for quantum mechanics, we start with a detailed presentation of our approach for the finite-dimensional quantum mechanics. We also separate real and complex cases, because the reproduction of the complex structure of quantum mechanics is a special problem which is not related to approximation of classical averages. In our approach quantum mechanics is an approximative theory. It predicts statistical averages only with some precision. In principle, there might be found deviations of averages calculated within the quantum formalism from experimental averages (which are supposed to be equal to classical averages given by our model). ?? 2007 Polish Scientific Publishers.
approximation; incompleteness of quantum mechanics; quantum and classical averages; quantum contribution into classical field average; small parameter; Taylor expansion; von Neumann trace formula
The writhing of circular cross-section rods: undersea cables to DNA supercoils
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
454
1976
2123-2156
1998
10.1098/rspa.1998.0252
The large de ection theory of circular cross-section elastic rods is used to consider the writhing of long straight rods subjected to tension and torque, such as undersea cables, and to closed loops with inserted twist, such as DNA supercoils. The writhed shape of the long straight rod under tension and torque is easily generated by twisting a piece of string with the ngers and consists of three separate parts: a balanced-ply region, a free end loop, and two tail regions. The solution for the rod shape in each of the regions is found. The results are then joined together to ensure continuity of the position and tangent vectors of the strand centreline through the introduction of point forces and moments at the points where the strands enter and exit the balanced ply. The results of the model are consistent with simple experiments on long braided rope. The writhed shape of the closed loop with twist inserted between the ends prior to closure is modelled as a balanced ply joined to two end loops. The analysis combines the mechanics solution with the conservation of topological link to provide a simple formula which quantitatively predicts the approximate shape and helix angle of the supercoil. The results are in good agreement with simple experiments on rope and with available data on DNA supercoils.
interwound supercoils; large deflection rods; linear elastic rods; link; tortuousity and writhe; twist; writhe
Three dimensional finite element analysis of the evolution of voids and thin films by strain and electromigration induced surface diffusion
Journal of the Mechanics and Physics of Solids
47
173-199
1999
10.1016/S0022-5096(98)00079-9
We describe a three-dimensional finite element method for predicting\nthe behavior of a solid which changes its shape as a result of strain\nand electromigration induced surface diffusion. The numerical procedure\nis described in detail. To demonstrate the accuracy and capabilities\nof the method, it is used to solve two problems of interest to the\nmicroelectronics industry. First, the method is used to predict the\nmotion and evolution of voids in an idealized interconnect line due\nto electromigration and strain induced surface diffusion. The results\nare compared and contrasted with existing two-dimensional finite\nelement simulations. In particular, we determine the conditions where\nthree-dimensional simulations are necessary to accurately predict\nthe behavior of the void. Secondly, the method is used to conduct\nfully three-dimensional simulations of strain induced roughening\non the surface of a thin epitaxial film. The results are compared\nwith the first order perturbation theory. It is shown that the first\norder theory provides a good approximation only for very small roughness\namplitudes. In addition, it is shown that the nature of the roughness\nthat develops on the surface is strongly sensitive to the three-dimensional\nshape of the initial imperfection on the surface, and is also influenced\nby the thickness of the epitaxial film.
elastic material; electromigration; finite elements; surface diffusion
Quantum-dressed classical mechanics: Theory and application
Physical Chemistry Chemical Physics
4
13
2865-2877
2002
10.1039/b202151j
A new method called “quantum dressed” classical mechanics has been formulated for treating problems within molecular dynamics, i.e. inelastic and reactive collisions, photodissociation, molecule–surface dynamics, non-adiabatic transitions etc. The method is based on an expansion of the wavefunction in a time-dependent basis set, the Gauss–Hermite basis set. From here it is possible to construct a discrete variable representation in which the grid points are defined by the Hermite part of the Gauss–Hermite basis set. The formulation introduces a set of grid points which follow the classical trajectory in space. With enough grid points the method approaches the exact quantum mechanical formulation. With just a single grid point in each dimension, we recover classical mechanics. Hence the new method adds a quantum option to ordinary Newtonian mechanics.
Noether ' s Theory iu Classical Nonconservative Mechanics
Acts Mechanics
27
17-27
1975
Noether's Theory in Classical Nonconservative Mechanics, Noether's theorem and ~Noether's inverse theorem for mechanical systems with nonconservative forces are established. The existence of first integrals depends on the existence of solutions of the generalized Noether- Bessel-ttagen equation or, which is the same, on the existence of solutions of the Killing system of partial differential equations. The theory is based on the idea that the transfor- mations of time and generalized coordinates together with dissipative forces determine the transformations of generalized velocities, as it is the case with variations in a variational principle of Hamilton's type for purely nonconservative mechanics [17], [18]. Using the theory a few new first integrals for nonconservative problems are obtained.
Relativistic Bohmian interpretation of quantum mechanics
AIP Conference Proceedings
844
1
272-280
2006
10.1063/1.2219368
I present a relativistic covariant version of the Bohmian interpretation of quantum mechanics and discuss the corresponding measurable predictions. The covariance is incoded in the fact that the nonlocal quantum potential transforms as a scalar, which is a consequence of the fact that the nonlocal wave function transforms as a scalar. The measurable predictions that can be obtained with the deterministic Bohmian interpretation cannot be obtained with the conventional interpretation simply because the conventional probabilistic interpretation does not work in the case of relativistic quantum mechanics.
Bohmian interpretation; Relativistic quantum mechanics
Physiological consequences of thin filament cooperativity for vertebrate striated muscle contraction: a theoretical study.
Journal of muscle research and cell motility
27
1
21-35
2006
10.1007/s10974-005-9049-y
Bindings of both myosin and Ca(2+) to the thin filament of vertebrate striated muscle are known to be strongly cooperative. Here the relation between these two sources of cooperativity and their consequences for physiological properties are assessed by comparing two models, with and without Monod-type myosin-binding cooperativity. In both models a thin filament regulatory unit (RU) is in either 'off' or 'on' state, and the equilibrium between them (K (on)) is [Ca(2+)]-dependent. The calculations predict the following: (1) In both models, myosin binding stabilizes the RU in the 'on' state, causing troponin to trap Ca(2+). This stabilization in turn increases the Ca(2+)-binding cooperativity, ensuring efficient regulation to occur in a narrow [Ca(2+)] range. (2) In the cooperative model, the RU is stabilized with a relatively low myosin affinity for actin (K approximately approximately 1), while the non-cooperative model requires a much higher affinity (K approximately approximately 10) to produce the same effect. (3) The cooperative model reproduces the known effects of [Ca(2+)] on the rate of force development and shortening velocity with a low K, but again the non-cooperative model requires a higher value. (4) Because of the finite value of K (on), the thin filaments can never be fully activated by increasing [Ca(2+)], indicating that contracting muscles are under strong influence of thin-filament cooperativity even at saturating [Ca(2+)]. Interpretation of data on muscle mechanics without considering these cooperative effects could therefore lead to a substantial (10-fold) overestimate of cross-bridge binding properties.
Actin Cytoskeleton; Actin Cytoskeleton: metabolism; Animals; Binding Sites; Binding Sites: physiology; Calcium; Calcium: metabolism; Calcium Signaling; Calcium Signaling: physiology; Humans; Models, Biological; Muscle Contraction; Muscle Contraction: physiology; Muscle, Skeletal; Muscle, Skeletal: physiology; Myosins; Myosins: metabolism; Protein Binding; Protein Binding: physiology; Stress, Mechanical; Troponin; Troponin: metabolism
The ballistic resistance of thin aluminium plates with varying degrees of fixity along the circumference
International Journal of Impact Engineering
74
46-56
2014
10.1016/j.ijimpeng.2014.01.007
The ballistic performance of thin aluminium targets and influence thereon of different circumferential fixity conditions were studied both experimentally and by finite element simulations. A pressure gun was employed to carry out the experiments while the numerical simulations were performed on ABAQUS/Explicit finite element code using Johnson–Cook elasto-viscoplastic material model. 1 mm thick 1100-H12 aluminium plates of free span diameter 255 mm were normally impacted by 19 mm diameter ogive and blunt nosed projectiles. The boundary conditions of the plate were varied by varying the region of fixity along its circumference as 100%, 75%, 50% and 25% in experiments and the numerical simulations. Further, simulations were carried out to compare the response of the plates with 50% and 75% continuous fixity with those with two and three symmetrical intermittent regions of 25% fixity respectively. The variation in the boundary condition has been found to have insignificant influence on the failure mode of the target however; it significantly affected the mechanics of target deformation and its energy absorption capacity. The ballistic limit increased with decrease in the region of fixity. It decreased for intermittent fixity in comparison with equivalent continuous fixity. And, it has been found to be higher for the impact with projectile having blunt nose in comparison with the one having ogive nose.
Ballistic limit; Projectile shape; Thin plates; Varying fixity
Calvarial development: cells and mechanics
Current Opinion in Orthopaedics
16
5
331-337
2005
10.1097/01.bco.0000178254.09823.9d
... In development, mesenchymal cells derived from the neural crest and mesoderm differentiate to form most craniofacial structures, including calvarial bone and cranial sutures , teeth, periodontal ligament, cartilage, muscles and subcutaneous fibrous and adipose tissues. ... \n
Arrival time in quantum mechanics
Physical Review A
56
5
3425-3435
1997
10.1103/PhysRevA.56.3425
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a spatial point.
The effect of the thermal conductivity and thickness of the wall on the nonlinear instability of a thin film flowing down an incline
International Journal of Non-Linear Mechanics
47
1-7
2012
10.1016/j.ijnonlinmec.2012.02.008
The nonlinear thermal instability of a thin liquid film falling down a heated wall is investigated. In particular, the heat conductivity and the thickness of the wall are taken into account. It is found that these two effects are represented by only one parameter which is the ratio of the nondimensional thickness of the wall and the nondimensional heat conductivity of the wall, that is d/Qc. The longwave linear stability is described in a general form with respect to a wide range of values of this parameter in order to understand the behavior of the thin film. In the nonlinear case, the thin film instability is investigated in space and time for two examples of time dependent perturbations. The first one is at a perturbation frequency of 0.5 and the second one is at 2.5. The Reynolds numbers corresponding to the isothermal maximum growth rate are used and it is shown that they are located at important places of the k vs. R plane, where k is the wave number and R is the Reynolds number. It is found the important result that, for any fixed Marangoni number Ma, the increase of the parameter d/Qc stabilizes the flow and at the same time decreases the nonlinear amplitude of the perturbations. © 2012 Elsevier Ltd. All rights reserved.
Inclined plane; Thermocapillarity; Thin liquid film; Wall heat conductivity; Wall thickness
Joint mechanics in osteoarthritis.
Novartis Foundation symposium
260
79-95; discussion 95-99, 100-104, 277-279
2004
The primary goal of our research has been to quantify the in vivo loading of normal and osteoarthritic (OA) joints, and to determine the corresponding biological responses. Much of the research in this area has been performed using articular cartilage explants. We feel that, although critically important to our understanding of cartilage mechanics and biology, these experiments may not be directly transferable to interpreting the in vivo joint mechanics and elucidating the detailed mechanisms of onset and progression of OA. Therefore, we have attempted to measure the loading of the knee in freely moving feline and lapine models of OA. We have found that, upon anterior cruciate ligament transection in the cat, knee joints are more flexed, muscle forces are decreased and muscle control patterns are destroyed. Articular cartilage initially becomes thicker, softer and more permeable, resulting in generally increased joint contact areas and decreased peak pressures in the initial stages of joint degeneration compared to control values. Based on our results, we speculate that unloading of the joint (rather than overloading), combined with poor muscular control and weakness, might constitute risks for the onset of joint degeneration.
Animals; Anterior Cruciate Ligament; Biomechanical Phenomena; Cartilage, Articular; Cats; complications; Electromyography; etiology; Humans; injuries; Joint Instability; Joints; Knee Injuries; Models, Animal; Osteoarthritis; physiopathology; Weight-Bearing
Quantum mechanics on manifolds
Acta Applicandae Mathematicae
56
2-3
231-251
1999
In this paper, we investigate the relationships between quantum mechanics and the theory of partial differential equations. We closely follow the De Broglie and Schrödinger picture. Namely, we consider the well-known wave-particle duality as a relation between solutions of partial differential equations, describing waves, and singularities of solutions, that is particles. Our analysis of these relations shows that the necessary ingredients of any quantum mechanical picture are two connections. The first one is a connection in the tangent bundle of the configuration manifold and the second one is a connection in the trivial linear bundle. We also consider mechanical systems equipped with an inner structure and show that quantization of these systems requires a linear connection in the corresponding vector bundle. These are gravity and electromagnetic fields, or Yang-Mills fields if the configuration space is the Minkowski space. In the case of general mechanical systems, they should be considered as natural generalizations of these fields. Explicit formulas for quantizations of some mechanical systems and the corresponding starproducts are given.
Connections; Minkowski space; Partial differential equations; Poisson structures; Quantization; Quantum mechanics; Yang-Mills fields
Statistical mechanics and population biology
Journal of Statistical Physics
30
3
709-753
1983
10.1007/BF01009685
This paper exploits the connection between statistical mechanics and stochastic processes in order to derive a class of macroscopic observables for populations. This review treats the dynamics of populations in both constant and variable environments and derives in each case the thermodynamic analogs of the population parameters.
adaptive value; density dependence; effective size; Entropy; Gibbs measures; Malthusian parameter; Mathematical and Computational Physics; phase transition; Physical Chemistry; quantum physics; Statistical Physics
Evaporation and combustion of thin films of liquid fuels
Journal of Fluid Mechanics
435
351-376
2001
10.1017/S002211200100413X
We consider the evaporation and subsequent burning of thin films of liquid fuels. Previous studies on liquid films, with and without evaporation, have primarily con- sidered the gas phase to be passive. The new element in this study is the introduction of combustion and the examination of both the liquid and gas phases and their effect on the film’s behaviour. For the case of a liquid film burning in quiescent air we show that the problem can be simplified to a single nonlinear evolution equation for the film thickness. All remaining variables, which are simply expressed in terms of the function describing the instantaneous position of the liquid–vapour interface, are subsequently determined. This equation is then solved in order to understand the dynamics of the film in the presence of evaporation and combustion. The planar configuration is discussed first. Predictions for the total evaporation time are obtained, along with the time history of the film thickness, the interfacial surface temperature, the flame standoff distance and its temperature, and the mass burning rate. The dependence of the burning characteristics on the fuel and oxidizer Lewis numbers, which measure the relative importance of thermal and molecular diffusivities, is also determined. Second, we analyse the case of a non-planar interface, where temperature variations along the film’s surface cause fluid motion in the liquid that could either dampen or amplify spatial non-uniformities. We show that, while thermocapillarity has the tendency to destabilize the planar interface, combustion acts to reduce this effect. In particular, when the heat release by combustion is substantial, all disturbances are obliterated, the film remains nearly planar and the burning occurs along nearly horizontal surfaces.
The aero-mechanics of low aspect ratio compliant membrane wings, with applications to animal flight
46th AIAA Aerospace Sciences Meeting and Exhibit
January
AIAA 2008-517
2008
Bats and other flying mammals are distinguished by thin, compliant membrane wings. In an effort to understand the dependence of aerodynamic performance on membrane compliancy, wind tunnel tests of low-aspect-ratio, compliant wings were conducted for Reynolds numbers ranging from 0.7 - 2.0 × 10\n 5. The lift and drag was measured for wings of varying aspect ratio (AR = 0.9, 1.4, 1.8), compliancy (membrane thickness = 0.10, 0.15, 0.25 mm), and pre-strain values (ε\n 0 = 0%,4%). In addition to the lift and drag measurements, the static and dynamic deformations of compliant membrane wings were measured using stereo photogrammetry. A theoretical model for the membrane camber due to aerodynamic loading is presented, indicating that the appropriate non-dimensional parameter describing the problem is a Weber number, comparing the aerodynamic load to the membrane elasticity. Excellent agreement between theory and experiments is found. Measurements of the aerodynamic performance show that, in comparision with rigid wings, the compliant wings have a higher lift slope, reach larger values of CL\n max and have softer stall at higher angles of attack. Drag for compliant wings is also increased and they exhibit a strong hysteresis both around zero angle of attack as well as around the stall angle. Unsteady membrane motions are also measured, and it is observed that the membrane vibrates with spatial structure that is closely related to the free eigenmodes of the membrane under tension, and that the Strouhal number at which the membrane vibrates rises with the freestream velocity, coinciding with increasing multiples of the natural frequency of the membrane. Copyright © 2008 by Kenneth Breuer.
UV damage and sun care: deciphering mechanics of skin to develop next generation therapies.
Journal of the mechanical behavior of biomedical materials
28
471-3
2013
10.1016/j.jmbbm.2013.02.008
Some ultraviolet radiation (UV) is essential to the body as it stimulates the production of vitamin D, yet overexposure has deleterious consequences for the skin. UV induces structural and cellular changes across the different layers of skin tissue leading to mechanical and oxidative stress. Both are critical parameters that can help us better understand and assess dermatological photodamage. While there is a developing body of research to quantify biomarkers of oxidative stress in skin, our knowledge of the magnitude of mechanical stresses in skin has been limited until recently due to the scarcity of methods to quantify the stress state of the tissue. In this regard, what is really exciting is that thin-film characterization and image correlation techniques have recently been successful in measuring the stress state of the tissue both in vitro and in vivo. In the next decade, quantifying UV-induced damage and the efficacy of sunscreens in preventing and treating photodamage will become an increasing focus in skin science research. An improved understanding of the magnitude of skin stresses will help us to better understand skin damage and appearance processes, such as cracking and wrinkling, and measure with accuracy both short-term and long-term effects of treatments.
Drug Discovery; Humans; Skin; Skin: drug effects; Skin: metabolism; Skin: radiation effects; Sunscreening Agents; Sunscreening Agents: pharmacology; Ultraviolet Rays; Ultraviolet Rays: adverse effects
Fuzziness in Quantum Mechanics
PHYSICS ESSAYS
9
3
496-505
1996
10.4006/1.3029260
It is shown that quantum mechanics can be regarded as what one could call a ''fuzzy'' mechanics, that is, the mechanics whose underlying logic is not Aristotelian binary logic of classical mechanics but, rather, fuzzy logic. From this point of view, classical mechanics is a crisp limit of a more general quantum mechanics based on the fuzzy logic. Using such an approach, the Schrodinger equation is derived from the Hamilton-Jacobi equation. The deep underlying unity between these equations is connected to the fact that a unique ''crisp'' trajectory of a classical particle is ''selected'' out of many-continuum paths according to the principle of least action. This can be interpreted as a consequence of the assumption that a classical particle ''resides'' in every path of a set of many-continuum paths that collapse to a single trajectory of an observed classical motion. The wave function is treated as a quantity describing a deterministic entity possessing a fuzzy character. As a logical consequence of such an interpretation, the complementarity principle and wave-particle duality concept can be abandoned in favor of an idea of a fuzzy deterministic microobject. In optical computing the undetectable quantum phase and its global information are lost in the process of defuzzification leading to its ''final'' product, that is, the probability density. Since in optical computing we are interested only in this product, we do not need to register all the intermediate results that contribute to the generation of the product. The lost information then can be viewed as ''garbage.''
Quantum Mechanics
American Journal of Physics
53
9
925
2011
10.1119/1.14383
The identification of BACE-1, a key enzyme in the production of Amyloid-β (Aβ) peptides, generated by the proteolytic processing of amyloid precursor protein, was a major advance in the field of Alzheimer's disease as this pathology is characterized by the presence of extracellular senile plaques, mainly comprised of Aβ peptides. Hydroxyethylamines have demonstrated a remarkable potential, like candidate drugs, for this disease using BACE-1 as target. Density Functional Theory calculations were employed to estimate interaction energies for the complexes formed between the hydroxyethylamine derivated inhibitors and 24 residues in the BACE-1 active site. The collected data offered not only a general but a particular quantitative description that gives a deep insight of the interactions in the active site, showing at the same time how ligand structural variations affect them. Polar interactions are the major energetic contributors for complex stabilization and those ones with charged aspartate residues are highlighted, as they contribute over 90% of the total attractive interaction energy. Ligand-ARG296 residue interaction reports the most repulsive value and decreasing of the magnitude of this repulsion can be a key feature for the design of novel and more potent BACE-1 inhibitors. Also it was explained why sultam derivated BACE-1 inhibitors are better ones than lactam based. Hydrophobic interactions concentrated at S1 zone and other relevant repulsions and attractions were also evaluated. The comparison of two different theory levels (X3LYP and M062X) allowed to confirm the relevance of the detected interactions as each theory level has its own strength to depict the forces involved, as is the case of M062X which is better describing the hydrophobic interactions. Those facts were also evaluated and confirmed by comparing the quantitative trend, of selected ligand-residue interactions, with MP2 theory level as reference standard method for electrostatic plus dispersion energies.
Incipient yielding behavior during indentation for gold thin films before and after annealing
Journal of Materials Research
21
10
2480-2492
2006
10.1557/JMR.2006.0303
We studied the deformation mechanisms and mechanics during indentation of polycrystalline gold thin films at depths below 100 nm. The measured material hardness decreased from 2.1 ± 0.1 to 1.7 ± 0.1 GPa after annealing for 4 h at 177 °C. Upon closer inspection, the hardness trends in the gold thin films were discovered to vary according to the indentation depth. At nanometer depths, the material hardness was quantified using multiple parameters, some of which were independent of the area calibration for the tip. The annealed specimen was very "hard" at low indentation depths, relatively soft at moderate indentation depths, and finally harder until the grain-size limit was reached. The as-deposited specimen demonstrated a relatively continuous harness trend as function of indentation depth, exhibiting monotonic convergence to Hall-Petch limited behavior. Discrete displacement jump events (excursions or "pop-ins") were frequently observed for the annealed specimen but not for the as-deposited specimen. Variation in hardness, excursion activity, and displacement during the hold at maximum load was observed according to the applied loading, which was parametrically varied at constant strain rates. Hardness results are explained in terms of the population and evolution of defects present within the specimens. The population of point defects is also influential, and critical thermal fluctuations, as well as the thermally activated process of diffusion, are believed to influence hardness at the specimen's free surface and further into its volume. After converging to a monotonic trend (proper tip engagement), the modulus of the gold was measured to be 106.0 ± 12.9 and 101.3 ± 6.0 GPa for the respective Au/Cr/Si specimens. These values exceeded predictions from the aggregate polycrystalline material theory, a representation used to estimate results for anisotropic single crystals. Exaggerated modulus measurements are explained as the result of the contribution of modulus mismatch with the substrate, pileup at the indentor tip, residual stress in the films, and crystallographic anisotropy of the gold. © 2006 Materials Research Society.
Anisotropy; Crystallography; Deformation; Diffusion; Gold; Gold thin films; Grain size and shape; Hall-Petch; Hardness; Indentation; Polycrystalline materials; Strain rate; Thin films
Synthesis of cobalt doped silica thin film for low temperature optical gas sensor
Journal of Sol-Gel Science and Technology
60
3
388-394
2011
10.1007/s10971-011-2483-y
A modified sol-gel method was used to prepare cobalt doped silica thin film with a cobalt content of 10, 20 and 30 mol% (10Co, 20Co and 30Co). The prepared films were annealed at different temperatures in the range 400-1,000 A degrees C, and their structural evolution examined. The mixed valence cobalt oxide, Co(3)O(4), crystallizes only in the sample with the higher cobalt content, while cobalt silicate is the only crystalline phase detected in the sample 10Co and 20Co. Both the cobalt content and the temperature of heat treatment resulted to affect the nature of cobalt species dispersed in the silica matrix. The 30Co was selected for further investigations by FTIR spectroscopy to follow the structural evolution of 30Co film as function of the temperature and UV-Vis to get information on the cobalt valence state. The optical gas-sensing properties of 30Co films, containing Co(3)O(4) as the major cobalt phase, were studied through the measuring of the film transmittance in dry air and in presence of dry air containing variable concentrations of polluting gases, CO and NO(2). The 30Co samples resulted to be highly sensitive to CO at room temperature. An explanation for the CO sensing characteristics, at low temperature, was proposed by referring to the physisorption-related mechanics of CO.
gel; optical gas sensing á; oxide á; sol; thin films á cobalt
Small scale membrane mechanics
Biomechanics and Modeling in Mechanobiology
13
4
697-711
2014
10.1007/s10237-013-0528-6
Large scale changes to lipid bilayer shapes are well represented by the Helfrich model. However, there are membrane processes that take place at smaller length scales that this model cannot address. In this work, we present a one-dimensional continuum model that captures the mechanics of the lipid bilayer membrane at the length scale of the lipids themselves. The model is developed using the Cosserat theory of surfaces with lipid orientation, or 'tilt', as the fundamental degree of freedom. The Helfrich model can be recovered as a special case when the curvatures are small and the lipid tilt is everywhere zero. We use the tilt model to study local membrane deformations in response to a protein inclusion. Parameter estimates and boundary conditions are obtained from a coarse-grained molecular model using dissipative particle dynamics (DPD) to capture the same phenomenon. The continuum model is able to reproduce the membrane bending, stretch and lipid tilt as seen in the DPD model. The lipid tilt angle relaxes to the bulk tilt angle within 5-6 nm from the protein inclusion. Importantly, for large tilt gradients induced by the proteins, the tilt energy contribution is larger than the bending energy contribution. Thus, the continuum model of tilt accurately captures behaviors at length scales shorter than the membrane thickness.
Curvature; Lipid bilayers; Mathematical model; Membranes
Simulated Dark-Matter Halos as a Test of Nonextensive Statistical Mechanics
0801.2504
2008
doi:10.1103/PhysRevE.77.022106
In the framework of nonextensive statistical mechanics, the equilibrium structures of astrophysical self-gravitating systems are stellar polytropes, parameterized by the polytropic index n. By careful comparison to the structures of simulated dark-matter halos we find that the density profiles, as well as other fundamental properties, of stellar polytropes are inconsistent with simulations for any value of n. This result suggests the need to reconsider the applicability of nonextensive statistical mechanics (in its simplest form) to equilibrium self-gravitating systems.
Introduction to Quantum Mechanics
AIP Conference Proceedings
1023
1
107-117
2008
10.1063/1.2958160
Thepurpose of this contribution is to give a very briefintroduction to Quantum Mechanics for an audience of mathematicians. Iwill follow Segal's approach to Quantum Mechanics paying special attentionto algebraic issues. The usual representation of Quantum Mechanics onHilbert spaces is also discussed.\n\n \n ©2008 American Institute of Physics
classical mechanics; Hilbert spaces; Lie algebras; quantum theory
2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending
Applied Mathematics and Mechanics
34
8
1017-1030
2013
10.1007/s10483-013-1724-x
A new numerical manifold (NMM) method is derived on the basis of quartic\nuniform B-spline interpolation. The analysis shows that the new interpolation\nfunction possesses higher-order continuity and polynomial consistency\ncompared with the conventional NMM. The stiffness matrix of the new\nelement is well-conditioned. The proposed method is applied for the\nnumerical example of thin plate bending. Based on the principle of\nminimum potential energy, the manifold matrices and equilibrium equation\nare deduced. Numerical results reveal that the NMM has high interpolation\naccuracy and rapid convergence for the global cover function and\nits higher-order partial derivatives. © 2013 Shanghai University\nand Springer-Verlag Berlin Heidelberg.
The Physical Pendulum in Quantum Mechanics
Physical Review
31
5
891-894
1928
10.1103/PhysRev.31.891
It is pointed out that the Mathieu functions of even order are the characteristic functions of the physical pendulum in the sense of Schrödinger's wave mechanics. The relation of various properties of the functions, as known from purely analytical investigations of them, to the pendulum problem is discussed.
Quantum Mechanics and 3N‐Dimensional Space
Philosophy of Science
73
5
778-789
2006
10.1086/518633
I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three‐dimensional space, not the wave function evolving in 3N‐dimensional space. CR - Copyright © 2006 Philosophy of Science Association
Fabrication of piezoelectric AlN thin film for FBARs
Science in China Series G: Physics, Mechanics and Astronomy
52
2
226-232
2009
10.1007/s11433-009-0021-5
This paper focuses on the fabrication of film bulk acoustic-wave resonator (FBAR) comprising an aluminum nitride (AlN) piezoelectric thin film sandwiched between two metal electrodes and located on a silicon substrate with a low-stress silicon nitride (Si3N4) support membrane for high frequency wireless applications, and analyzes the optimization of the thin AlN film deposition parameters on Mo electrodes using the reactive RF magnetron sputter system. Several critical parameters of the sputtering process such as RF power and Ar/N-2 flow rate ratio were studied to clarify their effects on different electrodes characteristics of the AlN films. The experiment indicated that the process for Mo electrode was easier compared with that of the Pt/Ti or Au/Cr bi-layer electrode as it entailed only one photo resist and metal deposition step. Besides, Pt/Ti or Au/Cr electrodes reduced the resonance frequency due to their high mass density and low bulk acoustic velocity. Compared with the case of the Al bottom electrode, there is no evident amorphous layer between the Mo bottom electrode and the deposited AlN film. The characteristics of the FBAR devices depend not only upon the thickness and quality of the AlN film, but also upon the thickness of the top electrode and the materials used. The results indicate that decreasing the thickness of either the AlN film or the top electrode increases the resonance frequency. This suggests the potential of tuning the performance of the FBAR device by carefully controlling AlN film thickness. Besides, increasing either the thickness of the AlN film or higher RF power has improved a stronger c-axis orientation and tended to promote a narrower rocking curve full-width at half-maximum (FWHM), but increased both the grain size and the surface roughness. An FBAR device fabricated under optimal AlN deposition parameters has demonstrated the effective electromechanical coupling coefficient (k(eff)(2)) and the quality factor (Q(fx)) are about 1.5% and 332, respectively.
Orbit Mechanics for Engineering Students
Orbital Mechanics for Engineering Students
367-404
2005
10.1016/B978-0-08-097747-8.00007-4
Up to now, we have mostly referenced the motion of orbiting objects to a nonrotating coordinate system fixed to the center of attraction (e.g., the center of the earth). This platform served as an inertial frame of reference, in which Newton's second law can be written as Fnet=maabsolute.
Angular acceleration of comoving frame; Angular velocity of comoving frame; Clohessy–Wiltshire equations; Clohessy–Wiltshire matrices; LVLH frame; r-bar; Relative acceleration in the comoving frame; Relative acceleration in the inertial frame; Two-impulse rendezvous
Positive inotropic effects of low dATP/ATP ratios on mechanics and kinetics of porcine cardiac muscle.
Biophysical journal
91
6
2216-26
2006
10.1529/biophysj.105.079061
Substitution of 2'-deoxy ATP (dATP) for ATP as substrate for actomyosin results in significant enhancement of in vitro parameters of cardiac contraction. To determine the minimal ratio of dATP/ATP (constant total NTP) that significantly enhances cardiac contractility and obtain greater understanding of how dATP substitution results in contractile enhancement, we varied dATP/ATP ratio in porcine cardiac muscle preparations. At maximum Ca(2+) (pCa 4.5), isometric force increased linearly with dATP/ATP ratio, but at submaximal Ca(2+) (pCa 5.5) this relationship was nonlinear, with the nonlinearity evident at 2-20% dATP; force increased significantly with only 10% of substrate as dATP. The rate of tension redevelopment (k(TR)) increased with dATP at all Ca(2+) levels. k(TR) increased linearly with dATP/ATP ratio at pCa 4.5 and 5.5. Unregulated actin-activated Mg-NTPase rates and actin sliding speed linearly increased with the dATP/ATP ratio (p < 0.01 at 10% dATP). Together these data suggest cardiac contractility is enhanced when only 10% of the contractile substrate is dATP. Our results imply that relatively small (but supraphysiological) levels of dATP increase the number of strongly attached, force-producing actomyosin cross-bridges, resulting in an increase in overall contractility through both thin filament activation and kinetic shortening of the actomyosin cross-bridge cycle.
Actins; Actins: chemistry; Actins: physiology; Actomyosin; Actomyosin: physiology; Adenosine Triphosphate; Adenosine Triphosphate: metabolism; Animals; Biomechanical Phenomena; Calcium; Calcium: physiology; Deoxyadenine Nucleotides; Deoxyadenine Nucleotides: metabolism; Hydrolysis; Kinetics; Male; Muscle, Skeletal; Muscle, Skeletal: chemistry; Myocardial Contraction; Myocardium; Myocardium: metabolism; Myosins; Myosins: physiology; Rabbits; Swine
Niels Bohr?s Generalization of Classical Mechanics
Foundations of Physics
35
3
347-371
2005
10.1007/s10701-004-1979-5
We clarify Bohr\textquoteright{}s interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible
bohm; bohr; classical mechanics; copenhagen interpretation; intertheoretic relations; quantum mechanics
Two-ply biodegradable nerve guide: Basic aspects of design, construction and biological performance
Biomaterials
11
286-290
1990
10.1016/0142-9612(90)90012-F
A synthetic biodegradable nerve guide was constructed of two polymeric layers: an inner microporous layer prepared from a copolymer of L-lactide and epsilon-caprolactone (pore size range 0.5-1 micron) and an outer microporous layer prepared from a polyurethane/poly(L-lactide) mixture (pore size range 30-70 microns). This nerve guide was used to bridge a 7 mm gap in the right sciatic nerve of rats. It enabled the sciatic nerve to regenerate across the gap, forming a new, well-defined nerve that effectively re-established the contact between the proximial and distal nerve end, as effective as an autograft.
A micromechanistic-based approach to fatigue life modeling of titanium-matrix composites
Composites Part B: Engineering
28
96
507-521
1997
10.1016/S1359-8368(96)00083-2
Fatigue life modeling of titanium-based metal-matrix composites (MMCs) was accomplished by combining a unified viscoplastic theory, a non-linear micromechanics analysis and a damage accumulation model. The micromechanics analysis employed the Bodner-Partom unified viscoplastic theory with directional hardening. This analysis was then combined with a life-fraction fatigue model to account for the time-dependent component of fatigue damage. The life-fraction fatigue model involved the linear summation of damage from the fiber and matrix constituents of the composite. A single set of empirical constants for the life-fraction fatigue model were established for each of two titanium MMCs reinforced with silicon carbide fibers: SCS-6/Ti-15-3 and SCS-6/ TIMETAL�21s. The predicted fatigue lives were within one order of magnitude of the experimental data for different loading conditions: isothermal fatigue, and both in-phase and out-of-phase thermomechanical fatigue. MMCs modeled included cross-ply, quasi-isotropic and unidirectional SCS-6/TIMETAL�21s, and cross-ply and quasi-isotropic SCS-6/Ti-15-3 laminates.
a; b; c; d; damage mechanics; fatigue; metal-matrix composites; mmcs; thermomechanical
Thermally induced damage in composite laminates: Predictive methodology and experimental investigation
Composites Science and Technology
56
10
1209-1219
1996
http://dx.doi.org/10.1016/S0266-3538(96)00089-9
A general analysis method is presented to predict matrix cracks in a composite laminate, together with the resulting degradations of laminate properties, as functions of temperature or thermal cycles. All plies except the surface plies are considered. A shear-lag solution for the stresses in the vicinity of cracks and a fracture mechanics crack formation criterion are used to predict cracks. Damage is modeled incrementally, which allows the inclusion of the effects of temperature-dependent material properties and softening of the laminate due to previous cracking. The analysis is incorporated into an easy-to-use computer program. Experimentally, crack densities are measured in a variety of laminates exposed to decreasing temperatures. Crack densities are measured at the edges of specimens by microscopic inspection, and throughout the specimen volumes by X-radiography and sanding down of the edges. In specimens with thick ply groups (several plies of the same angle stacked together), cracks behave ‘classically’, running the width of the specimens. In specimens with single ply groups, smaller, discontinuous cracks developed. Correlation between the analytical results and the edge crack densities were reasonable for those specimens which behaved classically. Crack densities measured at specimen edges do not agree with internal crack densities (or analyses) in specimens with non-classical cracks. A free-edge stress analysis clarifies the reasons for these discrepancies.
analysis; composites; damage; microcracking; thermal stresses
Thermal post-buckling analysis of imperfect laminated plates using a higher-order shear deformation theory
International Journal of Non-Linear Mechanics
32
6
1035-1050
1997
10.1016/S0020-7462(96)00135-7
Thermal post-buckling analysis is presented for a simply supported, composite laminated plate subjected to uniform or non-uniform tent-like temperature loading. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reddy's higher-order shear deformation plate theory, and include thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine thermal buckling loads and post-buckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, antisymmetrically angle-ply and symmetrically cross-ply laminated plates. The effects played by transverse shear deformation, thermal load ratio, plate aspect ratio, total number of plies, fiber orientation and initial geometrical imperfections are studied. Typical results are presented in dimensionless graphical form.
composite laminated plate; Galerkin-perturbation technique; higher-order shear deformation plate theory; structural stability; thermal post-buckling
Finite element method of B-spline wavelet on the interval for thin plate bending and vibration analysis
Gongcheng Lixue/Engineering Mechanics
24
2
56-61
2007
Based on two-dimensional tensor product B-spline wavelet on the interval (BSWI) and wavelet finite element method (WFEM), a finite element method (FEM) of BSWI is investigated to solve the static and vibration problems of thin plates. In the progress of WFEM formulation for thin plate analysis, BSWI scaling functions are employed to approximate the transverse displacements field. From the generalized function of potential energy for rectangle and skew plates, we can obtain the solving equation of WFEM via variational principle. The method combined the versatility of the accuracy of B-spline function approximation and various basis functions for structural analysis. Some numerical examples are studied to verify the proposed method. With few computational degree of freedoms (DOFs), the numerical results of the presented method are in good agreement with the solutions of other methods.
B-spline wavelet on the interval; Computational mechanics; Finite element method; Modal analysis; Thin plate bending
Noether conservation laws in classical mechanics
eprint arXivmathph0302027
6
1
12
2003
In Lagrangian mechanics, Noether conservation laws including the energy one are obtained similarly to those in field theory. In Hamiltonian mechanics, Noether conservation laws are issued from the invariance of the Poincare-Cartan integral invariant under one-parameter groups of diffeomorphisms of a configuration space. Lagrangian and Hamiltonian conservation laws need not be equivalent.
The mechanics of elastic contact with film-covered surfaces
Journal of Applied Physics
45
3
1041
1974
10.1063/1.1663365
Solutions to the Hertz problem, which predict the contact area between cylindrical or spherical bodies elastically loaded against one another, have frequently been applied to situations in which one of the bodies is coated with a thin film of different material, notably in the analysis of bearings lubricated with thin solid films. In reality the film may often exert a profound influence on the contact area and the Hertzian assumption will be inappropriate. The present work offers approximate analytical solutions for film‐coated cylindrical and spherical contacts, that are valid provided the contact dimensions are large compared to the film thickness and provided also that the Young's modulus of the film material is less than that of the surfaces with which it interacts. It is hoped that the expressions derived here will prove to be particularly useful in the study of lubricant films deposited by such processes as sputtering and ion plating, where a knowledge of the true area of contact is a crucial factor in the understanding of the mechanics involved.
Continuum Damage Mechanics: When and How?
International Journal of Damage Mechanics,
4
3
217-229
1995
10.1177/105678959500400302
The present paper reflects on the state of the development of damage mechanics initiated in 1958 by Lazar M. Kachanov who we commemorate with this series of four issues of the International Journal of Damage Mechanics. This paper presents a personal view and an assessment of the accomplishments of a group of dedicated people interested in this new field of solid mechanics. In particular, the paper focuses on the establishment of criteria needed to define the circumstances allowing for the application of a deterministic and local continuum model of traditional type.
The varieties of mechanics by 1800
Historia Mathematica
17
4
313-338
1990
10.1016/0315-0860(90)90025-9
After an exploration of some of the basic categories attending mechanics, Newtonianism, and physics, a survey is given of the range of subjects covered by mechanics at the end of the 18th century, and the three main traditions operative in the subject are stressed. A few major French figures of that time are then noted, and also some views evident in certain other countries. The appendix of the paper is concerned with bibliographical questions; and an extensive bibliography, mostly of secondary litetature, is appended.
history of mechanics; mechanics; sec 18
An initial flexural failure analysis of symmetrically laminated cross-ply rectangular plates
International Journal of Solids and Structures
16
5
451-463
1980
10.1016/0020-7683(80)90043-8
It is shown that by combining the exact (Navier) solution of the specially orthotropic plate equilibrium equations with the Tsai-Hill failure criterion the initial failure analysis of fibre reinforced laminated plates may be transformed into an optimisation problem. A simple trial and error procedure is used to locate and evaluate the maximum value of an initial failure function from which the initial failure load and the corresponding plate deflections may be evaluated. This approach is used to provide design data for the initial failure condition in GFRP and CFRP simply supported, rectangular plates subjected to uniform, uniform square patch and hydrostatic (linearly varying) load distributions.
On the Theory of Quantum Mechanics
Proceedings of the Royal Society of London. Series A
1926
661 On the Theory of Quantum Mechanics. By PAM DIRAC, St. John's College, Canbridge. (Communicated by RH Fowler, FRS-Received August 26, 1926.) 1. Introduction and SummTary. The new mechanics of the atom introduced by
Mechanics of manifold flow
ASCE Transactions
119
1103-1142
1954
Flow characteristics of branch points in manifolds involve complexities that the author has studied by combining results of experiment and of simplified analysis. The variation in head is studied for lfow in a circular conduit with lateral inflow or outflow at right angles thereto. Theoretical results are shown to be insufficiently accurate for practical use except in a few instances. The systematized empirical results presented for the various types of flow should be helpful in teh design of a veriety of manifold systems.
Abuses of Molecular Mechanics: Pitfalls to Avoid
Journal of Chemical Education
72
12
1070-1075
1995
10.1021/ed072p1070
A tutorial on common pitfalls to avoid when using molecular mechanics is presented. The author divides these problems into those derived from the software like using inadequate potential functions, poor parameters, wrong optimizers, and those originating from the scientist who introduces computational artifacts and improperly compares or interprets results.
The strange world of quantum mechanics
The strange world of quantum mechanics
xiv + 154
2000
10.1017/CBO9781107050709
"Entanglement is a strange feature of quantum physics, the science of the very small. It’s possible to link together two quantum particles – photons of light or atoms, for example – in a special wa...
The Solution Asymptotics of Classical and Nonclassical, Static and Dynamic Boundary-Value Problems for Thin Bodies
International Applied Mechanics
38
7
765-782
2002
10.1023/A:1020877123771
An asymptotic method for solution of classical and nonclassical boundary-value problems of the theory of elasticity for thin bodies (beams, rods, plates, and shells) is expounded. Studies on the asymptotic theory of thin bodies are reviewed. Asymptotic results are compared with those obtained by other applied theories. The asymptotic approach has been found out to be related to Saint Venant's principle. The correctness of this principle is mathematically proved for one class of problems. A fundamentally new asymptotics in the components of the stress tensor and the displacement vector is revealed in considering new classes of problems. On their basis, the applicability domains are outlined for various models of understructures. Solutions are obtained to certain classes of dynamic problems for thin bodies, particularly, those simulating seismic effects. The resonance conditions are established and ways of preventing them are pointed out.
Corotational mixed finite element formulation for thin-walled beams with generic cross-section
Computer Methods in Applied Mechanics and Engineering
199
49-52
3197-3212
2010
10.1016/j.cma.2010.06.026
The corotational technique is adopted here for the analysis of three-dimensional beams. The technique exploits the technology that applies to a two-noded element, a coordinate system which continuously translates and rotates with the element. In this way, the rigid body motion is separated out from the deformational motion. In this paper, a mixed formulation are adopted for the derivation of the local element tangent stiffness matrix and nodal forces. The mixed finite element formulation is based on an incremental form of the two-field Hellinger-Reissner variational principle to permit elasto-plastic material behavior. The local beam kinematics is based on a low-order nonlinear strain expression using Bernoulli assumption. The present formulation captures both the Saint-Venant and warping torsional effects of thin-walled open cross-sections. Shape functions that satisfy the nonlinear local equilibrium equations are selected for the interpolation of the stress resultants. In particular, for the torsional forces and the twist rotation degree of freedom, a family of hyperbolic interpolation functions is adopted in lieu of conventional polynomials. Governing equations are expressed in a weak form, and the constitutive equations are enforced at each integration cross-section along the element length. A consistent state determination algorithm is proposed. This local element, together with the corotational framework, can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with generic cross-section. The present corotational mixed element solution is compared against the results obtained from a corotational displacement-based model having the same beam kinematics and corotational framework. The superiority of the mixed formulation is clearly demonstrated. ?? 2010 Elsevier B.V.
Elasto-plastic material behavior; Generic cross-section; geometrically nonlinear beam; Geometrically nonlinear beam; mixed finite element analysis; Mixed finite element analysis; three-dimensional corotational formulation; Three-dimensional corotational formulation; Two-field Hellinger-Reissner variational principle
Determination of the elastic moduli of thin samples and adherent cells using conical atomic force microscope tips
Nature Nanotechnology
7
11
733-736
2012
10.1038/nnano.2012.163
The atomic force microscope can detect the mechanical fingerprints of normal and diseased cells at the single-cell level under physiological conditions. However, atomic force microscopy studies of cell mechanics are limited by the 'bottom effect' artefact that arises from the stiff substrates used to culture cells. Because cells adhered to substrates are very thin, this artefact makes cells appear stiffer than they really are. Here, we show an analytical correction that accounts for this artefact when conical tips are used for atomic force microscope measurements of thin samples. Our bottom effect cone correction (BECC) corrects the Sneddon's model, which is widely used to measure Young's modulus, E. Comparing the performance of BECC and Sneddon's model on thin polyacrylamide gels, we find that although Sneddon's model overestimates E, BECC yields E values that are thickness-independent and similar to those obtained on thick regions of the gel. The application of BECC to measurements on live adherent fibroblasts demonstrates a significant improvement on the estimation of their local mechanical properties. © 2012 Macmillan Publishers Limited. All rights reserved.
Asynchronous Variational Integration of Interaction Potentials for Contact Mechanics
arXiv.org
math.NA
706
2009
Asynchronous Variational Integrators (AVIs) have demonstrated long-time good energy behavior. It was previously conjectured that this remarkable property is due to their geometric nature: they preserve a discrete multisymplectic form. Previous proofs of AVIs' multisymplecticity assume that the potentials are of an elastic type, i.e., specified by volume integration over the material domain, an assumption violated by interaction-type potentials, such as penalty forces used to model mechanical contact. We extend the proof of AVI multisymplecticity, showing that AVIs remain multisymplectic under relaxed assumptions on the type of potential. The extended theory thus accommodates the simulation of mechanical contact in elastica (such as thin shells) and multibody systems (such as granular materials) with no drift of conserved quantities (energy, momentum) over long run times, using the algorithms in [3]. We present data from a numerical experiment measuring the long time energy behavior of simulated contact, comparing the method built on multisymplectic integration of interaction potentials to recently proposed methods for thin shell contact.
Creep analysis of thin-walled structures
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
82
8
507-533
2002
10.1002/1521-4001(200208)82:8<507::aid-zamm507>3.0.co;2-y
In addition to the elastic behavior, engineering materials at elevated temperatures tend to creep or, with other words, a spontaneous and a time-dependent material response can be observed. Due to the increasing safety requirements for power plants, aircraft components, equipment for chemical processes, etc. the time-dependent material behavior should be taken into account in the design process. Since many structural elements working under creep conditions can be classified as thin-walled structures the analysis is connected with the following three items: the choice of a suitable material behavior model, the choice of an adequate structural analysis model, and the choice of a suitable numerical solution technique. All three items are interlinked. For example, the choice of the structural analysis model (beam, plate, shell, etc.) has a significant influence on the numerical effort. On the other hand, the accuracy of the calculations is influenced by the material behavior model taking into account more or less effects. Creep mechanics is a branch of solid mechanics with a history of more than 100 years. After a brief discussion of the historical development and the introduction of some important references two creep behavior models are presented. For the first one the material behavior is not influenced by the kind of stress state while in the second case significant differences in dependence on the kind of the stress state can be observed. A typical example of such behavior is the different behavior in tension and compression. This behavior can be observed, for example, for the tertiary creep characterized by the damage evolution under tensile conditions. If we establish compression conditions, the creep deformations are changing but the damage state is partly frozen (no nucleation of new voids, for instance). The last part is devoted to the structural models. For thin-walled structures all simplifications of the analysis equations are founded on the assumptions with respect to the "thinness" of the structure. In this case, for instance, one can introduce some hypotheses for the stresses, strains and/or displacements in the thickness direction, and with the help of these hypotheses governing equations, reduced with respect to the dimension, can be established (instead of a system of three-dimensional equations we have a system of two- or one-dimensional equations). On the correctness and accuracy of such an approach will be reported. © WILEY-VCH Verlag Berlin GmbH.
Matrix Analysis of Shear Lag and Shear Deformation in Thin-Walled Box Beams
Journal of Engineering Mechanics
129
8
944-950
2003
10.1061/(ASCE)0733-9399(2003)129:8(944)
This paper presents an initial value solution of the static equilibrium differential equations of thin-walled box beams, considering both shear lag and shear deformation. This solution was used to establish the related finite element stiffness matrix and equivalent nodal forces vector. In the procedure a special shear-lag-induced bimoment is introduced, so that the analysis of shear lag and shear deformation of thin-walled box beams is admitted into the program system of the matrix-displacement method. The present procedure can be used to analyze accurately the shear lag and shear deformation effects for thin-walled box beams, especially for some complex structures ~such as continuous box girders and box beams with varying cross section, etc.!. The numerical results obtained by the present procedure are consistent with the results of model tests and predictions of the finite shell element method or finite difference approach.
Box beams,Shear lag,Shear deformation,Matrix metho
Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium
European Journal of Mechanics - A/Solids
46
42-53
2014
10.1016/j.euromechsol.2014.02.008
A semi-analytical approach eccentrically stiffened functionally graded circular cylindrical shells surrounded by an elastic medium subjected to external pressure is presented The elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman–Donnell sense, the smeared stiffeners technique and Galerkin method, this paper deals the nonlinear dynamic problem. The approximate three-term solution of deflection shape is chosen and the frequency–amplitude relation of nonlinear vibration is obtained in explicit form. The nonlinear dynamic responses are analyzed by using fourth order Runge–Kutta method and the nonlinear dynamic buckling behavior of stiffened functionally graded shells is investigated according to Budiansky–Roth criterion. Results are given to evaluate effects of stiffener, elastic foundation and input factors on the frequency–amplitude curves, natural frequencies, nonlinear responses and nonlinear dynamic buckling loads of functionally graded cylindrical shells.
Functionally graded material; Nonlinear dynamic analysis; Stiffened circular cylindrical shell
Complete set of circuit equations for stabilizer quantum mechanics
Physical Review A - Atomic, Molecular, and Optical Physics
90
1-11
2014
10.1103/PhysRevA.90.012109
We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on the completeness of the graphical ZX language for quantum processes. The complexity of the circuit equations, as opposed to the very intuitive reading of the much smaller number of ZX-equations, advocates the latter for performing computations with quantum circuits.
Space charge distribution in multi-ply LDPE
[Proceedings] 1992 Annual Report: Conference on Electrical Insulation and Dielectric Phenomena
1992
10.1109/CEIDP.1992.283219
The authors present experimental results on space charge\ndistribution at the metal-polymer interface and the polymer-polymer\ninterface by a pulsed electroacoustic method. In order to determine how\nmuch influence impurity diffusion has on the original material, two\nkinds of molding LDPE (low-density polyethylene) samples were used in\nthe experiment. One was a molding sample generated without polyethylene\nterephthalate film (PET), and the other was generated with PET film.\nMolding board materials are shown to have a strong effect on the space\ncharge distribution. Heterocharge distribution is dominant in the sample\nwith PET film processing, whereas homocharge distribution is dominant in\nthe sample without PET film processing. For the hot pressing sample, the\nspace charge distribution at the polymer-polymer interface looks like\nthat at the metal-polymer interface. This may imply that the\ncharacteristic fluctuations of the space charge distribution are\nstrongly dependent on the materials themselves and the preparation\nprocess
Mechanics of fretting fatigue-Oxford's contribution
Tribology International
76
1-5
2013
10.1016/j.triboint.2013.09.015
This article presents an historical review of studies of the mechanics of fretting fatigue, concentrating on those carried out at the University of Oxford. It includes, particularly, the seminal initial studies conducted under the direction of Prof J.J.O'Connor in the early 1970s, and brings the picture up to date. It concludes with some consideration of what the next stage of challenges facing fundamental studies are. ?? 2013 Elsevier Ltd. All rights reserved.
Contact mechanics; Fretting; Fretting fatigue; Partial slip
Nanoscale Fluid Mechanics and Energy Conversion
Applied Mechanics Reviews
66
5
50803
2014
10.1115/1.4026913
Under nanoconfinement, fluid molecules and ions exhibit radically\ndifferent configurations, properties, and energetics from those of\ntheir bulk counterparts. These unique characteristics of nanoconfined\nfluids, along with the unconventional interactions with solids at\nthe nanoscale, have provided many opportunities for engineering innovation.\nWith properly designed nanoconfinement, several nanofluidic systems\nhave been devised in our group in the past several years to achieve\nenergy conversion functions with high efficiencies. This review is\ndedicated to elucidating the unique characteristics of nanofluidics,\nintroducing several novel nanofluidic systems combining nanoporous\nmaterials with functional fluids, and to unveiling their working\nmechanisms. In all these systems, the ultra-large surface area available\nin nanoporous materials provides an ideal platform for seamlessly\ninterfacing with nanoconfined fluids, and efficiently converting\nenergy between the mechanical, thermal, and electrical forms. These\nsystems have been demonstrated to have great potentials for applications\nincluding energy dissipation/absorption, energy trapping, actuation,\nand energy harvesting. Their efficiencies can be further enhanced\nby designing efforts based upon improved understanding of nanofluidics,\nwhich represents an important addition to classical fluid mechanics.\nThrough the few systems exemplified in this review, the emerging\nresearch field of nanoscale fluid mechanics may promote more exciting\nnanofluidic phenomena and mechanisms, with increasing applications\nby encompassing aspects of mechanics, materials, physics, chemistry,\nbiology, etc.
Recent advances in the mechanics of boundary layer flow
Advances in Applied Mechanics
1
1-40
1948
10.1016/S0065-2156(08)70097-8
The concept of a boundary layer was proposed near the surface of a body moving through a fluid, a region of comparatively small thickness within which the viscous forces are comparable to the inertial forces and within which the relative speed between the body and the fluid decreases rapidly to zero is discuss in this chapter. The equations of flow is derived in the boundary layer from the Navier–Stokes equations to obtain solution for the special case of flow along a thin flat plate parallel to the direction of flow in an air stream of uniform speed. The theory gives both the skin friction and the velocity distribution within the layer. Comparisons of skin friction data soon showed certain discrepancies and it became clear that the boundary layer flow did not always conform to the Prandtl equations. This concept of Prandtl has been extraordinarily fruitful in the development of fluid mechanics. Many puzzling phenomena have been clarified by a study of the nature of the flow within the boundary layer and its effect on the general flow around the body.
Fractional Odd-Dimensional Mechanics
Advances in Difference Equations
2011
1-12
2011
10.1155/2011/526472
The classical Nambu mechanics is generalized to involve fractional derivatives using two different methods. The first method is based on the definition of fractional exterior derivative and the second one is based on extending the standard velocities to the fractional ones. Fractional Nambu mechanics may be used for nonintegrable systems with memory. Further, Lagrangian which is generate fractional Nambu equations is defined. Copyright © 2011 Ali Khalili Golmankhaneh et al.
An Analysis of the System Effects in Woven Fabrics Under Ballistic Impact
Textile Research Journal
62
495-509
1992
10.1177/004051759206200902
Following a brief review of prior work on fabric-based armor systems, the systemeffects that occur during the ballistic impact of woven fabric body armor materialsare discussed from a conceptual framework developed to relate single yam impact U,)mechanics to fabric impact mechanics. The consequence of assembling yarns intosingle-ply fabric structures is discussed from this perspective. A steep strain gradient 0along yams in the region of the transverse deflection of the fabric is related to the Yconstraint imposed on them by neighboring yams. Striking and residual A.lo city data,collected for single-ply fabric systems of Spectra{\textregistered}, Kevlar{\textregistered} 29, and nylon with various |different yam deniers and weave types, are used to establish the response of spacedarmor systems. The system effects of assembling fabric plies into body armor systems 0arn, determined by comparing the response of spaced armor systems to actual multipleplysystems. There is a pronounced decrease in energy absorption capacity for theSpectra and nylon systems; this deleterious effect is ascribed to increased transversestresses and possible interference of the deflection characteristics of fabric plies bysubsequent plies.
Design and Analysis of a Morphing Composite Airfoil Using Unbalanced Layup and Unconventional Ply Angles
TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES
57
2
79-85
2014
10.2322/tjsass.57.79
Design of morphing wings is being considered as a potential way to improve aircraft performance. Composite materials are identified as suitable candidates to achieve some of the future morphing capabilities of aircraft wings. In this work, a morphing airfoil is designed and manufactured using a woven carbon fiber reinforced plastic (CFRP) composite material and a vacuum bagging technique. The layup arrangement and stacking sequence are chosen for maximum out-of-plane deflection under the applied actuation force using finite element analysis (FEA) and composite plate bending experiments. Additionally, manual actuation loads are applied simultaneously at various feasible locations on the airfoil top surface. The morphed airfoil new shape is studied using a JavaFoil airfoil analysis program to investigate its aerodynamic characteristics in terms of lift vs. angle of attack and lift-to-drag ratio vs. angle of attack. It is found that the numbers and locations of actuation forces depend on the flight envelope stage (e.g., take-off and cruising). In general, four factors are identified to have significant effects on the maximum deflection and consequently the ease of the airfoil to morph. These factors are the ply angles, the unbalanced stacking sequence, and the number of actuation forces and their location along the airfoil skin. © 2014 The Japan Society for Aeronautical and Space Sciences.
Carbon Fibre; Drag; Finite Element; Lift; Morphing Airfoil
Continuum Damage Mechanics: Present State and Future Trends
Nuclear Engineering and Design
105
309-319
1987
10.1016/0029-5493(87)90225-1
Mechanics (CDM) has developed since the initial works of Kachanov and Rabotnov. The paper gives a review of its main features, of the present possibilities and of further developments. &x02022; - use of CDM for local approaches of fracture.
Information Theory and Statistical Mechanics
Physical Review Online Archive (Prola)
106
4
620-630
1957
citeulike-article-id:695031
Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available.It is concluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists only of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.
maxent; rationality_constraints
RITZ-TYPE DYNAMIC ANALYSIS OF CROSS-PLY LAMINATED CIRCULAR CYLINDERS SUBJECTED TO DIFFERENT BOUNDARY CONDITIONS
Journal of Sound and Vibration
227
4
749-768
1999
10.1006/jsvi.1999.2347
This paper extends the applicability of the Ritz-type method presented in a previous publication [1] towards an advanced study of the influence of the edge boundary conditions on the vibration characteristics of complete, cross-ply laminated cylindrical shells. The analysis is based on a combination of the Ritz method with appropriate, complete bases of orthonormal polynomials and its subsequent application on the energy functional of the love-type version of a unified shear-deformable shell theory. As a result, two different kinds of shear deformable Love-type shell theories are employed, including versions that either fulfil or violate the continuity of the interlaminar stresses through the shell thickness. Apart from the study of the physical problem itself, several features related to the theoretical model as well as to the analytical procedure are further addressed and investigated. As far as the modelling is concerned, particular emphasis is given to the version of the parabolic shear deformable shell theory that considers continuity of interlaminar stresses. Moreover, the relation of this version of the theory as well as its performance with respect to the corresponding older version that violates this continuity requirement [8] is further investigated. It is concluded that the accurate modelling of the interlaminar stress distribution may become a serious issue for further investigation, as it already is for the stress analysis of laminated composite structural elements.
Nonholonomic constraints in time-dependent mechanics
J. Math. Phys.
40
1376-1390
1999
10.1063/1.532808
The constraint reaction force of ideal nonholonomic constraints in time-dependent mechanics on a configuration bundle Q –>R is obtained. Using the vertical extension of Hamiltonian formalism to the vertical tangent bundle VQ of Q –> R, the Hamiltonian of a nonholonomic constrained system is constructed. The present setting is more general than the one usually considered in the literature on nonholonomic mechanics.
constraint; Nonholonomic; time-dependent mechanics
An introductory approach to fracture mechanics analyses
Engineering Fracture Mechanics
132
85-92
2014
10.1016/j.engfracmech.2014.09.008
This paper explores an introduction to the field of fracture mechanics by means of calculating the J-integral for a steel 1018 single edge notched bend specimen. The experimental methodology was primitive, nevertheless yielded acceptable results in comparison to the analytical method, giving the students first-hand experience in performing such studies.
CMOD; Crack; CTOD; Fracture; Notch; Steel
Computational Fluid Mechanics and Heat Transfer
Computational and Physical Processes in Mechanics and Thermal Sciences
791
1997
This comprehensive text provides basic fundamentals of computational theory and computational methods. The book is divided into two parts. The first part covers material fundamental to the understanding and application of finite-difference methods. The second part illustrates the use of such methods in solving different types of complex problems encountered in fluid mechanics and heat transfer. The book is replete with worked examples and problems provided at the end of each chapter.
Application of Fracture Mechanics to Anisotropic Plates
Journal of Applied Mechanics
967-974
1967
The conditions necessary for tlte application of fracture mechanics to anisotropic materials were examined and verified experimentally on orthotropic plates. It was observed that crack extension, by opening and forward sliding, occurred independently and the associated stress-intensity factors at the state of incipient fracture are material constants. An empirical relation (k1/k1c) + (k2/k2c)2 = 1 was found to be a fracture criterion for both balsa wood and fiher-glass-reinforced plastic plates, inferring the existence of a general law of fracture for orthotropic materials.
Quantum mechanics from a Heisenberg-type equality
Fortschritte der Physik
50
5-7
646-651
2002
10.1002/1521-3978(200205)50:5/7<646::AID-PROP646>3.0.CO;2-7
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states, and is sufficiently strong to provide an axiomatic basis for moving from classical mechanics to quantum mechanics. In particular, the assumption of a nonclassical momentum fluctuation, having a strength which scales inversely with uncertainty in position, leads from the classical equations of motion to the Schroedinger equation.
An innovative approach to thin coal seam mining of complex geological conditions by pressure regulation
International Journal of Rock Mechanics and Mining Sciences
71
249-257
2014
10.1016/j.ijrmms.2014.05.021
The hard rock parting contained in thin coal seams constrains the development of high-efficiency mining due to high level of equipment wear and low mining advance rate. To achieve safe and high-efficiency mining in thin coal seam with such complex geological conditions, an innovative mining approach using pressure regulation was proposed to substitute traditional deep-hole blasting technique to pre-break the coal and hence promote the flaking of hard parting during mining. Firstly, the strata pressure behaviors in the thin coal seam containing hard iron sulphide concretion parting were investigated by field monitoring and modeling study. Then, the feasibility of abutment pressure regulation via supporting force adjustment to pre-break the coal was proved by numerical experiments. The results show that the existence of hard iron sulphide concretions resulted in localized stress concentration by 30% and the profile of damage zone transforms to be radial and discontinuous. However, it does not enlarge the size of effective damage zone much. The results also reveal that the width of damage zone increases linearly with the decrease of supporting force at the logarithmic scale. This provides a theoretical guidance for the fully-mechanised thin coal seam mining face with hard rock parting. The implementation of pressure regulation in actual mining demonstrates that it can effectively enhance the mining advance rate and significantly reduce mining machine wear.
Damage zone; Fully-mechanised mining; Iron sulphide concretion; Pressure regulation; Thin coal seam
Computer applications in mechanics
Computers and Education
3
3
145-157
1979
10.1016/0360-1315(79)90040-X
This paper reviews the various ways in which the computer can be used within the mechanics section of a typical beginning physics course. While the authors are concerned primarily with the introductory college level course, many of the details would also be applicable to high school physics courses. © 1979.
A mechanics model of erosion of ductile materials by backward extrusion
Proceedings of the 1998 International Conference on Erosive and Abrasive Wear (ICEAW) - 9th International Conference on Erosion by Liquid and Solid Impact (ELSI IX)
233-235
Journal Article
182-190
1999
10.1016/S0043-1648(99)00169-6
Examination of eroded surfaces of ductile materials under a scanning electron microscope typically shows thin slivers or platelets; these subsequently break off to provide wear debris. Cousens and Hutchings [A.K. Cousens, I.M. Hutchings, Wear 88 (1983) 335-348] have studied this phenomenon in careful experiments, in which commercially pure aluminium and aluminium alloys were eroded by using glass beads and iron shot in an air blast erosion tester. It was observed that a thin surface layer hardened both due to embedding of the fragments of erodent and due to work hardening. The repeated impacts by erodents, then, caused the softer material to extrude out backwards, from discontinuities in the hardened layer. It is proposed that this 'backward extrusion' is due to 'plastic ratchetting' of the material below the hardened layer, which is progressively compressed and extruded out. The proposed mechanism has been modelled by using kinematical shakedown theorem of the theory of plasticity and the impact pressure which needs to be exceeded for the process to continue has been evaluated. By expressing the impact pressure in terms of impact velocity and material properties of the shot and the eroding surface a non-dimensional velocity is defined and related to the shakedown behaviour of the eroding system. It is shown that for the backward extrusion process to continue the non-dimensional impact velocity must be above a critical value. Examination of eroded surfaces of ductile materials under a scanning electron microscope typically shows thin silvers or platelets; these subsequently break off to provide wear debris. Cousens and Hutchings [A.K. Cousens, I.M. Hutchings, Wear 88 (1935) 335-348] have studied this phenomenon in careful experiments, in which commercially pure aluminium and aluminium alloys were eroded by using glass beads and iron shot in an air blast erosion tester. It was observed that a thin surface layer hardened both due to embedding of the fragments of erodent and due to work hardening. The repeated impacts by erodents, then, caused the softer material to extrude out backwards, from discontinuities in the hardened layer. It is proposed that this 'backward extrusion' is due to 'plastic ratchetting' of the material below the hardened layer, which is progressively compressed and extruded out. The proposed mechanism has been modelled by using kinematical shakedown theorem of the theory of plasticity and the impact pressure which needs to be exceeded for the process to continue has been evaluated. By expressing the impact pressure in terms of impact velocity and material properties of the shot and the eroding surface a non-dimensional velocity is defined and related to the shakedown behaviour of the eroding system. It is shown that for the backward extrusion process to continue the non-dimensional impact velocity must be above a critical value.
Air blast erosion tester; Aluminum; Aluminum alloys; Backward extrusion; ductile material; Ductile materials; Ductility; Erosion; Extrusion; Hardening; Impact testing; Kinematics; mathematical modeling; Mathematical models; Plasticity; Plastic ratchetting; Pressure; Scanning electron microscopy; Surfaces
Particle mechanics model for the effects of shear on solute retardation coefficient in rock fractures
International Journal of Rock Mechanics and Mining Sciences
52
92-102
2012
10.1016/j.ijrmms.2012.03.001
International Journal of Rock Mechanics and Mining Sciences, 52 + (2012) 92-102. doi:10.1016/j.ijrmms.2012.03.001
Fracture surface damage; Particle mechanics model; Retardation coefficient; Shear; Solute transport; Wear
Quantum Mechanics without Waves: A Generalization of Classical Statistical Mechanics
Annals of Physics
273
99-113
1999
10.1006/aphy.1998.5892
We generalize classical statistical mechanics to describe the kynematics\nand the dynamics of systems whose variables are constrained by a\nsingle quantum postulate (discreteness of the spectrum of values\nof at least one variable of the theory). This is possible provided\nwe adopt Feynman's suggestion of dropping the assumption that the\nprobability for an event must always be a positive number. This approach\nhas the advantage of allowing a reformulation of quantum theory in\nphase space without introducing the unphysical concept of probability\namplitudes, together with all the problems concerning their ambiguous\nproperties.
Experimental study on creep deformation of thin-walled tubes under pure bending
Structural Engineering and Mechanics
9
4
339-347
2000
The creep deformation of pure bending (hold constant moment for a period of time) tests were conducted in this paper. Thin-walled tubes of 304 stainless steel were used in this investigation. The curvature-ovalization measurement apparatus, designed by Pan et al. (1998), was used for conducting the present experiments. It has been found that as soon as the creep deformation is started, the magnitudes of the tube curvature and ovalization of tube cross-section quickly increase. The magnitudes of the creep curvature and ovalization of tube cross-section increase fast with a higher hold moment than that with a lower one. Owing to the continuously increasing curvature during the creep deformation, the tube specimen buckles eventually.
Bending (deformation); Creep; Stainless steel; Structural analysis; Thin walled tubes; Tubes (components)
OH- Effect on the Growth and Structural Properties of Chemical Bath Deposited ZnS Quantum Thin Films
Applied Mechanics and Materials
281
523-526
2013
Zinc sulfide (ZnS) quantum thin films have been deposited from precursors with a variety of OH- concentration onto microscope glass substrates by chemical bath deposition method. The growth and structural properties have been investigated. XRD patterns of ZnS films obtained from acidic solution showed a favorable wurtzite structure, while for those obtained from alkaline solution, showed a sphalerite structure. The growth studied of the deposited films has also shown that the OH- played a vital role in nucleation and the film growth.
Growth; OH-; Structure; ZnS Quantum Thin Film
Minimum size of 180 degree domains in ferroelectric thin films covered by electrodes
Applied Mathematics and Mechanics
27
8
1031-1036
2006
10.1007/s10483-006-0803-1
Ferroelectric domain switching under low voltage or short pulsesis of interest for the development of high-density random access memory (FRAM) devices. Being necessarily very small in size, instability and backswitching often occur when the external voltage is removed, which creates serious problems. In this investigation, a general approach to determine the minimum size of ferroelectric domain to avoid backswitching was developed, and as an example, a 180◦ domain in a ferroelectric thin film covered by the upper and lower electrodes was considered in detail. We note that our approach is generally applicable to many other fields, including phase transformation, nucleation and expansion of dislocation loops in thin films, etc.
Study morphology evolution in self-assembled block copolymer thin films in virtue of carbon nanotube
Advances in Heterogeneous Material Mechanics 2008
1358-1361
2008
In order to study systemically the morphology evolution in self-assembled block copolymer thin films induced by solution annealing, a simple relocation technique for atomic force microscopy, which takes advantage of carbon nanotube, is used for investigating repeatedly the imaging of some specific species on the whole substrate with a high relocation accuracy of tens of nanometers. As an example of the application of this technique, TappingMode AFM Ex-situ study of the morphology transition induced by solvent treatment in a triblock copolymer thin film has been carried out.
afm; block copolymer; carbon nanotube; self-assembled
Probabilistic evaluation of fuselage-type composite structures
Probabilistic Engineering Mechanics
14
1-2
179-187
1999
10.1016/S0266-8920(98)00027-7
\nA methodology is developed to simulate computationally the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, natural frequencies, displacements, stress/strain, etc., which are the consequences of the random variation (scatter) of the primitive (independent random) variables in the constituent, ply, laminate and structural levels. This methodology is implemented in a computer code IPACS (integrated probabilistic assessment of composite structures). A fuselage-type composite structure is analyzed to demonstrate the code's capability. The probability distribution functions of the buckling loads, natural frequency, displacement, strain and stress are computed. The sensitivity of each primitive (independent random) variable to a given structural response is also identified from the analyses.
{Cyclic plasticity modelling for ANDES thin shell and line-spring finite elements}
International Journal of Applied Mechanics
01
01
201-232
2009
10.1142/S1758825109000101
This paper presents a proposed methodology to account for cyclic plastic response of the thin shell ANDES and line-spring finite elements. A through thickness integration scheme is employed for the shell element and stress resultant plasticity is used for the line-spring element. A simplified contact formulation to account for crack closure in the line-spring element is also presented. Numerical comparisons between the proposed models and detailed 3D analyses (pipes) are carried out and presented herein. A comparison between the present implementation and large scale experiment of a surface cracked pipe subjected to large cyclic plastic strains is also presented. The purpose of the presented implementation is to account for cyclic loading in pipeline technology where significant amount of plasticity in the loading cycles occurs.
Kinematic hardening; line-spring; low; thin shell
Analysis of the hydrodynamic interaction between cascades of thin profiles taking account of vortex wake evolution
Journal of Applied Mechanics and Technical Physics
17
4
502-506
1977
10.1007/BF00851999
The papers [1-5] are devoted to an investigation of aspects of the hydrodynamic interaction of cascades of profiles in a nonlinear formulation: it is shown experimentally in [1] and theoretically in [2] that the free vortex sheet ruptures upon meeting a profile; taking account of the evolution of vortex wakes, the flows around two cascades of solid profiles of infinitesimal [3] and finite [4] density are computed; results of an experimental investigation of the dynamic reactions of the flow on two mutually moving cascades of thin profiles are presented in [5]. The interference between two cascades of thin profiles in an inviscid, incompressible fluid flow is examined in this paper, where a modified method from [6] is used. © 1977 Plenum Publishing Corporation.
Measurement on asymmetric transition of a hypersonic boundary layer using a high frequency thin-film sensor system
New Trends in Fluid Mechanics Research
186-189
2007
A very high frequency-responding thin film sensor system is developed and applied to measure mean and fluctuation value of heat flux rate about the hypersonic flow over two slender cones. Experiments are having performed in a piston shot tunnel at Mach number 6. Measurements are asymmetric transition of the boundary layer over the slender cone. The time averaged heat flux and the heat flux rate fluctuation have been measured with this system. Time-averaged heat flux rate gives the boundary layer transition onset and peak position clearly. Heat flux rate fluctuation reveals the turbulent characteristic in spectrum analysis. Heat flux rate fluctuation has a wide frequency range in hypersonic boundary-layer.
asymmetric; fluctuation; hypersonic; slender cone; thin-film sensor
Elements of Quantum Mechanics
A Trajectory Description of Quantum Processes. I. Fundamentals
850
75-119
2012
Bohmian mechanics constitutes a different way to understand quantum mechanics, where the role of an external observer is not present, and quantum phenomena and processes are explained in a causal way, connecting system configurations at different times by means of trajectories. However, in order to better understand the ideas and concepts behind this approach to the quantum world, in this chapter some relevant ingredients from the standard quantum mechanics are briefly revisited. In this regard, special emphasis is made on trajectory-based approaches or their use to obtain quantum-mechanical information directly (calculation of observables) or inferring it from quantum-classical correspondence arguments (phase–space distributions, such as the Wigner and Husimi distributions). Thus, apart from general quantum concepts, the derivation of Schrödinger’s equation by means of the Hamiltonian analogy, the Feynman path integral formulation, the semiclassical route to quantum mechanics or the eikonal approach, will be also briefly exposed.
Mathematical and Computational Physics; quantum physics; Theoretical
Particle finite element methods in solid mechanics problems
Computational Plasticity
7
87-103
2007
10.1007/978-1-4020-6577-4_6
The paper examines the possibilities of extending the Particle finite element methods (PFEM), which have been successfully applied in fluid mechanics, to solid mechanics problems. After a review of the fundamentals of the method, their specific features in solid mechanics are presented. A methodology to face contact problems, the anticipating contact interface mesh, is presented oil the basis of a penalty-like constitutive models for imposing the contact and friction conditions. Finally, the PFEM is applied to same representative solid mechanics problems to display the capabilities of the method and some final conclusions are obtained.
fluid-flow; point method; powder compaction processes; simulation; transport
A classical interpretation of quantum mechanics and the measurement problem
Measurement
76
August
10
2010
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented which is motivated by retaining the point of view of classical mechanics as much as possible, and which is consistent with relativity theory. Everything can be written down in terms of well-known mathematical formulations that can be found in every textbook about quantum mechanics. Therefore, in this version, almost no formulas are used.
Nonlinear stability analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads
European Journal of Mechanics - A/Solids
50
28-38
2015
http://dx.doi.org/10.1016/j.euromechsol.2014.10.004
Abstract To increase the thermal resistance of various structural components in high-temperature environments, the present research deals with nonlinear stability analysis of thin annular spherical shells made of functionally graded materials (FGM) on elastic foundations under external pressure and temperature. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Classical thin shell theory in terms of the shell deflection and the stress function is used to determine the buckling loads and nonlinear response of the FGM annular spherical shells. Galerkin method is applied to obtain closed – form of load – deflection paths. An analysis is carried out to show the effects of material, geometrical properties, elastic foundations and combination of external pressure and temperature on the nonlinear stability of the annular spherical shells.
Elastic foundations; FGM annular spherical shells; Nonlinear stability analysis; Thermo-mechanical loads
Modelization and numerical approximation of piezoelectric thin shells Part II: Approximation by finite element methods and numerical experiments
Computer Methods in Applied Mechanics and Engineering
192
4045-4073
2003
10.1016/S0045-7825(03)00362-1
A two-dimensional modelization of piezoelectric thin shells has been developed in the first part of this work. Three equivalent variational formulations have been considered: ??? an homogeneous one (with respect to the potential) the bilinear form of which is positive definite but not symmetric; ??? the associated nonhomogeneous one which is directly related to the natural boundary conditions on the potential; ??? a third one, whose bilinear form is now symmetric but no longer positive definite. In this second part of this work, the approximation of the second formulation by a conforming finite element method is analyzed. It takes into account the use of numerical integration techniques and gives criteria on the choice of suitable numerical schemes. Moreover, the drawbacks linked to the unsymmetrical character of the associated square matrix of the linear system are circumvent by using a condensation method which consists to eliminate the potential and then to only solve a symmetrical and elliptic linear system with respect to the displacement. This method is most effective than a full implementation of the third variational formulation. Finally some numerical experiments on plate and thin cylindrical shells prove the effectiveness of this method. ?? 2003 Elsevier B.V. All rights reserved.
Transparent thin film thermocouple
Thin Solid Films
176
73-78
1989
10.1016/0040-6090(89)90365-9
A transparent thin film thermocouple has been produced by reactive sputtering which has a Seebeck coefficient of 0.14 mV °C−1. The positive leg of the thermocouple is indium tin oxide (ITO) and the negative leg is In2O3. The In2O3 and ITO thin films were also tested with sputtered thin film platimun to obtain their individual thermoelectric potentials. Stability of the transparent thermocouple at 575 K and the calibration data of sputtered ITO and platinum are also reported.
An introduction to mathematical modeling : a course in mechanics
Wiley series in computational mechanics
xiv, 334 p.
2011
10.1002/9781118105733
"An important resource, this book provides a short-course in nonlinear continuum mechanics, contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics, and presents a brief introduction to statistical mechanics of systems in thermodynamic equilibrium. Also included is information on continuum mechanics, electrodynamics, quantum mechanics, and statistical mechanics. The author approaches mechanics as the branch of physics and mathematical science concerned with describing the motion of bodies, including their deformation and temperature changes, under the action of forces, and if the study of the propagation of waves and the transformation of energy in physical systems are added, then the term mechanics does indeed apply to everything that is covered within the book. "-- "An important resource, this book provides a short-course in nonlinear continuum mechanics, contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics, and presents a brief introduction to statistical mechanics of systems in thermodynamic equilibrium. Also included is information on continuum mechanics, electrodynamics, quantum mechanics, and statistical mechanics"--
MATHEMATICS / General.; Mechanics, Analytic.
Biofluid mechanics: innovations and challenges
Journal of Biomechanics
46
207
2013
10.1016/j.jbiomech.2012.11.034
This special issue on 'Biofluid Mechanics' is dedicated to Professor Shmuel Einav on the occasion of his 70 th birthday. It is a tribute to his leading role in the development of the field of biomedical engineering and his seminal contributions to biofluid mechanics in general and to cardiovascular bioengineering in particular. This issue is the outcome of a special international meeting that was held in March 2012 in the Dead Sea in Israel. The meeting was a conjunc-tion of the 1 st Conference on Computational Fluid Dynamics in Medicine and Biology and the 7 th International Biofluid Mechanics Symposium, a series of scientific symposia that Professor Einav was leading during the past decade. Biofluid mechanics is a vast discipline of bioengineering in which fundamental principles of fluid mechanics are utilized to elucidate underlying mechanisms of biological flows and their interrelation-ships with physiological processes, in health and in sickness. It spans from cells to organs, covering diverse aspects of functionality of systemic physiology, including cardiovascular, respiratory, reproduc-tive, urinary, musculoskeletal, neurological, ocular, lymphatic, and auditory systems. The application of its principles is crucial for designing experimental systems in which new aspects of flow driven physiological processes can be studied and tested, as well as for designing successful artificial replacements and devices used in regenerative medicine. Biofluid mechanics and its simulations apply to internal flows such as cardiovascular blood flow and respiratory airflow, as well as external flows such as flying and aquatic locomo-tion (i.e., swimming). Biological flows involve complex fluids flowing through three dimensional (3D) deformable and permeable tissues and organs. Initially, the mathematical and computational modeling of the non-linear equations governing such flows was limited to sim-plified models and geometries. The development of innovative numerical techniques, incorporating multidisciplinary computa-tional fluid dynamics (CFD) models, made the simulation of complex transport phenomena in medicine and biology feasible. Tackling more challenging and clinically relevant problems in realistic physiologic geometries was achieved by concomitant advancements in high performance computing (HPC) and the development of cutting edge clinical visualizing modalities and graphics software. Presently, those are readily integrated into numerical simulations of physiological flows. It opens tremen-dous opportunities for harnessing the power of biofluid mechanics analysis to solving problems at the clinical forefront. It led to breakthroughs such as patient specific fluid–structure interactions (FSI) modeling of disease processes for improving clinical diagnostics, designing optimized implantable prosthetic devices, and improving outcomes of surgical procedures. In the last decade it also extended to the role of flow in processes such as mechanotransduction of biological signals through the interaction with cellular and subcellular structures. The latter pre-sents yet another challenge of innovative multiscale modeling approaches which integrate elements of continuum mechanics with molecular dynamics. A major aim is bridging the gap between the disparate spatiotemporal scales characterizing flow driven and bio-chemical processes governing physiological response. Medicine and biology are progressively entering into the in silico modeling era, of which several of the more significant contributions emerge from the biofluid mechanics community. Modeling of complex flows allows for deep insight into multifaceted phenomena within any biofluid system, enabling the exploration of new biological and physiological aspects of health and disease processes. It provides effective meth-odologies for predicting the performance of devices during the design stage while accelerating the regulatory phase of these devices by offering new virtual testing and validation techniques. There are many challenges that the biofluids community faces in defining critical questions, identifying tools that are required to answer these questions, and synthesizing individual biological path-ways into successful predictive models of flow driven biological phenomena. By combining cellular and molecular approaches we can address biofluid mechanics issues at levels extending from the subcellular nanoscales through higher organizational levels of regional cellular phenotypes to macroscopic organ systems and whole body scales. The relationships between biological flows, mechanotransduc-tion, and the localization of arterial lesions can now be advanced by the incorporation of new technologies and the refinement of existing methods in imaging, computational modeling, and high throughput genomics and proteomics. These challenges will further encompass extracorporeal biofluid mechanics, regenerative medicine, clinical devices, mass and heat transfer and imaging modalities. This special issue is composed of reviews and original research articles of the state-of-the-art in CFD applications to biological flows, including integration of numerous modalities that enable patient-specific simulations, leading to enhanced clinical diagnostics and improved outcomes of clinical interventions. These articles, which represent a snapshot of the cutting edge research currently conducted in biofluid mechanics, were contributed by leading groups in the field who participated in this special international conference and work-shop organized by Engineering Conferences International.
Quantum mechanics/molecular mechanics study of oxygen binding in hemocyanin.
The journal of physical chemistry. B
118
19
5034-43
2014
10.1021/jp5003885
We report a combined quantum mechanics/molecular mechanics (QM/MM) study on the mechanism of reversible dioxygen binding in the active site of hemocyanin (Hc). The QM region is treated by broken-symmetry density functional theory (DFT) with spin projection corrections. The X-ray structures of deoxygenated (deoxyHc) and oxygenated (oxyHc) hemocyanin are well reproduced by QM/MM geometry optimizations. The computed relative energies strongly depend on the chosen density functional. They are consistent with the available thermodynamic data for oxygen binding in hemocyanin and in synthetic model complexes when the BH&HLYP hybrid functional with 50% Hartree-Fock exchange is used. According to the QM(BH&HLYP)/MM results, the reaction proceeds stepwise with two sequential electron transfer (ET) processes in the triplet state followed by an intersystem crossing to the singlet product. The first ET step leads to a nonbridged superoxo CuB(II)-O2(•-) intermediate via a low-barrier transition state. The second ET step is even more facile and yields a side-on oxyHc complex with the characteristic Cu2O2 butterfly core, accompanied by triplet-singlet intersystem crossing. The computed barriers are very small so that the two ET processes are expected to very rapid and nearly simultaneous.
Natural element approximation of Reissner–Mindlin plate for locking-free numerical analysis of plate-like thin elastic structures
Computer Methods in Applied Mechanics and Engineering
256
17-28
2013
10.1016/j.cma.2012.12.015
A rotation-free mixed natural element approximation of Reissner–Mindlin plate for the locking-free numerical analysis of plate-like thin elastic structures is presented, motivated by the rotation-free approximation for plate- and shell-like elastic structures and the high smoothness of Laplace interpolation functions used in natural element method. The mid-surface deflection and the rotation of shear are directly approximated using Laplace interpolation functions, while the Voronoi polygon-wise constant curvatures and bending moments are indirectly computed by area-averaging the boundary integrals of deflection derivatives and rotation of shear. The present approximation of the deflection and rotation of shear of discretized Reissner–Mindlin plate bending problem is formulated according to the modified mixed Hu-Washizu principle. Through the numerical results, it is verified that the rotation-free mixed natural element approximation of only the deflection and rotation of shear successfully prevents shear locking in the numerical analysis of plate-like thin elastic structures.
Constant curvature; Laplace interpolation function; Reissner–Mindlin plate; Rotation-free mixed natural element approximation; Shear locking; Voronoi polygons
Asymptotic solutions of coupled dynamic problems of thermoelasticity for thin bodies of anisotropic inhomogeneous-in-plan materials
Journal of Applied Mathematics and Mechanics
75
601-611
2011
10.1016/j.jappmathmech.2011.11.015
Two-dimensional recurrence resolvents for an inhomogeneous thin body (plates of variable thickness and shells) are derived by an asymptotic method based on the three-dimensional equations of the coupled dynamic problem of the thermoelasticity of an anisotropic body, which are solved in the case of anisotropy, having, at each point, one plane of symmetry perpendicular to the transverse axis. Recurrence formulae are derived in a general formulation for determining the components of the stress tensor, the strain vector and the function of the change in the temperature field, when different boundary conditions of dynamic problems of the theory of coupled thermoelasticity and thermal conductivity are given on the end surfaces of a thin body. An algorithm for determining the analytical and numerical (necessary) solutions of these boundary-value problems with an arbitrarily specified accuracy is developed. ?? 2011 Elsevier Ltd. All rights reserved.
Two-parameter asymptotic approximations in the analysis of a thin solid fixed on a small part of its boundary
Quarterly Journal of Mechanics & Applied Mathematics
60
4
457-471
2007
10.1093/qjmam/hbm019
Planar elasticity problems are considered for thin domains fixed along a small part of the end region boundary. The analysis involves two small parameters: the normalized thickness of the body and the normalized length of the fixed part of the boundary. The aim of the paper is to derive an asymptotic approximation of the solution to a boundary-value problem in such a domain and, in particular, analyze the ‘effective boundary conditions’, which occur for the leading-order terms of the asymptotics. We include applications for problems of both anti-plane shear and plane strain elasticity. [ABSTRACT FROM PUBLISHER] Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
ALGORITHMS; BOUNDARY value problems; ELASTICITY; FUNCTIONS; GEOMETRY
Supersymmetric quantum mechanics in graphene
Journal of the Korean Physical Society
50
6
1678-1682
2007
10.3938/jkps.50.1678
To understand the unusual quantum Hall effects in graphene, we exploit the supersymmetric quantum mechanics on the basis of the index theorem and a higher degree of symmetry. The index theorem relates the zero-energy states to the topology of the compact lattice. We claim that the zero-energy state emerges naturally, provided the Zeeman splitting becomes as large as the Landau level separation at the Fermi points in graphene. This results in the fact that supersymmetry is a good symmetry. In the case of nonzero energy, the up-spin and the down-spin states provide the exact higher symmetry of spin, forming a supersymmetric multiplet. We describe briefly a unified picture for the peculiar and unconventional quantum Hall effects in graphene on the basis of the supersymmetric quantum mechanics.
Quantum Mechanics and Metaphysical Indeterminacy
Australasian Journal of Philosophy
88
2
227-245
2010
10.1080/00048400903097786
There has been recent interest in formulating theories of non-representational indeterminacy. The aim of this paper is to clarify the relevance of quantum mechanics to this project. Quantum-mechanical examples of vague objects have been offered by various authors, displaying indeterminate identity, in the face of the famous Evans argument that such an idea is incoherent. It has also been suggested that the quantum-mechanical treatment of state-dependent properties exhibits metaphysical indeterminacy. In both cases it is important to consider the details of the metaphysical account and the way in which the quantum phenomenon is captured within it. Indeed if we adopt a familiar way of thinking about indeterminacy and apply it in a natural way to quantum mechanics, we run into illuminating difficulties and see that the case is far less straightforward than might be hoped.
Quantum Mechanics on Noncommutative Spacetime
Physical Review D
74
3
8
2006
10.1103/PhysRevD.74.037901
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note however that noncommutative intrinsic dipole moments are not observable in present experiments searching for an EDM of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moment are thus incorrect.
Response of moderately thick laminated composite plates on elastic foundation subjected to moving load
Composite Structures
97
286-295
2013
10.1016/j.compstruct.2012.10.017
Dynamic response of moderately thick antisymmetric cross-ply laminated rectangular plates on elastic foundation is investigated. The governing equations are based on the higher order shear deformation theory (HSDT). Two-parameter elastic foundation (Pasternak type) is considered. Modal analysis in conjunction with the incremental differential quadrature method (IDQM), as an efficient and stable numerical tool for temporal domain discretization, are employed to solve the governing differential equations. Much lower computational time of the DQM with respect to Newmark’s method is exhibited. The convergence of the method is demonstrated and its accuracy is shown by comparing the results with those of exact solution for thin plate obtained using the classical plate theory (CPT). Also, comparison between the results of different theories, i.e. the classical thin plate theory (CPT), the first order shear deformation theory (FSDT) and the higher order shear deformation theory (HSDT), is made. The effects of different parameters on dynamic response of the antisymmetric cross-ply plates are studied. The results can be used as benchmark solution for future works.
Cross-ply laminated plates; Dynamic response; Elastic foundation; Higher order shear deformation theory; Incremental differential quadrature
Mode interaction in thin-walled I-section struts with semi-rigid flange–web joints
International Journal of Non-Linear Mechanics
69
71-83
2015
10.1016/j.ijnonlinmec.2014.11.023
A recently developed variational model that describes the non-linear interaction between the global and local buckling of a thin-walled I-section strut under pure compression is extended to include semi-rigid flange–web connections. A formulation combining the Rayleigh–Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Cellular buckling, observed in the case where the web is assumed to provide no more than a simple support to the flanges, is found to be rapidly eroded by increasing the connection rigidity, although the local buckling wavelength still reduces as the post-buckling deformation is increased. The model is validated using finite element analysis; the results compare very well particularly when a high rigidity between the section web and flanges is simulated.
Global buckling; Local buckling; Mode interaction; Non-linear mechanics; Snaking
Symmetries in discrete-time mechanics
Annals Of Physics
252
2
357-361
1996
Based on a general formulation for discrete-time quantum mechanics,\nintroduced by M. Khorrami (Annals Phys. 224 (1995), 101), symmetries\nin discrete-time quantum mechanics are investigated. It is shown\nthat any classical continuous symmetry leads to a conserved quantity\nin classical mechanics, as well as quantum mechanics. The transformed\nwave function, however, has the correct evolution if and only if\nthe symmetry is nonanomalous. (C) 1996 Academic Press, Inc.
The Mechanical Behavior of Short-Fiber-Elastomer Composites
Rubber Chemistry and Technology
49
5
1167-1181
1976
10.5254/1.3535004
Abstract The measured elastic and strength properties of angle-ply composites of short fibers and rubber depend on test-piece geometry. In general, higher tensile moduli and strengths are obtained when plies are both thin and wide. Once the effects of test-piece geometry are taken into account, elastic properties can be calculated as functions of the properties of a single ply. Classical compliance transformation equations can be used. However, because of the invariance of shear modulus in aligned composites, the tensor transformation equations are somewhat simplified. Tensile strengths of off-axis unidirectional composite plates and balanced-angle plies can be fitted by Hill's criterion. Unidirectional composites tend to fail in the weakest mode, depending on the angle of stress, but laminating causes all principal stresses in a ply to be near their ultimate limit at the time of failure.
Statistical Mechanics: Fundamentals and Modern Applications (Wilde, Richard E.; Singh, Surjit)
Journal of Chemical Education
76
6
761
1999
10.1021/ed076p761.2
The book is split into three sections: Essentials, Equilibrium Statistical Mechanics, and Non-Equilibrium Statistical Mechanics.\nThe book is split into three sections: Essentials, Equilibrium Statistical Mechanics, and Non-Equilibrium Statistical Mechanics.
Nanorheology of molecularly thin films of n-hexadecane in Couette shear flow by molecular dynamics simulation
Journal of Non-Newtonian Fluid Mechanics
77
1-2
53-78
1998
10.1016/S0377-0257(97)00094-3
In this work the rheological and structural properties of n-hexadecane\nhave been studied by molecular dynamics simulation. The model consists\nof two structured atomic walls between which the fluid is sheared\nby moving the walls in opposite directions. The fluid consists of\nchains of n-hexadecane molecules. Each molecule has 16 interaction\nsites where each site on the molecule represents a CH2 or CH3 group.\nThe Lennard-Jones potential governs the intermolecular interactions.\nStretching, angular and torsional potentials are used for the intramolecular\ninteractions to preserve the integrity of the molecules. An isothermal\nsimulation of the Couette shear flow is conducted to reveal the rheological\nproperties of n-hexadecane at high Weissenberg numbers in films as\nthin as 1 nm. The results obtained show an increase in the average\nviscosity of hexadecane as the film thickness is decreased to scales\ncomparable to the molecular diameter of the chain segments. These\nresults agree with recent experimental findings for very thin films,\nrevealing shear thinning and normal stress difference effects which\nare an indication of non-Newtonian behaviour. Structural properties\nsuch as the density profiles, bond angle and dihedral angle distribution\nfunctions and average end-to-end distance of the molecules are obtained\nfor films of different thickness and at different shear rates. The\neffects of the wall-fluid interaction strength on the fluid properties\nare also investigated in different adsorption limits. It seems that\nadsorption is a determining factor in the properties of these ultrathin\nfilms. The results indicate different shear responses depending on\nthe adsorption limit of the surface.
couette shear flow; nanorheology; n -hexadecane
Comparative study on vibration control methodologies applied to adaptive thin-walled anisotropic cantilevers
European Journal of Mechanics - A/Solids
24
4
661-675
2005
10.1016/j.euromechsol.2004.12.006
A study of the vibrational control of adaptive doubly-tapered cantilevered\nbeams, simulating an aircraft wing, exposed to time-dependent external\npulses is presented. Whereas the beam structure encompasses non-classical\nproperties such as transverse shear and anisotropy of their constituent\nmaterials, the active control capabilities are based upon the implementation\nof the adaptive materials technology. Herein, the adaptive feature\nis achieved through the converse piezoelectric effect that consists\nof the generation of localized strains in response to an applied\nvoltage. Piezoactuators in the form of patches or spread all over\nthe beam span are considered. The active control involves the dynamic\nresponse to arbitrary time-dependent external pulses. The closed-loop\ndynamic response time-histories are obtained via the use of the piezoelectrically\ninduced moment control, and through the implementation of a modified\nbang-bang control strategy that involves a maximum value constraint\nimposed on the input voltage. In addition to this active feedback\ncontrol methodology, a passive one based upon the use of the directionality\nproperty of anisotropic composite material structures is also implemented.\nMoreover, the results are compared to those obtained via the implementation\nof other two feedback control methodologies, namely the Linear Quadratic\nRegulator (LQR) and the Fuzzy Logic Control (FLC). Numerical simulations\nemphasizing the performance of the adopted control strategies intended\nto contain and even suppress the oscillations when time unfolds are\npresented, and pertinent conclusions are outlined.
adaptive cantilevers; bang; converse piezoelectric effect; lqr and flc controls; thin-walled beams
Combining Quantum Mechanics Methods with Molecular Mechanics Methods in ONIOM
Journal of Chemical Theory and Computation
2
3
815-826
2006
10.1021/ct050289g
The purpose of this paper is 2-fold. First, we present several extensions to the ONIOM(QM:MM) scheme. In its original formulation, the electrostatic interaction between the regions is included at the classical level. Here we present the extension to electronic embedding. We show how the behavior of ONIOM with electronic embedding can be more stable than QM/MM with electronic embedding. We also investigate the link atom correction, which is implicit in ONIOM but not in QM/MM. Second, we demonstrate some of the practical aspects of ONIOM(QM:MM) calcns. Specifically, we show that the potential surface can be discontinuous when there is bond breaking and forming closer than three bonds from the MM region. [on SciFinder (R)]
combining quantum mech MM method ONIOM electronic; Molecular mechanics; Molecular orbital methods; Quantum chemistry; Reaction mechanism (combining quantum mechanics me
Contact mechanics
Adhesion Science and Engineering
1
Mechanics of Adhesion
577-604
2002
A review provides an up-to-date description of contact mechanics methods in the context of adhesion science, focusing on the underlying math. description of the most relevant contact problems. The fundamental expressions of contact mechanics for axially sym. geometries are presented. The effects of adhesive forces on these geometries are also discussed. The contact of linear viscoelastic materials is described. [on SciFinder (R)]
Modeling crack propagation for advanced 4-point bending testing of metal-dielectric thin film stacks
Engineering Fracture Mechanics
96
490-499
2012
10.1016/j.engfracmech.2012.08.018
For monitoring and improving mechanical properties of BEoL (back-end of line) interconnect structures in microprocessor technology, it is crucial to analyze their adhesion and crack propagation properties. In the present investigation, a camera assisted 4-point bending beam technique has been used to obtain fast and reliable adhesion measurements including locally resolved crack length information. To interpret the obtained crack propagation data, a finite-element modeling approach has been utilized. The combination of local measurement of the crack energy release rate and modeling enables to evaluate measurement curves for both symmetric and asymmetric crack propagation modes and to describe the crack propagation properties of the involved film stacks not attainable in such detail by conventional 4-point bending technique. © 2012 Elsevier Ltd.
4-Point bending; Adhesion; Finite-element modeling; On-chip interconnects
Critical Assessment of the Mandrel Peel Test for Fiber Reinforced Thermoplastic Laminates
Engineering Fracture Mechanics
101
96-108
2013
10.1016/j.engfracmech.2012.07.005
The applicability of the mandrel peel test for thermoplastic composites was investigated experimentally by comparing the fracture toughness to the values obtained by the double cantilever beam (DCB) and end loaded split (ELS) beam test. Two laminates were considered: a unidirectionally carbon-PPS laminate and a carbon-PPS hybrid laminate, in which the interface consisted of a woven fabric and a unidirectionally reinforced ply. The mandrel peel results on the unidirectionally reinforced laminate compared well with the DCB and ELS test results. The fracture toughness of the hybrid interface could not be quantified by the DCB or ELS test, whereas this was possible using the mandrel peel test.
Fracture mechanics; Interface fracture; Polymer matrix composites; Toughness testing
Mass transport in water waves over a thin layer of soft viscoelastic mud
Journal of Fluid Mechanics
573
105
2007
10.1017/S0022112006003508
A theory is presented for the mass transport induced by a small-amplitude\nprogressive wave propagating in water over a thin layer of viscoelastic\nmud modelled as a Voigt medium. Based on a sharp contrast in length\nscales near the bed, the boundary-layer approximation is applied\nto the Navier-Stokes equations in Lagrangian form, which are then\nsolved for the first-order oscillatory motions in the mud and the\nnear-bed water layers. On extending the analysis to second order\nfor the mass transport, it is pointed out that it is inappropriate,\nas was done in previous studies, to apply the complex viscoelastic\nparameter to a higher-order analysis, and also to suppose that a\nVoigt body can undergo continuous steady motion. In fact, the time-mean\nmotion of a Voigt body is only transient, and will stop after a time\nscale given by the ratio of the viscosity to the shear modulus. Once\nthe mud has attained its steady deformation, the mass transport in\nthe overlying water column can be found as if it were a single-layer\nsystem. It is found that the near-bed mass transport has non-trivial\ndependence on the mud depth and elasticity, which control the occurrence\nof resonance. Even when the resonance is considerably damped by viscosity,\nthe mass transport in water over a viscoelastic layer can be dramatically\ndifferent, in terms of magnitude and direction, from that over a\nrigid bed.
2-layer viscous system interfacial waves surface-w
Acoustic implications of a thin viscous boundary layer over a compliant surface or permeable liner
Journal of Fluid Mechanics
678
348-378
2011
10.1017/jfm.2011.116
This paper considers the implications of a high-Reynolds-number thin parallel boundary layer on fluid–solid interaction. Two types of boundaries are considered: a compliant boundary which is flexible but impermeable, such as an elastic sheet or elastic solid, and a permeable boundary which is rigidly fixed, such as a perforated rigid sheet. The fluid flow consists of a steady flow along the boundary and a small time-dependent perturbation, with the boundary reacting to the perturbation. The fluid displacement due to the perturbation is assumed to be much smaller than the boundary-layer thickness. The analysis is equally valid for compressible and incompressible fluids. Numerical examples are given for compressible flow along a cylindrical duct, for both permeable and compliant cylinder walls. The difference between compliant and permeable walls is shown to be dramatic in some cases. High- and low-frequency asymptotics are derived, and shown to compare well to the numerics. When used with a mass–spring–damper boundary, this model is shown to lead to similar, but not identical, temporal instability with unbounded growth rate to that seen for slipping flow using the Myers boundary condition. It is therefore suggested that a regularization of the Myers boundary condition removing the unbounded growth rate may lead to, or at least inform, a regularization of the model presented here.
Mechanics of interface fracture with applications in electronic packaging
IEEE Transactions on Device and Materials Reliability
3
4
129-143
2003
10.1109/TDMR.2003.820623
The purpose of this paper is to present a brief review of the mechanics of interface fracture, with a focus on applications in electronic packaging. From a structural mechanics perspective, electronic devices can be thought of as composite structures to thermomechanical loading. The mechanics of interface fracture is a specialized subtopic within the discipline of fracture mechanics and the nonspecialist may be unaware of some of the subtle differences encountered in applying interface fracture concepts. The mechanics associated with interface fracture introduces certain mathematical concepts that may seem to be unnecessarily complicated, but are essential for its proper application. It is important that the electronic packaging reliability engineer be aware of these concepts, understanding the most important implications.. This review will focus on the. mechanics and computational aspects of interface I. fracture in electronic structures, with a particular emphasis on some details that the nonexpert could only obtain after an extensive review of the available literature. Numerical results are. presented for the important problem of corner cracking between silicon and epoxy materials subjected to thermomechanical loading. These new results provide insight into the three-dimensional nature of interfacial,. crack propagation at bimaterial corners.
The Universal Arrow of Time II: Quantum mechanics case
Quantum
43
2011
The given paper is natural continuation of our previous paper arXiv:1011.4173 We have illustrated earlier, that in the classical Hamilton mechanics for an overwhelming majority of real chaotic macroscopic systems there is alignment of their thermodynamic time arrows because of their small interaction. This fact and impossibility to observe entropy decrease at introspection explain the second low of thermodynamics. In a quantum mechanics the situation even is little bit easier - all closed systems of finite volume are periodic or nearly periodic. The proof in a quantum mechanics is in many respects similar to the proof in the classical Hamilton mechanics - it also uses small interaction between subsystems and impossibility to observe entropy decrease at introspection. However there are special cases which were not in the classical mechanics. In these cases a one microstate corresponds to a set of possible macrostates (more precisely their quantum superposition). Consideration this property with using decoherence theory and taking into account of thermodynamic time arrows introduces new outcomes in quantum mechanics. It allows to resolve the basic paradoxes of a quantum mechanics: (a) to explain paradox of wave packet reduction at measurings when the observer is included in system (introspection) (paradox of the Schrodinger cat); (b) to explain unobservability of superposition of macroscopic states by the external observer in real experiments (paradox of Wigner's friend); (c) to prove the full equivalence of multiworld and Copenhagen interpretations of quantum mechanics; (d) to explain deviations from the exponential law at decay of particles and pass from one energy level on another (paradox of a kettle which never will begin to boil).
General Physics; Quantum Physics; Statistical Mechanics
Mechanics of the meristems
Mechanical Integration of Plant Cells and Plants
9
133-172
2011
10.1007/978-3-642-19091-9
In this chapter, the structure, function, and growth of apical meristems and cambium are discussed from a perspective of mechanics. We first characterize the meristems and point to implications of the symplasm, apoplasm, and organismal concepts for our understanding of plant morphogenesis. Then we discuss the symplastic (coordinated) growth and a putative role of principal directions of growth and mechanical stress tensor in the meristem function, also explaining how the principal directions are manifested in cellular pattern and cell behavior. The present knowledge on the mechanics of meristems, in particular on the distri- bution of mechanical stress and on the mechanical properties of the meristems, is to a large extent speculative. Our objectives are to present and discuss the available empirical data and hypotheses on the meristem mechanics, and the evidence on the role of mechanical factors in plant morphogenesis.
Is quantum mechanics exact?
Journal of Mathematical Physics
54
6
062107
2013
10.1063/1.4811217
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Statistical Mechanics of Complex Networks
Review of Modern Physics
74
1
67-97
2002
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the networks robustness against failures and attacks.
networks; statistical mechanics
POST FIRST-PLY FAILURE MODELLING OF GLASS REINFORCED THERMOPLASTIC COMPOSITES
FRC 2000–Composites for the Millennium
505-511
2000
http://dx.doi.org/10.1533/9780857093134.505
ABSTRACT Aligned fibre glass reinforced thermoplastics composites manufactured from commingled glass and polypropylene offer improved mechanical properties and potential for structural parts moulded in high volumes. It is important that the behaviour of such materials under large deformation conditions can be modelled. The modelling of first-ply failure and post failure material behaviour is critical in determining the overall performance of any structural composites component. Typically, the material model is required to include various modes of failure and mode-dependent, non-linear post failure behaviour. The post failure behaviour requirements can range from a slight reduction in modulus to a rapid drop-off in load carrying ability. The paper describes a simple implicit finite element damage model for commingled glass reinforced thermoplastic composite. The model is implemented as a user subroutine within the ABAQUS code, and is based on the well-known Chang and Lessard approach for thermosets. Element stresses are evaluated and the failure criteria are applied to identify the onset of damage at a single element level. Criteria for laminate tensile failure, laminate compressive failure, fibre-matrix shear failure and fibre buckling are included. In subsequent steps (load or displacement increment) of the analysis the element stiffnesses are adjusted to represent damage which has accumulated. The damage model is calibrated with manufacturer's data and experimental coupon data for +45°/- 45° and 0°/90° reinforcement architecture. The model is validated by comparison of experimental and finite element results of a plate with a hole, under in-plane compression. The results are also discussed in terms of implementing the model in the design/analysis of automotive impact structures.
Fracture mechanics and microstructural design
Fracture Mechanics of Ceramics, Vol. 4, Proceedings International Symposium on the Fracture Mechanics of Ceramics Pennsylvania State University, University Park PA, U.S.A. 27-29 July 1977
799-819
1978
Several means are proposed whereby fracture mechanics concepts can govern the design of ceramic microstructures for optimum mechanical integrity. These means take into account the size effects on the formation of microcracks as well as toughening mechanisms based on controlled microstructures. Theory should be implemented whenever manufacturing new ceramic materials free of microcracks.
fracture; snow mechanics
Contact Mechanics
Journal of the American Chemical Society
37
452
1987
10.1115/1.3261297
This treatise is concerned with the stresses and deformation of solid\nbodies in contact with each other, along curved surfaces which touch\ninitially at a point or along a line. Examples are a railway wheel\nand rail, or a pair of gear wheel teeth. Professor Johnson first\nreviews the development of the theory of contact stresses since the\nproblem was originally addressed by H. Hertz in 1882. Next he discusses\nthe influence of friction and the topographical roughness of surfaces,\nand this is incorporated into the theory of contact mechanics. An\nimportant feature is the treatment of bodies which deform plastically\nor viscoelastically. In addition to stationary contact, an appreciable\nsection of the book is concerned with bodies which are in sliding\nor rolling contact, or which collide.
Average absorption coefficient for optically thin media
Journal of Applied Mechanics and Technical Physics
11
1
10-13
1972
10.1007/BF01102667
Modifications are considered of the mean Planck absorption coefficient for a section of an absorbing medium adjacent to a source section, taking into account temperature inequalities of blackbody radiation and the absorption cross section of the medium, as well as the effect of the length of the section, which is small. Equations are presented for an analogous coefficient determining self-absorption of radiation by the gas. © 1972 Consultants Bureau.
Dynamic stabilization of thin plasma filaments
Journal of Applied Mechanics and Technical Physics
11
1
21-27
1972
10.1007/BF01102669
The Routh function is found for a fine plasma filament (toroidal and rectilinear), experiencing smooth long-wave hosepipe and constrictive perturbations in the case in which the external magnetic field is a combination of quadrupole and longitudinal fields. Different variants of dynamic stabilization of a filament are briefly discussed. Combined dynamic stabilization of a straight filament with an alternating current by means of constant quadrupole and longitudinal fields is investigated by averaging with respect to rapid oscillations. © 1972 Consultants Bureau.
Statistical mechanics of complex networks
Rev Mod Phys
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers
Our experience in combining mechanics
American Journal of Orthodontics and Dentofacial Orthopedics
110
6
575-589
1996
http://dx.doi.org/10.1016/S0889-5406(96)80033-3
The use of more than one orthodontic technique in an orthodontic practice can significantly increase treatment capability. Being able to carry out the efficient and effective use of multiple techniques, however, requires that the appliance and the force systems are designed to do both tipping and translation in an optimal manner, either individually or in a variable combination. The application of this philosophy of combining treatment mechanics has been very favorable in our practice. The case reports and mechanics described were selected from our practice to show the diversity and potential that is possible with combination anchorage treatment mechanics. The key to success in a multiattachment straight wire system is to have the ability to use light tipping movements in combination with rigid translation and to be able to vary the location of either, at any time the need arises during treatment.
Mechanics of Laminates
Advanced Mechanics of Composite Materials
243-297,
2013
10.1016/B978-0-08-098231-1.00005-4
A typical composite structure consists of a system of layers bonded together. The layers can be made of different isotropic or anisotropic materials, and have different structures, thicknesses, and mechanical properties. The topic of this chapter is to provide equations allowing us to predict the behavior of a laminate as a system of layers with given properties. The only restriction that is imposed on the laminate as an element of a composite structure concerns its total thickness, which is assumed to be much smaller than the other dimensions of the structure.
antisymmetric laminates; fiber metal laminates; laminate; quasi-homogeneous layers; Sandwich structure; symmetric laminates
Concrete–ice abrasion mechanics
Cement and Concrete Research
73
79-95
2015
10.1016/j.cemconres.2015.01.001
The mechanisms of abrasion of concrete by ice are investigated by review of lab and field studies, wear theory, fracture-, contact- and poromechanics. Experience indicates that ice abrasion does not require freeze/thaw cycles. Three distinct mechanisms may contribute to abrasion damage of concrete: (1) asperities of ice sliding on concrete can create tensile stresses sufficient to initiate cracks (with fatigue from repeated contacts playing an important role); (2) debris released from the surface of the concrete can act as sharp abrasive particles that enhance the damage as the ice drags them along the surface; and (3) water forced into surface defects can create pressure that propagates cracks. Topics for further research and recommendations for minimizing abrasion are suggested.
Concrete (E); Degradation (C); Durability (C); Mechanical Properties (C)
Renormalization in quantum mechanics
Physical Review D
48
12
5940-5945
1993
10.1103/PhysRevD.48.5940
We implement the concept of Wilson renormalization in the context of simple quantum mechanical systems. The attractive inverse square potential leads to a $\b$ function with a nontrivial ultraviolet stable fixed point and the Hulthen potential exhibits the crossover phenomenon. We also discuss the implementation of the Wilson scheme in the broader context of one dimensional potential problems. The possibility of an analogue of Zamolodchikov's $C$ function in these systems is also discussed.
On nonlocal fluid mechanics
International Journal of Engineering Science
10
561-575
1972
10.1016/0020-7225(72)90098-5
A continuum theory of nonlocal fluid dynamics is proposed. The balance laws, jump conditions, and the constitutive equations are obtained generalizing classical stokesian fluids to include the nonlocal effects. Thermodynamical restrictions are used to obtain the specific forms of the constitutive equations and the nonlocal field residuals. The nonlocal effects are shown to include the surface tension and surface stresses. Steady channel flow and shear flow problems are solved. © 1972.
Quantum causality : conceptual issues in the causal theory of quantum mechanics
Studies in history and philosophy of science,
23
xi, 230 p.
2009
There is no sharp dividing line between the foundations of physics and philosophy of physics. This is especially true for quantum mechanics. The debate on the interpretation of quantum mechanics has raged in both the scientific and philosophical communities since the 1920s and continues to this day. (We shall understand the unqualified term ‘quantum mechanics’ to mean the mathematical formalism, i. e. laws and rules by which empirical predictions and theoretical advances are made. ) There is a popular rendering of quantum mechanics which has been publicly endorsed by some well known physicists which says that quantum mechanics is not only 1 more weird than we imagine but is weirder than we can imagine. Although it is readily granted that quantum mechanics has produced some strange and counter-intuitive results, the case will be presented in this book that quantum mechanics is not as weird as we might have been led to believe! The prevailing theory of quantum mechanics is called Orthodox Quantum Theory (also known as the Copenhagen Interpretation). Orthodox Quantum Theory endows a special status on measurement processes by requiring an intervention of an observer or an observer’s proxy (e. g. a measuring apparatus). The placement of the observer (or proxy) is somewhat arbitrary which introduces a degree of subjectivity. Orthodox Quantum Theory only predicts probabilities for measured values of physical quantities. It is essentially an instrumental theory, i. e.
Causality (Physics); Quantum theory.
Measurement of the in-situ transverse tensile strength of composite plies by means of the real time monitoring of microcracking
Composites Part B: Engineering
649-659
2014
10.1016/j.compositesb.2014.02.001
Failure of a ply due to transverse loading is one of the mechanisms that was taken into account in physically-based failure criteria, used in composites design. However, experimental data are scarce and the measurement techniques used in the past are time consuming and involve a lot of specimen handling during testing. While some physical information is currently well consolidated (such as the dependence of the strength on ply thickness, or in-situ strength), there still remain relevant open questions. This work presents a methodology, which does not interfere with the tensile test, to detect transverse cracks by optical means. Four different configurations of CFRP are considered. The results show that the in-situ strength depends on the thickness of the ply and the orientation of the adjacent layers. In the case of thick transverse plies, the strength is controlled by full-width transverse cracks whereas, in thin plies cracking parallel to the specimen’s mid-plane occurs before transverse matrix cracking.
Short-term plyometric training improves running economy in highly trained middle and long distance runners.
Journal of strength and conditioning research / National Strength & Conditioning Association
20
4
947-54
2006
10.1519/R-18235.1
Fifteen highly trained distance runners VO(2)max 71.1 +/- 6.0 ml.min(-1).kg(-1), mean +/- SD) were randomly assigned to a plyometric training (PLY; n = 7) or control (CON; n = 8) group. In addition to their normal training, the PLY group undertook 3 x 30 minutes PLY sessions per week for 9 weeks. Running economy (RE) was assessed during 3 x 4 minute treadmill runs (14, 16, and 18 km.h(-1)), followed by an incremental test to measure VO(2)max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km.h(-1) (4.1%, p = 0.02), but not at 14 or 16 km.h(-1). This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p = 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p = 0.09), and a lower VO(2)-speed slope (14%, p = 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or VO(2)max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics.
Adult; Analysis of Variance; Humans; Lactates; Lactates: blood; Male; Muscle Strength; Muscle Strength: physiology; Oxygen Consumption; Oxygen Consumption: physiology; Physical Education and Training; Physical Education and Training: methods; Physical Endurance; Physical Endurance: physiology; Running; Running: physiology
Short-term plyometric training improves running economy in highly trained middle and long distance runners
Journal of Strength & Conditioning Research
20
4
947-954
2006
Fifteen highly trained distance runners (Vo<sub>2</sub>max 71.1 ± 6.0 ml · min<sup>-1</sup> · kg<sup>-1</sup>, mean ± SD) were randomly assigned to a plyometric training (PLY; n = 7) or control (CON; n = 8) group. In addition to their normal training, the PLY group undertook 3 x 30 minutes PLY sessions per week for 9 weeks. Running economy (RE/was assessed during 3 x 4 minute treadmill runs (14, 16, and 18 km · h<sup>-1</sup>), followed by an incremental test to measure Vo<sub>2</sub>max. Muscle power characteristics were assessed on a portable, unidirectional ground reaction force plate. Compared with CON, PLY improved RE at 18 km · h<sup>-1</sup> (4.1%, p = 0.02), but not at 14 or 16 km · h<sup>-1</sup> This was accompanied by trends for increased average power during a 5-jump plyometric test (15%, p = 0.11), a shorter time to reach maximal dynamic strength during a strength quality assessment test (14%, p = 0.09), and a lower Vo<sub>2</sub>speed slope (14%, p = 0.12) after 9 weeks of PLY. There were no significant differences in cardiorespiratory measures or Vo<sub>2</sub>max as a result of PLY. In a group of highly-trained distance runners, 9 weeks of PLY improved RE, with likely mechanisms residing in the muscle, or alternatively by improving running mechanics. ABSTRACT FROM AUTHOR
*AEROBIC capacity; elite runners; *LONG-distance running; oxygen consumption; *PHYSICAL fitness testing; *PLYOMETRICS; *RUNNERS (Sports); strength training; *WEIGHT training
Thin boron nitride nanotubes with exceptionally high strength and toughness.
Nanoscale
5
11
4840-6
2013
10.1039/c3nr00651d
Bending manipulation and direct force measurements of ultrathin boron nitride nanotubes (BNNTs) were performed inside a transmission electron microscope. Our results demonstrate an obvious transition in mechanics of BNNTs when the external diameters of nanotubes are in the range of 10 nm or less. During in situ transmission electron microscopy bending tests, characteristic "hollow" ripple-like structures formed in the bent ultrathin BNNTs with diameters of sub-10 nm. This peculiar buckling/bending mode makes the ultrathin BNNTs hold very high post-buckling loads which significantly exceed their initial buckling forces. Exceptional compressive/bending strength as high as ∼1210 MPa was observed. Moreover, the analysis of reversible bending force curves of such ultrathin nanotubes indicates that they may store/adsorb strain energy at a density of ~400 × 10(6) J m(-3). Such nanotubes are thus very promising for strengthening and toughening of structural ceramics and may find potential applications as effective energy-absorbing materials like armor.
Identification and design of novel polymer-based mechanical transducers: A nano-structural model for thin film indentation
Journal of Applied Physics
116
10
104307
2014
10.1063/1.4895338
Mechanical characterization is important for understanding small-scale systems and developing devices, particularly at the interface of biology, medicine, and nanotechnology. Yet, monitoring sub-surface forces is challenging with current technologies like atomic force microscopes (AFMs) or optical tweezers due to their probe sizes and sophisticated feedback mechanisms. An alternative transducer design relying on the indentation mechanics of a compressible thin polymer would be an ideal system for more compact and versatile probes, facilitating measurements in situ or in vivo. However, application-specific tuning of a polymer's mechanical properties can be burdensome via experimental optimization. Therefore, efficient transducer design requires a fundamental understanding of how synthetic parameters such as the molecular weight and grafting density influence the bulk material properties that determine the force response. In this work, we apply molecular-level polymer scaling laws to a first order elastic foundation model, relating the conformational state of individual polymer chains to the macroscopic compression of thin film systems. A parameter sweep analysis was conducted to observe predicted model trends under various system conditions and to understand how nano-structural elements influence the material stiffness. We validate the model by comparing predicted force profiles to experimental AFM curves for a real polymer system and show that it has reasonable predictive power for initial estimates of the force response, displaying excellent agreement with experimental force curves. We also present an analysis of the force sensitivity of an example transducer system to demonstrate identification of synthetic protocols based on desired mechanical properties. These results highlight the usefulness of this simple model as an aid for the design of a new class of compact and tunable nanomechanical force transducers.
How a singularity forms in continuum damage mechanics
Mechanics Research Communications
55
86-88
2014
10.1016/j.mechrescom.2013.10.001
In this work we show how a singularity arises in a continuous region within the framework of continuum damage mechanics. We postulate and illustrate mathematically the internal damage processes leading to a singularity. It is not the aim of this work to show where, when, or why the singularity forms - just how it forms. The singularity could be interpreted in various ways - it could be the crack tip of a forming micro-crack, the tip of a forming micro-void, or the tip of other types of micro-defects. It is understood that when the singularity forms the process of fracture initiates. Thus this work could potentially provide a crucial link between the subjects of damage mechanics and fracture mechanics. ?? 2013 Elsevier Ltd.
Damage mechanics; Fracture mechanics; Singularity
A new direction in computational fracture mechanics in materials science: Will the combination of probabilistic and fractal fracture mechanics become mainstream?
Computational Materials Science
69
197-203
2013
10.1016/j.commatsci.2012.11.018
Continuum mechanics-based approximation is too often unsatisfactory for solution of real material problems especially in experimental as well as computational fatigue applications. Various methods of classical-deterministic analyses often produce inconclusive or conflicting estimates of the fatigue life of a component. In addition, the classical Griffith-Irwin-Orowan concept that assumed the phenomena based on homeomorphism mathematics cannot be developed any closer to the experimental results anymore. It has already reached its saturation point. This note discusses the fundamental reasons of the limitations of classical fracture mechanics and subsequently predicts alternatives. Application of classical fracture mechanics to engineering problems is discussed along with possible alternatives employing probabilistic and fractal fracture mechanics in materials engineering. ?? 2012 Elsevier B.V. All rights reserved.
Fractal; Fracture mechanics; Non-Euclidean; Probability
Lunar soil mechanics
British Interplanetary Society
48
1
43-48
1995
Determination of the mechanical and physical properties of the lunar soil as a function and depth beneath the surface assists in the interpretation of experiments such as active and passive seismology, heat flow and core sampling, which have been conducted on the Moon and will be resumed when lunar development is underway in the next century. Such data on the mechanical and physical properties are required for the construction of a lunar base. We anticipate using soil mechanics data to design foundations for telescopes and other structures on the Moon. The predictions of the performance of lunar vehicles rest upon an understanding of lunar soil properties.
CORE SAMPLING; DRILLING; GEOTECHNICAL ENGINEERING; LUNAR BASES; LUNAR GEOLOGY; LUNAR SOIL; PENETROMETERS; REGOLITH; SOIL MECHANICS; STRATIGRAPHY; SUBSTRATES; SURFACE PROPERTIES
Geometrically-exact sandwich shells: The static case
Computer Methods in Applied Mechanics and Engineering
189
167-203
2000
10.1016/S0045-7825(99)00294-7
The present formulation offers a general method for analyzing the static response of geometrically-exact sandwich shells undergoing large deformation. The layer directors at a point in the reference surface are connected to each other by universal joints, and form a chain of rigid links. Finite rotations of the directors in every layer are allowed, with shear deformation independently accounted for in each layer. The thickness and the length of each layer can be arbitrary, thus allowing the modeling of an important class of multilayer structures having ply drop-offs. The present formulation is thus suitable to model shell structures with patches of constrained viscoelastic materials or of piezoelectric materials. The nonlinear weak form of the governing equations of equilibrium is constructed here, and then the linearization of the weak form and the associated inextensible directors update are derived, leading to a symmetric tangent stiffness matrix. A Galerkin finite element projection of the linearized equilibrium equations results in a system of nonlinear algebraic equations, in which the interpolation accounts for the finite rotations of the directors. We present extensive numerical examples, including sandwich shells with three identical layers and ply drop-offs, to illustrate the applicability and versatility of the proposed formulation.
Research on the principles and mechanics of cracking and extracting the kernel of the soft-walnut.
Transactions of the Chinese Society of Agricultural Engineering
11
4
164-169
1995
Walnuts are classified by variety and the importance of cracking soft-walnuts by machine is emphasized. Measurement of the physical characteristics of the soft-walnut showed that the nut could be regarded as a homogeneous thin shell. Based on an analysis of the internal forces according to thin-shell theory, the principles of cracking and extraction of the kernel were proposed and a machine with a double serrated plate and a serrated arc was designed. Experimental testing confirmed the theoretically determined optimum parameters for the cracking unit. The performance of the cracking machine was: cracking rate >90%, high-grade kernel rate 70-90%, and first-grade kernel rate 30-40%.\n
An accurate modeling of thin film flows down an incline for inertia dominated regimes
European Journal of Mechanics - B/Fluids
24
1
49-70
2005
10.1016/j.euromechflu.2004.06.001
An accurate modeling of a wavy film flow down an inclined plane is developed using the weighted residual technique which was first proposed by Ruyer-Quil andManneville [Eur. Phys. J. B 15 (2000) 357]. The model includes third order terms in order to better capture the effects of smallWeber and high Reynolds numbers. This is made possible by an appropriate refinement of the velocity profile. To this end, a free parameter α acting on the flexibility of the velocity profile is introduced. It is shown, from linear stability analysis that the model follows quite closely, for a suitable choice of α, the Orr–Sommerfeld equation for all Weber and Kapitza numbers. The improvement is of course more substantial in the inertia dominated regimes. Some prominent qualitative and quantitative characteristics of traveling wave solutions are then derived from a simplified version of the model that is before hand converted into a three dimensional dynamical system.
chaotic attractors; film flow; inclined plane; stationary waves
An advanced rough surface continuum-based contact and sliding model in the presence of molecularly thin lubricant
Tribology Letters
49
1
227-238
2013
10.1007/s11249-012-0060-3
A model of molecularly thin lubricant layer behavior for rough, sliding contact is presented in this work as a function of lubricant layer morphology. Building on previous work by the authors where the lubricant layer was assumed to be uniform in thickness and morphology, lubricant contributions to contact are presently treated at the asperity level and the effects of lubricant bonding ratio and coverage are accounted for. Effective stiffnesses for lubricated asperities are used to calculate the bearing and shear forces, while variable surface energy is modeled at the asperity level and used within an improved continuum adhesive formulation. Contributions from asperities in lubricant and solid contact for partial coverage are determined within the context of a statistical mechanics model. The proposed model can be used to study the mixed nanolubrication regime expected during light contact or "surfing" recording in magnetic storage, where sustained nanolubricant contact would partially deplete mobile molecules from the contact interface. © Springer Science+Business Media New York 2012.
Adhesion; Boundary lubrication friction; Magnetic data storage; Nanotribology; Roughness effects
Effects of mechanical characteristics on the chemical-mechanical polishing of dielectric thin films
Thin Solid Films
290-291
458-463
1996
10.1016/S0040-6090(96)09020-7
The effects of as-deposited (intrinsic) stress, externally applied (extrinsic) stresses, hardness, and modulus of various dielectric films on chemical-mechanical polishing (CMP) removal and post-CMP cleaning processes are studied in this article. Intrinsic stresses of the polished dielectrics do not contribute directly to the CMP removal rate. Extrinsic stresses including normal and shear components are calculated using principles of elasticity and fluid mechanics respectively and their roles in the material removal process are discussed. Theoretical evaluation and experimental results both suggest that hardness and modulus are the two most important material characteristics affecting the CMP process. Efficiency of post-CMP particle extraction can be monitored using an adhesion probability which is related to the hardness of wafer and pad. In addition, particle removal rate can be remarkably enhanced by increasing pressure (normal stress) while increasing pad rotation speed (shear stress) contributes little to reduce the particle count.
Chemical-mechanical polishing; Dielectrics; Hardness; Stress
Explicit Robin–Neumann schemes for the coupling of incompressible fluids with thin-walled structures
Computer Methods in Applied Mechanics and Engineering
267
566-593
2013
10.1016/j.cma.2013.09.020
We introduce a class of explicit coupling schemes for the numerical solution of fluid–structure interaction problems involving a viscous incompressible fluid and a general thin-walled structure (e.g., including damping and non-linear behavior). The fundamental ingredient in these methods is a (parameter free) explicit Robin interface condition for the fluid, which enables the fluid–solid splitting through appropriate extrapolations of the solid velocity and fluid stress on the interface. The resulting solution procedures are genuinely partitioned. Stability and error estimates are provided for all the variants (depending on the extrapolations), using energy arguments within a representative linear setting. In particular, we show that one of them simultaneously yields added-mass free unconditional stability and optimal (first-order) time accuracy. A comprehensive numerical study, involving different examples from the literature, supports the theory.
Explicit coupling scheme; Fluid–structure interaction; Incompressible fluid; Non-linear shell; Robin–Neumann scheme; Visco-elasticity
Thin-walled curved beams. II: analytical solutions for buckling of arches
Journal of Engineering Mechanics
120
10
2102-2125
1994
In recent years, after Yoo queried the validity of Vlasov's equations regarding the lateral buckling of a circular arch, there has been a number of papers published with a certain degree of disagreement among various researchers. Based on a comprehensive and consistent formulation of curved beam theory presented in the previous paper, closed-form solutions thus obtained are used for comparison of the present theoretical study to others. In the present paper, major potential sources of discrepancies are traced, thereby the rigor and validity of the present formulation is demonstrated. Also, the study on the buckling modes of arches subjected to the condition of uniform bending gives an insight for better understanding of lateral buckling characteristics of arches.
Arches; Bending (deformation); Buckling; Closed form solutions; Convergence of numerical methods; Curved beams and girders; Curved beam theory; Numerical methods; Thin walled curved beams
An Experimental, Numerical and SEM Study of Fracture in a Thin Polymer Film
Key Engineering Materials
592-593
225-228
2013
10.4028/www.scientific.net/KEM.592-593.225
Observations and analysis of samples from scanning electron microscopic (SEM) micrographs has been concerned in this work. The samples originate from fractured mechanical mode I tensile testing of a thin polymer film made of polypropylene used in the packaging industry. Three different shapes of the crack; elliptical, circular and flat, were used to investigate the decrease in load carrying capacity. The fracture surfaces looked similar in all studied cases. Brittle-like material fracture process was observed both by SEM micrographs and the experimental mechanical results. A finite element model was created in Abaqus as a complementary tool to increase the understanding of the mechanical behaviour of the material. The numerical material models were calibrated and the results from the simulations were comparable to the experimental results.
Abaqus; Brittle; Fracture Mechanics; Fracture Surface; Polypropylene (PP); SEM
Development of a concept inventory for fluid mechanics
33rd Annual Frontiers in Education, 2003. FIE 2003.
1
T3D_23-T3D_28
2003
10.1109/FIE.2003.1263340
Concept inventories are assessment tools designed to determine the degree to which students understand the concepts of a subject and to identify the misconceptions that students hold. The results of a concept inventory can be used to change the methods of instruction to overcome student misconceptions. A cooperative effort between mechanical engineering faculty at the Universities of Wisconsin-Madison and Illinois, Champaign-Urbana has been directed toward development of a fluid mechanics concept inventory (FMCI). Fluid mechanics typically follows thermodynamics in the sequence of courses in thermal sciences, involves both the mechanics and dynamics of fluids, and builds on basic physics and Newtonian mechanics. This paper describes the process used for development of the FMCI, the details of how we determined the content, and examples of actual content of the instrument itself.
Applications of Nambu mechanics to systems of hydrodynamical type II
Journal of Nonlinear Mathematical Physics
11
2
223-232
2004
10.1063/1.1481955
In this paper we further investigate some applications of Nambu mechanics in hydrodynamical systems. Using the Euler equations for a rotating rigid body Nevir and Blender [J. Phys. A 26 (1993), L1189-L1193] had demonstrated the connection between Nambu mechanics and noncanonical Hamiltonian mechanics. Nambu mechanics is extended to incompressible ideal hydrodynamical fields using energy and helicity in three dimensional (enstrophy in two dimensional). In this paper we discuss the Lax representation of systems of Nevir-Blender type. We also formulate the three dimensional Euler equations of incompressible fluid in terms of Nambu-Poisson geometry. We discuss their Lax representation. We also briefly discuss the Lax representation of ideal incompressible magnetohydrodynamics equations.
euler equations; fluid; hamiltonian mechanics; lie; poisson structures
Determination of elastic moduli of thin layers of soft material using the atomic force microscope
Biophys J
82
5
2798-2810
2002
S0006-3495(02)75620-8 [pii]\n10.1016/S0006-3495(02)75620-8
We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels.
Atomic Force; Atomic Force: methods; Atomic Force/*methods; Calibration; Elasticity; Electron; Electron: methods; Electron/methods; Gels; *Gels; Microscopy; Microspheres; *Microspheres; Models; Reproducibility of Results; Theoretical
On the Failure Work and Modulus of Composites Reinforced by Thin Elastomer-Coated Fibers
Journal of Composite Materials
26
18
2632-2654
1992
Doi 10.1177/002199839202601801
Fiber reinforced composites have high specific strength, excellent fatigue resistance and variable directional freedom in property control, allowing for optimal structural design. A deficiency in stiff fiber reinforced composites is poor low-speed impact resistance (i.e., low energy absorption before major failure). This has been experimentally shown to be remediable by coating the reinforcing fibers with an elastomeric coating. However, the stiffness of the composites is decreased because of reduced efficiency in interface load transfer in the soft coating. This can be improved by making the coating very thin. For practical design, it is necessary therefore to provide an analytical relation between the increase in failure work and the corresponding decrease in stiffness with the coating properties. Interface stress concentration is parametrically studied in this paper. A formula for calculating the longitudinal modulus of composites reinforced by aligned coated fibers is proposed. The formula is based on a combination of both composite mechanics and finite-element stress analysis. The results provide fundamental guidelines to practical engineering applications of composites of elastomer-coated fibers.
energy absorption; glass fiber composite; graphite fiber composites; impact strength; longitudinal modulus; rubber-coated fibers; rubber coating; stress; stress concentration
Study of polygonal water bells: inertia-dominated thin-film flows over microtextured surfaces
Journal of Fluid Mechanics
721
46-57
2013
10.1017/jfm.2013.60
Microtextured surfaces are commonly used to study complex hydrodynamic phenomena such as spreading and splashing of liquid droplets. However, although surface topography is known to modify near-surface flow, there is no theory able to quantitatively predict the dramatic changes in dynamics of liquid spreading and splashing. Here, we investigate experimentally water bells formed on micropatterned surfaces in order to characterize the hydrodynamics of inertia-dominated flows through regular porous layers. Water bells are self-suspended catenary-shaped liquid films created when a jet impinges on a horizontal disc called an impactor. We show that the presence of micrometre-sized posts regularly arranged on the impactor results in a decrease of the water bell radius and the loss of axisymmetry as open water bells adopt polygonal shapes. We introduce a simple model that captures the main features of the inertia-dominated flow and reveals the role of the hydrodynamic interactions between neighbouring posts. In addition to their applications for tunable jet atomization, these polygonal sheets provide a paradigmatic system for understanding inertia-dominated flow in porous media.
interfacial flows (free surface); porous media; thin films
Observation of Stress Field Around an Oscillating Crack Tip in a Quenched Thin Glass Plate
Experimental Mechanics
48
3
367-374
2008
10.1007/s11340-007-9078-0
The variation of stress field around an oscillating crack tip in a\nquenched thin glass plate is observed using instantaneous phase-stepping\nphotoelasticity. The successive images around the propagating crack\nare recorded by a CCD camera that is equipped with a pixelated micro-retarder\narray. Then, the phase maps of the principal stress difference and\nthe principal direction are easily obtained even though the photoelastic\nfringes cannot be visualized. The path of the crack growth as well\nas the stress intensity factors and the crack tip constraint are\nobtained from these phase distributions. Results show that the mode\nI stress intensity factor and the crack tip constraint vary remarkably\nwith the crack growth. In addition, the results show that the mode-II\nstress intensity factor exists even though the crack propagates smoothly.
Breakdown of continuum fracture mechanics at the nanoscale.
Scientific reports
5
8596
2015
10.1038/srep08596
Materials fail by the nucleation and propagation of a crack, the critical condition of which is quantitatively described by fracture mechanics that uses an intensity of singular stress field characteristically formed near the crack-tip. However, the continuum assumption basing fracture mechanics obscures the prediction of failure of materials at the nanoscale due to discreteness of atoms. Here, we demonstrate the ultimate dimensional limit of fracture mechanics at the nanoscale, where only a small number of atoms are included in a singular field of continuum stress formed near a crack tip. Surprisingly, a singular stress field of only several nanometers still governs fracture as successfully as that at the macroscale, whereas both the stress intensity factor and the energy release rate fail to describe fracture below a critically confined singular field of 2-3 nm, i.e., breakdown of fracture mechanics within the framework of the continuum theory. We further propose an energy-based theory that explicitly accounts for the discrete nature of atoms, and demonstrate that our theory not only successfully describes fracture even below the critical size but also seamlessly connects the atomic to macroscales. It thus provides a more universal fracture criterion, and novel atomistic insights into fracture.
The Relation Between Classical and Quantum Mechanics
American Journal of Physics
32
8
597
1964
10.1119/1.1970870
It is pointed out that, if classical mechanics is to be regarded as a limiting case of quantum mechanics, then it must admit superpositions of states, which are generally regarded as unacceptable. To avoid this it is proposed that classical mechanics be described by a nonlinear equation which is equivalent to the Hamilton-Jacobi equation and is not always the limit of the Schrödinger equation. It is conjectured that the transition from the wave-mechanical equation to the classical equation is characterized by a mass m 0 = ħc/γ 1 2 ≈ 10 −5 g . This nonlinear equation may help one to understand the process of measurement of a quantum-mechanical system by means of a classical measuring instrument.
Computational mechanics applied to interaction problems
International Journal for Numerical Methods in Engineering
60
1
361-379
2004
Doi 10.1002/Nme.966
This paper presents a general discussion on the application of computational mechanics concepts to solve engineering problems involving interaction effects between different media-for example, structure-soil/rock interaction and/or different phases such as solid-fluid interaction. The discussion includes illustrations based on numerical analyses of such problems using coupled finite element and boundary element, coupled finite element and infinite element methods. A few of the other mechanics concepts such as damage mechanics and optimization are also included in the discussion. Copyright (C) 2004 John Wiley Sons, Ltd.
2-dimensional medium; boundary element method; dams; dependent infinite elements; dynamic analysis; dynamic-response; earthquake; finite element method; foundation interaction; infinite element; interaction between two media and two phases; soil-structure interaction; structural control; time-domain; vibration
Quantum Mechanics on Manifolds and Topological Effects
Letters in Mathematical Physics
82
2-3
219-236
2007
10.1007/s11005-007-0188-5
A unique classification of the topological effects associated to quantum mechanics on manifolds is obtained on the basis of the invariance under diffeomorphisms and the realization of the Lie-Rinehart relations between the generators of the diffeomorphism group and the algebra of infinitely differentiable functions on the manifold. This leads to a unique ("Lie-Rinehart") C algebra as observable algebra; its regular representations are shown to be locally Schroedinger and in one to one correspondence with the unitary representations of the fundamental group of the manifold. Therefore, in the absence of spin degrees of freedom and external fields, the first homotopy group of the manifold appears as the only source of topological effects.
high energy physics theory; lie; manifolds; mathematical physics; quantum mechanics; quantum topological effects; rinehart
Mechanics of fluids, Volume 1
Taylor Francis
2006
Presenting material on the mechanics of fluids which is needed for an honours-degree course in civil or mechanical engineering, this text also provides relevant ...
science
The mechanics of wool carpets
The Mechanics of Wool Structures
411-435
1988
This book forms an advanced textbook on the methodology used in the study of fibre assemblies, whether wool or other fibres. - Journal of the Textile Institute, 80(1), 1989, 165
Channel-cracking of thin films with the extended finite element method
Engineering Fracture Mechanics
70
18
2513-2526
2003
Doi 10.1016/S0013-7944(03)00083-3
The recently developed extended finite element method (XFEM) is applied to compute the steady-state energy release rate of channeling cracks in thin films. The method is demonstrated to be able to model arbitrary singularities by using appropriate enriching functions at selected nodes with a relatively coarse mesh. The dimensionless driving force for channeling cracks is obtained as a function of elastic mismatch, crack spacing, and the thickness ratio between the substrate and the film. The results are compared with those from several previous studies when available. Emphasis is placed on the cases with compliant substrates, for which much less information is available from previous studies. It is found that, while it is quite challenging to model the cases with very compliant substrates using regular finite element method because of the strong singularities, the present approach using XFEM is relatively simple and straightforward. (C) 2003 Elsevier Ltd. All rights reserved.
channeling crack; compliant substrate; discontinuities; elastic wedges; fracture; growth; mechanics; thin film; xfem
A General Method to Study Very Thin Cellular Structures
Nonlinear Partial Differential Equations and their Applications. College de France Seminar, Vol. X
1991
The authors consider a method of obtaining effective coefficients for cellular structures. The materials under study are thin cellular materials that are periodic in one or two directions. The thickness of the materials is small compared with the size of the cell, and the material in the cell is concentrated in thin layers along the cell boundaries or in the diagonal direction. The authors use homogenization in open sets with holes to obtain effective coefficients for the periodic structures. In the directions where the width of the material is equal to that of the cell they use dilatations and apply homogenization methods to the dilated domain. Solving the partial differential system defined on the cell to obtain the effective coefficients, the authors consider the material in the cell as a superposition of several layers or bars. They demonstrate the method for the Laplace operator with Neumann conditions on the boundaries of the holes. The mathematics is difficult.
Composite Structures and Materials; Homogenization; Mechanics of Solids; Mechanics of Structures; Partial Differential Equations; Partial Differential Equations in Media with Peri; Qualitative Properties of Solutions
Evolution of transverse cracking in CF/Epoxy cross-ply laminates under creep loading
Journal of Composite Materials
33
928-940
1999
The fastener design for the transfer of concentrated transverse (out of plane, pull-out) loads to random glass fiber reinforced thermoset polymers was investigated. The elastic material properties, void content,a nd glass content of the composite were determined and a finite element model was used to analyze and compare the performance of the various washer designs for reducing the stress and strain levels near the edge of the washer at a bolted joint. Experimental studies were conducted to verify the finite element model.
Uniformly loaded, antisymmetric cross-ply laminated, rectangular plates: An initial flexural failure analysis
Fibre Science and Technology
16
1
1-10
1982
10.1016/0015-0568(82)90010-0
An exact equilibrium solution is combined with the Tsai-Hill failure criterion to produce initial flexural failure loads and associated central deflections for simply supported, antisymmetrically laminated rectangular plates fabricated from CFRP and GFRP and subjected to a uniform lateral pressure. These quantities are presented in dimensionless graphical form for plates comprising up to eight laminae and varying in aspect ratio from 0·5 to 4. A significant feature of the study is that these quantities are very dependent on the direction of the applied loading.
Mechanisms of polymer degradation in implantable devices 2. Ply(DL-lactic acid)
Journal of biomedical materials research
27
1409-1418
1993
The hydrolytic degradation of poly(DL-lactic acid) in an aqueous environment in which hydroxyl radicals have been generated has been investigated. Different methods (gel permeation chromatography, differential scanning calorimetry, and scanning electron microscopy) were employed to study the mechanisms of degradation of this amorphous physiologicaly absorable polymer. The data indicated that the hydroxyl radical is likely to be a significat factor in the degradation of this polymer.
Fracture Mechanics Ch03
Fracture Mechanics
25-75
2012
10.1016/B978-0-12-385001-0.00003-1
Brittle fracture in a solid in the form of crack growth is governed by the stress field around the crack tip and by parameters that describe the resistance of the material to crack growth. Thus, the analysis of stresses near the crack tip constitutes an essential part of fracture mechanics. There are three independent movements corresponding to three fundamental fracture modes. These basic fracture modes are usually called Mode I, Mode II, and Mode III, respectively, and any fracture mode in a cracked body may be described by one of the three basic modes, or their combinations. The three basic modes of crack deformation can be more precisely defined by the associated stresses ahead of the crack front, which are considered as the crack, tip in two-dimensional problems. In addition, method of complex potential for plane elasticity is discussed. Among various mathematical methods in plane elasticity, the complex potential function method by Kolosov and Muskhelishvili are one of the powerful and convenient methods to treat two-dimensional crack problems. In the complex potential method, stresses and displacements are expressed in terms of analytic functions of complex variables. The problem of obtaining stresses and displacements around a crack tip is converted to finding some analytic functions subjected to appropriate boundary conditions.
asymptotic expansion method; crack tip field; fracture toughness; fundamental solution; K-dominance; Kolosov-Muskhelishvili complex potentials; stress intensity factor; superposition method; Westergaard function method
Correlation of vibration and cutting forces in thin-walled machining
Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012
175-180
2012
The lack of stiffness of thin-walled parts results in easy deflection under the cutting forces during the milling process. In this case, it is important to predict the cutting forces of milling thin-walled sections so that the wall sections are maintained at high accuracy. The prediction and analysis of cutting forces could play an essential role to select the cutting conditions, tooling and the system of machining used. Furthermore, the prevention of vibration, chatter, deformation, dimensional error and the maintenance of stable conditions of machining can be obtained by predicting the cutting forces. Many researchers have taken this topic into account and applied the theoretical concepts, simulation and other technical approaches to predict the cutting forces during machining operations so that good machining results can be obtained. In this paper a methodology is developed to correlate the vibrational characteristics of the cutting process with the forces developed by the process. If this correlation exists then it is possible to develop a modelling approach to determine the characteristics of the thin walled sections can be determined. The work that will be described in this paper will present a technique to correlate the data and the use of the data for the development of the modelling approach. The experimental set-up and procedure will be presented and discussed. From this information it will be shown which characteristics can be correlated. Finally the feasibility of the process will be discussed.
Correlation; Cutting forces; Machining; Thin-walled; Vibration
Failure analysis of polymer composite stiffened laminates using the finite element method
Journal of Reinforced Plastics and Composites
18
1
2-14
1999
A finite element method is adopted to study the initiation of damage (ply failure) of polymer composite stiffened laminates under static loading. Lightweight and high strength advanced composite materials are nowadays extensively used in aircraft and automobile industry. These structures on various occasions are subjected to point load or uniformly distributed load. Under these loads the stress level at a point may be high enough to initiate a local failure and a reduction in strength. So, a first-ply failure analysis (initiation of damage) of plated structures are often necessary. The procedure adopted here is based on the first-order shear deformation theory and a tensor polynomial failure criteria. As a special case, Tsai-Wu failure criteria is incorporated in the computer code. A number of problems for which experimental and theoretical results are available, have been analysed in the present investigation to check the code developed, and finally, analysis of stiffened composite plate problems with various laminae orientation, stiffener eccentricity etc. have been put forward for first ply failure load as new results for future reference. The results can be compared to find the best possible ply group against failure under transverse loading. According to author's knowledge, this is perhaps the first attempt to apply first ply-failure analysis in any stiffened configuration
failure analysis; finite element analysis; fracture mechanics; laminates; shear deformation; stress analysis
Une approche integrale de la theorie des profiles minces (An integral method to derive thin-airfoil theory)
C. R. Acad. Sci. Paris, Mecanique des fluides/Fluid Mechanics
t. 322
Serie IIb
809-815
1996
On présente une théorie des profils minces applicable à tout ordre. La démarche proposée consiste à écrire et à résoudre asymptotiquement un système d'équations intégrales singulières et couplées ayant pour inconnues des densités linéiques de sources et de tourbillons à répartir sur la frontière exacte du profil. Aformal thin-airfoil theory is built that can apply to any order. Theproposed method consists in asymptotically solving a system of singular and integral equations where the unknownquantities are distributions of sources and vortices to be spread over the exact boundary of the airfoil.
aerodynamics; thin airfoils
Thin concrete shells reinforced with glass fibers. Manufacturing technology and mechanical properties
Book of Abstracts: Seventeenth International Conference Mechanics of Composite Materials
128
2012
Pneumatic mould use is an approach with a set of advantages among thin wall structural element fabrication technologies. In the reported work, on the flat surface of a non-inflated pneumatic mould was imposed and smoothed down (forming a thin layer) glass fiberconcrete mix. Before concrete binding, mould was inflated by air forming a moderate curvature shell. After that, concrete was hardened, during concrete hardening air pressure in pneumatic mould was kept constant value. Then, an air in the pneumatic mould was blown out and shell was demolded. Two variants were observed: (a) shell is reinforced by uniformly distributed short glass fibers (concretes with three different fiber concentrations were investigated); (b) shell is reinforced by weft knitted glass fiber textiles (were fabricated in the laboratory). Simultaneously flat material samples were fabricated and experimentally tested. Composite materials elastic moduli as well as tensile strength were obtained. With the goal to predict mechanical behavior of produced thin fiberconcrete shells, a detailed micromechanical investigation for single fiber and few fibers bundle pull-out micro-mechanics was performed numerically (using FEM modeling) and experimentally. Macro-crack opening structural model, based on data sets with information about single fiber and few fibers bundle pull-out micro-mechanics, (was elaborated earlier [1]) was exploited predicting shell load bearing facility depending on opening of a crack in the loaded shell. Theoretical results were compared with the data obtained in experiments.
Pneumatic mould
Path integral methods in statistical mechanics
Physics Reports
16
2
57-114
1975
10.1016/0370-1573(75)90030-7
We derive various rigorous representations of the partition function of a many body system as a path integral. Most of the approximation methods for the evaluation of path integrals are discussed. Applications are made to the condensation of classical gases, to the configurational statistics of macromolecules, and to the interacting Bose fluid.
GBT-based structural analysis of elastic–plastic thin-walled members
Computers & Structures
136
1-23
2014
10.1016/j.compstruc.2014.01.001
Structural systems made of high-strength and/or high-ductility metals are usually also rather slender, which means that their structural behaviour and ultimate strength are often governed by a combination of plasticity and instability effects. Currently, the rigorous numerical analysis of such systems can only be achieved by resorting to complex and computationally costly shell finite element simulations. This work aims at supplying to designers/researchers with an efficient and structurally clarifying alternative to assess the geometrically and/or materially non-linear behaviour (up to and beyond the ultimate load) of prismatic thin-walled members, such as those built from cold-formed steel. The proposed approach is based on Generalised Beam Theory (GBT) and is suitable for members exhibiting arbitrary deformation patterns (e.g., global, local, distortional, shear) and made of non-linear isotropic materials (e.g., carbon/stainless steel grades or aluminum alloys). The paper begins by providing an overview of the physically and geometrically non-linear GBT formulation recently developed and validated by the authors, which is followed by the presentation and thorough discussion of several illustrative numerical results concerning the structural responses of 5 members (beams and columns) made of distinct (linear, bi-linear or highly non-linear) materials. The GBT results consist of equilibrium paths, modal participation diagrams and amplitude functions, stress contours, displacement profiles and collapse mechanisms – some of which are compared with Abaqus shell finite element analysis (SFEA) values. An excellent correlation is found in all cases and, moreover, it is shown that GBT analyses including judiciously selected deformation mode sets involve only 25% (on average) of the number of d.o.f. required by similarly accurate SFEA. Moreover, it is clearly evidenced that the GBT modal nature makes it possible to acquire in-depth knowledge on the member behavioural mechanics in the elastic and elastic–plastic regimes.
Arbitrary deformation patterns; Collapse and post-collapse deformed configurations; First and second-order analyses; Generalised Beam Theory (GBT); J2-flow plasticity with strain-hardening; Thin-walled members
Thin Films
J. Natn. Sci. Coun. Sri Lanka
24
4
299-308
1996
Current-potential scam were used to investigate the electrodeposition of cuprous oxide thin films in an acetate bath. YJe found that a narrow potential domain, from 0 V vs SCE to -300 mV vs SCE, is available for the potentiostatic electrodeposition of cuprous oxide thin films and extension of this domain towards more cathodic potentials will result in theco-deposition of copper. These results were further verified by the X-ray diffraction measurements on the thin films formed by the electrodeposition at various electrode potentials. Optical transmission studies revealed that electrodeposited cuprous oxide is a direct band gap semiconductor of 2.0 eV. Key
cuprous oxide; electrodeposition; thin films
End forming of thin-walled tubes using a die
International Journal of Mechatronics and Manufacturing Systems
1
2/3
183
2008
10.1504/IJMMS.2008.020504
The aim of this paper is to evaluate the applicability of tube end-forming processes, currently applied in metals, to polyvinyl chloride (PVC). The presentation is focused on four different processes (expansion, reduction, internal and external inversion) and its contents are expected to provide new fundamental level of knowledge and understanding about the mechanics of deformation and the expected modes of deformation of PVC tubes. The formability limits are defined in terms of the major operating variables with the purpose of predicting the behaviour of PVC tubes across a wide range of working conditions. The experimental findings are interpreted in the light of an innovative extension of the finite clement flow formulation that is capable of modelling cold plastic deformation of pressure-sensitive materials under a non-associated flow rule. Special emphasis is placed on the analysis of load-displacement, local buckling, ductile damage and crazing. The overall results confirm that end-forming of thin-walled PVC tubes at room temperature have potential for the manufacture of custom and specific shapes
2008; a; alves; and martins; b; c; end forming of thin-walled; end forming of tubes; experimentation; f; finite element method; follows; gouveia; int; j; l; m; mechatronics and; p; r; reference to this paper; rodrigues; rosa; should be made as; tubes using a die
Adhesion thin ductile films using stressed overlayers and nanoindentation
Surface Engineering 2002 - Synthesis, Characterization and Applications. Symposium, 2-5 Dec. 2002
750
33-38
2002
Differently stressed films of tungsten on silicon dioxide have been studied to determine the interfacial fracture toughness and the Mode I fracture energy release rate of tungsten on glass. Tungsten films with a low compressive stress (less than 1 GPa) had nanoindentation tests performed on them to induce buckling. Using mechanics based models and the dimensions of the buckles the fracture energy release rate and the phase angle of loading () were calculated to be between 3.8 and 13 J/m2. By varying the residual stress in the film it was possible to examine regions of pure shear (Mode II) interfacial fracture as well as mixed mode interfacial fracture toughness of this system. A similar tungsten film was then used as stressed overlayer on sputtered Pt films on silicon dioxide to determine the fracture energy release rate. Nanoindentation was required to induce buckling, as the overlayer alone did not cause spontaneous buckling. The stressed overlayer method and nanoindentation were used to determine the interfacial toughness of the Pt/silica system to be 1.4 J/m2
adhesion; Adhesion; buckling; Buckling; compressive strength; ductility; Ductility; fracture toughness; Fracture toughness; indentation; internal stresses; materials testing; plasticity; platinum; Residual stresses; Silica; silicon compounds; sputter deposition; thin films; Thin films; tungsten
Postbuckling Behavior of Thin-Walled Open Cross-Section Compression Members
Journal of Structural Mechanics
7
2
143-159
1979
10.1080/03601217908905317
ABSTRACT The postbuckling behavior of simply supported columns with thin-walled open cross section is investigated by means of the general nonlinear theory of elastic stability. Fourth-order terms in the series expansion of the total potential energy are disregarded. It is shown that interaction between linearly independent simultaneous buckling modes is responsible for neutral equilibrium at bifurcation if the column cross section has two axes of symmetry, and unstable if it has only one. If the buckling modes are not simultaneous, the equilibrium is neutral in both cases. Finally, the equilibrium at bifurcation is usually unstable if the cross section has no axis of symmetry.\nABSTRACT The postbuckling behavior of simply supported columns with thin-walled open cross section is investigated by means of the general nonlinear theory of elastic stability. Fourth-order terms in the series expansion of the total potential energy are disregarded. It is shown that interaction between linearly independent simultaneous buckling modes is responsible for neutral equilibrium at bifurcation if the column cross section has two axes of symmetry, and unstable if it has only one. If the buckling modes are not simultaneous, the equilibrium is neutral in both cases. Finally, the equilibrium at bifurcation is usually unstable if the cross section has no axis of symmetry.
Cracks Pattern Formation and Spalling in Functionalized Thin Films
Procedia Materials Science
3
104-109
2014
10.1016/j.mspro.2014.06.020
Functionalized thin films of ceramic material are used in catalytic converters as a catalyst support. A degradation of the catalytic performances can be caused by thermal and chemical effects leading to the formation of cracks and the detachment of fragments. Understanding the formation of the lattice of cracks and the spalling is challenging in fracture mechanics. The need for two conditions for predicting crack nucleation, one involving energy and the other stresses, is shown. The stress condition defines a threshold below which the pattern formation is inhibited. As long as it is not reached, the energy accumulates. Then, at onset, depending on the strength and toughness of the material, the amount of energy can be sufficiently large to give rise to a more or less dense lattice of cracks. Following initiation, the newly created small fragments tend to separate from it by debonding.
ageing; brittle materials; cracks pattern.; Thin films
SMA-thin film composites providing traveling waves
Smart Structures and Materials 2003: Active Materials: Behavior and Mechanics
5053
110-118
2003
Doi 10.1117/12.498571
Actuators providing traveling waves are attractive for several industrial applications, like active skins for turbulent drag reduction or transport devices for assembling processes. Traveling waves require a flexible structure in contrast to standing waves which contain knots without vertical motion. Therefore, different concepts to realize these waves have been developed. This work presents the functional principle of wave generation by means of shape memory alloy (SMA) thin film composites and the conditions that have to be considered for the performance of traveling waves with continuous wave flow. Devices using temperature inhomogeneities, an arrangement of separately addressed SMA composites as well as structures using different SMAs have been investigated and their feasibility is discussed.
composite; drag reduction; shape memory alloy; traveling wave
Quantum mechanics: The reality gap
New Scientist
207
2774
32-36
2010
10.1016/S0262-4079(10)62036-2
How can a theory that describes nature so well have no roots in reality? ?? 2010 Reed Business Information Ltd, England.
Phase Space Quantum Mechanics - Direct
Quantum
16
2006
10.1063/1.2345109
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of non commuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
Towards Adelic Noncommutative Quantum Mechanics
Arxiv preprint hepth0412088
8
2004
A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools embedded in q-deformed and noncommutative quantum mechanics. A rather fundamental approach, called deformation quantization, is noted. A few relations between noncommutativity and nonarchimedean spaces as well as similarities between corresponding quantum theories on them are pointed out. An extended Moyal product in a proposed form of adelic noncommutative quantum mechanics is considered. We suggest some question for future investigations.
high energy physics theory; mathematical physics
p-Mechanics and Field Theory
Representations
12
2004
10.1016/S0034-4877(05)80068-0
The orbit method of Kirillov is used to derive the p-mechanical brackets math-ph/0007030, quant-ph/0212101. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder-Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with Galilean. Keywords: Classic and quantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg group, orbit method, deformation quantisation, representation theory, De Donder-Weyl field theory, Galilean group, Clifford algebra, conformal M"obius transformation, Dirac operator.
classical quantum mechanics; clifford algebra; commutator; conformal m; de donder; deformation quantisation; galilean group; heisenberg group; moyal brackets; obius transformation; orbit method; phrases; poisson brackets; representation theory; weyl field theory
Crack face sliding effect on stiffness of laminates with ply cracks
Composites Science and Technology
66
1444-1454
2006
10.1016/j.compscitech.2005.08.016
The rate of stiffness reduction in damaged laminates with increasing transverse crack density in plies depends on two micromechanical parameters: normalized crack face opening displacement (COD) and crack face sliding displacement (CSD). A FE-based parametric study shows that the only properties that affect the CSD are the thickness ratio and the in-plane shear stiffness ratio of the damaged and neighboring undamaged layers. The dependence is described by a power function with respect to the above mentioned properties. This relationship and the previously obtained power law for COD [Lundmark P, Varna J. Constitutive relationships for damaged laminate in in-plane loading. Int J Dam Mech 2005:14(3):235-59] are used in the damaged laminate constitutive relationships [Lundmark P, Varna J. Constitutive relationships for damaged laminate in in-plane loading. Int J Dam Mech 2005:14(3):235-59], which are closed form exact expressions for general symmetric laminates in in-plane loading. The model is validated analyzing reduction in shear modulus of [Sn,90m]s laminates and comparing with direct FE-calculations. The results are excellent in case of cracks in one layer only. For laminates with two orthogonal systems of cracks, the power law underestimates the CSD. To account for interaction between both systems of cracks, which is of importance for crack face sliding, the power law is modified using the effective shear modulus of the cracked neighboring layer. ?? 2005.
Homogenization; Intralaminar cracks; Laminate stiffness; Sliding displacements
Experimental investigation of the very high cycle fatigue of GFRP [90/0]s cross-ply specimens subjected to high-frequency four-point bending
Composites Science and Technology
101
62-70
2014
10.1016/j.compscitech.2014.06.023
In contrast to low cycle and high cycle fatigue, very high cycle fatigue of fibre-reinforced composites has only been explored in part. Knowledge of degradation behavior, damage mechanisms and phenomenology of damage initiation and growth in the range up to 108 cycles and beyond is rare. A special high-frequency four-point bending test rig has been set up to circumvent common problems such as specimen heating. As tests can be conducted in a frequency range between 50 and 80Hz, load cycle numbers of up to 108 are reached within acceptable testing times. In the presented test series, the very high cycle fatigue behavior of a [90/0]s glass fibre-reinforced laminate is tested at six different load levels. The use of online transmitted light photography and stiffness monitoring provides the correlation of stiffness degradation with transverse cracking and delamination. The effect of load level is examined. Damage growth differs for high- and low load levels. At low loads, degradation is shifted to higher cycle numbers. Delamination onset is delayed by slower crack growth in thickness direction. At the lowest loads, cracks initiate marginally indicating a threshold for transverse cracking in fatigue.
a; matrix composites; polymer
Transformational-Generative Syntax and the Teaching of Sentence Mechanics.
Journal of Basic Writing
6
2
26-36
1987
Argues that, from a transformational-generative perspective, errors in writing mechanics (such as run-on sentences, comma splices, and errors in subject-verb agreement) persist because writing instructors do not exploit students' language ability. Describes how transformational grammar is useful in correcting errors in sentence mechanics. (MM)
Basic Writing; Error Correction (Language); Senten; Elementary Secondary Education; Higher Education;
Speakable in quantum mechanics
Synthese
190
15
3265-3286
2012
10.1007/s11229-012-0158-z
At the 1927 Como conference Bohr spoke the now famous words "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature." However, if the Copenhagen interpretation really holds on to this motto, why then is there this feeling of conflict when comparing it with realist interpretations? Surely what one can say about nature should in a certain sense be interpretation independent. In this paper I take Bohr's motto seriously and develop a quantum logic that avoids assuming any form of realism as much as possible. To illustrate the non-triviality of this motto a similar result is first derived for classical mechanics. It turns out that the logic for classical mechanics is a special case of the derived quantum logic. Finally, some hints are provided in how these logics are to be used in practical situations and I discuss how some realist interpretations relate to these logics.
Mechanics of materials.
Studies in health technology and informatics
152
13-26
2010
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
Tribological characterization of thin hard coatings by reciprocating sliding tests
Tribology Letters
1
4
265-276
1995
10.1007/BF00174254
Thin hard coatings on metal or ceramic surfaces offer a large spectrum of improvements of the friction and/or wear behaviour of tribosystems. The development of coatings and the tailoring of their properties require test methods providing information about their friction and wear behaviour. A new wear test standard (ASTM) is under development for the evaluation of friction and wear quantities for sliding motions using the reciprocating sliding mode. The applicability of this test method to coated specimens was checked by testing uncoated and coated steel specimens in contact with alumina balls, whereby lower loads were used than in the ASTM proposal for bulk materials. Additionally, the influence of the relative humidity of the surrounding air at room temperature on friction and wear results was examined.
Analysis of the spontaneous interfacial decohesion of a thin surface film
Journal of the Mechanics and Physics of Solids
40
1
75-103
1992
10.1016/0022-5096(92)90254-Y
Results of a numerical and experimental study of thin film delamination are reported. Spontaneous delamination is induced by a cut in a thin film attached to a substrate. The delamination is driven by the residual stress caused by thermal strain mismatch between the film and substrate. From the measured shape of the delamination, interfacial fracture criteria are examined. Parametric studies of fracture criteria are carried out numerically using a boundary integral equation (BIE) formulation. The analysis includes a new numerical scheme, based on the M-integral, for evaluating the stress intensity factor at the ends of the cut. Experiments are conducted with a polyimide film on a glass substrate. The level of residual stress is controlled by thermal strain mismatch between the film and substrate, varying the test temperature in the range of 20-255[degree sign]C. Both numerical and experimental studies cover delamination of large extent. The experiment shows that the polyimide--glass interface is much tougher in the anti-plane shearing mode (mode 3). The measured interface toughness is 4.1-4.5 J/m2 for plane strain crack growth caused by tensile residual stress of the film. On the other hand, the measured mode 3 fracture toughness of the interface is 14.9-16.5 J/m2.
An experimental and computational study of the elastic-plastic transition in thin films
Dislocations and Deformation Mechanics in Thin Films and Small Structures
673
Generic
2001
Nanoindentation studies of thin metal films have provided insight into the mechanisms of plasticity in small volumes, showing a strong dependence on the film thickness and grain size. It has been previously shown that an increased dislocation density can be manifested as an increase in the hardness or flow resistance of a material, as described by the Taylor relation [1]. However, when the indentation is confined to very small displacements, the observation can be quite the opposite; an elevated dislocation density can provide an easy mechanism for plasticity at relatively small loads, as contrasted with observations of near-theoretical shear stresses required to initiate dislocation activity in low-dislocation density materials. Experimental observations of the evolution of hardness with displacement show initially soft behavior in small-grained films and initially hard behavior in large-grained films. Furthermore, the small-grained films show immediate hardening, while the large grained films show the 'softening' indentation size effect (ISE) associated with strain gradient plasticity. Rationale for such behavior has been based on the availability of dislocation sources at the grain boundary for initiating plasticity. Embedded atom method (EAM) simulations of the initial stages of indentation substantiate this theory; the indentation response varies as expected when the promixity of the indenter to a Σ79 grain boundary is varied.
Computer simulation; Crack initiation; Dislocation density; Dislocations (crystals); Elasticity; Elastic-plastic transition; Embedded atom method; Flow resistance; Grain size and shape; Hardness; Mechanical variables measurement; Phase transitions; Plasticity; Shear stress; Softening indentation size effect; Thickness measurement; Thin films
A continuum damage model for composite laminates: Part I – Constitutive model
Mechanics of Materials
39
10
897-908
2007
10.1016/j.mechmat.2007.03.005
A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level.
composite materials; continuum damage mechanics; fracture mechanics
A continuum damage model for composite laminates: Part I – Constitutive model
Mechanics of Materials
39
10
897-908
2007
10.1016/j.mechmat.2007.03.005
A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level.
composite materials; continuum damage mechanics; fracture mechanics
Extension of Murray's law including nonlinear mechanics of a composite artery wall.
Biomechanics and modeling in mechanobiology
14
1
83-91
2015
10.1007/s10237-014-0590-8
A goal function approach is used to derive an extension of Murray's law that includes effects of nonlinear mechanics of the artery wall. The artery is modeled as a thin-walled tube composed of different species of nonlinear elastic materials that deform together. These materials grow and remodel in a process that is governed by a target state defined by a homeostatic radius and a homeostatic material composition. Following Murray's original idea, this target state is defined by a principle of minimum work. We take this work to include that of pumping and maintaining blood, as well as maintaining the materials of the artery wall. The minimization is performed under a constraint imposed by mechanical equilibrium. We derive a condition for the existence of a cost-optimal homeostatic state. We also conduct parametric studies using this novel theoretical frame to investigate how the cost-optimal radius and composition of the artery wall depend on flow rate, blood pressure, and elastin content.
artery; constrained; goal function; mixture theory; murray; s law
A SURVEY OF LAGRANGIAN MECHANICS AND CONTROL ON LIE ALGEBROIDS AND GROUPOIDS
International Journal of Geometric Methods in Modern Physics
03
03
509-558
2006
10.1142/S0219887806001211
In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach. © World Scientific Publishing Company.
Classical Field Theory; Discrete Mechanics; Hamiltonian Mechanics; Lagrangian Mechanics; Lie algebroids; Lie groupoids; Mechanical control systems; Nonholonomic Lagrangian systems
Three-dimensional analysis of reinforced concrete frames based on lumped damage mechanics
International Journal of Solids and Structures
40
19
5109-5123
2003
10.1016/S0020-7683(03)00258-0
This paper presents a general formulation for the analysis of reinforced concrete frames. The model has been developed within the framework of lumped damage mechanics. This is a theory based on the methods of continuum damage mechanics, fracture mechanics and the concept of plastic hinge. The paper also describes the numerical implementation of the model in the finite element programs. The model is evaluated by the numerical simulation of three tests reported in the literature. Two of them deal with a column subjected to variable axial loads and biaxial flexure. The third is a two-story three-dimensional frame subjected to earthquake loadings outside the principal directions of the frame. © 2003 Elsevier Ltd. All rights reserved.
Biaxial bending; Damage mechanics; Fracture mechanics; Reinforced concrete; Structural analysis
Comment on "Arrival time in quantum mechanics" and "Time of arrival in quantum mechanics"
Physical Review A
59
1
897
1999
10.1103/PhysRevA.59.897
Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the “time operator,” which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.
Arterial hemodynamics and wall mechanics
Seminars in Vascular Surgery
11
3
169-180
1998
Arterial hemodynamics and wall mechanics are important considerations for the vascular clinician for a number of reasons. Hemodynamics and wall mechanics both have been shown to be affecters of disease formation. It is important for the practicing vascular surgeon to know how disease affects both blood flow and wall mechanics and to understand the consequence of hemodynamics on arterial reconstructions. In this article, we summarize the basic concepts of arterial hemodynamics and wall mechanics as they relate to the development of arterial pathology. A few practical mathematical relationships and examples are provided for both illustration and utilization. We also discuss the use of computer models for the estimation of wall stresses in individual abdominal aortic aneurysms.
A MULTISCALE ANALYSIS OF THE MECHANICAL BEHAVIOR OF A THERMO-OXIDIZED C/EPOXY LAMINA
MECHANICS OF COMPOSITE MATERIALS
46
1
101-112
2010
10.1007/s11029-010-9130-5
The mechanical behavior of carbon-fiber-reinforced polymer matrix composites having undergone a thermo-oxidation process is studied. The purpose is to perform a multiscale analysis of the consequences of oxidation on the intrinsic mechanical properties of the external composite ply and on the internal mechanical states experienced by the structure under mechanical loads. The effective mechanical properties of oxidized composite plies are determined according to the Eshelby-Kroner self-consistent homogenization procedure, depending on evolution of the oxidation process. The results obtained are compared with estimates found by the finite-element method. The macroscopic mechanical states are calculated for a unidirectional composite and laminates. The macroscopic stresses in each ply of the structure are determined by the classical lamination theory and the finite-element method, whereas the local stresses in the carbon fiber and epoxy matrix are calculated by using an analytical stress concentration relation.
carbon-fiber-reinforced polymer matrix composites; external composite ply and; having undergone a; local stresses; mechanical properties of the; of the consequences of; on the internal mechanical; oxidation on the intrinsic; perform a multiscale analysis; polymer matrix composites; scale transition models; the mechanical behavior of; the purpose is to; thermo-oxidation; thermo-oxidation process is studied
Statistical analysis of oblique crack evolution in composite laminates
Composites Part B: Engineering
65
34-39
2014
10.1016/j.compositesb.2014.01.038
A previously developed statistical model for transverse cracking in cross ply laminates is extended to oblique cracking in multidirectional laminates. The oblique cracks are assumed to form in a ply when the local in-plane tensile stress normal to fibers exceeds the transverse strength of the ply. This strength is assumed to have a statistical distribution given by a two-parameter Weibull function. The model is applied to a glass-epoxy [0/602/0/-602]s laminate in which cracking evolution of the four -60?? plies in the middle of the laminate is examined. The local stress field in the cracked -60?? plies is calculated by a three-dimensional finite element method based on a unit cell construction developed by Li et al. [1]. The measured crack density is found to agree well with that calculated by the statistical model. ?? 2014 Elsevier Ltd.
A. Polymer-matrix composites; B. Defects; C. Damage mechanics; C. Statistical properties/methods
MODELING AND ANALYSIS OF BIAS-PLY MOTORCYCLE TIRES. BT - Nonlinear Finite Elem Anal and ADINA, Proc of the ADINA Conf, 4th, June 15, 1983 - June 17, 1983
Computers and Structures
17
5-6
653-658
1983
10.1016/0045-7949(83)90078-0
Physical properties of motorcycle tire structures are considered to help select a good and true-to-life mechanistic model suitable for finite element analysis of tires. Rubber and bias-ply layered-cord together make the inflated unhomogeneous tire structure anisotropic and geometrically highly nonlinear. A mathematical model made of three-dimensional solid and truss elements is discussed, and presented as realistic and adequate to accommodate the anisotropy and nonlinearity inherent in the tire problem. Various loading cases, including a cambered tire with inflation pressure and vertical load on contact patch, are studied and evaluated of force and moment acting on the tire.
MATHEMATICAL TECHNIQUES - Finite Element Method; mechanical engineering computing; MOTOR CYCLES; TIRES
Statistical mechanics of complex networks
Arxiv preprint cond-mat
2001
Page 1. arXiv:cond-mat/0106096 v1 6 Jun 2001 of Reka Albert 1,2 and Albert-Laszlo Barabasi 2
Buckling of orthotropic plates with free and rotationally restrained unloaded edges
Thin-Walled Structures
24
1
83-96
1996
10.1016/0263-8231(95)00036-4
Solutions and parametric studies are presented for the buckling of rectangular plates whose axes of material orthotropy coincide with the axes of the plate. The results presented apply to homogeneous orthotropic plates, stiffened orthotropic plates, and laminated composite material plates having flexural orthotropy (i.e. single ply and multiply unidirectional, and symmetric cross-ply composite plates). The plates considered are subjected to uniform uniaxial compression and simply supported on the loaded edges. The boundary conditions are different on the two unloaded edges; one edge being free and the other edge being elastically restrained against rotation. Parametric studies showing the effect of the orthotropic properties of the plate materials, the plate aspect ratio, the rotational restraint of the one unloaded edge and the buckle half-wavelength are discussed. Results in the form of nondimensional buckling curves are given in terms of orthotropy ratios and in terms of properties of common unidirectionally reinforced composite material. The use of the solution in conjunction with experimental data to predict the edge rotational restraint coefficient for thin-walled composite material beams is described.
ANALYSIS OF ORTHOGONALLY CRACKED LAMINATES UNDER TENSION.
Journal of Applied Mechanics, Transactions ASME
54
4
872-879
1987
10.1115/1.3173131
The problems of stiffness reduction and stress analysis of cross-ply fiber composite laminates, where all plies are cracked in fiber directions, are treated by a variational method on the basis of the principle of minimum complementary energy. The Young's modulus obtained is a strict lower bound but is expected to be close to the true value on the basis of experience with a previous analysis. Approximate values of Poisson's ratio and internal stresses have been obtained. The latter reveal important tendencies of continued failure by delamination.
Analysis of wrinkled membrane structures by thin-shell elements
Gongcheng Lixue/Engineering Mechanics
27
8
2010
The membrane structure is a new type of space structure, whose load-bearing members are compose of flexible membranes. When a thin-film membrane structure is subjected to external loading, wrinkles usually appear on local areas, which significantly affect the performance and reliability of membrane structures. So the study on wrinkled membrane structures is desirable and essential. The thin shell elements was adopted to simulate the wavelength, amplitude and direction of wrinkled rectangle tensioned membrane structures based on buckling theory under in-plane loading. A comparison with the corresponding experimental data proved that the method were correct and effective. The form-state model of an air-inflated membrane structure was given according to the quasi-static assumption. The simulation of cushion under the combined action of in-plane loading and normal loading was carried out to illustrate the wrinkles distribution and stress state. The results showed that the thin-shell elements can be adopted to simulate the deformation, wrinkle areas and stress distribution of tensioned membrane structures and air-inflated membrane structures under external loadings.
Air-inflated membrane structure; Explicit finite element; Tensioned membrane structure; Thin-shell element; Wrinkles
The onset of yield in the cold rolling of thin strip
Journal of the Mechanics and Physics of Solids
17
4
253-264
1969
stresses in a thin strip as it passes between rolls have been studied with a view to predicting the onset of plastic reduction. It has been shown that the load to initiate plastic reduction of hard materials increases very rapidly for thin gauges but, how ever thin the strip, some reduction is shown to be theoretically possible. The stresses in the strip which control the onset of plastic flow are critically dependent upon the frictional conditions at the interface between the rolls and the strip. It is shown that friction at the interface between the rolls and a thin strip leads to an appreciable region in the centre of the arc of contact where the strip does not slip relative to the rolls. Under these conditions plastic reduction occurs at entry and at exit to the roll bite but does not occur in the central region of no relative motion.
Generalized Bundle Quantum Mechanics
Quantum
July
19
2003
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes the base space of the fibre bundle in question in a more natural way. It starts off with a review of the mathematical tools needed and then moves on to build the objects necessary.
Mechanics of the lung in the 20th century.
Comprehensive Physiology
1
4
2009-27
2011
10.1002/cphy.c100067
Major advances in respiratory mechanics occurred primarily in the latter half of the 20th century, and this is when much of our current understanding was secured. The earliest and ancient investigations involving respiratory physiology and mechanics were frequently done in conjunction with other scientific activities and often lacked the ability to make quantitative measurements. This situation changed rapidly in the 20th century, and this relatively recent history of lung mechanics has been greatly influenced by critical technological advances and applications, which have made quantitative experimental testing of ideas possible. From the spirometer of Hutchinson, to the pneumotachograph of Fleisch, to the measurement of esophageal pressure, to the use of the Wilhelmy balance by Clements, and to the unassuming strain gauges for measuring pressure and rapid paper and electronic chart recorders, these enabling devices have generated numerous quantitative experimental studies with greatly increased physiologic understanding and validation of mechanistic theories of lung function in health and disease.
Animals; History, 20th Century; Humans; Lung; Lung: physiology; Physiology; Physiology: history; Respiratory Function Tests; Respiratory Function Tests: history; Respiratory Mechanics; Respiratory Mechanics: physiology
Computational Mechanics ©
Computational Mechanics
4
401-408
1989
In the development of a viscoplasticity theory without a yield surface and without a loading and unloading condition, the properties of a uniaxial constitutive model consisting of two coupled nonlinear differential equations are examined. The critical points of the system of differential equations are evaluated for monotonic loading, creep and relaxation conditions and are shown to be stable. The conditions necessary for the elimination of stable but oscillatory solutions are given. Also given are the asymptotic solutions valid near the critical points. The analytical predictions are confirmed by numerical results.
A comparison of the models of a thin and a complete viscous shock layer in the problem of the supersonic flow of a viscous gas past blunt cones
Journal of Applied Mathematics and Mechanics
53
6
762-767
1989
The flow of a viscous heat conducting supersonic gas past spherically blunted cones is used to compare the solutions of the equations of a thin (hypersonic) viscous shock layer (TVSL) with a given form of the shock wave (SW), with the solutions of the complete equations of a viscous shock layer (CVSL) in which the assumption that the shock layer is thin is not made and, which is important, the form of the SW is determined in the course of solving the problem. It is shown that a "successful" description of the form of the SW in solving the problem of hypersonic flow past a blunt cone within the framework of the equations of a TVSL provides, firstly, the possibility of obtaining the solution at considerable distances downstream and secondly, of sharpening the solution considerably, assuming that it can be obtained at all within the framework of the equations of the TVSL, compared with the commonly used asymptotic approach in which the form of the SW is assumed, in solving these equations, to be an equidistant form of the body.
How thin is a thin bed?
Geophysics
38
6
1176
1973
10.1190/1.1440403
Based on reflective properties, a thin bed may be conveniently defined as one whose thickness is less than about X*/8, where At, is the (predomi- nant) wavelength computed using the velocity of the bed. The amplitude of a reflection from a thin bed is to the first order of approximation equal to 4nAb,h,, where b is the thickness of the bed and A is the amplitude of the reflection if the bed were to be very thick. The equation shows that a bed as thin as 10 ft has, for typical frequency and velocity, considerably more reflective power than is usually attributed to it.
Statistical mechanics of anharmonic lattices
Contemporary Mathematics
327
1-16
2003
This paper is a review on the statistical mechanics of anharmonic oscillators coupled to heat reservoirs. We discuss stationary states (existence and ergodic properties) and entropy production (positivity, Green-Kubo formulas and the Gallavotti-Cohen fluctuation theorem).This review will appear in the Proceedings of the 2002 UAB International Conference on Differential Equations and Mathematical Physics.
A continuum damage model for composite laminates: Part I - Constitutive model
Mechanics of Materials
39
10
897-908
2007
10.1016/j.mechmat.2007.03.005
A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level. © 2007 Elsevier Ltd. All rights reserved.
Composite materials; Continuum damage mechanics; Fracture mechanics
A continuum damage model for composite laminates: Part I – Constitutive model
Mechanics of Materials
39
897-908
2007
http://dx.doi.org/10.1016/j.mechmat.2007.03.005
A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level.
Composite materials; Continuum damage mechanics; Fracture mechanics
CTOA of a stable crack in a thin aluminum fracture specimen
Engineering Fracture Mechanics
70
3-4
427-442
2003
10.1016/S0013-7944(02)00129-7
A crack tip opening angle (CTOA) resistance curve was generated from the moir?? interferometry data of thin single edge notched (SEN) and central notched (CN), 2024-T3 aluminum fracture specimens. This CTOA resistance curve, which has a steady state value of 6??, was then used to propagate the cracks in elasti-plastic finite element models of the CN specimen and a CN specimen with a simulated multiple site damage. The CTOA of curved crack growth in a biaxial fracture specimen scattered between 4?? and 8?? but the resultant crack tip opening displacement, which is the vector sum of the mode-I and the mode-II crack tip sliding displacement, remained a constant 0.18 mm. The CTOA of a rapidly propagating crack in 1.6 mm thick, 7075-T6 SEN specimens in reased from 4.5?? at a low-crack velocity to a constant 7?? at the terminal crack velocity. ?? 2002 Elsevier Science Ltd. All rights reserved.
COD; CTOA; Dynamic crack growth; Finite element analysis; Moir?? interferometry; Stable crack growth
Continuum damage mechanics modeling for fatigue life of elastomeric materials
International Journal of Structural Integrity
1
1
63-72
2010
10.1108/17579861011023801
Continuum damage mechanics modeling for fatigue life of elastomeric materials
elastomers; fatigue; modelling; paper type research paper; rubbers
Quantum dressed classical mechanics: application to non-adiabatic processes
Chemical physics letters
343
July
130-138
2001
10.1021/jp013206a
A newly formulated theory for time-dependent molecular quantum mechanics is used to study processes involving more than one potential energy surface. Good agreement with exact numbers is obtained using one trajectory and just two grid points.
Predicting fracture of layered composites caused by internal instability
Composites - Part A: Applied Science and Manufacturing
32
9
1243-1253
2001
10.1016/S1359-835X(01)00077-X
The present paper estimates the critical strain at which ply instability occurs in compressible layered composites under uniaxial or biaxial compression. This is achieved by using two methods: the continuum approach and the model of piecewise-homogeneous medium in conjunction with the three-dimensional stability theory. The accuracy of the continuum theory is examined by taking into account the influence of layer thickness, stiffness properties and biaxiality of loads. Also, upper and lower bounds for the critical buckling strain of laminates with interfacial defects (cracks with connected edges) are determined using the results for perfectly bonded and sliding layers. ?? 2001 Elsevier Science Ltd. All rights reserved.
A. layered structures; B. buckling; B. fracture; C. analytical modelling; C. micro-mechanics
A Bridge between quantum computation and statistical mechanics
Arxiv
1-63
2012
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Second, we show another interesting technique to employ quantum nature, quantum annealing. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.
Nonlinear Control and Analytical Mechanics: A Computational Approach
Applied Mechanics Reviews
54
4
B63
2001
10.1115/1.1383676
Nonlinear control and analytical mechanics come together in areas such as space systems design, robotics, vehicle design, and biomechanics. This easily accessible book gives an integrated treatment of non-linear control and analytical mechanics, highlighting the computational infrastructure common to both areas. The authors introduce computer algebra tools that facilitate model building, systems design and code generation, and present many illustrative examples.
On the Fluid Mechanics of Fires 1
Annual review of fluid mechanics
33
1
67–92
2001
Fluid mechanics research related to fire is reviewed with a focus on canonical flows, multiphysics coupling aspects, and experimental and numerical tech- niques. Fire is a low-speed, chemically reacting flow in which buoyancy plays an important role. Fire research has focused on two canonical flows, the reacting bound- ary layer and the reacting free plume. There is rich, multilateral, bidirectional coupling among fluid mechanics and scalar transport, combustion, and radiation. There is only a limited experimental fluid mechanics database for fire owing to measurement diffi- culties in the harsh environment and to the focus within the fire community on ther- mal/chemical consequences. Increasingly, computational fluid dynamics techniques are being used to provide engineering guidance on thermal/chemical consequences and to study fire phenomenology.
and experimental and numerical; boundary layers; buoyancy; canonical flows; focus on; is reviewed with a; multiphysics coupling aspects; nonpremixed combustion; plumes; research related to fire; s abstract fluid mechanics; tech-; turbulence
Total solution for structural mechanics problems
Computer Methods in Applied Mechanics and Engineering
191
989-1012
2001
10.1016/S0045-7825(01)00314-0
A concept of total solution for structural mechanics problems is proposed in this paper, it aims to establish a systematic approach to provide a comprehensive solution for practical structural mechanics problems, especially for traditional forward problems with incomplete input information (load, material property, boundary condition) and inverse problems with insufficient observations of effects (displacement, acceleration, stress, etc.). The approach for a total solution is to formulate such a structural mechanics problem as a parameter identification problem based on the forward solver of problem. All the unknown parameterized information in this forward model is determined through an iterative procedure of conducting alternately forward and inverse (or mixed) analyses. Algorithms of implementing inverse and mixed analyses are developed, which include a sensitivity matrix-based method and a modified adaptive neural networks method. Numerical investigations have been made to demonstrate the feasibility and validity of the proposed approach as well as the implementation algorithms. ?? 2001 Elsevier Science B.V. All rights reserved.
Inverse problems; Mathematical models; Neural networks; Sensitivity matrix; Structural mechanics
An Experimental Study of the Microformability of Very Thin Materials
Experimental Mechanics
53
2
155-162
2013
10.1007/s11340-012-9623-3
This article extends the concept of forming limit curves to very\nthin (0.1 mm) metallic materials. The forming limit curves for these\nmaterials are referred in this paper as microforming limit curves.\nTo study the microformability of such materials, a microdrawing press\nbased on the Marciniak principle, coupled with an image acquisition\nsystem, was designed and built in the laboratory. Images of the sample\nsurface were obtained during the microdrawing process and processed\nusing a deformation measurement system based on image correlation.\nThe microformability of aluminium 1050A (99.5%) and aluminiumalloy\n(Al-3%Mg) were characterised in tests at three different geometries\nand then analysed. Besides, a new technique for estimating the strain\nat the onset of necking was developed and tested against a proven\nmethod. This technique is more easily automated because it does not\nrely on subjective criteria. Thus, it is possible to have the microforming\nlimit curve for very thin sheet by a rapid and objective experimental\nmethod.
Forming limit curves of microdrawing; Microdrawing
Blast loaded thin composite plates - An experimental study
Proceedings of the 2006 SEM Annual Conference and Exposition on Experimental and Applied Mechanics 2006
4
1801-1807
2006
In recent times, E-Glass and Carbon fiber based composites have found extensive use in naval structures and there are various studies in literature, which intend to characterize these materials under different quasi-static and ballistic loadings. But, often these materials are subjected to blast loadings occurring from warheads and torpedoes during service or regular war exercises. In this study, thin plates of composite materials were subjected to dynamic loading under shock blast and explosive blast conditions. The plates were held in special fixtures, which ensured fixed-free boundary conditions. The plates were held in the top and bottom and were free along the sides. The deflections incurred in these plates were recorded real time using a high-speed camera and were analyzed for velocity and acceleration of the plate during the deflection. The damage initiation and progression in the plates were observed real time. Typical velocity of Carbon Fiber based composite was 80 m/s and deflection was 16 mm when subjected to explosive blast loads. These data were utilized for comparing the relative performance of the two different composite materials while subjected to identical load intensity and form.
Antibiotics: start-ups ply novel targets and technologies
Start-Up
2003
Microbial drug resistance is a real and growing problem, but drugmakers face disincentives: a plethora of products already on the market, the difficulty of differentiating drugs, and the habit of reserving truly new drugs for emergencies. Big Pharmas are backing out, creating opportunities for small companies who feel they can play successfully. But lack of interest from large partners means biotechs can't access the assets those firms hold, so many start-ups are pairing up with peers. Some firms are building businesses around an abundance of targets derived through genomics. But others are deliberately avoiding working with novel genetic code and instead studying whole cells and physiological changes in organisms. Many firms are addressing the lack of chemical diversity against targets. Some of these are pursuing diversity through natural products like marine microbes, insisting they'll fare better than earlier firms did, in part because of technological advances. Others are trying to create diversity synthetically, by taking structural approaches to understanding targets new and old, as well as compounds. Crystallography, in silico libraries, computational models and mass spectroscopy are key tools in iterative development processes that remain unproven in the anti-infectives field. Some firms are seeking to minimize the risks of novelty, by putting their efforts into developing new versions of antibiotics that worked well before resistance grew. No matter what technological approach start-ups take to developing antibiotics, all face similar challenges external to themselves-primarily in regulatory affairs and funding, but also in hunting Big Pharma partnerships.
Fracture Mechanics
Fracture Mechanics
378
2002
10.1007/978-3-642-19240-1
While teaching a course on fracture mechanics at Delft University of Technology we discovered that although there are a few excellent textbooks, their subject matter covers developments only up to the early 1970s. Consequently there was no systematic treat- ment of the concepts of elastic-plastic fracture mechanics. Also the description of frac- ture mechanics characterisation of crack growth needed updating, especially for sus- tained load fracture and unstable dynamic crack growth. In the present textbook we have attempted to cover the basic concepts of fracture mechanics for both the linear elastic and elastic-plastic regimes, and three chapters are devoted to the fracture mechanics characterisation of crack growth (fatigue crack growth, sustained load fracture and dynamic crack growth). There are also two chapters concerning mechanisms of fracture and the ways in which actual material behaviour influences the fracture mechanics characterisation of crack growth. The reader will find that this last topic is treated to some way beyond that of a basic course. This is because to our knowledge there is no reference work that sys- tematically covers it. A consequence for instructors is that they must be selective here. However, any inconvenience thereby entailed is, we feel, outweighed by the importance of the subject matter. This textbook is intended primarily for engineering students. We hope it will be use- ful to practising engineers as well, since it provides the background to several new de- sign methods, criteria for material selection and guidelines for acceptance of weld de- fects. Many people helped us during preparation of the manuscript. We wish to thank par- ticularly J. Zuidema, who made vital contributions to uniform treatment of the energy balance approach for both the linear elastic and elastic-plastic regimes; R.A.H. Ed- wards, who assisted with the chapter on sustained load fracture; A.C.F. Hagedorn, who drew the figures for the first seven chapters; and the team of the VSSD, our publisher, whose patience was sorely tried but who remained unbelievably co-operative. Finally, we wish to thank the National Aerospace Laboratory NLR and the Boiler and Pressure Vessel Authority ‘Dienst voor het Stoomwezen’ for providing us the op- portunity to finish this book, which was begun at the Delft University of Technology.
Molecular mechanics of single molecules
Structure
14
3
390-391
2006
10.1016/j.str.2006.02.003
The mechanics of single molecules of bacteriorhodopsin interacting with purple membrane have been investigated from both sides of the membrane by Kessler and Gaub (2006) in this issue of Structure. Remarkably, barriers can be associated with specific amino acid sequences to an accuracy of ??3 amino acids. ??2006 Elsevier Ltd. All rights reserved.
Wave Mechanics and the Fifth Dimension
arXiv.org
gr-qc
2013
Replacing 4D Minkowski space by 5D canonical space leads to a clearer derivation of the main features of wave mechanics, including the wave function and the velocity of de Broglie waves. Recent tests of wave-particle duality could be adapted to investigate whether de Broglie waves are basically 4D or 5D in nature.
{Navier-Stokes} Analog of Quantum Mechanics
Physical Review
152
4
1115
1966
10.1103/PhysRev.152.1115
Bohm's formulation of quantum mechanics as a modified set of {Hamilton-Jacobi} equations is rewritten as a quantum-mechanical {Navier-Stokes} equation.
Ricci Curvature and the Mechanics of Solids
The Australian Mathematical Society
37
4
238-241
2010
We discuss some differential geometry pertaining to continuum mechanics and the route recently taken by D.N. Arnold, R.S. Falk, and R. Winther in deriving new improved finite element schemes in linear elasticity from constructions in projective geometry.
Behaviour of laminated plates subjected to conventional blast
International Journal of Impact Engineering
6
3
145-155
1987
10.1016/0734-743X(87)90018-2
Response of simply supported anti-symmetrically laminated angle-ply plates to explosive blast loading is considered. A closed-form solution is obtained for thick plates, it being assumed that the material remains in the elastic range. The effect of transverse shear deformations on the response of thick plates is taken into consideration. The behaviour of thin laminated plates subjected to blast is studied using geometrically non-linear theory. Initial imperfections, which can be important for thin plates, are included in the analysis. The solution for thin elastic laminated plates is obtained numerically using a Runge-Kutta method. The analysis yields the non-dimensional deflection vs time relationship which can be used to determine the stresses and strains in the layers of the plate.
Gravity and inertia in quantum mechanics
Physical Review A
21
5
1419-1438
1980
10.1103/PhysRevA.21.1419
The experiments described in this paper probe the simultaneous effects of gravity, inertia, and quantum mechanics on the motion of the neutron. Using a neutron interferometer of the type developed by Bonse and Hart for x rays, we have observed quantum-mechanical interference phenomena induced by the gravitational field of the Earth and by the Earth's rotation relative to the fixed stars. The importance of these experiments with regard to the role of the principle of equivalence in quantum mechanics is discussed.
Advances in Applied Mechanics Volume 25
Advances in Applied Mechanics
25
47-181
1987
10.1016/S0065-2156(08)70277-1
This chapter discusses the modern corner, edge, and crack problems in linear elastodynamics involving transient waves. The solution of corner, edge, and crack problems based on the equations of motion from the linear theory for a homogeneous, isotropic elastic material, is an important topic of long-standing interest, difficulty, and challenge. The basic difficulty in these problems is exhibited in the waveguide example of Love's treatment of the free longitudinal vibration of a finite-length, circular section, cylindrical rod. It is suggested that for a long, thin rod, this shear stress could be assumed to be zero because its mate on the neighboring lateral surface is zero. This type of approximation, with the simplifying features brought forth by the low-frequency long waves it represents, has led to a great deal of work on the creation and use of approximate one-dimensional theories for treating waveguide and vibration problems in the rod, plate, and shell. The formal solutions for the present mixed edge condition plate problems for the longitudinal impact problem and the analogous one for the mixed pressure shock both have in them the lowest branch-type integral. A method for obtaining wavefront approximations that is applicable to a broader class of waveguide problems than the Cagniard–deHoop method is presented. The transient response of two-dimensional cantilevered plates subjected to base motions is also elaborated.
HAMILTON'S PRINCIPLE APPLIED TO FLUID MECHANICS
Quarterly Journal of Mechanics and Applied Mathematics
30
pt 1
107-130
1977
10.1109/TSP.2008.925261
Hamilton's principle is rigorously applied to fluid systems to yield initially the equations of motion of a real (compressible, viscous) fluid. The assumptions of incompressibility and inviscidity are considered within the context of the variational principle. The principle is then used directly to obtain equations of motion for various fluid systems. These equations are approximate in that only the first terms of a set of admissible functions are considered; closure of the set leads to exact solutions.
S-Matrix Formulation fo Statistical Mechanics
Physical Review
187
1
345
1969
10.1103/PhysRev.187.345
We have formulated the statistical mechanics in terms of the S matrix, which describes the scattering processes taking place in the thermodynamical system of interest. Such a formulation is necessary for studying the systems whose microscopic constituenss behace according to the laws of relaticistic quantum mechanics. Our result is a simple prescription for calculating the grand canonical potential of any faseous system given the free-particle energies and S-matriz elements....
Non-extensive statistical mechanics of compressible turbulence
Physica A: Statistical Mechanics and its Applications
318
3-4
358-370
2003
10.1016/S0378-4371(02)01368-7
Non-extensive statistical mechanics approach to fully developed compressible turbulence is considered and is shown to be even more viable than that for incompressible turbulence. This approach affords a whole new perspective to spatial intermittency aspects in fully developed compressible turbulence on the one hand, and provides results that are consistent with those obtained previously by multi-fractal formulations. The results confirm uniformly that compressibility effects tend to reduce spatial intermittency in fully developed turbulence.
47.27.Gs
Information theory and statistical mechanics. II
Physical Review
108
2
171-190
1957
10.1103/PhysRev.106.620
Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between irreversibility and information loss. A principle of "statistical complementarity" is pointed out, according to which the empirically verifiable probabilities of statistical mechanics necessarily correspond to incomplete predictions. A preliminary discussion is given of the second law of thermodynamics and of a certain class of irreversible processes, in an approximation equivalent to that of the semiclassical theory of radiation.
Enhancing the learning of fluid mechanics using computer simulations
Journal of Engineering Education
96
4
381-388
2007
10.1002/j.2168-9830.2007.tb00946.x
This paper reports the results of a study into the impact of computer simulations on the understanding of fluid mechanics by engineering students. A "lesson study" approach was taken, using constructivist educational theory combined with the variation theory of learning from phenomenography to inform the design of learning activities and to assess their impact. Student difficulties with fluid mechanics concepts were assessed using questions from the Fluid Mechanics Concept Inventory (FMCI). Students had the greatest difficulties with pressure measurement, fluid flow through pipes with changing diameter, and velocity profiles for fluid between flat plates. We developed a set of three simulations to address these difficulties. The impact of the simulations was gauged by a second administration of the FMCI. Most of the students in the sophomore fluid mechanics class participated in the whole of this exercise. Students showed significant improvement in two of the three areas of difficulty. Student feedback on this as an additional learning exercise was very positive.
computer simulations; concept inventory; economic concepts; fluid mechanics
Superconvergent Perturbation Method in Quantum Mechanics
Physical Review Letters
74
9
1495-1499
1995
10.1103/PhysRevLett.74.1495
An analog of Kolmogorov's superconvergent perturbation theory in classical mechanics is constructed for self-adjoint operators. It is different from the usual Rayleigh-Schrödinger perturbation theory and yields expansions for eigenvalues and eigenvectors in terms of functions of the perturbation parameter.
Coherent states for the quantum mechanics on a torus
Arxiv
December 2006
1-15
2007
The coherent states for the quantum mechanics on a torus and their basic properties are discussed.
A New Interpretation on Quantum Mechanics
Philosophy
January
8
2002
Based on new experiments about the "macroscopic Schrodinger's cat state" etc., a self-consistent interpretation on quantum mechanics is presented from the new point of view combining physics, philosophy and mathematics together.
Development of a high cycle fatigue testing system and its application to thin aluminum film
Engineering Fracture Mechanics
75
17
4958-4964
2008
10.1016/j.engfracmech.2008.06.015
The principal goal of this investigation was to develop a feedback controlled high cycle fatigue testing system and to demonstrate its usefulness by acquiring a preliminary stress-life curve of an aluminum film in a very short period of time. A high cycle fatigue testing system having 2.5 N load capacities was constructed and proved reliable, stable and useful in doing long-run fatigue tests. A set of stress-life curves was collected under a mean stress level with 1.16 μm thick aluminum films under closed-loop load control. The system is compact enough to set it up on subsidiary equipment like an optical microscope. A white light interferometric microscope was utilized to observe a specimen’s surface morphology change with fatigue cycles in-situ. The surface roughness was decreased or remained constant in the beginning but started to increase in the later stage.
Statical and dynamical behaviour of thin fibre reinforced composite laminates with different shapes
Computer Methods in Applied Mechanics and Engineering
194
17
1797-1822
2005
10.1016/j.cma.2004.06.009
Based on the classical laminated plate theory, a variational approach for the study of the statical and dynamical behaviour of arbitrary quadrilateral anisotropic plates with various boundary conditions is developed. The analytical formulation uses the Ritz method in conjunction with natural coordinates to express the geometry of general plates in a simple form. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram-Schmidt procedure. The algorithm developed is quite general and can be used to study fibre reinforced composite laminates with symmetric lay-ups, which may have general anisotropy and any combinations of clamped, simply supported and free edge support conditions. Various numerical applications are presented and some results are compared with existing values in the literature to demonstrate the accuracy and flexibility of the present method. New results were also determined for plates with different geometrical shapes, combinations of boundary conditions, several stacking sequences and various angles of fibre orientation. ?? 2004 Elsevier B.V. All rights reserved.
composite plates; free vibration; laminates; mode shapes; ritz method; static analysis
Monitoring patient mechanics during mechanical ventilation.
Critical care clinics
14
4
629-53, vi
1998
This article provides a review of respiratory mechanics that can be monitored in ventilator-dependent patients during passive and spontaneous breathing. Special focus is placed on resistance, compliance, and work of breathing. A description of methods and techniques, and a summary of clinical observations and applications in critically-ill patients are also included.
Artificial; Artificial: methods; Humans; Intrinsic; Intrinsic: etiology; Monitoring; Physiologic; Physiologic: methods; Positive-Pressure Respiration; Respiration; Respiratory Function Tests; Respiratory Insufficiency; Respiratory Insufficiency: physiopathology; Respiratory Insufficiency: therapy; Respiratory Mechanics
Doing quantum mechanics with control theory
IEEE Transactions on Automatic Control
45
1
73-77
2000
10.1109/9.827357
Bellman and Dreyfus (1964) showed how classical mechanics can be obtained from Hamilton's principle by dynamic programming. If we add noise in a particular way, we obtain Schrodinger's equation and many other results from the elementary theory of quantum mechanics. Some new results can also be obtained, and there are important consequences for the philosophy of science.
Development of celestial mechanics in Japan
Planetary and Space Science
46
8
1031-1036
1998
10.1016/S0032-0633(98)00033-6
In this article, a brief history of Japanese astronomy before the Meiji restoration is described at the beginning. Then the development of celestial mechanics research in Japan after the Meiji is traced until the 1950s by describing, particularly, the careers and works of H. Terao, K. Hirayama and Y. Hagihara, the three consecutive professors of celestial mechanics at Tokyo University, as well as those by their students.
Quantum mechanics in multiply-connected spaces
Journal of Physics A: Mathematical and General
29
1497-1510
1996
10.1088/0305-4470/29/7/019
This paper analyses quantum mechanics in multiply-connected spaces. It is shown that the multiple connectedness of the configuration space of a physical system can determine the quantum nature of physical observables, such as the angular momentum. In particular, quantum mechanics in compactified Kaluza - Klein spaces is examined. These compactified spaces give rise to an additional angular momentum which can adopt half-integer values and therefore, may be identified with the intrinsic spin of a quantum particle.
Conventional quantum mechanics without wave function and density matrix
The XXXI latin american school of physics (Escuela Latinoamericana de fisica, ELAF) new perspectives on quantum mechanics
464
1
191-220
1999
10.1063/1.58229
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schrödinger evolution equation and to the energy level equation written for the positive probability distribution are discussed. Instead of the transition probability amplitude (Feynman path integral) a transition probability is introduced. A new formulation of the conventional quantum mechanics (without wave function and density matrix) based on the “probability representation” of quantum states is given. An equation for the propagator in the new formulation of quantum mechanics is derived. Some paradoxes of quantum mechanics are reconsidered.
On the thermodynamic consistency of the equivalence principle in continuum damage mechanics
Journal of the Mechanics and Physics of Solids
59
5
1115-1120
2011
10.1016/j.jmps.2011.01.015
We consider theories of continuum damage mechanics involving damage effect variables of different tensorial ranks. It turns out that orthotropic damage together with the use of Lemaitre's equivalence principle for the elastic part does not allow thermodynamic potentials such as the free enthalpy to exist. As the existence of these potentials is, however, a strict thermodynamic requirement, a theory employing orthotropic damage in this way is inconsistent. We show that the use of a rank-4 damage effect variable allows a consistent use of the equivalence principle.
Anisotropic material; Damage mechanics; Elastic material; Microcracking
Quantum Mechanics and Frequentism: A Reply to Ismael
British Journal for the Philosophy of Science
47
4
575-577
1996
Ismael (BJPS, 196) has argued that frequentism is not a viable option for the interpretation of the probabilities of quantum mechanics. The argument assumes that the quantum probabilities are intrinsic properties of systems. I show that the formalism of quantum mechanics suggests no such fact.
Quantum Mechanics
Relative non-relativistic mechanics
arXiv
11
2007
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame, inertial force, free motion equation, and inertial frame are discussed.
Passing from mechanics of the special theory of relativity to newtonian mechanics, and the relativistic effects
Journal of Applied Mathematics and Mechanics
45
6
742-748
1981
10.1016/0021-8928(81)90112-X
A general method of passing from mechanics of the special theory of relativity to Newtonian mechanics is considered together with various relativistic effects.
A constitutive framework for modelling thin incompressible viscoelastic materials under plane stress in the finite strain regime
Mechanics of Time-Dependent Materials
15
4
389-406
2011
10.1007/s11043-011-9159-4
Rubbers and soft biological tissues may undergo large deformations\nand are also\n\nviscoelastic. The formulation of constitutive models for these materials\nposes special challenges.\n\nIn several applications, especially in biomechanics, these materials\nare also relatively\n\nthin, implying that in-plane stresses dominate and that plane stress\nmay therefore be\n\nassumed. In the present paper, a constitutive model for viscoelastic\nmaterials in the finite\n\nstrain regime and under the assumption of plane stress is proposed.\nIt is assumed that the\n\nrelaxation behaviour in the direction of plane stress can be treated\nseparately, which makes it\n\npossible to formulate evolution laws for the plastic strains on explicit\nform at the same time\n\nas incompressibility is fulfilled. Experimental results from biomechanics\n(dynamic inflation\n\nof dog aorta) and rubber mechanics (biaxial stretching of rubber sheets)\nwere used to assess\n\nthe proposed model. The assessment clearly indicates that the model\nis fully able to predict\n\nthe experimental outcome for these types of material.
finite strain; large deformation; plane stress; rubber; viscoelastic
Mesothelioma in vehicle mechanics: Is the risk different for Australians?
Occupational Medicine
57
8
581-589
2007
10.1093/occmed/kqm114
BACKGROUND: The question of whether vehicle mechanics have an increased risk of mesothelioma has important public health implications. Calculations of relative risk using case reports from the Australian Mesothelioma Registry (AMR) indicate increased risks; however, this contrasts with the results of 19 epidemiologic studies that have found no association. AIM: To evaluate potential explanations for the discrepancy of findings from epidemiologic studies and AMR reports. METHODS: We evaluated three hypotheses as possible explanations for the inconsistency between the AMR-based calculations and the findings from published epidemiologic studies: (i) differences in exposure characteristics of Australian vehicle mechanics versus vehicle mechanics in North America and Europe, (ii) limitations of the AMR data and (iii) errors in the risk calculations based on AMR data. We reviewed available exposure information specific to Australian vehicle mechanics and AMR data, obtained from the Australian National Occupational Health and Safety Commission, for this evaluation. RESULTS: We did not identify differences in workplace exposures, processes or fibre type among Australian vehicle mechanics compared to vehicle mechanics in other countries. Our analysis of primary AMR data identified several errors in exposure classification and in the assumptions used to calculate relative risk. CONCLUSIONS: Discrepancies between epidemiologic studies and AMR-based calculations cannot be explained by differences in exposure. These discrepancies are most likely attributable to inadequate occupational information and classification in the AMR from 1986 forward and to erroneous assumptions used to derive relative risk estimates for mesothelioma among Australian vehicle mechanics.
Asbestos; Brakes; Epidemiology; Mesothelioma registry; Motor mechanics; Motor vehicle mechanics
On the ( Non ) Equivalence of the Schr ¨ odinger and Heisenberg Pictures of Quantum Mechanics
arXiv
1
2
1-6
2014
The aim of this short Note is to show that the Schrödinger and Heisenberg pictures of quantum mechanics are not equivalent unless one uses a quantization rule clearly stated by Born and Jordan in their famous 1925 paper. This rule is sufficient and necessary to ensure energy conservation in Heisenberg's matrix mechanics. It follows, in particular, that Schrödinger and Heisenberg mechanics are not equivalent if one quantizes observables using the Weyl prescription.
A quantum mechanical method for calculating nonlinear optical properties of condensed phase molecules coupled to a molecular mechanics field: A quadratic multiconfigurational self-consistent-field/molecular mechanics response method
The Journal of Chemical Physics
115
17
7843-7851
2001
10.1063/1.1400138
An approach for determining nonlinear optical properties within a quantum mechanics/molecular mechanics method is presented. The response equations in the multiconfigurational self-consistent-field/molecular mechanics approach that includes polarization effects are derived and implemented for second order in response theory. The method is employed to calculate frequency-dependent first hyperpolarizabilities and two-photon absorption properties for H 2 O in aqueous solution. The results are in close agreement with experimental measurements.
Non-linear elastic analysis of thin rods subjected to bending with arbitrary kinetic conditions of their cross-sections
International Journal of Non-Linear Mechanics
17
2
119-128
1982
10.1016/0020-7462(82)90043-9
In this paper problems concerning the non-linear analysis of thin rods due to pure bending with constant initial curvatures and twist and with arbitrary kinetic conditions of their cross-sections are presented. Couples are not considered as being applied to the rods except at their ends. The solutions developed in this paper, which determine the curvature components and the twist of the rod after deformation, are exact in the form of elliptic integrals. Le modèle simple de von Karman d' une calotte plate élastique encastrée soumise à une pression externe est reformulé e en tant que catastrophe élémentaire. En résultat, on améliore substantiellement l' appréhension conceptuelle du comportement en déflexion sous charge. On identifie trois modes distincts de comportement en déflexion. On justifie un comportement du type de retournement par comparaison à des données expérimentales. Das einfache Modell nach von Kármán für eine eingespannte flache elastische Schale unter Aussendruck wird als eine elementare Katastrophe beschrieben. Das grundlegende Verständnis des Auslenkungsverhaltens unter der Last wird in der Folge wesentlich verbessert. Drei eindeutige Arten von Auslenkungsverhalten werden identifiziert. Durch Vergleich mit experimentellen Ergebnissen wird eine Art von Verhalten, nämlich ein Durchschlagen der Schale, untermauert.
Simulation of flow around a thin, flexible obstruction by means of a deforming grid overlapping a fixed grid
International Journal for Numerical Methods in Fluids
56
6
723-738
2008
Doi 10.1002/Fld.1552
This paper presents a numerical method for simulation of coupled flows, in which the fluid interacts with a thin deformable solid, such as flows in cardiovascular valves. The proposed method employs an arbitrary Lagrangian-Eulerian (ALE) method for flow near the solid, embodied in the outflow domain in which the mesh is fixed. The method was tested by modelling a two-dimensional channel flow with a neo-Hookean obstacle, an idealization of the coupled flow near a cardiovascular valve. The effects of the Reynolds number and the dimensionless elastic modulus of the material on the wall shear stress, the size of the downstream reverse flows, and the velocity and pressure profiles were investigated. The deformation of the obstacle, the pressure drop across the obstacle, and the size of the top reverse flow increased as the Reynolds number increased. Conversely, increasing the elastic modulus of the obstacle decreased the deformation of the obstacle and the size of the top reverse flows, but did not affect the pressure drop across the obstacle over the range studied. Copyright (C) 2007 John Wiley & Sons, Ltd.
aortic-valve; domain decomposition; fluid-solid interaction; fluid-structure interaction; heart-valves; incompressible navier-stokes equations; mechanics; overlapping grid
On the Mechanics of Development
Journal of Monetary Economics
22
3-42
1988
This paper considers the prospects for constructing a neoclassical theory of growth and international trade that is consistent with some of the main features of economic previous termdevelopment.next term Three models are considered and compared to evidence: a model emphasizing physical capital accumulation and technological change, a model emphasizing human capital accumulation through schooling, and a model emphasizing specialized human capital accumulation through learning-by-doing.
Robert Lucas 1988
FLUID MECHANICS
RADIANT HEATING AND COOLING HANDBOOK
864
2002
* Covers designing, sizing, and positioning radiant heating and cooling systems in industrial, commercial, residential buildings, and facilities* Describes the underlying principles of radiant heating and cooling relating to thermal comfort
Experimental investigation into the effect of edge stitching on the tensile strength and fatigue life of co-cured joints between cross-ply adherends
Advanced Composites Letters
13
3
151-161
2004
An experimental study was conducted to investigate the effect of stitching on the static and fatigue response and related failure modes of co-cured single-lap joints between composite adherends. Two cross-ply layups, [0 2/90]s and [90/02]s, were selected for the adherends, with the aim of studying the influence of the layer orientation at the joining interface (0'I-0I for joints between [0 2/90]s adherends and 90'I-90'I for joints with [90/0 2]s adherends). It was found that stitching did not affect the static behaviour of [02/90]s joints, but it resulted in a 36% increase in the static strength of joints between [90/0 2]s adherends. However, stitching significantly improved the fatigue life of both [02/90]s and [90/0 2]s joints by extending the durations of both the crack nucleation and propagation stages. Direct observations indicated that the bridging action of stitches (which remained intact throughout the entire fatigue life of the joints) on delaminated adherends is the physical mechanism responsible for the extension of the crack propagation phase.
Co-curing; Cross-ply; Single-lap joints; Stitching, fatigue
Fracture Prediction of Dissimilar Thin Film Materials in Cu/low-k Packaging
Journal of Materials Science: Materials in Electronics
21
8
787-795
2010
10.1007/s10854-009-9994-0
For current semiconductor technology, interfacial crack in stacked thin films of Cu/low-k damascene integration is a critical reliability issue that needs to be urgently resolved. In addition to the measurement of 4-point bending test, how to precisely estimate the adhesion energy between dissimilar films through simulation, based on fracture mechanics is important while designing robust interconnect structures as well as developing next-generation low-k materials. Distinct from the former studies, this research proposes a novel tie-release crack prediction technique based on finite element calculations in order to consider the stress-induced impacts on the thermo-mechanical reliability of the microelectronic package with a low-k chip during the different cracking length of film interfaces. To ensure the correctness and feasibility of the presented technique, a plastic ball array (PBGA) package with stacked Cu/low-k interconnects is implemented as test vehicle to validate actual testing data of experiments and evaluate the variation of interfacial cracking energy while silicon chip becomes thinner. Through the combination of J-integral approach with the technique of global-local sub-modeling, all the predicted results for the forgoing referred cases reveal a good agreement with the physical behaviors of devices. Therefore, it can be concluded that the proposed methodology is highly reliable in estimating the occurrence opportunities of interfacial crack.
Advertising Appeals; Advertising Attitude; Advertising Spokespersons; Purchase Intention
A study of stationary crack-tip deformation fields in thin sheets by computer vision
Experimental Mechanics
34
2
125-140
1994
10.1007/BF02325709
Abstract The in-plane deformation fields near a stationary crack tip for thin, single edge-notched (SEN) specimens, made from Plexiglas, 3003 aluminum alloy and 304 stainless steel, have been successfully obtained by using computer vision. Results from the study indicate that (a) in-plane deformations ranging from elastic to fully plastic can be obtained accurately by the method, (b) for xx xy , the size of the HRR dominant zone is much smaller than forV yy , respectively. Since these results are in agreement with recent analytical work, suggesting that higher order terms will be needed to accurately predict trends in the data, it is clear that the region where the first term in the asymptotic solution is dominant is dependent on the component of the deformation field being studied, (c) the HRR solution can be used to yy only in regions where theplastic strains strongly dominate the elastic strain components (i.e., textbackslashvarepsilon yytextasciicircumel /textbackslashleft. textbackslashvarepsilon yytextasciicircumpl .03 - .05 ); forV, the HRR zone appears to extend somewhat beyond this region, (d) the displacement componentU does not have the HRR singularity anywhere within the measurement region for either 3003 aluminum or 304 SS. However, the displacement componentV agrees with the HRR slope up to the plastic-zone boundary in 3003 aluminum $5textbackslashtext J/textbackslashsigma 0textless rtextless 2textbackslashtext5 J/textbackslashsigma 0 and over most of the region where measurements were obtained 0textless rtextless 8textbackslashtext J/textbackslashsigma 0 in 304 SS and (e) the effects of end conditions must be included in any finite-element model of typical SEN specimen geometries to accurately calculate theJ integral and the crack-tip fields.
Experimental and theoretical/numerical investigations of thin films bonding strength
Theoretical and Applied Fracture Mechanics
31
47-59
1999
10.1016/S0167-8442(98)00066-4
A laser spallation facility has been developed to measure the strength of planar interfaces between a substrate and a thin coating. This quantity is a central requirement in contemporary thin film and protective coatings technology and its successful measurement should improve the scientific/technological potential for the design of advanced composites, protective coatings of composites that operate in hostile environments, and in joining of dissimilar materials. The technique involves impinging a laser pulse of ultra short duration on the rear surface of the substrate, which is coated by a thin layer of energy absorbing metal such as Sn and Pb. The explosive evaporation of the metallic layer, confined between a fused quartz crystal and the substrate, induces a compressive shock wave, which propagates through the substrate toward the material interface. Upon reflection from the free surface of the coating, the pressure pulse is converted into a tensile wave which, under certain conditions, can lead to spallation at the interface. It is shown by mathematical simulation that atomic bond rupture is the mechanism of separation in this experiment. Since the interaction of laser energy with matter is a complicated, highly non-linear process, our investigations, at first, were based on measurement of the pressure pulse generated by the threshold flux level that leads to spallation, by using a microelectronics device with a piezo-electric crystal, and on computation of the tensile stress experienced at the material interface, by numerical simulation of the induced stress wave propagation. Several substrate/coating (ceramic/ceramic and ceramic/metal) systems have been investigated such as, 1-15 ??m SiC by CVD, 1-4 ??m TiC and TiN by PVD coatings on sapphire substrates, as well as 1-2 ??m Au, Sn and Ag coatings by sputtering on sapphire, fused quartz and glass substrates. For indentically prepared specimens, the measured threshold energy levels are reproducible, thus leading to reproducible bond strength values, while the spall size, as expected, is dependent on the laser pulse energy level. Finally, the bond strength values obtained are in very good agreement with similar data derived by direct experimental techniques based on Laser-Doppler-Interferometry.
The borderland between quantum and classical mechanics
Physica Scripta
T70
7-13
1997
10.1088/0031-8949/1997/T70/001
A derivation of non-relativistic quantum mechanics is based on classical Newtonian mechanics.
The borderland between quantum and classical mechanics
Physica Scripta
T70
7-13
1997
10.1088/0031-8949/1997/T70/001
A derivation of non-relativistic quantum mechanics is based on classical Newtonian mechanics.
Fracture Mechanics for Failure of Concrete
Annual Review of Materials Science
24
293-320
1994
10.1146/annurev.ms.24.080194.001453
Failure of concrete structures is usually accompanied by cracking of concrete. Understanding and modeling of how and when concrete fails are not only critical for designingconcrete structures, but are also important for developing new cement-based materials. Recent publication (1,2) have shown that fracture mechanics has now been established as a fundamental apporach that can explain certain nonlinear aspects of concrete behavior, help to preven brittle failures of structures, and be an important aid in materials engineering. In this paper we discuss applications of fracture mechanics to failure of concrete structures. Thewse topics include internal microstructure of concrete; the concept osf strain localization, which is a typical feature of concrete behavior; the principles of linear elastic fracture mechanichs (LEFM); fracutre processes and toughening mechanisms in concrete; nonlinear fracutre mechanics approaches used to describe fracture of concrete; the determination of material fracutre parameters of concrete and derivation of an R-curve. We demonstrate that many experimental phenomena associated with failure of concrete, such as size effect on tensile strengh and brittleness of high strength concrete, can be interpreted by fracutre mechanics.
concrete; crack; fracture process; fracture resistance; localization; micro; strain; stress; structure
Geometric variables and yield criteria in damage mechanics
Computational Plasticity X - Fundamentals and Applications
2009
A consistent framework to describe the anisotropic damaging of elastic-plastic materiasl is developed within Continuum Mechanics in large strains. © CIMNE.
Continuum mechanics;Porous materials;
Mechanics of filled carbon nanotubes
Diamond and Related Materials
44
11-25
2014
10.1016/j.diamond.2014.01.015
The benefits of filling carbon nanotubes (CNTs) with assorted molecular and crystalline substances have been investigated for the past two decades. Amongst the study of new structural phases, defects, chemical reactions and varied types of host–guest interactions, there is one fundamental characterisation aspect of these systems that continues to be overlooked: the mechanical behaviour of filled CNTs. In contrast to their empty counterparts, the mechanics of filled CNTs is a subject where reports appear far and apart, this despite being key to the application of these materials in technological devices. In the following paragraphs, we review the work that has been carried out up to the present on the mechanics of filled CNTs. The studies discussed range from experimental resonant frequency essays performed within electron microscopes to modelling, via molecular dynamics, of three-point bending of nanotubes filled with gases.
Carbon Nanotubes; Encapsulation; Filled Carbon Nanotubes; Mechanical Properties; Mechanics
Fluid mechanics
Academic Press 4th ed
891
2012
Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situationswhether in the liquid or gaseous state or ...
technology & engineering
Fracture Mechanics
Spon Press - Taylor Fr. Gr.
378
2005
In this second edition, which is the result of numerous revisions, updates and additions, the authors cover the basic concepts of fracture mechanics for both the linear elastic and elastic-plastic regimes. The fracture mechanics parameters K, G, J and CTOD are treated in a basic manner along with the text methods to determine critical values. The development of failure assessment based on elastic-plastic fracture mechanics is reflected in a comprehensive treatment. Three chapters are devoted to the fracture mechanics characterisation of crack growth. Fatigue crack growth is extensively treated and attention is paid to the important topic of the initiation and growth of short fatigue cracks. Furthermore, sustained load fracture and dynamic crack growth are discussed, including various test techniques, e.g. the determination of the crack arrest toughness. Finally, there are two chapters dealing with mechanisms of fracture and the ways in which actual material behaviour influences the fracture mechanics characterisation of crack growth. This textbook is intended primarily for engineering students.
book + Fracture analysis +; fracture analysis; Fracture mechanics; Fracture Mechanics; Mechanisms of Fracture in Metallic Materials; pipelines; SBD; sent testing; TECHNOLOGY & ENGINEERING; unloading compliance technique
Fracture Mechanics
Spon Press - Taylor & Francis Group
378
2005
In this second edition, which is the result of numerous revisions, updates and additions, the authors cover the basic concepts of fracture mechanics for both the linear elastic and elastic-plastic regimes. The fracture mechanics parameters K, G, J and CTOD are treated in a basic manner along with the text methods to determine critical values. The development of failure assessment based on elastic-plastic fracture mechanics is reflected in a comprehensive treatment. Three chapters are devoted to the fracture mechanics characterisation of crack growth. Fatigue crack growth is extensively treated and attention is paid to the important topic of the initiation and growth of short fatigue cracks. Furthermore, sustained load fracture and dynamic crack growth are discussed, including various test techniques, e.g. the determination of the crack arrest toughness. Finally, there are two chapters dealing with mechanisms of fracture and the ways in which actual material behaviour influences the fracture mechanics characterisation of crack growth. This textbook is intended primarily for engineering students.
fracture analysis; Fracture mechanics; Fracture Mechanics; Mechanisms of Fracture in Metallic Materials; pipelines; SBD; sent testing; TECHNOLOGY & ENGINEERING; unloading compliance technique
Fracture Mechanics
Spon Press - Taylor & Francis Group
378
2005
In this second edition, which is the result of numerous revisions, updates and additions, the authors cover the basic concepts of fracture mechanics for both the linear elastic and elastic-plastic regimes. The fracture mechanics parameters K, G, J and CTOD are treated in a basic manner along with the text methods to determine critical values. The development of failure assessment based on elastic-plastic fracture mechanics is reflected in a comprehensive treatment. Three chapters are devoted to the fracture mechanics characterisation of crack growth. Fatigue crack growth is extensively treated and attention is paid to the important topic of the initiation and growth of short fatigue cracks. Furthermore, sustained load fracture and dynamic crack growth are discussed, including various test techniques, e.g. the determination of the crack arrest toughness. Finally, there are two chapters dealing with mechanisms of fracture and the ways in which actual material behaviour influences the fracture mechanics characterisation of crack growth. This textbook is intended primarily for engineering students.
fracture analysis; Fracture mechanics; Fracture Mechanics; Mechanisms of Fracture in Metallic Materials; pipelines; SBD; sent testing; TECHNOLOGY & ENGINEERING; unloading compliance technique
Effects of oxygen on prismatic faults in α-Ti: a combined quantum mechanics/molecular mechanics study
Scripta Materialia
98
32-35
2015
10.1016/j.scriptamat.2014.11.008
The mechanical properties of α-Ti are greatly affected by the presence of oxygen impurities. Here we focus on the interaction of oxygen with prismatic faults and oxygen diffusion barriers in α-Ti using a multiscale quantum mechanics/molecular mechanics approach. We show that a one-sixth monolayer of oxygen addition increases the Peierls stress 4-fold and reduces the dislocation core width by 18%. The calculated hardening effect due to oxygen and the oxygen diffusion barriers are consistent with experiments.
Dislocation; First principles; Oxygen; Peierls stress
Uncertainty relations of statistical mechanics
Physical Review A
31
5
3237-3239
1985
10.1103/PhysRevA.31.3237
Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum Mechanics. Such a complementarity is expressed as the impossibility of perform an exact simultaneous determination of the system energy and temperature by using an experimental procedure based on the thermal equilibrium with other system regarded as a measure apparatus (thermometer). In this work, we provide a simple generalization of this latter approach with the consideration of a thermodynamic situation with several control parameters.
Classical mechanics
Nature
278
5699
680
1960
For thirty years this has been the acknowledged standard in advanced classical mechanics courses. This classic book enables readers to make connections between classical and modern physics - an indispensable part of a physicist's education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the book to include the latest topics, applications, and notation, to reflect today's physics curriculum. They introduce readers to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help readers to develop skills in how to use computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the book remains fully accessible to readers who have not had an intermediate course in classical mechanics. For college instructors and students.
Classical mechanics; Rutherford scattering
Introduction to Quantum Mechanics and the Quantum-Classical transition
Proc. XV International Workshop on Geometry and Physics
1
3-42
2006
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the action of the unitary group on the Hilbert space allows to relate both approaches. We also study Weyl-Wigner approach to Quantum Mechanics and discuss the implications of bi-Hamiltonian structures at the quantum level.
Quantum Physics
Not-so-classical mechanics: unexpected symmetries of classical motion
Canadian Journal of Physics
83
2
91-138
2005
10.1139/p05-003
A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central-force problem; inequivalent Lagrangians and Hamiltonians; constants of central-force motion; a general discussion of higher order Lagrangians and Hamiltonians, with examples from Bohmian quantum mechanics, the Kortewegde Vries equation, and the logistic equation; gauge theories of Newtonian mechanics; and classical spin, Grassmann numbers, and pseudomechanics.
Another Survey of Foundational Attitudes Towards Quantum Mechanics
arXiv
10
2013
Although it has been almost 100 years since the beginnings of quantum mechanics, the discussions about its interpretation still do not cease. Therefore, a survey of opinions regarding this matter is of particular interest. This poll was conducted following an idea and using the methodology of Schlosshauer et al. (arXiv:1301.1069 [quant-ph]), but among a slightly different group. It is supposed to give another snapshot of attitudes towards the interpretation of quantum mechanics and keep discourse about this topic alive.
Development of mechanics and pulmonary reflexes
Respiratory Physiology and Neurobiology
149
1-3
143-154
2005
10.1016/j.resp.2005.05.028
The mechanical properties of the respiratory system are paramount in converting neural output into ventilation. The highly compliant chest wall of the newborn results in chest distortion and volume loss during inspiration and, as the chest is also unable to resist the inward recoil of the lung, there is a reduction in lung volume at end expiration (functional residual capacity) and a tendency for alveoli to collapse. Vagal innervation of the lungs and airways is responsible for eliciting various reflexes that result in the dynamic modification of respiratory mechanics and an improvement in ventilation. From the first breath, the newborn increases the frequency of augmented breaths to improve lung compliance and prolongs the expiratory time constant in order to increase the amount of air remaining in the lung at end expiration and help prevent lung collapse. This review examines the respiratory mechanics of the mammalian neonate at birth and during early development together with the vagal reflexes that are responsible for the dynamic modification of respiratory mechanics in order to ensure that effective gas exchange occurs from birth. ?? 2005 Elsevier B.V. All rights reserved.
Respiratory mechanics: lung compliance, chest wall
Interference in Bohmian mechanics with complex action.
The Journal of chemical physics
127
16
161101
2007
10.1063/1.2794029
In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of Bohmian mechanics in which the quantum action S is taken to be complex [Y. Goldfarb et al., J. Chem. Phys. 125, 231103 (2006)]. In the alternative formulation there is a significant reduction in the magnitude of the quantum force as compared with the conventional Bohmian formulation, at the price of propagating complex trajectories. In this paper we show that Bohmian mechanics with complex action is able to overcome the main computational limitation of conventional Bohmian methods-the propagation of wave functions once nodes set in. In the vicinity of nodes, the quantum force in conventional Bohmian formulations exhibits rapid oscillations that present a severe numerical challenge. We show that within complex Bohmian mechanics, multiple complex initial conditions can lead to the same real final position, allowing for the accurate description of nodes as a sum of the contribution from two or more crossing trajectories. The idea is illustrated on the reflection amplitude from a one-dimensional Eckart barrier. We believe that trajectory crossing, although in contradiction to the conventional Bohmian trajectory interpretation, provides an important new tool for dealing with the nodal problem in Bohmian methods.
Fractal materials, beams, and fracture mechanics
Zeitschrift fur Angewandte Mathematik und Physik
60
1194-1205
2009
10.1007/s00033-009-8120-8
Continuing in the vein of a recently developed generalization of continuum ther- momechanics, in this paper we extend fracture mechanics and beam mechanics to materials described by fractional integrals involving D, d and R. By introducing a product measure in- stead of a Riesz measure, so as to ensure that the mechanical approach to continuum mechanics is consistent with the energetic approach, speci¯c forms of continuum-type equations are derived. On this basis we study the energy aspects of fracture and, as an example, a Timoshenko beam made of a fractal material; the local form of elastodynamic equations of that beam is derived. In particular, we review the crack driving force G stemming from the Gri±th fracture criterion in fractal media, considering either dead-load or ¯xed-grip conditions and the e®ects of ensemble averaging over random fractal materials.
Beams; Fractal materials; Fracture mechanics
Elastic-plastic dynamic analysis of anisotropic laminated plates
Computer Methods in Applied Mechanics and Engineering
70
3
349-365
1988
10.1016/0045-7825(88)90025-4
This paper presents the application of a refined finite element model to the elastic and elastic-plastic dynamic analysis of anisotropic laminated plates. Dynamic analysis is based on Newmark's algorithm used in conjunction with the Hughes and Liu predictor-corrector scheme resulting in an ‘effective static problem’ which is solved using a Newton-Raphson-type process. Flow theory is used in the inelastic range and the Huber-Mises yielding surface extended by Hill for anisotropic materials is adopted. Numerical results obtained for two categories of anisotropic structures, namely cross-ply laminated plates and angle-ply laminated plates, are presented and the effects of anisotropy and bending/ stretching coupling on the dynamic elastic and elastic-plastic responses are discussed. The effects of lamina stack sequences and lamina angle sequences on the dynamic responses are also considered.
Transverse shear and normal deformation theory for bending analysis of laminated and sandwich elastic beams
Mechanics of Composite Materials and Structures
6
3
267-283
1999
10.1080/107594199305566
The influence of transverse normal strain on bending analysis of cross-ply laminated and sandwich beams is presented. A higher-order shear deformation beam theory is developed. Euler-Bernoulli classical, Timoshenko first-order and simple higher-order theories have been also used in the analysis. The governing equations for a beam composed of orthotropic layers and subjected to any given mechanical load distribution are derived. Making use of Navier-like approach, exact solutions are obtained for cross-ply laminated and sandwich beams subjected to arbitrary loadings. Numerical results for beams with the simply-supported boundary conditions are presented. The effects due to transverse normal strain, transverse shear deformation and number of layers on the static response of the beams are investigated.
Tensile testing and non-destructive evaluation scanning of varied Ply CFRP laminates with embedded magnetostrictive particles
54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
2013
10.2514/6.2013-1661
One method for Nondestructive Evaluation (NDE) of Carbon Fiber Reinforced Polymers (CFRP) is the integration of magnetostrictive particles (MSP) into CFRP laminates. In order to ensure that integration of MSP would be a feasible method of nondestructive evaluation, the structural intrusiveness of the particles must be investigated. Since one of the major benefits of CFRP is its strength to weight ratio, the inclusion of a foreign material must be minimally intrusive on the material properties of the laminate. This paper details several analyses meant to quantify the affect of integrating MSP into unidirectional CFRP laminates on the quasi-static tensile properties. First, the material properties of both the MSP and CFRP laminate were used in conjunction with the constitutive equations to estimate the ultimate tensile strength of symmetric laminates with and without MSP. Once a prediction of the failure stress had been determined, laminates were fabricated and tested under quasi-static tension. Finally, the experimental tests were correlated with a Finite Element Model. The laminates tested ranged from two plies to ten plies with a single layer of MSP embedded in the center of laminates. The results from experimental testing of carbon fiber-reinforced polymer composite beams with and without a layer of magnetostrictive particles showed that the particle layer was minimally intrusive on the quasi-static tension properties of the beam. Analysis of the results revealed that the addition of a layer of MSP caused a slight increase in the ultimate tensile strength of the beams, while the modulus saw an equivalent drop. Based on the number of samples tested, the amount of change seen in both the tensile strength and the modulus was statistically negligible. An investigation using scanning electron microscopy shed light on the change in the material properties. It was seen that during the curing process the epoxy matrix flowed into the voids between particles in the particle layer, which caused an increase in the fiber volume in the ply region. Previous research has shown that an increase in fiber volume in fiber reinforced composites leads to an improvement in ultimate tensile strength. This is because tensile strength is a fiber-dominated property. The microscopy analysis also showed that while there was flow over of epoxy resin into the particle layer, there were still large voids present. The presence of voids inside a laminate would reduce the incubation time for matrix cracks, limiting the matrix's ability to transfer stress between fibers and reducing the stiffness of the laminate. The results from the analytical model proved to overestimate both the ultimate tensile strength and the modulus. The analytical model was based on equations and material properties for ideal laminates. Experimental testing tends to encounter issues such as material flaws, fabrication inconsistencies, and testing inconsistencies, which cause the results to deviate from the analytical model. While the experimental results and analytical model did not completely agree, the difference was not an order of magnitude in size. On the other hand, the results from the finite element analysis were in close agreement with the experimental data. For laminates with ply numbers of fewer than the data was statistically equivalent to the FEA model, with the higher laminate numbers seeing a slight overestimation in the ultimate tensile strength. The overestimation was likely the result of a difference in the theoretical thickness and fabricated thickness of the laminates. The thickness used in the finite element model was based on the manufacturer's recommended thickness, which, due to epoxy flow out, would differ from the thickness of fabricated laminates. In lower ply laminates the thickness difference would not be pronounced, but in laminates with more plies the difference is compounded and would have a greater affect. While this research shows that the addition of a layer of magnetostrictive particles does not have an appreciable affect on the quasi-sic tension properties of fiber reinforce composites, future research will have to be conducted to investigate it's affects in different loading scenarios. The results gained from this research are promising for the performance of these laminates under compressive loading. A fiber reinforced laminate's compressive properties, like its tensile properties, are fiber dominated. Since the addition of a particle layer resulted in an increased fiber volume in the ply region, it is postulated that compression testing will also reveal the particle layer is minimally intrusive. The results of the microscopy study reflect poorly on the performance of laminates under the action of bending forces. Bending of beams involves the upper and lower surfaces of the laminate being under the action of opposing stress states. One surface is under the action of compressive stress, while the other is under the action of a tensile stress and the center of the beam is integral in the transfer of these two stress states. The microscopy study revealed that the particle layer, located in the center of the beam, is riddled with voids. This presence of voids would inhibit the layer's ability to transfer the stress effectively between the two surfaces. It is believed that a laminate containing a layer of magnetostrictive particles under the action of a bending stress would delaminate along the centerline, resulting in premature failure. Additionally, in this paper, experimental and numerical results of damage sensing tests using magnetostrictive particles embedded in fiber reinforced polymer laminates, are presented. For the experimental results, carbon fiber reinforced polymer (CFRP) laminates (Hexcel AS4/3501-6) are embedded with Terfenol-d particles and the ply count is varied to observe the change in the sensing. Sensing is observed using a non-contacting magnetostrictive strain sensor setup. The sensing parameter observed is the voltage induced in the secondary circuit. Two of the three batches presented have laminates that are embedded with.5"x.5", release agent coated patches that prevent bonding between the Terfenol-d and the CFRP layer. The laminate ply count ranges from 2-14 unidirectional plies. Two fabrication methods are used to distribute the particles in the laminate. The experimental results from the three batches reveal that the fabrication technique has a significant effect on the sensing signal. The effect of particle accumulation in the magnetic flux path significantly affects the sensing signal and makes the presence of a delamination difficult to assess. The experiments also show that when the ply count is varied, there is not much variation in the sensing signal. For the numerical simulation, finite element models are constructed to analyze the magneto-mechanical interaction in a laminate embedded with terfenol-D (TD) for sensing purposes. The model examines the mechanical parameters that affect sensing by observing the parameters in the Terfenol-d layer around a delamination. The results of the model show that the magnetic field produces a local change in strain and stress in the region of the delamination. The strain in the delamination region is greater than the strain in the bonded regions. The stress in the delamination region is lower than the stress in the bonded regions. For the magnetic parameters, a constant magnetic permeability was used in the constitutive magnetostriction equation, which inhibits the magnetic flux density from varying as a function of stress/strain. The data shows that the distribution method used to distribute the particles have a dominant effect on the sensing signal. Attempts were made to refine the distribution method, but it is highly suggested that an automated method be used to distribute these particles. The effect of ply variation cannot be distinguished due to inconsistencies in the sensing signal. The delamination also could not be clearly distinguished from a change in particle density. Future work will focus on finding new ways to distribute particles and differentiate particle clumping from a delamination. The multiphysics FEA model reveals that there is a drop in stress and strain in the region of the delamination for a laminate that has a delamination against the magnetostrictive layer. © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Analytical models; Beams and girders; Carbon fibe; Carbon fiber reinforced polymer; Compressive prope; Laminates
Carrier generation in polycrystalline MgIn2O4 thin films by proton implantation
Philosophical Magazine B: Physics of Condensed Matter: Statistical Mechanics, Electronic, Optical and Magnetic Properties
82
10
1155-1162
2002
Doi 10.1080/13642810210126689
Thin films of polycryst. MgIn2O4 (spinel structure; bandgap, 3.5 eV) were prepd. on silica glass by the rf sputtering technique. The thin films were insulating in the as-deposited state, and proton implantation was carried out in the fluence range from 1 * 1015 to 1 * 1018 cm-2 at room temp. to introduce carrier electrons in the films. Upon implantation at a fluence of 1 * 1015 cm-2, the elec. cond. increased to as high as approx. 3 * 10 S cm-1 and satd. at this level even for higher fluences. Carrier generation efficiency was about 100% at a fluence of 1 * 1015 cm-2 but monotonically decreased with increasing fluence. Nuclear reaction anal. on deuteron-implanted specimens revealed that the depth profile of D concn. for all specimens was almost the same in the as-implanted state, and the D fraction retained in the films was about 80% for a D+ fluence of 1 * 1016 cm-2, about 70% for 1 * 1017 cm-2, and about 65% for 1 * 1018 cm-2. After post-annealing at 300 Deg, the width of the D distribution became broader, and the retained D fraction was reduced to 50% for a D+ fluence of 1 * 1017 cm-2 or 17% for 1 * 1018 cm-2. These results strongly suggest that the majority of H+ ions implanted at high fluences are present in the films as neutral species such as H2 mols. Therefore, the formation of these species, which are inactive for carrier generation, is responsible for the decrease in carrier generation efficiency. [on SciFinder (R)]
Band gap (band gap of polycryst. MgIn2O4 thin film; carrier generation in polycryst. MgIn2O4 thin film; carrier generation proton implantation band gap po; Electric conductivity; Electric current carriers (generation; Ion implantation; Polycrystalline materials (carrier generation in p; Sputtering (sputter-deposition of polycryst. MgIn2
Effect of radial load on the flexural stiffness of a thin disc
Journal of the Mechanics and Physics of Solids
13
4
237-245
1965
10.1016/0022-5096(65)90013-X
A disc gripped at its centre was loaded with radial and transverse loads acting simultaneously at a point on the periphery. By calculating the strain energy absorbed by the disc and work done by applied forces, the effect of radial load on transverse stiffness was evaluated. The values obtained were confirmed experimentally.
円板; 曲げ剛性
Electromagnetics as Fluid-Mechanics
Physics Essays
7
4
450-452
1994
Electromagnetic field potentials are modeled as analogs in fluid mechanics.
classical electromagnetism; ether; maxwell equations
Fatigue of laminated composite structures with stress concentrations
Composites Part B: Engineering
65
11-16
2013
10.1016/j.compositesb.2013.10.020
A model defined at the ply scale to predict the failure of laminated composites for static and fatigue loadings has been proposed. The model describes the loss of strength in the fibre direction for high levels of transverse damage. This phenomenon can be observed in a 0?? tube by applying a cyclic torsion loading up to a high level of damage followed by a tensile test. The model includes an original approach based on a Fracture Characteristic Volume (FCV) to predict the fibre failure of laminated structures with stress concentrations. The FCV is a cylinder defined at the ply scale where the average stress is calculated and compared to the maximal strength of the material. The fibre failure model and an application to open hole plates loaded in fatigue are presented in this paper. ?? 2013.
A. Laminates; B. Fatigue; B. Stress concentrations; C. Damage mechanics
Geometrically non-linear dynamics of composite four-bar mechanisms
International Journal of Non-Linear Mechanics
47
8
837-850
2012
10.1016/j.ijnonlinmec.2012.05.002
This work intends to demonstrate the importance of a geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional non-linearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the non-linear, flexible four-bar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we identify and investigate a few four-bar mechanism problems where the cross-sectional non-linearities are significant in predicting better and critical system dynamic characteristics. This is carried out by varying stacking sequences (i.e. the arrangement of ply orientations within a laminate) and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form non-linear beam stiffness matrix. A numerical example is presented which illustrates the importance of 2-D cross-sectional non-linearities and the behavior of the system is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS).
Erwin Schrodinger and the rise of wave mechanics. III. Early response and applications
Foundations of Physics
18
2
107-184
1988
http://dx.doi.org/10.1007/BF01882930
Th& article (Part III) deals with the early applications of wave mechanics to atomic problems--including the demonstration of the formal mathematical equivalence of wave mechanics with the quantum mechanics of Born, Heisenberg, and Jordan, and that of Dirac--by Schr6dinger himself and others. The new theory was immediately accepted by the scientific community.
Fluid mechanics , turbulent flow and turbulence modeling
Production
2011
This course material is used in three courses in the International Masters pro- gramme Solid and fluid mechanics at Chalmers. The three courses are TME075 Mechanics of solids and fluids (Part II: Fluidmechanics),MTF256 Turbulent Flow and MTF270 Turbulence Modeling. MSc students who follow these courses are supposed to have taken at least one course in fluid mechanics.
Evading quantum mechanics
Quantum
1-6
2012
Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.
Contact Mechanics
Tribology for Scientists and Engineers
93-140
2013
10.1007/978-1-4614-1945-7_3
This book describes available tribology technologies and introdces a comprehensive overview of tribology. General, up-to-date knowledge on how tribology is approached in various related areas of research, both experimental and computational is provided.
Whole bladder mechanics during filling.
Scandinavian journal of urology and nephrology. Supplementum
201
27
51-58; discussion 76-102
1999
In addition to molecular and cellular properties, elemental and whole bladder properties are important to the function of the bladder during filling. The bladder pressure volume filling relation is dependent on all aspects of bladder tissue. Elemental mechanics properties include elasticity, viscoelasticity, and plastic deformation of bladder tissue. Whole bladder properties include bladder shape, mass, and distension. This paper reviews work on mathematical model aimed at determining the effect of whole bladder properties on bladder filling mechanics and outlines directions for the future.
151; 202-; 202-5817; 5771; 708; biomechanics; bladder; com; damaser; decades; e-mail; fax; filling; hines; hines va hospital; il; in the last few; margot s; mass; mdamaser; phd; pressure; research service; shape; significant; surfnetcorp; tel; there has been a; usa
The classical N-body problem within a generalized statistical mechanics
Journal of Physics A: Mathematical and General
27
17
5707-5714
1994
10.1088/0305-4470/27/17/008
The modifications that must be introduced within the framework of standard, classical N-body statistical mechanics techniques, in order to deal with the recently proposed generalized scenario of non-extensive statistical mechanics are discussed. A generalized version of the equipartition theorem is shown to hold. The ideal gas is revisited as a simple application.
Phase Space Quantum Mechanics
Quantum
327
00
94
2003
The paper review and develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative star-product and the deformation of the Poisson bracket to an appropriate Lie bracket is the key element in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of Hamiltonian systems without any constrains and for a very wide class of deformations. The considered class of deformations and the corresponding star-products contains all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of star-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the star-multiplication. The most important result of the paper shows that developed formalism is more fundamental then the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. In addition, examples of a free particle and a simple harmonic oscillator illustrating the formalism of the deformation quantization and its classical limit are given.
Cold expansion and reduction of thin-walled PVC tubes using a die
Journal of Materials Processing Technology
209
9
4229-4236
2009
http://dx.doi.org/10.1016/j.jmatprotec.2008.11.015
The production of sound thin-walled tubular parts by expansion and reduction using a die is generally limited to metals. Current research work in the field follows the same trend as that of industry and, therefore, there is no accumulated experience, no practical design rules and no information available in the specialized literature concerning the utilization of polyvinyl chloride (PVC) tubes (as well as other polymers). As far as authors are aware no technology validation studies have ever been performed with the objective of employing cold expansion and reduction forming processes for shaping the end of thin-walled PVC tubes. This paper is concerned with the abovementioned lack of knowledge and is a first step towards the understanding of the mechanics of deformation of tube end forming applied to PVC (and polymers, in general). The presentation addresses the influence of major process parameters on the formability limits of the expansion and reduction of thin-walled PVC tubes using a die and proposes an innovative extension of the flow formulation that is capable of modelling cold plastic deformation of pressure-sensitive polymers under a non-associated flow rule. The overall investigation is assessed with experimental data obtained under laboratory-controlled conditions and results show that free expansion and reduction of thin-walled PVC tubes using a die can be successfully utilized for producing custom and specific shapes at the tube ends.
End forming of tubes; Experimentation; Finite element method; PVC
Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT
Computer Methods in Applied Mechanics and Engineering
193
4763-4779
2004
10.1016/j.cma.2004.03.013
A Ritz method based on kernel particle approximation for the field variables is proposed for the postbuckling analysis of laminated composite plates. The first-order shear deformation plate theory (FSDT) is employed to model the plate flexure. The Ritz method is used to obtain the discretized non-linear equations. A geometrically non-linear analysis is used to trace the postbuckling paths of the plate. Typical numerical examples including isotropic plates, and cross-ply and angle-ply laminated composite plates have been solved using the proposed method. The results are in close agreement with the series solution as well as previous finite element results available in the literature.
Large deflection of unsymmetric laminates with mixed boundary conditions
International Journal of Non-Linear Mechanics
20
4
273-282
1985
http://dx.doi.org/10.1016/0020-7462(85)90035-6
This paper is analytically concerned with non-linear bending of an unsymmetrically laminated angle-ply rectangular plate under lateral load. The plate edges are subjected to the varying rotational constraints. A series solution satisfying the von Karman-type non-linear equations and the required boundary conditions of the plate is presented. In the formulation the edge moments are replaced by an equivalent lateral pressure near the plate edges. Governing equations are reduced to a set of algebraic equations. Numerical results for maximum deflection, bending moment and inplane force of unsymmetric angle-ply plates are graphically presented for various high-modulus materials, aspect ratios, geometries of lamination and boundary conditions. Present results are also compared with available data.
Is thermodynamics mechanics?
Journal of Engineering Education
29
5
423-429
1939
Argument presented to prove that study of thermodynamics is essentially branch of mechanics. Before Soc Promotion Eng Education.
Thermodynamics
Effects of Interaction Between Chemical Kinetics and Fluid Mechanics in a Stagnation Point Boundary Layer
Combustion Science and Technology
3
6
267-272
1971
10.1080/00102207108952294
Abstract In the present study the mutual effects between thin-flame kinetics and fluid mechanics have been studied Tor a stagnation point flow with boundary layer approximations. The effects of fluid mechanics on the flame properties have been studied with three models (a) Blasius flow model (or Lees' approximation), (b) Falkner-Skan model and (c)?Exact? model. II is shown that Blasius flow model overestimates the flame position by a large amount (much larger than 50% over most of the range). The Falkner-Skan model and ?Exact? model overestimate and underestimate, respectively, the flame position by roughly equal amounts (?20-30%). It is, however, shown by heuristic arguments that predictions of flame position will be more accurate provided actual Lewis number values (0.5-0.7) are used with the exact model. The fuel and product concentrations at the wall are under- and overestimated respectively by the Falkner-Skan model compared to the ?Exact? values. Finally, the velocity profile for a realistic case (with temperature profiles due to the experiments of Tsuji and Yamaoka) has been computed and presented.
Three-dimensional analysis of multi-layered functionally graded anisotropic cylindrical panel under thermomechanical loading
Mechanics of Materials
40
235-254
2008
10.1016/j.mechmat.2007.06.008
A general method is presented for the analysis of a thermoelastic multi-layered cylindrical panel made of an oblique pile of functionally graded layers having orthotropic material properties. The two edges of the panel are under simply-supported and zero temperature conditions. Steady-state thermal and mechanical boundary conditions can be applied on the innermost and outermost surfaces of the cylindrical panel. In addition, the functionally graded material is assumed to be of a power law type in the radial direction and the homogeneous solution in each layer is obtained in terms of the pseudo-Stroh formalism. The solution for the multi-layered cylindrical panel is derived based on the transfer matrix method. Novel to this work, is an alternative but equivalent formulation for the transfer matrix method which is more concise in expression. The derived solution is subsequently applied to investigate a five-layered cylindrical panel. The influence of the gradation of the material and ply angle on the distribution of temperature, displacements and stresses are investigated. The results clearly show that material gradation and ply angle significantly influence the elastic fields and temperature. ?? 2007 Elsevier Ltd. All rights reserved.
Cylindrical panel; Functionally graded material; Generalized plane strain; Pseudo-Stroh formalism; Thermoelasticity; Transfer matrix method
Hygrothermal Effects on the Nonlinear Bending of Shear Deformable Laminated Plates
Journal of Engineering Mechanics
128
April
493-496
2002
10.1061/(ASCE)0733-9399(2002)128:4(493)
The influence of hygrothermal effects on the postbuckling of shear deformable laminated plates subjected to a uniaxial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory that includes hygrothermal effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, fiber volume fraction and initial geometric imperfections are studied.
Symplectic Reduction and the Problem of Time in Nonrelativistic Mechanics
The British Journal for the Philosophy of Science
63
4
789-824
2012
10.1093/bjps/axr045
The deep connection between the interpretation of theories invariant under local symmetry transformations (i.e. gauge theories) and the philosophy of space and time can be illustrated nonrelativistically via the investigation of reparameterization-invariant reformulations of Newtonian mechanics, such as Jacobi's theory. Like general relativity, the canonical formulation of such theories feature Hamiltonian constraints; and like general relativity, the interpretation of these constraints along conventional Dirac lines is highly problematic in that it leads to a nonrelativistic variant of the infamous problem of time. I argue that, nonrelativistically at least, the source of the problem can be found precsely within the symplectic reduction that goes along with strict adherence to the Dirac view. Avoiding reduction, two viable alternative strategies for dealing with Hamiltonian constraints are available. Each is found to lead us to a novel and interesting re-conception of time and change within nonrelativistic mechanics. Both these strategies and the failure of reduction have important implications for the debate concerning the relational or absolute status of time within physical theory.\n1 Introduction 2 Mechanics with a Fixed Parameterization 2.1 Lagrangian mechanics 2.2 Hamiltonian mechanics 2.3 Symplectic mechanics 2.4 Presymplectic geometry and symplectic reduction 3 Reductionism, Haecceitism, and Gauge Symmetry 4 Reparameterization-Invariant Mechanics 4.1 Extended Lagrangian mechanics 4.2 Extended Hamiltonian mechanics 4.3 Jacobi's principle and timeless theory 4.4 Degeneracy, indeterminacy, and triviality 5 Representing Change and Observables in Timeless Mechanics 5.1 The emergent time strategy 5.2 The correlation strategy 6 Interpretational Implications 6.1 The relationalist versus substantivalist dispute with regard to time 6.2 An ontology of timeless change?
Fluid mechanics , turbulent flow and turbulence modeling
Production
2010
This course material is used in three courses in the International Master’s pro- gramme Solid and fluid mechanics at Chalmers. The three courses are TME075 Mechanics of solids and fluids (Part II: Fluidmechanics),MTF256 Turbulent Flow and MTF270 Turbulence Modeling. MSc students who follow these courses are supposed to have taken at least one course in fluid mechanics.
Low-Velocity Impact Response of Cross-Ply Laminated Sandwich Composites with Hollow and Foam-Filled Z-Pin Reinforced Core
Journal of Composites Technology and Research
21
2
84
1999
10.1520/CTR10950J
Sandwich composites offer unique lightweight and high bending stiffness advantages for a wide variety of engineered structures. Traditional foam core sandwich constructions exhibit low transverse stiffness and catastrophic compression failure of the core, besides being inaccessible in terms of space, In this study, two configurations including a hollow truss/Z-pin core comprising a three-dimensional (3-D) open network of titanium pins and a foam core reinforced with a 3-D arrangement of titanium pins have been considered in conjunction with traditional foam core sandwich composites. These innovative core designs have the potential to enhance the impact damage resistance, and provide damage containment mechanisms and space/core accessibility advantages. The top and bottom facesheets in all three types of sandwich constructions are made from 16 layers of E-glass/epoxy prepregs stacked in crossly orientation. The low-velocity impact response of the composites is studied at five energy levels, ranging from I 1 to 40 J. with an intention of investigatin the damage initiation, damage propagation and failure mechanisms. The influence of spacing the Z-pins in a foam core has also been studied at the same five energy levels. Detailed microscopic inspection has been conducted to determine the impact failure characteristics of the three types of sandwich composites. For the energy levels considered, the results demonstrate that by reinforcing the foam cells with Z-pins, low-velocity impact damage is contained effectively and is limited to the localized dimensions of the core and facesheet that lie within a pin cluster dimension.
Geometric continuum mechanics
Meccanica
49
1
111-133
2014
10.1007/s11012-013-9777-9
Geometric Continuum Mechanics ( GCM) is a new formulation of Continuum Mechanics ( CM) based on the requirement of Geometric Naturality ( GN). According to GN, in introducing basic notions, governing principles and constitutive relations, the sole geometric entities of space-time to be involved are the metric field and the motion along the trajectory. The additional requirement that the theory should be applicable to bodies of any dimensionality, leads to the formulation of the Geometric Paradigm ( GP) stating that push-pull transformations are the natural comparison tools for material fields. This basic rule implies that rates of material tensors are Lie-derivatives and not derivatives by parallel transport. The impact of the GP on the present state of affairs in CM is decisive in resolving questions still debated in literature and in clarifying theoretical and computational issues. As a consequence, the notion of Material Frame Indifference ( MFI) is corrected to the new Constitutive Frame Invariance ( CFI) and reasons are adduced for the rejection of chain decompositions of finite elasto-plastic strains. Geometrically consistent notions of Rate Elasticity ( RE) and Rate Elasto-Visco-Plasticity ( REVP) are formulated and consistent relevant computational methods are designed.
Continuum mechanics; Frame Invariance; Integrability; Lie derivatives; Rate-Elasticity; Rate-Visco-Elasto-Plasticity
Quantum statistical mechanics and class field Theory
New York
1-9
2007
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be realized in terms of the structure of equilibrium states of a quantum statistical mechanical system.
explicit class field theory; number field; phrases; quantum statistical mechanics
Base plate mechanics of the barnacle Balanus amphitrite (=Amphibalanus amphitrite).
Biofouling
24
2
109-18
2008
10.1080/08927010701882112
The mechanical properties of barnacle base plates were measured using a punch test apparatus, with the purpose of examining the effect that the base plate flexural rigidity may have on adhesion mechanics. Base plate compliance was measured for 43 Balanus amphitrite (=Amphibalanus amphitrite) barnacles. Compliance measurements were used to determine flexural rigidity (assuming a fixed-edge circular plate approximation) and composite modulus of the base plates. The barnacles were categorized by age and cement type (hard or gummy) for statistical analyses. Barnacles that were 'hard' (> or =70% of the base plate thin, rigid cement) and 'gummy' (>30% of the base plate covered in compliant, tacky cement) showed statistically different composite moduli but did not show a difference in base plate flexural rigidity. The average flexural rigidity for all barnacles was 0.0020 Nm (SEM +/- 0.0003). Flexural rigidity and composite modulus did not differ significantly between 3-month and 14-month-old barnacles. The relatively low flexural rigidity measured for barnacles suggests that a rigid punch approximation is not sufficient to account for the contributions to adhesion mechanics due to flexing of real barnacles during release.
Adhesiveness; Animals; Biological; Biomechanical Phenomena; Larva; Larva: growth & development; Models; Surface Properties; Thoracica; Thoracica: growth & development
Torsion of Open and Closed Thin-Walled Laminated Composite Sections
Journal of Composite Materials
39
6
497-524
2005
10.1177/0021998305047097
Vlasov’s theory is expanded to perform the linear analysis of open\nand closed sections made of general laminated composites. Following\nthe guidelines of Mechanics of Laminated Beams, the transverse shear\ndeformations are included in the formulation. To overcome the overestimation\nof stiffness by the often assumption of negligible tangential stress,\nthe laminate resultant force and moment are instead set to zero in\nthis paper. The present model accounts for all possible elastic couplings\nin composite sections, such as extension- and bending-torsion. Applications\nof the formulation to flanged and box sections are presented and\nguidelines are provided on how to evaluate the torsional stiffness\ncoefficients of the beam. A general solution for a fixed composite\nbeam under tip torsional loads is derived, and the steps can be used\nto derive solutions for any other boundary conditions. The effect\nof warping-torsion on the torsional stiffness of the beam is investigated.\nComposite beams were tested in torsion and the angle of twist and\nshear strains were measured for verification of the analytical model\npredictions, which agree closely with the experimental results and\nfinite element results.
Interfacial characterization of 2D woven SiC/SiC and cross-ply 0°/90° CAS/SiC composites
Composites Part A: Applied Science and Manufacturing
27
9 PART A
787-792
1996
A study has been made on the micromechanical behaviour of the interfaces present in two silicon carbide fibre (Nicalon) reinforced ceramic matrix composites: a cross-ply 0°/90° composite with a calcium-aluminium silicate (CAS) glass matrix and a 2D woven composite with a chemical vapour infiltrated silicon carbide matrix. The interfacial properties were determined from fibre push-down tests performed with a nano-indentation system. Several micromechanical models have been fitted to the experimental data to obtain the interfacial mechanical parameters of sliding resistance, debond energy and residual stress. For both materials, the validity of the assumptions of these models is discussed.
Calcium aluminium silicate glass matrix; Ceramic matrix composites; Characterization; Chemical vapour infiltrated silicon carbide matrix; Debond energy; Fiber push down tests; Fibre push-down tests; Glass; Interfaces; Interfaces (materials); Mathematical models; Mechanical properties; Mechanical testing; Micromechanical behaviour; Micromechanical models; Nano indentation system; Physical properties; Residual stresses; Silicon carbide fibre reinforced ceramic matrix co; Sliding resistance
Effect of ply thickness on longitudinal splitting and delamination in graphite/epoxy under compressive cyclic load
Composite Materials: Fatigue and Fracture
335-360
1986
The initiation and growth of damage due to compressive cyclic loading was investigated in left bracket plus or minus 45//n/0//n right bracket //s graphite/epoxy laminates where the 'effective ply thickness' was varied by allowing n to take on the values 1, 2, and 3. A total of 35 axially loaded sandwich specimens with 6. 35-mm-diameter holes were cycled at 7 Hz at peak stress levels of 52% to 72% of the static ultimate compressive stress of 425 MPa (which was experimentally determined to be independent of the value of n). Out-of-plane moire interferometry and pulse-echo ultrasound techniques were used to nondestructively inspect the specimens and showed that three distinct modes of damage growth occur in these laminates.
INTERFEROMETRY; NONDESTRUCTIVE EXAMINATION; PLASTICS LAMINATES; SANDWICH STRUCTURES - Testing
ENERGY BALANCE METHOD FOR PREDICTING CRACKING IN CROSS-PLY LAMINATES DURING BEND DEFORMATION
ICF10, Honolulu, Hawaii - 2001
2001
Microstructural damage in composite structures arising from the application of mechanical and/or thermal loads is often unavoidable and its effects need to be taken into account when assessing structural performance, especially the occurrence of ply crack formation and delamination. For structures subject to fatigue loading it is desirable to avoid damage occurrence of any kind as it can act as nucleation sites for the growth of macroscopic damage (e.g. delaminations) that eventually leads to the catastrophic failure of the structure. As many structures experience some form of bend deformation during service it is vital that damage formation in the presence of bending is well understood. Of particular relevance to the performance of structures is the prediction of the occurrence of microstructural damage in complex loading modes where out-of-plane bending modes of deformation occur in conjunction with in-plane biaxial and through-thickness loading.
Low velocity impact properties of intra-ply hybrid composites based on basalt and nylon woven fabrics
Materials & Design
31
8
3835-3844
2010
DOI 10.1016/j.matdes.2010.03.033
In this paper, the low velocity impact behavior of homogenous and hybrid composite laminates reinforced by basalt-nylon intra-ply fabrics was experimentally investigated. Epoxy resin was used as matrix material. The purpose of using this hybrid composite is to combine the good mechanical properties of basalt fiber with the excellent impact resistant of nylon fiber. Five different types of woven fabrics were used as reinforcement with different volume percentages of nylon (0%, 25%, 33.3%, 50% and 100%). The effect of nylon/basalt fiber content on maximum force, maximum deflection, residual deflection, total absorbed energy, elastic energy, size and type of damage were studied at several low velocity impact nominal energy levels (16, 30 and 40J). The results indicate that impact performance of these composites is significantly affected by the nylon/basalt fiber content. The visual inspection and ultrasonic C-scan of the impact damaged specimens reveals that content of nylon/basalt fiber controls the type and size of damage. (C) 2010 Elsevier Ltd. All rights reserved.
behavior; carbon; composites; compression; fabric; fiber composites; glass; impact; performance; plates; reinforcement; stress-concentrations; tensile
Manufacturing and Mechanical Evaluation of HRBP/PPTA Intra-Ply Hybrid Nonwovens for Protecting Cushioning Composites
Advanced Materials Research
910
254-257
2014
10.4028/www.scientific.net/AMR.910.254
In this study, high-resilience bonding polyester/Poly-paraphenylene terephthalamid intraply hybrid nonwovens with various fiber blending ratios and thermal treatment conditions were prepared through needle-punching and thermal-bonding. The mechanical characteristics including tensile strength, tear strength, puncture resistance and bursting strength were investigated. The results showed that the addition of Kevlar fibers enhanced the mechanical properties of hybrid nonwovens. The tensile strength, puncture resistance and bursting strength also improved with the increase in thermal treatment duration and temperature while the tear strength had lower strength when treated at 180°C than at 170°C. The reason was thermal bonding points restricted the slippage of the fibers leading the fibers to break in sequence instead of sustaining the tension together. © (2014) Trans Tech Publications, Switzerland.
Bursting strength; Intra-ply; Puncture resistance; Thermal-bonding
Bending response of cross-ply laminated composite plates with diagonally perturbed localized interfacial degeneration.
The Scientific World Journal
350890
2013
10.1155/2013/350890
A laminated composite plate element with an interface description is developed using the finite element approach to investigate the bending performance of two-layer cross-ply laminated composite plates in presence of a diagonally perturbed localized interfacial degeneration between laminae. The stiffness of the laminate is expressed through the assembly of the stiffnesses of lamina sub-elements and interface element, the latter of which is formulated adopting the well-defined virtually zero-thickness concept. To account for the extent of both shear and axial weak bonding, a degeneration ratio is introduced in the interface formulation. The model has the advantage of simulating a localized weak bonding at arbitrary locations, with various degeneration areas and intensities, under the influence of numerous boundary conditions since the interfacial description is expressed discretely. Numerical results show that the bending behavior of laminate is significantly affected by the aforementioned parameters, the greatest effect of which is experienced by those with a localized total interface degeneration, representing the case of local delamination.
On the enhancement of impact damage tolerance of composite laminates
Composites Engineering
3
5
383-394
1993
10.1016/0961-9526(93)90076-V
This paper examines the use of a thin layer of Ultra High Molecular Weight Polyethylene (UHMWPE) on the outer surface of carbon/epoxy composite materials as a method of improving impact resistance and damage tolerance through hybridization. Flat 16-ply laminates as well as honeycomb sandwich structures with eight-ply facesheets were tested in this study. Instrumented drop-weight impact testing was used to inflict damage upon the specimens. Evaluation of damage resistance included instrumented impact data, visual examination, C-scanning and compression after impact (CAI) testing. The results show that only one lamina of UHMWPE did not improve the damage tolerance (strength retention) of the 16-ply flat laminate specimens or the honeycomb sandwich beams, however, a modest gain in impact resistance (detectable damage) was found for the honeycomb sandwich specimens that contained an outer layer of UHMWPE.
Nonlinear wave mechanics
Annals of Physics
100
1-2
62-93
1976
10.1016/0003-4916(76)90057-9
Nonlinear wave mechanics is constructed, based on Schrödinger-type equation with nonlinearity −bψ ln | ψ |2. This nonlinearity is selected by assuming the factorization of wavefunctions for composed systems. Its most attractive features are: existence of the lower energy bound and validity of Planck's relation E = h̵ω. In any number of dimensions, soliton-like solutions (gaussons) of our equation exist and move in slowly varying fields like classical particles. The Born interpretation of the wavefunction is consistent with logarithmic nonlinearity and we tentatively estimate the order of magnitude of the universal constant b.
Wave mechanics of breakdown
Journal of Fluid Mechanics
56
04
775
2006
10.1017/S0022112072002654
Kinematic wave theory is used to determine under what conditions breakdown of a steady or unsteady laminar flow into high frequency oscillations should occur. The analysis of a small-scale secondary wave riding on a large- scale inhomogeneity, such as that produced by a finite amplitude primary instability wave, reveaos that the breakdown mechanism has three basic ingredients: (i) a self-excited secondary wave with a group velocity near the propagation velocity (phase velocity) of the primary wave, (ii) space- time focusing of the secondary wave train of the primary wave crest and (iii) a nonlinear filtering mechanism leading to rectification of the secondary wave (25 Refs.)
Quantum Mechanics and Computation
Foundations of Science
9
4
387-404
2004
10.1007/s10699-005-4827-y
In quantum computation non classical features such as superposition states and entanglement are used to solve problems in new ways, impossible on classical digital computers.We illustrate by Deutsch algorithm how a quantum computer can use superposition states to outperform any classical computer. We comment on the view of a quantum computer as a massive parallel computer and recall Amdahls law for a classical parallel computer. We argue that the view on quantum computation as a massive parallel computation disregards the presence of entanglement in a general quantum computation and the non classical way in which parallel results are combined to obtain the final output.
algorithm; law; quantum computation; quantum mechanics; States
Delamination identification of cross-ply graphite/epoxy composite beams using electric resistance change method
Journal of Composite Science and Technology
62
629-639
2002
10.1016/S0266-3538(02)00013-1
Detection of delaminations is a difficult task for visual inspections. Difficulty of detection underlines the importance of development of smart structures for monitoring delaminations of graphite/epoxy laminated composites. This study employs an electric resistance change method for identification of delamination location and size; applicability of the method is investigated experimentally using beam-type specimens fabricated from cross-ply laminates. On the specimen surface, multiple electrodes are mounted by co-curing copper foil to measure electric resistance changes. Interlamina shear tests are conducted to create a practical delamination crack in a beam-type specimen. Five beam specimen types were made and tested. A large number of tests were conducted to obtain a data set for solving inverse problems to estimate delamination location and size from measured electric resistance changes. Response surfaces are employed for a solver of inverse problems instead of well-known artificial neural networks. As a result, the method successfully identifies delamination location and size for these beam type specimens. To obtain practically efficient estimation performance, at least five electrodes are indispensable for these beam type specimens. # 2002 Elsevier Science Ltd. All rights reserved.
Disc-like angle-ply structures for intervertebral disc tissue engineering and replacement.
U.S. Pat. Appl. Publ.
US20110098826A1
34pp.
2011
Provided are implant scaffolds comprising angle-ply arrays of two or more layers of substantially aligned fiber, methods of making and using said scaffolds, and kits comprising such scaffolds. Thus, aligned nanofibrous scaffolds were generated via electrospinning; briefly, poly(ε-caprolactone) were dissolved at 143 mg/mL in equal parts THF and N,N-dimethylformamide, then extruded at 2.5 mL/h through a spinneret charged to 13 kV; the resulting nanofibrous jet was collected on a grounded mandrel rotating at 10 m/s and located 20 cm from the spinneret; aluminum shields on either side of the spinneret were charged to +9 kV to focus the jet; the spinneret was fanned back and forth to ensure uniform fiber deposition; mats of ca. 250 μm thickness were electrospun to match the natural lamellar thickness of the annulus fibrosus. [on SciFinder(R)]
Process technology and mechanical properties of polylactic acid ply yarns and 316L stainless steel braids
Advanced Materials Research
287-290
2656-2659
2011
Biodegradable polymer has been widely used in surgical suture, dressing, artificial bone and other bone-related applications. However, when compared with the human cortical bone, the pure polymer obviously did not have enough strength. The present study aimed to give preliminary insights from a pilot study of designing a scaffold of polylactic acid ply yarns composited with stainless steel (SS) braids. To evaluate the fabrication processes and alkali effects on the individual materials, the different heating temperature and alkali treating time and alkali concentration were applied to clarify the changes in mechanical strength. The experimental results showed that the strength was not significant declined with alkali and heating treatments. The retained mechanical strength was kept at 100-120 MPa and ultimately led to bone-like mechanical properties. © (2011) Trans Tech Publications.
316 L stainless steel; 316L stainless steel; Alkali concentrations; Alkali effects; Alkali treating; Artificial bone; Artificial bones; Biodegradable polymers; Bone; Braid; Corrosion resistant alloys; Fabrication process; Heating; Heating temperatures; Heating treatments; Human cortical bone; Mechanical properties; Pilot studies; Polylactic acid; Process Technologies; Pure polymers; Scaffolds; Stainless steel; Surgical sutures; Weaving
Effect of fibre waviness on compression failure of cross-ply carbon/epoxy laminates
Trends in Advanced Materials and Processes
352
189-194
2000
Composites were made as cross-ply laminates with artificially introduced waviness near the middle, with different severity of waviness and different fractions of wavy layers. The laminates had configuration (0/(90 0(2))(n) /core/ (0(2) 90)(n)/ 0) with n = 2, 4, and 6 in samples with 24, 36, and 48 layers respectively. The fraction of wavy layers varied from 6 to 37%, and the severity of waviness, measured as the ratio of amplitude over half wavelength - 2a/lambda, varied from 0.03 to 0.08, which corresponded to the angular deviations from 7 to 14 degrees. The composites were tested in compression to determine the effect of wave severity and fraction of wavy layers on compression strength. Failure of tested coupons was examined to establish the mechanism of fracture initiation and propagation. Two compression failure mechanisms were observed.
carbon/epoxy laminates; composites; compression failure; compression strength; wavy layers
Vibration of axisymmetric shear deformable cross-ply laminated cylindrical shells - A variational approach
International journal of engineering science
36
3
219-231
1998
10.1016/s0020-7225(97)00076-1
A free vibration analysis of axisymmetric shear deformable laminated circular cylindrical shells is presented. A third-order shear deformation theory of elastic shells is developed and its application is presented for circular cylindrical shells laminated of orthotropic layers. The effects of inplane deformation and inertia, shear deformation and rotatory inertia are all included. Maupertuis-Lagrange (M-L) mixed variational formula is utilized to formulate the governing equations. Analytical solutions for simply-supported, clamped and free boundary conditions are also developed. Numerical results of the third-order theory for natural frequencies of cross-ply laminated circular cylindrical shells are compared with those obtained using the classical and first-order shell theories. The effects due to shear deformation, boundary conditions, lamination schemes, mode number and material anisotropy on the natural frequencies are investigated. The sample numerical results presented herein for free vibration analysis of axisymmetric shear deformable laminated circular cylindrical shells should serve as references for future comparisons. (C) 1998 Elsevier Science Ltd. All rights reserved.
Indices in classical mechanics
Journal of Physics A: Mathematical and General
24
18
4335-4348
1991
10.1088/0305-4470/24/18/020
The authors discuss the linearization of the equations of motion around a periodic orbit in a\r conservative two degree of freedom Hamiltonian system, with an emphasis on computationally useful\r formulae. Indices are defined using singularities in projections. Conjugate points, self-conjugate\r points and the possibility of assigning a symbolic code are discussed.
Quantum mechanics of baryogenesis
Physics Letters B
483
1-3
217-224
2000
10.1016/S0370-2693(00)00573-6
The cosmological baryon asymmetry can be explained as remnant of heavy Majorana neutrino decays in the early universe. We study this out-of-equilibrium process by means of Kadanoff-Baym equations which are solved in a perturbative expansion. To leading order the problem is reduced to solving a set of Boltzmann equations for distribution functions.
Fracture Mechanics: Fundamentals and Applications
Aerospace Engineering
2
688
1995
With its combination of practicality, readability, and rigor that is characteristic of any truly authoritative reference and text, Fracture Mechanics: Fundamentals and Applications quickly established itself as the most comprehensive guide to fracture mechanics available. It has been adopted by more than 100 universities and embraced by thousands of professional engineers worldwide. Now in its third edition, the book continues to raise the bar in both scope and coverage. It encompasses theory and applications, linear and nonlinear fracture mechanics, solid mechanics, and materials science with a unified, balanced, and in-depth approach.Reflecting the many advances made in the decade since the previous edition came about, this indispensable Third Edition now includes: A new chapter on environmental cracking Expanded coverage of weight functions New material on toughness test methods New problems at the end of the book New material on the failure assessment diagram (FAD) method Expanded and updated coverage of crack closure and variable-amplitude fatigue Updated solutions manualIn addition to these enhancements, Fracture Mechanics: Fundamentals and Applications, Third Edition also includes detailed mathematical derivations in appendices at the end of applicable chapters; recent developments in laboratory testing, application to structures, and computational methods; coverage of micromechanisms of fracture; and more than 400 illustrations. This reference continues to be a necessity on the desk of anyone involved with fracture mechanics.
Structural forms of green fluorescent protein by quantum mechanics/molecular mechanics calculations
Russian Chemical Bulletin
59
1
61-65
2010
DOI 10.1007/s11172-010-0045-z
The molecular modeling of structural forms of the green fluorescent protein (GFP) with the Ser65Thr single-site mutation was performed by the quantum mechanics/molecular mechanics (QM/MM) method. Two model systems were constructed based on the crystallographic structure from the Protein Data Bank (PDB entry code 1EMA.) The model systems differ in the initial protonation state of the side chain of the amino acid residue Glu222 near the chromophore. The atomic coordinates of the protein macromolecule corresponding to the equilibrium geometric configurations were determined by total energy minimization using the QM/MM method within the density functional theory approximation PBE0/cc-pVDZ for the quantum subsystem that consists of the chromophore, a water molecule, and the side chains of Arg96, Glu222, and Ser205, and with the parameters of the AMBER force field for the molecular mechanics subsystem. In the analysis of the results, particular attention was given to the hydrogen bond redistribution in the chromophore-containing region of the protein caused by a change in the protonation state of the chromophore. The results obtained from the model containing the initially protonated side chain of Glu222 suggest a new interpretation of the photophysical processes in the green fluorescent protein.
absorption-spectra; asfp595; environment; excited-state dynamics; gfp chromophore; green fluorescent protein; hybrid quantum mechanics/molecular mechanics metho; molecular modeling; operation; proton-transfer; simulation; wire
Higher order mechanics on graded bundles
Journal of Physics A: Mathematical and Theoretical
48
20
205203
2015
10.1088/1751-8113/48/20/205203
Options for access to Higher order mechanics on graded bundles
Quantum mechanics: last stop for reductionism
arXiv
2
2012
The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.
Advances in Fluid Mechanics V; Proceedings
Sci-Tech News
58
4
43
2004
Reviews the book "Advances in Fluid Mechanics V: Proceedings," edited by M. Rahman et al.
ADVANCES in Fluid Mechanics V: Proceedings (Book); BOOKS -- Reviews; NONFICTION; RAHMAN, M.
{Transition probability and interference in stochastic mechanics}
Physical Review A
38
10
5401-5403
1988
10.1103/PhysRevA.38.5401
{A functional-integral expression for the stochastic-mechanics transition probability is obtained. The form of this transition probability indicates that; contrary to the general consensus; interference plays an essential role in the evolution of the probability density in stochastic mechanics.}
Journal of the Mechanics and Physics of Solids The bimodal theory of plasticity : A form-invariant generalisation
Journal of the Mechanics and Physics of Solids
59
8
1576-1595
2011
10.1016/j.jmps.2011.04.019
The bimodal plasticity model of fibre-reinforced materials is currently available and applicable only in association with thin-walled fibrous composites containing a family of straight fibres which are conveniently assumed parallel with the x1-axis of an appropriately chosen Cartesian co-ordinate system. Based on reliable experimental evidence, the model suggests that plastic slip in the composite operates in two distinct modes; the so-called matrix dominated mode (MDM) which depends on a matrix yield stress, and the fibre dominated mode (FDM) which depends also on the fibre yield stress. Each mode is activated by different states of applied stress, has its own yield surface (or surfaces) in the stress space and has its own segment on the overall yield surface of the composite. This paper employs theory of tensor representations and produces a form-invariant generalisation of both modes of the model. This generalisation furnishes the model with direct applicability to relevant plasticity problems, regardless of the shape of the fibres or the orientation of the co-ordinate system. It thus provides a proper mathematical foundation that underpins important physical concepts associated with the model while it also elucidates several technical relevant issues. A most interesting of those issues is the revelation that activation of the MDM plastic regime is possible only if the applied stress state allows the fibres to act like they are practically inextensible. Moreover, activation of the more dominant, among the two MDM plastic slip branches is possible only if conditions of material incompressibility hold, in addition to the implied condition of fibre inextensibility. A direct mathematical connection is thus achieved between basic, experimentally verified concepts of the bimodal plasticity model and a relevant mathematical model originated earlier from the theory of ideal fibre-reinforced materials. An additional issue of discussion involves the number of independent yield stress parameters that the bimodal theory needs to take into consideration. Moreover, an analytical expression is provided of a relatively simple mathematical surface that possesses all known features of the FDM yield surface; currently captured with the aid of both experimental and computational means. The present study is guided by the existing relevant experimental evidence which, however, is principally associated with the plastic behaviour of solids reinforced by strong fibres. Nevertheless, several of the outlined developments are expected to be applicable to composite materials containing a single family of more compliant or even weak fibres.
Bimodal theory; Fibre-reinforced materials; Plasticity; Thin-walled composites; Yield surfaces
Fracture behavior of thin-walled Zircaloy fuel clad tubes of Indian pressurized heavy water reactor
International Journal of Fracture
173
2
175-188
2012
DOI 10.1007/s10704-012-9678-2
For structural integrity analysis of thin walled tubular components such as fuel claddings used in nuclear reactors, knowledge of valid fracture mechanics parameters are required. As axially-cracked thin tubes possess a non-standard geometry from the point of view of specimen fabrication, there is no direct straight forward way to derive their fracture mechanics parameters with known functions as can be done for standard test methods. In the present work, the J-R curve for an axially cracked fuel pin from Indian 220 MWe pressurized heavy water reactor is derived after experimental and analytical derivation of the required parameters and the results are compared with earlier published data for similar material.
embrittlement; fuel cladding tube; indian phwr; j-r curve; j-r curves; load normalization technique; load separation; mechanical-properties; normalization method; sra zircaloy-4; temperature; tension; tests; toughness; zirconium alloys
Introduction to Quantum Mechanics
arXiv
math-ph
2008
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
81Q; math.MP; math-ph
Effect of surface treatment and Z-axis reinforcement on the interlaminar fracture of jute/epoxy laminated composites
Engineering Fracture Mechanics
114
104-114
2013
10.1016/j.engfracmech.2013.10.015
This study examines the effects of preform architecture, surface treatment, and z-directional micro-fiber reinforcement on the interlaminar fracture performance of jute/epoxy laminated composites. Laminated composites were fabricated using an optimized vacuum infusion process. Fracture characterization studies showed surface treatments increased fracture toughness as a result of improved interfacial adhesion. Unidirectional preforms were found to decrease fracture toughness as compared to plain weave preforms due to reduced inter-ply interaction. The addition of z-direction reinforcement increased the composites' Mode-I fracture toughness by 80% and increased interlaminar shear strength (ILSS) at the cost of decreased tensile strength and modulus. © 2013 Elsevier Ltd. All rights reserved.
jute fiber composite; z -axis reinforcement
Advances in Wind Turbine Blade Design and Materials
Advances in Wind Turbine Blade Design and Materials
251-297
2013
10.1533/9780857097286.2.251
Fatigue life prediction of wind turbine rotor blades is a very challenging task, as blade failure is led by different failure types that act synergistically. Inherent defects like wrinkles, fiber misalignments and voids, that can be introduced during fabrication, can constitute potential damage initiation points and rapidly develop to failure mechanisms like matrix cracking, transverse-ply cracking, interface cracking, debonding, fiber breakage, etc. Different methods have been established to address this problem, some based on phenomenological and others on actual damage mechanics modeling. This chapter aims to provide an overview of fatigue life modeling and prediction methodologies for the composite materials and structural composite elements that compose a wind turbine rotor blade under complex loading conditions.
fatigue life prediction; fracture; phenomenological fatigue modeling; residual stiffness; residual strength
MODIFIED BLISTER TESTS FOR EVALUATION OF THIN FLEXIBLE MEMBRANE ADHESION ON RIGID SUBSTRATE
Materials science research international
1
2
78-81
1995
10.2472/jsms.44.501Appendix_78
The blister test geometry commonly used for the measurement of interfacial work of adhesion W has been re-examined and new fracture mechanics analyses are given for thin flexible membranes on rigid substrates in which the stretching deformations are predominant. Two loading configurations are considered. (1)The blister is pressurized under an internal expansion of a fixed mass of working gas. Gere stable crack propagation and multiple measurements per specimen are allowed. (2)The blister is loaded by a shaft at its apex, which also gives stable interface crack propagation. The fracture mechanics analyses are verified with simple experiments using sticky tapes on an aluminium plate based on these two test methods. Additional shaft-loaded blister experiments of nylon 6 films on surface treated aluminium substrates have also been studied and compared to the double cantilever geometry.
Blister test; Debonding; Gas pressure; Shaft-loading; Thin flexible membrane
The High-Energy Interpretation of Quantum Mechanics
Euresis Journal
6
49-61
2013
We address the issue of the interpretation of quantum mechanics by asking why the issue never arises in the description of high-energy interactions. We argue that several tenets of quantum mechanics, specifically the collapse of the wave function, follow directly once one accepts the essential randomness of fundamental interaction events. We then show that scale separation of fundamental interactions ensures that decoherent measurement can be unambiguously separated from the random quantum events. Finally, we argue that the fundamental symmetries of space and time guarantee the existence of a unique preferred basis. We argue that this set of ideas might lead to an interpretation of quantum mechanics, or rather, show in which sense an "interpretation" is (or is not) necessary.
Pulmonary mechanics in lymphangioleiomyomatosis.
The American review of respiratory disease
143
5 Pt 1
1030-3
1991
10.1164/ajrccm/143.5_Pt_1.1030
Standard pulmonary function and mechanics studies were done in eight female patients with lymphangioleiomyomatosis diagnosed by open-lung biopsy. Five patients were studied before hormone treatment. The mean age of the patients was 40 +/- 3 (SEM) years. Two of the eight had a smoking history of 10 pack-years or more, but all had quit smoking several years before evaluation. There was a trend toward increased total lung capacity (114 +/- 7% expressed as mean of percentage predicted +/- SEM) and increased residual volume (207 +/- 24%). Of the eight patients seven had expiratory obstruction as evidenced by the reduced forced expiratory volume in 1 s/forced vital capacity ratio [( FEV1/FVC] 61 +/- 6%). Steady-state diffusing capacity for carbon monoxide was reduced in seven of the patients (57 +/- 12%). Pulmonary mechanics studies performed in a body plethysmograph revealed a modest reduction in retractive force both at total lung capacity and at 90% total lung capacity (67 +/- 10 and 59 +/- 9%, respectively). Static compliance tended to be increased (128 +/- 19%). Pulmonary flow resistance was markedly elevated (266 +/- 46%). Maximal flow-static recoll curves revealed that in the seven patients with expiratory obstruction the cause was predominantly airway narrowing rather than loss of lung elastic forces. We conclude that in this group of patients with lymphangioleiomyomatosis there was no evidence for significant restriction. Although there was some decrease in retractive force consistent with emphysema, expiratory flows were reduced predominantly because of airway narrowing or obstruction rather than loss of pulmonary elastic recoil forces.
Adult; Biopsy; Female; Humans; Lung; Lung Neoplasms; Lung Neoplasms: pathology; Lung Neoplasms: physiopathology; Lung: pathology; Lung: physiopathology; Lung Volume Measurements; Lymphangiomyoma; Lymphangiomyoma: pathology; Lymphangiomyoma: physiopathology; Pulmonary Ventilation; Pulmonary Ventilation: physiology; Respiratory Mechanics; Respiratory Mechanics: physiology
Van der Waals Effects between Hydrogen and First-Row Atoms in Molecular Mechanics (MM3/MM4)
Journal of Computational Chemistry
21
14
1229-1242
2000
10.1002/1096-987X(20001115)21:14<1229::AID-JCC2>3.0.CO;2-9
The van der Waals energy functions used in molecular mechanics have long been known to be reasonably good. However, much recent work suggests that the situation is more complicated than has been earlier assumed. In the present work, various nb initio studies have been carried out, and have been compared with results from experiment and current molecular mechanics data (MM3/MM4) to provide a basis for improving the way molecular mechanics deals with these quantities. (C) 2000 John Wiley & Sons, Inc.
ab initio; alcohols; molecular mechanics; van der waals interactions
Delay time in quaternionic quantum mechanics
Journal of Mathematical Physics
53
2
022102
2012
10.1063/1.3684747
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.
Plasticity in rock mechanics
International Journal of Mechanical Sciences
13
4
291-297
1971
10.1016/0020-7403(71)90054-3
The Coulomb yield condition and its associated flow rule is used to solve the title problem, i.e. what internal supporting forces would be necessary to prevent granular rock from breaking into horizontal, rectangular section coal-mining tunnels. The analysis based upon an upper and lower bound approach, shows several peculiarities so that it could be of interest in itself. 1971.
Quantum Mechanics and the Brain
Spring
75-82
2007
10.1002/qua.560090728
... be- cause we believe they are better evolved to deal more effi- ciently with single - photons than the ... a very low dark-count rate (ie, false signals indicating the presence of a photon when in ... The esti- mated efficiency of the locust eye is about 0.6 (Lillywhite 1977), much higher then ...
Stochastic Computational Fluid Mechanics
Computing in Science and Engineering
9
2
21-29
2007
10.1109/MCSE.2007.38
Stochastic simulations in computational fluid dynamics let researchersmodel uncertainties beyond numerical discretization errors. The authors present examples of stochastic simulations of compressible and incompressible flows and provide analytical solutions for verifying these newly emerging methods for stochastic modeling.
In vivo measurement of bone deformations using strain gauges BT - Bone mechanics handbook
Bone mechanics handbook
8
1-41
2001
Fritton, S. P., and C. T. Rubin. "In vivo measurement of bone deformations using strain gauges." Bone mechanics handbook, 2nd edition. Boca Raton: CRC Press. p (2001): 8-91.
On the enhancement of impact damage tolerance of composite laminates
Composites Engineering
3
5
383-394
1993
This paper examines the use of a thin layer of Ultra High Molecular Weight Polyethylene (UHMWPE) on the outer surface of carbon/epoxy composite materials as a method of improving impact resistance and damage tolerance through hybridization. Flat 16-ply laminates as well as honeycomb sandwich structures with eight-ply facesheets were tested in this study. Instrumented drop-weight impact testing was used to inflict damage upon the specimens. Evaluation of damage resistance included instrumented impact data, visual examination, C-scanning and compression after impact (CAI) testing. The results show that only one lamina of UHMWPE did not improve the damage tolerance (strength retention) of the 16-ply flat laminate specimens or the honeycomb sandwich beams, however, a modest gain in impact resistance (detectable damage) was found for the honeycomb sandwich specimens that contained an outer layer of UHMWPE.
Fracture Mechanics Ch02
Fracture Mechanics
11-24
2012
10.1016/B978-0-12-385001-0.00002-X
The theoretical strength of a solid is usually understood as the applied stress that fractures a perfect crystal of the material by breaking the atomic bonds along the fractured surfaces. The theoretical strength is estimated using the interatomic bonding force versus the atomic separation relation. Failure of a solid is characterized by separation of the body. At the atomistic level, the fracture strength of a “perfect” material depends on the strength of its atomic bonds. In addition, Griffith postulated that all bulk glasses contain numerous minute flaws in the form of microcracks that act as stress concentration generators. This new concept accompanied by the energy release approach that he introduced started the era of modern fracture mechanics. The Griffith theory for fracture of perfectly brittle elastic solids is founded on the principle of energy conservation, that is, energy added to and released from the body must be the same as that dissipated during crack extension.
energy conservation; Griffith theory; single-edge-cracked specimen; strain energy; surface energy; theoretical strength
Stochastic mechanics and quantum interference
Physics Letters A
141
8-9
370-376
1989
10.1016/0375-9601(89)90851-7
It is shown that in the framework of the stochastic interpretation of quantum mechanics it is always possible to determine correct real positive transition probabilities that can be added together to obtain the quantum interference patterns. The implication of this fact on the possibility that quantum micro-objects follow trajectories in space and time is discussed. A derivation is given of a path integral formula yielding these transition probabilities.
Quantum Mechanics and Information Retrieval
Advanced Topics in Information Retrieval
33
125-154
2011
10.1007/978-3-642-20946-8
This chapter aims at providing a survey of the body of scientific literature relevant to Quantum Mechanics (QM) and Information Retrieval (IR). The survey is illustrated with a common notation to fully grasp the contribution of each paper. In particular, the probability aspects of IR and those of QM are emphasized because probability is one of the most important topics of both disciplines.
Mechanics of Pressure Slip Casting
Journal of the American Ceramic Society
55
5
264-268
1972
10.1111/j.1151-2916.1972.tb11277.x
The quantitative mechanics of pressure slip casting an aqueous Al2O3 slip deflocculated with an organic polyelectrolyte were investigated at 50 to 500 psi. The specific resistance, casting rate, and microstructural characteristics of the resultant cakes were especially sensitive to the electrophoretic mobility of the slip. The mechanochemical action of the polyelectrolyte in effecting deflocculation was somewhat different from that of simple ionic electrolytes.
The Light of Quantum Mechanics
Dialectica
52
103
1998
Although classical probability theory, as it is encapsulated in the axioms of Kolmogorov and in his criterion for the independence of two events, can consistently be employed in quantum mechanics, this can only be accomplished at an exorbitant price. By considering first the classic two-slit experiment, and then the passage of one photon through three polarizers, the applicability of Kolmogorov's last axiom is called into question, but the standard rebuff of the Copenhagen interpretation is shown to be adequate to this challenge. (edited)
The Physical Principles of Quantum Mechanics
eprint arXiv:1112.1507
1930
1-27
2011
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.
Quantum Physics
Many-Worlds Interpretation of Quantum Mechanics
Stanford Encyclopedia of Philosophy
Spring
2009
10.1007/978-3-540-70626-7_113
The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.
Everett; quantum mechanics; quantum theory measurement
Fluid Mechanics
Book
17
179-191
2010
10.1111/j.1549-8719.2009.00016.x.Mechanobiology
Endothelial cells are stimulated by shear stress throughout the vasculature and respond with changes in gene expression and by morphological reorganization. Mechanical sensors of the cell are varied and include cell surface sensors that activate intracellular chemical signaling pathways. Here, possible mechanical sensors of the cell including reorganization of the cytoskeleton and the nucleus are discussed in relation to shear flow. A mutation in the nuclear structural protein lamin A, related to Hutchinson-Gilford progeria syndrome, is reviewed specifically as the mutation results in altered nuclear structure and stiffer nuclei; animal models also suggest significantly altered vascular structure. Nuclear and cellular deformation of endothelial cells in response to shear stress provides partial understanding of possible mechanical regulation in the microcirculation. Increasing sophistication of fluid flow simulations inside the vessel is also an emerging area relevant to the microcirculation as visualization in situ is difficult. This integrated approach to study-including medicine, molecular and cell biology, biophysics and engineering-provides a unique understanding of multi-scale interactions in the microcirculation.
Development of engineering mechanics
Journal of Engineering Education
21
6
457-463
1931
History of mechanics with reference to work of men who have either originated or made significant contributions to engineering mathematics. (see also Assn. Chinese and Am. Engrs. -- Jl., vol. 12, no. 4, Apr. 1931, pp. 26-33)
Mechanics
On the Ricci flow and emergent quantum mechanics
J Phys Conf Ser
174
12033
2009
10.1088/1742-6596/174/1/012033
The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential function that is proportional to the Ricci scalar curvature of configuration space. This allows one to obtain Schroedinger quantum mechanics from Perelman's action functional: the quantum-mechanical wavefunction is the exponential of i times the conformal factor of the metric on configuration space. We explore links with the recently discussed emergent quantum mechanics.
{S}tatistical mechanics of unsupervised learning
Europhys. Lett.
24
5
421-426
1993
10.1209/0295-5075/24/5/017
We study two different unsupervised learning strategies for a single-layer\nperceptron. The environment provides a set of unclassified training\nexamples, which belong to two different classes, depending on their\noverlap with an N-dimensional concept vector. By means of a statistical-mechanics\nanalysis, using the replica method, we investigate how well the perceptron\ninfers the unknown structure from the input data.
unsupervised
Computational explosion mechanics and related progress
Chinese Science Bulletin
56
33
3610-3613
2011
10.1007/s11434-011-4796-1
Explosion mechanics is the theoretical basis for the design of highly efficient arms and ammunition and industrial explosion safety. Because it involves the complex physical and mechanical behaviors of multi-materials under extreme conditions, such as high speed, high temperature and high pressure, it is almost impossible to give exact solutions for explosion problems. As explosion occurs in a very short time and has a strong destructive effect, there will be lim- ited amounts of experimental data obtained during the ex- plosion process. With the continuous development of numerical methods and computer performance, computational explosion mechanics has become a new interdisciplinary branch of explosion mechanics, material dynamics, compu- tational mathematics and computer technology, and greatly promoted the development of explosion mechanics and weapons equipment. Since the late 1960s, US-led western developed countries have developed more than one hundred calculation codes of explosion mechanics. Based on the simulation software for explosion mechanics, calculations about three-dimensional physical processes on a system scale during the course of weapon system development have been performed, which resulted in the development of a number of high efficiency arms and ammunition. Such research institutions as the Beijing Institute of Technology, the Chinese Academy of Engineering Physics, the Institute of Applied Physics and Computational Mathematics, the Institute of Mechanics of the Chinese Academy of Sciences, Peking University, the University of Science and Technology of China and other research institutions have developed different numerical methods for explosion mechanics, dynamic constitutive models and software development. Finite Difference Method and Finite Element Method are the most common methods of the discrete methods adopted in computational explosion mechanics. The former is a representative method by which time and space are covered with cells to gain approximate numerical solutions after partial differential equations (governing equations) are established. The latter is a representative method by which continuous space is decomposed into finite elements. Classed by coordinates, Eulerian method and Lagrangrian Method are two common methods utilized in computational explosion mechanics.
Description of many separated physical entities without the paradoxes encountered in quantum mechanics
Foundations of Physics
12
12
1131-1170
1982
10.1007/BF00729621
Abstract We show that it is impossible in quantum mechanics to describe two separated physical systems. This is due to the mathematical structure of quantum mechanics. It is possible to give a description of two separated systems in a theory which is a generalization of quantum mechanics and of classical mechanics, in the sense that this theory contains both theories as special cases. We identify the axioms of quantum mechanics that make it impossible to describe separated systems. One of these axioms is equivalent to the superposition principle. We show how these findings throw a different light on the paradox of Einstein, Podolsky, and Rosen.
Stability and dynamics of thin heated liquid films
International Journal of Fluid Mechanics Research
25
3
449+
1990
Some applications of the dynamical theory of thin liquid films on\na solid surfaces, subject to heat transfer, are presented. Thermocapillary\nand vapor recoil effects are destabilizing, while hydrostatic pressure\nand surface tension effects tend to stabilize the film. Gravitational\nsurface waves promote wave steepening and possible wave breaking.\nThe growth of nonlinear waves may result in equilibration and "permanent"\ntwo-dimensional waves, which can, however, be destroyed by secondary\nwave growth in the transverse direction. The phenomena which are\nfound include downwards fingering, which may lead to local dryout,\nand the formation of longitudinal rolls, which may lead to rivulet\nformation on a heated surface.
bankoff
Polygonal manifold element for thin plate-bending analysis
Gongcheng Lixue/Engineering Mechanics
29
10
249-256
2012
A triangular or rectangular element was used for the numerical computation\nin a general numerical manifold method (NMM). For many practical\nproblems, a polygonal element can adjust to the complicated configuration\nof a computational domain easily, hence a polygonal manifold element\nis analyzed for numerical computation. The convex polygonal mesh\nfor a manifold element is constructed based on a Delaunay triangulation\nmesh. An improved Wachspress shape function is used as a weight function\nof the numerical manifold method. The validity of the proposed numerical\nmanifold method is illustrated by the analysis of a thin plate bending\nproblem. Numerical manifold formulas and element matrices are also\nderived for the numerical example. The results show that this method,\ncompared with the finite element method, can improve accuracy and\nconvergence greatly.
Finite element method;
General thin rod model for preslip bending response of strand
JOURNAL OF ENGINEERING MECHANICS-ASCE
126
2
132-139
2000
10.1061/(ASCE)0733-9399(2000)126:2(132)
A general discrete thin rod model to study the preslip response of a\nstrand of helical wires having wires-to-core friction contacts under\nconstant curvature free bending has been developed for the case of\nCoulomb stick friction that considers together (a) all the three wire\nforces and three wire couples; (b) more appropriate equations for the\nwire shear forces; (c) the wire normal force as one of the contributors\nto strand bending moment; (d) wire external equilibrium; and (e) wire\nrolling with or without zero net shear on the strand cross section. The\nindividual contributions of wire forces and couples to the strand\nbending moment for 10 models including EPRI model are compared. Several\nearlier models are shown to be special cases of the present general\nmodel.
The irreversibility and classical mechanics laws
Physics
9
2004
The irreversibility of the dynamics of the conservative systems on example of hard disks and potentially of interacting elements is investigated in terms of laws of classical mechanics. The equation of the motion of interacting systems and the formula, which expresses the entropy through the generalized forces, are obtained. The explanation of irreversibility mechanism is submitted. The intrinsic link between thermodynamics and classical mechanics was analyzed.
Statistical Mechanics
Do We Understand Quantum Mechanics-Finally?
arXiv preprint arXiv:1203.3678
42
2012
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator algebras. We then review some basic aspects of quantum mechanics and, in particular, of its interpretation. We attempt to clarify what Quantum Mechanics tells us about Nature when appropriate experiments are made. We discuss the importance of the mechanisms of "dephasing" and "decoherence" in associating "facts" with possible events and rendering complementary possible events mutually exclusive.
Quantum Mechanics as a Complete Physical Theory
Theoretical and Mathematical Physics
132
3
1264-1276
2002
10.1023/A:1020272121372
We show that the principles of a complete physical theory and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that allow constructing a renewed mathematical scheme of quantum mechanics. This scheme involves the standard mathematical formalism of quantum mechanics. Simultaneously, it contains a mathematical object that adequately describes a single experiment. We give an example of the application of the proposed scheme.
Vehicle traction mechanics
Soil and Tillage Research
7
369-370
1986
10.1016/0167-1987(86)90024-3
The fundamental problem in the study of vehicle mobility is the development of traction between the vehicle and the supporting terrain. The mechanics of energy transfer will essentially control the final performance of the surficial machine. Determining and predicting the capability of a particular piece of machinery to traverse successfully a specific piece of terrain is very complex, particularly as the characteristics and properties of different types of terrain cover vary considerably, as do the many types of vehicle and their running gear. The material that forms the basis of this book has been gathered over many years of study both in the laboratory and in the field. It studies vehicle traction mechanics from the viewpoint of the interaction between the vehicle and the ground surface. The types of machines covered include earth-moving, forestry, agricultural, and construction machines. In addition, the mechanisms involved in the development of traction and the working of the terrain through cultivation, construction and surface disturbances are examined. The book also addresses the problems of off-road mobility and terrain trafficability, especially from the terrain-support and terrain interaction points of view. It is the authors' aim that the book will provide the reader with the ability to both analyze and predict the traction capability of his proposed machinery, and also to anticipate the kinds of reactions that will occur in the ground and at the ground surface.
Universal quantum mechanics
Physical Review D
78
8
15
2007
If gravity respects quantum mechanics, it is important to identify the essential postulates of a quantum framework capable of incorporating gravitational phenomena. Such a construct likely requires elimination or modification of some of the "standard" postulates of quantum mechanics, in particular those involving time and measurement. This paper proposes a framework that appears sufficiently general to incorporate some expected features of quantum gravity. These include the statement that space and time may only emerge approximately and relationally. One perspective on such a framework is as a sort of generalization of the S-matrix approach to dynamics. Within this framework, more dynamical structure is required to fully specify a theory; this structure is expected to lack some of the elements of local quantum field theory. Some aspects of this structure are discussed, both in the context of scattering of perturbations about a flat background, and in the context of cosmology.
A Multiscale Failure Model for Analysis of Thin Heterogeneous Plates
International Journal of Damage Mechanics
19
5
575-610
2009
10.1177/1056789509104729
This manuscript presents a new multiscale framework for the analysis of failure of thin heterogeneous structures. The new framework is based on the asymptotic homogenization method with multiple spatial scales, which provides a rigorous mathematical basis for bridging the microscopic scales associated with the periodic microstructure and thickness, and the macroscopic scale associated with the in-plane dimensions of the macrostructure. The proposed approach generalizes the Caillerie—Kohn—Vogelius elastostatic heterogeneous plate theory for failure analysis when subjected to static and dynamic loads. Inelastic fields are represented using the eigendeformation concept. A computationally efficient n-partition computational homogenization model is developed for simulation of large scale structural systems without significantly compromising on the solution accuracy. The proposed model is verified against direct 3D finite element simulations and experimental observations under static and dynamic loads.
Bending and Buckling of Thin-Walled Open-Section Rings
Journal of the Engineering Mechanics Division
89
5
17-44
1963
The Wagner theory for the bending and buckling of straight bars of thin-walled open section is extended to circular curved bars and rings. The differential equations of equilibrium are determined by a summation of force components, whereas the natural boundary conditions are derived by the minimum potential energy principle. The effects of nonuniform torsion, unsymmetrical loading, elastic foundation, and axial extension are included. The buckling of a ring subjected to a uniform external pressure is treated. The critical pressure is found to be the root of a cubic characteristic equation. Simplified solutions are found by restricting the generality, thereby reducing the characteristic equation to the first order.
Bending; Buckling; Rings
Relativistic Quantum Mechanics and Field Theory
Foundations of Physics
34
3
33
2004
10.1023/B:FOOP.0000019625.30165.35
The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality property and the gauge invariance encoded in the Gauss' law is discussed in connection with the various quantization choices for gauge fields
Bending analysis of thin functionally graded plates using generalized differential quadrature method
Archive of Applied Mechanics
81
11
1523-1539
2011
DOI 10.1007/s00419-010-0499-3
In this paper, the differential quadrature (DQ) method is presented for easy and effective analysis of isotropic functionally graded (FG) and functionally graded coated (FGC) thin plates with constant Poisson's ratio and varying Young's modulus in the thickness direction. The bending of FG and FGC plates under transverse loading has been studied using the polynomial differential quadrature (PDQ) and the harmonic differential quadrature (HDQ) methods. A three-dimensional elasticity solution for a moderately thick FG plate with exponential Young's modulus is used as the benchmark. Two examples, including a thin FG rectangular plate and a thin FGC rectangular plate with sigmoidal Young's modulus, are investigated. The numerical results of PDQ and HDQ methods reveal good agreement with other solutions. Also, it is shown that the formulations for thin FG plates and homogeneous plates are similar, except that the plane strain components of the middle surface in FG plates are not zero.
buckling analysis; crack problem; edge crack; elasticity solution; free-vibration analyses; functionally graded plate; harmonic differential quadrature method; mechanical-behavior; polynomial differential quadrature method; rectangular-plates; sigmoid function; structural components; thermal loads; transverse load
A systematic method for characterizing the elastic properties and adhesion of a thin polymer membrane
International Journal of Mechanical Sciences
47
3
319-332
2005
Doi 10.1016/J.Ijmecsci.2005.02.006
The elastic properties and adhesion of a thin silicone rubber membrane have been characterized. An effective instrumentation embodying a video-enhanced microscope, which meets force and displacement resolution of 0.1 mu N and 10 nm, was developed. It provides the capability of simultaneously measuring both the applied force and the resultant displacement of the thin polymer membrane. A linear theoretical elastic solution was applied to quantitatively interpret the measured central deflection of the membrane under a circular concentrical load. Young's modulus of the membrane can be,easily determined once the applied force and the central deflection, together with the essential dimensions, are known. The membrane jumped into an adhesion contact when the punch approached the range of the inter-surface force across the punch-membrane gap. A pull-off event was observed at a nonzero contact circle when the tensile load reached a critical threshold. The experiment is basically consistent with a theoretical model based on linear elasticity and an energy balance. The new method can be used to measure mechanical behavior of prestressed ultrathin biomembranes and thin walled biocapsules with a residual stress. (c) 2005 Elsevier Ltd. All rights reserved.
adhesion; cohesive zone; contact; deformation; elastic properties; elastography; films; flat punch; mechanical characterization; mechanics; microcapsule; solids; thin polymer membrane
Model for predicting thermal stresses in thin polycrystalline films
Journal of the Mechanics and Physics of Solids
45
4
511-534
1997
This paper reports the development of a numerical model to analyze thermal stresses induced in thin polycrystalline films deposited on thick substrates. The model accounts for viscoplastic deformations due to crystallographic slip in each grain of the polycrystal. The microstructural processes, which constrain dislocation slip due to the substrate, surface layer, and grain boundaries as well as due to hardening on the slip systems themselves, are considered and incorporated into the model. Using this model, the predicted stress-temperature curves for aluminium films with a natural oxide layer are in good agreement with the measured curves, especially for thicker films. It was found that the predictions of stress-temperature curves for fiber textured films are not substantially affected by reasonable deviations from a perfect fiber texture. Therefore, one can globally model the deformation of a textured polycrystalline film by assuming it to be a single crystal provided the film is in a state of equal biaxial strain. However, it is also shown that for an equal biaxial thermal strain, the local stress state at the grain level is more complicated due to the effect of the orientation of the individual grains, although the global stress state will be equal biaxial for a textured film. In fact, very high local stress gradients might have to be accommodated. © 1997 Elsevier Science Ltd. All rights reserved.
A. Strengthening mechanisms; A. Stress relaxation; A. Thin films; B. Polycrystalline material; B. Thermal stress; Crystallographic slip; Crystal microstructure; Crystal orientation; Dislocations (crystals); Grain boundaries; Mathematical models; Plastic deformation; Polycrystalline materials; Strengthening (metal); Stress concentration; Stress relaxation; Thermal stress; Thin films; Viscoplasticity
Classical paths and quantum mechanics
Annals of Physics
164
2
411-462
1985
10.1016/0003-4916(85)90021-1
In the semiclassical limit, the path integral description of quantum mechanics is dominated by classical paths. A classical path method is developed to extract energy levels and wavefunctions for a one-dimensional quantum system and it is shown that this method reproduces the results of the WKB approach. The classical path method generalizes the instanton method and provides new insights into instanton interactions. It provides a convenient and intuitive approach to many problems in quantum mechanics and field theory.
Statistical mechanics of powder mixtures
Physica A: Statistical Mechanics and its Applications
157
3
1091-1100
1989
10.1016/0378-4371(89)90035-6
In this paper we use a new formulation of the statistical mechanics of powders to develop a theory for a mixture of grains of two different sizes. We map this problem onto the spin formulation of the eight-vertex model and reproduce the features of the phase separation diagram of the powder mixture that we would intuitively be led to expect. Finally, we discuss the insight afforded by this solution on the "thermodynamic" quantities of interest in the powder mixture. © 1989.
Statistical mechanics of powder mixtures
Physica A: Statistical Mechanics and its Applications
157
3
1091-1100
1989
10.1016/0378-4371(89)90035-6
In this paper we use a new formulation of the statistical mechanics of powders to develop a theory for a mixture of grains of two different sizes. We map this problem onto the spin formulation of the eight-vertex model and reproduce the features of the phase separation diagram of the powder mixture that we would intuitively be led to expect. Finally, we discuss the insight afforded by this solution on the “thermodynamic” quantities of interest in the powder mixture.
Quantum mechanics: a systemic component of the modern physics paradigm
Physics Education
35
6
386-392
2000
10.1088/0031-9120/35/6/302
This article presents an epistemological approach to quantum mechanics teaching.
Fracture Mechanics and the Time Dependent Strength of Adhesive Joints
Journal of Composite Materials
5
2
176-192
1971
10.1177/002199837100500204
Fracture mechanics and time dependent strength of elastic or viscoelastic solids adhesively jointed by soft polymeric bonding layer
Soil Mechanics and Plasticity Analysis of Limit Design
Quarterly of Applied Mathematics
10
2
157-165
1952
... CiteULike is a free online bibliography manager. Register and you can start organising your references online. Tags. Soil mechanics and plastic analysis or limit design . ... \n
Analysis on cracking in hard thin films on a soft substrate under Berkovich indentation
Vacuum
112
29-32
2015
10.1016/j.vacuum.2014.11.013
The present work studied fracture behavior of a thin amorphous carbon film by nano-indentation using a sharp Berkovich indenter. The film was deposited onto a poly-ether-ether-ketone substrate using the plasma deposition method. After indentation tests, both radial cracks and picture-frame cracks were observed. A three-dimensional finite element (FE) model was developed to understand the stress evolution in the thin film under Berkovich indentation. The stress analysis showed that the maximum tensile stress in the film occurs along the indenter edge which contributes to the formation of radial cracks. It was also found that the picture-frame cracks can be developed, depending on the modulus ratio between the film and the substrate. The FE simulation results agree well with experimental observations and shed new insights into fracture mechanics of thin films under Berkovich indentation.
Finite element; Fracture; Hard thin films/soft substrate; Nano-indentation
The multiscale simulation of metal organic chemical vapor deposition growth dynamics of GaInP thin film
Science China-Physics Mechanics & Astronomy
53
8
1481-1490
2010
DOI 10.1007/s11433-010-4069-z
As a Group III-V compound, GaInP is a high-efficiency luminous material. Metal organic chemical vapor deposition (MOCVD) technology is a very efficient way to uniformly grow multi-chip, multilayer and large-area thin film. By combining the computational fluid dynamics (CFD) and the kinetic Monte Carlo (KMC) methods with virtual reality (VR) technology, this paper presents a multiscale simulation of fluid dynamics, thermodynamics, and molecular dynamics to study the growth process of GaInP thin film in a vertical MOCVD reactor. The results of visualization truly and intuitively not only display the distributional properties of the gas' thermal and flow fields in a MOCVD reactor but also display the process of GaInP thin film growth in a MOCVD reactor. The simulation thus provides us with a fundamental guideline for optimizing GaInP MOCVD growth.
computational analysis; computational fluid dynamics; gainp thin film growth; kinetic monte carlo; metal organic chemical vapor deposition; mocvd process; monte-carlo-simulation; multiscale simulation; rotating-disk reactors; virtual reality
Magnetic oxide thin films
Current Opinion in Solid State and Materials Science
4
1
24-27
1999
http://dx.doi.org/10.1016/S1359-0286(99)80006-0
Thin films of manganese or cobalt oxides exhibiting colossal magnetoresistance have been prepared using the same deposition methods as those used in the growth of superconducting cuprates. The thin film morphology, as well as the physical properties of the manganese oxide thin films, is shown to be strongly dependent on thin film growth. Devices, including these manganese oxides, have been grown to achieve a better sensitivity of their colossal magnetoresistance behavior to a magnetic field.
Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature
Journal of Fluid Mechanics
764
76-94
2015
DOI 10.1017/jfm.2014.703
Laminar helically-symmetric gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section is considered. We extend the work of Stokes et al. (Phys. Fluids, vol. 25 (8), 2013, 083103) and Lee et al. (Phys. Fluids, vol. 26 (4), 2014, 043302) to channels with arbitrary curvature and torsion or, equivalently, arbitrary curvature and slope. We use a non-orthogonal coordinate system and, remarkably, find an exact steady-state solution. We find that the free-surface shape and flow have a complicated dependence on the curvature, slope and flux down the channel. Moderate to large channel slope has a significant effect on the flow in the region of the channel near the inside wall, particularly when the curvature of the channel is large. This work has application to flow in static spiral particle separators used in mineral processing.
concentrators; finite curvature; fluid motion; lubrication theory; particle; pipe; simulation; spiral separators; thin films; waves/free-surface flows
Influence of nodule count on fatigue properties of ferritic thin wall ductile iron
Materials Science and Technology
23
8
1000-1004
2007
10.1179/174328407X185910
The present work focuses on the study of the influence of nodule count on the fatigue resistance of ductile iron. Fatigue tests were carried out on specimens taken from thin wall ductile iron plates of 2 and 4 mm thickness and standard Y blocks of 12?7 mm thickness, showing nodule counts ranging between 1800 and 300 nod mm22. All samples were ferritised before testing to obtain a homogeneous ferritic matrix. The results showed a large dispersion of fatigue strength values. Nevertheless, careful examination of the fracture surfaces showed the presence of very small casting defects on many test samples. When only the results measured on sound test samples were accounted for, a significant increase in fatigue strength was found as the nodule count increases. Casting defects, particularly microshrinkage, revealed by scanning electron micro- scopy on the fracture surfaces, were responsible for the premature failure, due to shortening of the crack initiation stage. The fatigue lives measured experimentally were compared with estimations based on the fracture mechanics theory.
Ductile iron; Fatigue strength; Nodule count influence; Thin wall
Prediction of thin-rimmed gear crack propagation from a factorial design approach
Fatigue & Fracture of Engineering Materials & Structures
34
7
470-486
2011
10.1111/j.1460-2695.2010.01540.x
Gear failure involving bending fatigue can have catastrophic consequences depending on the propagation path direction. Therefore, anticipating and preventing eventual critical fracture are crucial at the design stage. However, none of the methods available can give rapid and quantitative evaluation of gear fatigue crack evolution. Aiming to provide fast predictions of crack propagation paths, this paper proposes a factorial design approach for gear bending fatigue simulation. Six parameters related to gear geometry and initial crack configuration are considered in this study. Factorial design experiments are numerically conducted with an efficient 2D boundary element model assuming linear elasticity. Then, bending fatigue damage is modelled using polynomial functions. The resulting prediction model can instantly establish the crack trajectory in thin-rimmed gear for any cycle numbers. Application of the approach is illustrated by several case studies, while its precision and reliability are demonstrated through an exhaustive validation procedure. © 2011 Blackwell Publishing Ltd.
bending fatigue; boundary element method; crack propagation; factorial design; linear elastic fracture mechanics; thin-rimmed gear
The equivalence principle in classical mechanics and quantum mechanics
arXiv preprint gr-qc/9810087
1-21
1998
We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all.
Concrete with Nano-Additives in thin Wall Shell Structures
RTU Zinātniskie raksti: Mašīnzinātne un transports/Ražošanas tehnoloģija
6
46-52
2013
In the present paper physical and mechanical properties of glass fibre fibrous concrete as well as its technological possibilities in the production of definite shells have been studied. Production technology patented by RTU Concrete Mechanics Laboratory was used. This technology allows developing and obtaining different shells from fibrous concrete, including also dome structures and two-plane bended shells with smooth inner and outer surfaces. Concrete is spread in the necessary thickness on horizontal base, then the upper surface is leveled out and only then, applying pneumatic pressure, with the help of high elasticity material mould the necessary shell bending (height) is built. [1,2].
concrete with nano-additives; shell production technology
Microcontinuum fluid mechanics—A review
International Journal of Engineering Science
11
8
905-930
1973
10.1016/0020-7225(73)90038-4
In this survey developments in microcontinuum fluid mechanics have been reviewed and appropriate references are supplied throughout. We begin by considering the general theories of fluid microcontinua. In particular, the fundamental mechanics and general constitutive theories governing the behavior of such media are discussed. This is followed by a brief treatment of statistically based theories. The specialized microfluid continuum theories, many of which result upon simplification of the general theories, are also considered. Relations between the many different theories are demonstrated with the aid of various tables.
Quantum Mechanics, Orthogonality, and Counting
The British Journal for the Philosophy of Science
48
3
313-328
1997
In quantum mechanics it is usually assumed that mutually exclusive states of affairs must be represented by orthogonal vectors. Recent attempts to solve the measurement problem, most notably the GRW theory, require the relaxation of this assumption. It is shown that a consequence of relaxing this assumption is that arithmetic does not apply to ordinary macroscopic objects. It is argued that such a radical move is unwarranted given the current state of understanding of the foundations of quantum mechanics.
Combining Bohm and Everett : Axiomatics for a Standalone Quantum Mechanics
Arxiv Preprints
1-36
2012
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett’s “many-worlds” interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well as those of standard quantum mechanics. It has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Most importantly, the Born rule can be derived by straightforward application of the Laplacian rule, without reliance on a “quantum equilibrium hypothesis” that is crucial for Bohmian mechanics, and without reliance on a “branch weight” that is crucial for Everett-type theories. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no “splitting of worlds”, which is a typical feature of Everett-type theories. Altogether, the theory explains 1) the subjective occurrence of probabilities, 2) their quantitative value as given by the Born rule, 3) the identification of observables as self-adjoint operators on Hilbert space, and 4) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory
bohmian mechanics; born rule; everett interpretation; interpretation; interpretation of quantum mechanics; many-worlds
The post-buckling improvement of the shape memory alloy composite plates through the active strain energy tuning using finite element method
2011 IEEE Symposium on Business, Engineering and Industrial Applications (ISBEIA)
564-569
2011
10.1109/ISBEIA.2011.6088882
Shape memory alloy has been used as actuator parts in aerospace industry since the 1970s. In recent years, this smart material has been used to improve structural behaviours. Due to environmental heating, the problem of buckling of thin composite structures of aerospace vehicles becomes significant. A numerical study on the buckling and post-buckling improvements of composite plates due to shape memory effect behaviour of the shape memory alloy is presented. The shape memory alloy wires were embedded within laminated composite plates to exploit the recovery stress induced by the shape memory alloy to improve the stiffness of the plates. The study was conducted on symmetric and anti-symmetric angle-ply and cross-ply composite plates. The methods of active property tuning and active strain energy tuning were applied to show the various effects of the shape memory alloy on the studied behaviours. A geometric non-linear finite element model of the shape memory alloy composite plates and its source code were developed. It was found that significant improvements occurred in the critical loads and the post-buckling paths of the symmetric and anti-symmetric angle-ply and the symmetric cross-ply composite plates due to the active strain energy tuning method. In the case of the anti-symmetric cross-ply composite plate where bifurcation point did not exist, the post-buckling path improved substantially too.
active strain energy tuning; non linear finite element model; post buckling; shape memory alloy
Asymptotic analysis of the formation of thin liquid film in spin coating
Fluid Dynamics Research
30
2
107-125
2002
10.1016/S0169-5983(01)00041-7
Unsteady thin liquid film flow of non-uniform thickness on a rotating disk is analyzed by asymptotic methods. Short- and long-time-scale solutions for the transient film profile near the rotating axis are independently derived as a function of space and time. Analyses were performed for a case in which the initial film thickness is even in radial distance and the peripheral effects of the liquid film are assumed to be negligible., The result reveals the effects of the gravitational and surface tension forces, coupled with inertial force, on the film planarization and thinning process, (C) 2002 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.
asymptotic solutions; disks; dynamics; flat rotating-disk; flow; fluid flow; liquids; model; non-newtonian fluids; rotation; spin coating; thin films; transients
In situ studies of wear mechanisms in magnetic thin-film disks
Tribology Transactions
40
4
549-558
1997
Doi 10.1080/10402009708983692
Contact start-stop (CSS) tests and continuous drag tests are used for detailed in situ analysis of wear mechanisms in magnetic thin-film rigid disks. Coefficient of static friction and disk surface reflectance are measured during the contact start/stop tests and coefficient of kinetic friction, acoustic emission rms, acoustic emission count, and disk surface reflectance are all measured during the continuous drag tests. It is the first time that friction, acoustic emission and optical reflectance sensors are used simultaneously for wear studies. In situ measurements are used to determine precursors to failure of magnetic thin-film disks, to compare wear processes in CSS and drag tests, and to correlate CSS and drag tests. Disk. wear is seen to follow a pattern of lubricant depletion and/or localized polishing of overcoat asperities. The sliding distance associated with CSS tests is less damaging to disks than continuous drag sliding distances. A combination of sensors used in this study, in particular an optical sensor wed to measure changes in disk reflectance, has been demonstrated to be valuable in understanding the failure mechanisms.
acoustic diagnostics; acoustic-emission; contact mechanics; contact start stop; hard disks; head; magnetic data storage systems tribology; static friction; wear
Research of distributed curvature modal sensors with optical fiber on vibration measurement for thin structures
Fifth International Symposium on Instrumentation and Control Technology, October 24, 2003 - October 27, 2003
5253
471-475
2003
10.1109/ICICIC.2008.448
Thin structures have been applied widely in different areas of engineering. They are prone to elastic vibration when submit to external dynamic excitations or interference, which will not only lower system stability, but also threaten the people's lives. Thus, it is significant to research this topic in depth, Generally, many acceleration sensors are put on the cover of the structure to measure the vibrations. Also, strain sensors have been recently used for measuring vibration. However, strain is difficult to measure in thin structures and there are also limitations when applying multi-spot distributed measurement method. Based on the theory that the vibration of practical structure can be decoupled into multiple vibration modes, a new concept of curvature modal sensors with optical fiber is proposed to measure vibration modes.
Approximation theory; Computational methods; Degrees of freedom (mechanics); Image sensors; Optical fibers; Piezoelectric devices; Strain gages; Vibration control; Vibration measurement; Vibrations (mechanical); Wave interference
Regular hexagons and stripes on Marangoni and Rayleigh–Taylor unstable volatile thin films
European Journal of Mechanics - B/Fluids
47
48-56
2014
http://dx.doi.org/10.1016/j.euromechflu.2013.12.005
Thin volatile Newtonian liquid films with a free surface on a cooled horizontal substrate are studied theoretically and numerically. We show that if the fluid is initially in equilibrium with its own vapor in the gas phase, regular surface deformation patterns in the form of long-wave hexagons or stripes having a well defined lateral length scale are observed, depending on the instability mechanism. This is different to the case without evaporation where rupture or coarsening to larger and larger spatially disordered patterns is seen in the long time limit. We propose to use such a system to create a regular structuring of the film’s surface. Heat production by latent heat and the influence of a temperature dependent surface tension (Marangoni effect) are included as well. Special emphasis is laid on the so-called anomalous Marangoni effect. In this case a parameter region where stripes should occur already at threshold is found by means of a systematic weakly non-linear analysis.
Convection; Evaporation; Marangoni effect; Pattern formation; Rayleigh–Taylor instability; Thin films
Finite element modeling of the crushing behavior of thin-walled CFRP tubes under axial compression
Composites Part B: Engineering
64
50-58
2014
10.1016/j.compositesb.2014.04.008
A finite element modeling methodology was developed to study the crushing behavior and energy absorption characteristics of graphite/epoxy laminated circular tubes. Laminated tubes were modeled using multiple layers of shell elements with layers being tied together using tiebreak contact. A progressive damage model was used to simulate the failure within each layer while a mesh-independent energy-based failure criterion for the tiebreaks was implemented in the model to effectively simulate the delamination between layers during the crushing process. Simulation results compared very well with the experiments in terms of the load-displacement behavior, specific energy absorption, and surface strain distribution, and provided a good depiction of the failure process. © 2014 Elsevier Ltd. All rights reserved.
A. Carbon fiber; A. Laminates; C. Finite element analysis (FEA); C. Laminate mechanics
Classification of thin plate models by asymptotic expansion of non-linear three-dimensional equilibrium equations
International Journal of Non-Linear Mechanics
36
165-186
2001
10.1016/S0020-7462(00)00005-6
We present in this paper a new constructive method of classification of two-dimensional plate models from the applied forces level and the geometrical data. This approach which uses asymptotic methods is based on a dimensional analysis of the non-linear equilibrium equations. This dimensional analysis leads to dimensionless numbers which reflect the geometry of the structure and the applied forces. For a given forces level, the order of magnitude of the displacements and the corresponding two-dimensional model are deduced by asymptotic expansion of the three-dimensional equations. For decreasing forces level, we obtain successively the non-linear membrane model, another membrane model, the usual non-linear plate model and the linear Kirchhoff-Love model.
asymptotic methods; dimensional analysis; non-linear elasticity; plate theory
A geometric approach to the canonical reformulation of quantum mechanics
Theoretical and Mathematical Physics
147
3
847-853
2006
10.1007/s11232-006-0080-y
The measure of distinguishability between two neighboring preparations of a physical system by a measurement device naturally defines a line element on the preparation space of the system. We show that quantum mechanics can be derived from the invariance of this line element in the canonical formulation. We also discuss the canonical formulation of quantum statistical mechanics.
Respiratory mechanics after heart-lung and bilateral lung transplantation.
Thorax
52
8
718-22
1997
10.1136/thx.52.8.718
The factors determining respiratory mechanics following heart-lung transplantation (HLT) and bilateral lung transplantation (BLT) are incompletely understood.
Adult; Female; Heart-Lung Transplantation; Heart-Lung Transplantation: physiology; Humans; Lung Compliance; Lung Transplantation; Lung Transplantation: physiology; Lung Volume Measurements; Male; Postoperative Period; Regression Analysis; Respiratory Mechanics
On the Singularities in Fracture and Contact Mechanics
Journal of Applied Mechanics
75
5
051111
2008
10.1115/1.2936241
Generally, the mixed boundary value problems in fracture and contact mechanics may be formulated in terms of integral equations. Through a careful asymptotic analysis of the kernels and by separating nonintegrable singular parts, the unique features of the unknown functions can then be recovered. In mechanics and potential theory, a characteristic feature of these singular kernels is the Cauchy singularity. In the absence of other nonintegrable kernels, Cauchy kernel would give a square-root or conventional singularity. On the other hand, if the kernels contain, in addition to a Cauchy singularity, other nonintegrable singular terms, the application of the complex function theory would show that the solution has a non-square-root or unconventional singularity. In this article, some typical examples from crack and contact mechanics demonstrating unique applications of such integral equations will be described. After some remarks on three-dimensional singularities, the key examples considered will include the generalized Cauchy kernels, membrane and sliding contact mechanics, coupled crack-contact problems, and crack and contact problems in graded materials.
Capacitance computation of thin conductors with the fast multipole method
International Journal of Applied Electromagnetics and Mechanics
17
1-3
75-89
2003
Computing the capacitance coefficients of a multiconductor system embedded in multiple piecewise homogeneous dielectrics with the boundary element method in combination with the fast multipole method, the memory requirements and the computational cost for the solution of the system of linear equations are approximately proportional to the number of unknowns. In this paper it will be shown, that the calculation of the free charges on the conductors and with it the calculation of the capacitance coefficients can be accelerated, if the fast multipole method is also used for the post-processing.
bem computations
Atomic Layer Deposition of Molybdenum Nitride Thin Films.pdf
Applied Mechanics and Materials
492
375-379
2014
10.4028/www.scientific.net/AMM.492.375
This work focuses on synthesis of molybdenum oxide (MoO3)by Atomic layer deposition (ALD)using molybdenum hexacarbonyl [Mo(CO)6] and ozone. In-situ growth characteresticswerestudied by Quartz Crystal Microbalance (QCM). ALD temperature window for this material lies between 165 to 175°C giving a maximum growth rate of 0.45 Å per ALD cycle. Negligible nucleation was found by QCM studyindicating a linear growth of the film. Effect of different oxidants on the growth rate is also studied.As-deposited film is amorphous in nature which converts to monoclinic-MoO3 after annealing as seen by taransmission electron microscopy. © (2014) Trans Tech Publications, Switzerland.
Atomic layer deposition; Molybdenum oxide; Quartz crystal microbalance; Solar cell
Stochastic mechanics of relativistic fields
Journal of Physics: Conference Series
504
1
012013
2014
10.1088/1742-6596/504/1/012013
After a brief review of stochastic mechanics of nonrelativistic particle systems, the paper\r discusses in a qualitative way issues concerning the application of stochastic mechanics to\r relativistic fields and their relation to quantum field theory. It is suggested that gauge theories\r will be essential to this program.
Entangled states in stochastic mechanics
Journal of Physics A: Mathematical and General
33
33
5833-5848
2000
10.1088/0305-4470/33/33/304
An axiomatization of the core part of stochastic mechanics (SM) is proposed and this scheme is\r discussed as a hidden variables theory. We work out in detail an example with entanglement and\r rigorously prove that SM and quantum mechanics agree in predicting all the observed correlations at\r different times.
Analytical and numerical studies of the stability of thin-film rimming flow subject to surface shear
Journal of Fluid Mechanics
541
317
2005
10.1017/S0022112005006142
Motivated by applications in rapidly rotating\nmachinery, we have previously extended the lubrication model of the\nthin-film flow on the inside of a rotating circular cylinder to\nincorporate the effect of a constant shear applied to the free\nsurface of the film and discovered a system rich in film profiles\nfeaturing shock structures. In this paper, we extend our model to\ninclude the effects of surface tension at leading order and take\nInto account higher-order effects produced by gravity in order to\nresolve issues regarding existence, uniqueness and stability of\nsuch weak solutions to our lubrication model. We find, by\nanalytical and numerical means, a set of feasible steady\ntwo-dimensional solutions that fit within a rational asymptotic\nframework. Having identified mathematically feasible solutions, we\nstudy their stability to infinitesimal two-dimensional\ndisturbances. Based on our findings, we conjecture which of the\npossible weak solutions are physically meaningful.\n
Wave propagation in a fluid flowing through a curved thin-walled elastic tube
European Journal of Mechanics, B/Fluids
25
6
987-1007
2006
10.1016/j.euromechflu.2005.12.001
The pulsatile flow in a curved elastic pipe of circular cross section is investigated. The unsteady flow of a viscous fluid and the wall motion equations are written in a toroidal coordinate system, superimposed and linearized over a steady state solution. Being the main application relative to the vascular system, the radius of the pipe is assumed small compared with the radius of curvature. This allows an asymptotic analysis over the curvature parameter. The model results an extension of the Womersley's model for the straight elastic tube. A numerical solution is found for the first order approximation and computational results are finally presented, demonstrating the role of curvature in the wave propagation and in the development of a secondary flow. ?? 2006 Elsevier SAS. All rights reserved.
Arterial flow; Curved elastic tubes; Numerical methods; Perturbation methods
A novel semi energy finite strip method for post-buckling analysis of relatively thick anti-symmetric laminated plates
Advances in Engineering Software
48
32-39
2012
10.1016/j.advengsoft.2012.01.007
In the current paper, a novel semi-energy FSM is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for thin and relatively thick anti-symmetric angle-ply composite laminates subjected to uniform end-shortening. The laminated plates are assumed to be simply supported at their boundaries. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. The study of the results has provided confidence in the validity and capability of the developed FSM in handling the post buckling problem of anti-symmetric angle-ply laminates. ?? 2012 Elsevier Ltd. All rights reserved.
Angle ply composite plates; Finite strip method; First order shear deformation theory; Post buckling analysis; Semi-energy approach; Von-K??rm??n's compatibility equation
Micro-mechanics and continuum damage mechanics
Archive of Applied Mechanics
65
7
437-456
1995
10.1007/BF00835656
Continuum Damage Mechanics has been applied successfully to technical problems since the idea was introduced by Kachanov almost 40 years ago. In keeping with the traditions of mechanics, the formulation was based on the results of mechanical tests on specimens whose size is measured in centimeters. To model the observations which describe the deterioration of material properties it was found necessary to introduce internal variables referred to as ‘damage’. The approach is phenomenological, with only a minimal attempt to provide a physical interpretation of damage. For this reason the approach has had little appeal to those whose interest is in the physical mechanisms which cause material deterioration. In this presentation a description is given of attempts to develop continuum damage mechanics so that the relationship with the physical mechanism approach is less abrupt. The procedure is illustrated with reference to ceramic matrix composites.
No spin-statistics connection in nonrelativistic quantum mechanics
Quantum
77843
5
2
2003
We emphasize that there is no spin-statistics connection in nonrelativistic quantum mechanics. In several recent papers, including Phys. Rev. A 67, 042102 (2003) [quant-ph/0207017], quantum mechanics is modified so as to force a spin-statistics connection, but the resulting theory is quite different from standard physics.
Quantum Physics
Mixing and equilibrium probability densities in classical statistical mechanics
Physica A: Statistical Mechanics and its Applications
187
3-4
589-602
1992
http://dx.doi.org/10.1016/0378-4371(92)90012-F
The effects of the mixing property of the microscopic\ndynamics on the limiting behaviour of macroscopic and microscopic\nprobability densities in classical statistical mechanics are studied\nin detail.
Off-axis inelastic behavior of hybrid composite GLARE 2 and classical lamination theory taking into account ply failure
Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
62
601
2088-2096
1996
Inelastic and fracture behaviors of a new fiber-metal composite GLARE 2, a unidirectional hybrid laminate of glass/epoxy laminae and aluminum alloy sheets, have been examined under various off-axis static tensile loading conditions. The classical laminated plate theory (CLT) has been applied to describe the off-axis inelastic behavior of GLARE 2, in which the failure-induced elastic degradation of GFRP plies was taken into account. For all off-axis angles, a clear transition from the linear to nonlinear deformation regime appears. The stress level of this sharp transition almost coincides with the yield stress of the constituent aluminum layers. The anisotropy in the fracture stress can be predicted using the Tsai-Hill theory. Taking into account the observation that for a 90° off-axis specimen the tangent modulus in the nonlinear regime is almost in agreement with that of the monolithic aluminum alloy, we have considered transverse cracking in the GFRP plies and modified the CLT so as to include the instantaneous degradation of the transverse and shear elastic moduli due to the transverse fracture. The results obtained using the CLT with ply failure accurately described the characteristic behavior of GLARE 2.
Aluminum alloys; Classical lamination theory; Degradation; Elastic degradation; Elasticity; Elastic moduli; Epoxy resins; Failure (mechanical); Fiber metal laminates; Fracture; Glass fibers; Hybrid composite; Laminated composites; Laminating; Off axis inelastic behavior; Plastic deformation; Ply failure; Stresses; Tsai-Hill theory
Processing 20 ply clad plate by accumulative clad rolling from stainless steel/aluminum/aluminum alloy.../stainless steel sheets
Materials Science Forum
610-613
454-458
2009
10.4028/www.scientific.net/MSF.610-613.454
According to the principle of accumulative roll bonding(ARB),the 20 ply clad sheet from austenitic stainless steel (STS304)/pure aluminum(A11060)/ aluminum alloy(A13003).../austenitic stainless steel (STS304)sheets with excellent heat, anti-corrosion and mechanical properties of stainless steel and the high thermal and electrical conductivities of aluminum was fabricated by accumulative clad rolling (ACR). Well-bonded clad plate was successfully obtained in the procedure: A11060 sheets with a thickness of 0.5mm and A13003 sheets 0.5mm thick and STS304 sheets 0.5mm thick were employed. Basic clad sheet from different ply A11060/A13003 sheets was obtained with an initial rolling reduction of 44% at 450°C followed by annealing at 300°C, then ACR was with reduction of 50% at 550°C from STS304 on each side. The stretch property, bonding property, microscopic structure and interface composition were measured and analyzed. It was indicated that the best clad sheet had bonding strength of 129MPa and stretch strength of 225MPa. At the end,STS304 sheet with thickness of 3mm was taken the place of the clad sheet from STS304 sheets of 1mm and A11060 of 1mm and A13003 of 1mm. Therefore, it decreased by 44% in weight and economizes rare metal elements Cr and Ni of 66% in weight. © (2009) Trans Tech Publications, Switzerland.
Accumulative clad rolling (ACR); Accumulative roll; Alumina; Aluminum; Aluminum alloys; Architectural; Roll bonding
Identical probability distribution of first-ply failure strains and design allowables computation based on multi-sample data of composite laminates
Computers & Structures
61
2
225-230
1996
http://dx.doi.org/10.1016/0045-7949(96)00019-3
Design allowables are of great importance in designing composite structures. The design allowables of conventional metallic materials are easy to obtain. The design allowables of composite materials are generally calculated from the experimental data by using statistical methods. If the test data from different laminates are used as different samples, a great number of tests should be made to get reasonable allowables, or the size of each sample will be very small. A small sample size will result in overly conservative design allowables which may impose an unreasonable weight penalty on the design. Previous studies show that the first-ply failure (FPF) strains of composite laminates are almost the same for those laminates containing the same “weakest” ply. This paper analyzes the identity of the probability distribution of the FPF strains. The FPF strains of Pi4 symmetric composite laminates containing 90 ° plies are theoretically and experimentally studied. A nonparametric test is made to verify the hypothesis that the experimental data of these laminates are drawn from an identical population. The theoretical discussion and nonparametric test show that the FPF strains of these laminates usually have the same distribution, and the experimental data can be regarded as the observations from a single sample. Statistical methods for computing design allowables based on multi-sample data are discussed for the following two cases: (1) the multi-sample data can be used as a single sample or (2) these data cannot be regarded as being from a single sample.
A Reformulation of Quantum Mechanics
Modern Physics Letters A
6
3
225
1991
10.1142/S0217732391000191
We show that the phenomena explained by quantum mechanics can alternatively be explained as a breakdown of probability theory without the need for wave-particle duality or the idea that a particle does not have a unique path in space. The single-particle Lagrangian consistent with the reformulated quantum mechanics is derived and specialized to the Schrödinger and Klein-Gordon theories. The usual paradoxes of quantum mechanics are explained. A connection to gravity is proposed. Probability theory is restored in the classical limit.
Thin filament regulation
Comprehensive Biophysics
4
251-267
2012
10.1016/B978-0-12-374920-8.00416-1
The review summarizes the current state of knowledge of the calcium regulation of striated muscle contraction via the thin filament proteins, tropomyosin and troponin. The description focuses on in vitro studies of the thin filament and covers structural, biochemical and dynamic aspects of the thin filament's response to calcium binding. A reductionist approach has allowed many of the transitions to be defined at the level of a single structural unit. Here an emphasis is placed on the co-operative nature of the structural and biochemical transitions of the thin filament and the allosteric relationship between calcium and myosin binding to the thin filament. ?? 2012 Elsevier B.V. All rights reserved.
Actin; Allosteric; Calcium; Co-operativity; Coupled equilibria; E-F hand; Inhibitory peptide; Motility; Myosin; Persistence length; Signal peptide; Thin filament; Tropomyosin; Troponin
Numerical studies of transonic BZT gas flows around thin airfoils
Journal of Fluid Mechanics
396
109-141
1999
doi:10.2514/6.1998-2690
Numerical studies of two-dimensional, transonic flows of dense gases of retrograde type, known as BZT gases, around thin airfoils are presented. The computations are guided by a recent asymptotic theory of Rusak & Wang (1997). It provides a uniformly valid solution of the flow around the entire airfoil surface which is composed of outer and inner solutions. A new transonic small-disturbance (TSD) equation solver is developed to compute the nonlinear BZT gas flow in the outer region around most of the airfoil. The flow in the inner region near the nose of the airfoil is computed by solving the problem of a sonic flow around a parabola. Numerical results of the composite solutions calculated from the asymptotic formula are compared with the solutions of the Euler equations. The comparison demonstrates that, in the leading order, the TSD solutions of BZT gas flows represent the essence of the flow character around the airfoil as computed from the Euler equations. Furthermore, guided by the asymptotic formula, the computational results demonstrate the similarity rules for transonic flows of BZT gases. There are differences between the self-similar cases that may be related to the error associated with the accuracy of the asymptotic solution. A discussion on the flow patterns around an airfoil at transonic speeds and at various upstream thermodynamic conditions is also presented. The paper provides important guidelines for future studies on this subject.
Effect of lap-sheets on deep drawing of metallic foil cups
Journal of Materials Processing Technology
119
48-51
2001
10.1016/S0924-0136(01)00896-2
In order to improve the deep drawability of stainless-steel foil cups, foil-lap blanks in which thin sheet metals (lap-sheets) were lapped over the foils were used in the deep-drawing operations. In the deep-drawing process, aluminum sheets were used as lap-sheets. The following three foil-lap blanks were used. B-sheet type: a two-ply foil-lap blank in which an aluminum sheet is on the blank holder side. D-sheet type: a two-ply foil-lap blank in which an aluminum sheet is on the die side. Sandwich type: a three-ply foil-lap blank in which a stainless-steel foil blank is sandwiched between two aluminum lap-sheets. In the D-sheet type, cracks on the foil cups were prevented by the lap-sheet on the die side. In the B-sheet type, wrinkles on the foil cups were prevented by the lap-sheet on the blank holder side. The deep drawability of stainless-steel foil cups was improved effectively when using lap-sheets. The thickness and the strain-hardening characteristics of aluminum lap-sheets influenced the deep drawability of foil cups. © 2001 Elsevier Science B.V. All rights reserved.
Deep drawing; Drawability; Metal foil
Exact 3D stress analysis of laminated composite plates by sampling surfaces method
Composite Structures
94
12
3654-3663
2012
10.1016/j.compstruct.2012.06.006
A paper focuses on the use of the efficient approach to exact 3D elasticity solutions of cross-ply and angle-ply laminated composite plates. This approach is based on the new method of sampling surfaces (SaS) developed recently by the authors. We introduce inside the nth layer I n not equally spaced SaS parallel to the midsurface of the plate and choose displacements of these surfaces as fundamental plate unknowns. Such an idea permits the representation of the proposed higher order layer-wise plate theory in a very compact form. This fact gives in turn the opportunity to derive the exact 3D solutions of elasticity for thick and thin laminated composite plates with a prescribed accuracy by utilizing a sufficiently large number of SaS, which are located at interfaces and Chebyshev polynomial nodes. ?? 2012 Elsevier Ltd.
3D stress analysis; Angle-ply composite; Laminated plate; Layer-wise description; Sampling surfaces method
Pattern Discovery and Computational Mechanics
Physics
12
2000
Computational mechanics is a method for discovering, describing and quantifying patterns, using tools from statistical physics. It constructs optimal, minimal models of stochastic processes and their underlying causal structures. These models tell us about the intrinsic computation embedded within a process---how it stores and transforms information. Here we summarize the mathematics of computational mechanics, especially recent optimality and uniqueness results. We also expound the principles and motivations underlying computational mechanics, emphasizing its connections to the minimum description length principle, PAC theory, and other aspects of machine learning.
A monoparametric family of metrics for statistical mechanics
Physica A: Statistical Mechanics and its Applications
344
547-553
2004
10.1016/j.physa.2004.06.030
In a recent paper, we have studied a generalization of the Jensen-Shannon divergence (JSD) (Physica A 329 (2003) 81). This generalization was made in the context of Tsallis' statistical mechanics. The present work is devoted to an investigation of the metric character of the JSD generalization. © 2004 Elsevier B.V. All rights reserved.
Jensen-Shannon divergence; Metrics for probability spaces; Non-extensive statistical mechanics
The effects of pneumoperitoneum on respiratory mechanics during bariatric surgery.
Obesity surgery
12
3
376-9
2002
10.1381/096089202321088192
The aim of this study was to investigate the influence of laparoscopic and conventional open surgery on respiratory mechanics, and blood gases, and to determine convenient techniques from the point of view of intraoperative respiratory mechanics, for bariatric surgery.
Adult; Blood Gas Analysis; Female; Gastroplasty; Gastroplasty: adverse effects; Hemodynamics; Hemodynamics: physiology; Humans; Laparoscopy; Laparoscopy: adverse effects; Male; Middle Aged; Monitoring, Intraoperative; Obesity, Morbid; Obesity, Morbid: blood; Obesity, Morbid: physiopathology; Obesity, Morbid: surgery; Pneumoperitoneum, Artificial; Pneumoperitoneum, Artificial: adverse effects; Respiration Disorders; Respiration Disorders: blood; Respiration Disorders: etiology; Respiration Disorders: physiopathology; Respiratory Mechanics; Respiratory Mechanics: physiology
Survey of the Interpretations of Quantum Mechanics
American Journal of Physics
24
4
272
1956
10.1119/1.1934204
A survey is made of the hitherto proposed answers to the following crucial questions arising in the physical interpretation of the mathematical formalism of wave mechanics: (I) What is the meaning of the dynamical variables and of their eigenvalues? (II) What is the meaning of the wave function? (III) What is the nature and origin of Heisenberg's uncertainty relations? (IV) What is the nature of the systems dealt with by wave mechanics? Taking into account the interpretations that have been proposed in the last few years, a surprisingly large number of answers is found. The present situation in quantum mechanics is compared with similar crises in the past history of physics. The mere multiplicity of consistent interpretations of quantum mechanics is regarded as a warning against the dogmatic adherence to any one of them, to the exclusion of new possibilities.
Nelsonian Mechanics Revisited
Foundations of Physics
1-19
1998
10.1023/A:1021622603864
In de Broglie and Bohm's pilot-wave theory, as is well known, it is possible to consider alternative particle dynamics while still preserving the quantum distribution. I present the analogous result for Nelson's stochastic theory, thus characterising the most general diffusion processes that preserve the quantum equilibrium distribution, and discuss the analogy with the construction of the dynamics for Bell's beable theories. I briefly comment on the problem of convergence to the quantum distribution and on possible experimental constraints on the alternative dynamics.
Quantum Mechanics I
Quantum
789
7247
202
2010
This is the first Internet course on elementary quantum mechanics written in Spanish ("castellano") for the benefit of Spanish speaking students. I thank my eight Mexican students at the Institute of Physics, University of Guanajuato, Leon, (IFUG), for the collaboration that made this possible. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Experiments and numerical simulations of thermal shock crack patterns in thin circular ceramic specimens
Ceramics International
41
1
1107-1114
2015
10.1016/j.ceramint.2014.09.036
An attempt was made to explore the formation mechanism of thermal shock crack patterns in ceramics and to develop quantitative numerical simulations. A set of experiments on thin circular ceramic specimens yielded two-dimensional readings of thermal shock crack patterns with periodical and hierarchical characteristics. The numerical simulations of the thermal shock crack patterns are based on the minimum potential energy principle, where the convective heat transfer coefficient at high temperatures, which is difficult to measure, was inversely estimated by the crack spacing, which is easy to measure. Numerical simulation results were in good agreement with the experimental data. Several interesting thermal shock crack evolution phenomena were found. Two stability criteria of crack propagation, i.e. the minimum potential energy principle and the fracture mechanics bifurcation theory, were compared. It was found that the two criteria verify and complement each other. The present study leads to an improved understanding of the formation and evolution of thermal shock crack patterns in ceramics and can help engineers to assess the thermal shock failure of practical ceramic components.
ceramics; Ceramics; crack patterns; Crack patterns; numerical simulations; Numerical simulations; thermal shock; Thermal shock
Flow domain identification from free surface velocity in thin inertial films
Journal of Fluid Mechanics
720
338-356
2013
10.1017/jfm.2013.14
We consider the flow of a viscous liquid along an unknown topography. A new strategy is presented to reconstruct the topography and the free surface shape from one component of the free surface velocity only. In contrast to the classical approach in inverse problems based on optimization theory we derive an ordinary differential equation which can be solved directly to obtain the inverse solution. This is achieved by averaging the Navier–Stokes equation and coupling the function parameterizing the flow domain with the free surface velocity. Even though we consider nonlinear systems including inertia and surface tension, the inverse problem can be solved analytically with a Fourier series approach. We test our method on a variety of benchmark problems and show that the analytical solution can be applied to reconstruct the flow domain from noisy input data. It is also demonstrated that the asymptotic approach agrees very well with numerical results of the Navier–Stokes equation. The results are finally confirmed with an experimental study where we measure the free surface velocity for the film flow over a trench and compare the reconstructed topography with the measured one.
flow control; interfacial flows (free surface); thin films
Buckling instability and pattern around holes or cracks in thin plates under a tensile load
European Journal of Mechanics A Solids
11
1
65-89
1992
We present a novel experimental situation in which an applied tensile stress creates a complex spatial buckling pattern resembling a 'Maltess cross' around a defect such as a hole or a crack in a thin plate. In contrast to usual situations in which large scale buckling occurs, the applied macroscopic load has no compressive component and is thus globally stabilizing with respect to the buckling instability. The observed instability stems from a compressive stress induced by the presence of the defect. The effect of imperfect boundary conditions and of the finite size of the plate are analyzed by comparing a numerical finite element computation and some experiments carried out in the simplest case of a circular hole. Experiments with cracks clearly show the distorsion of the buckling pattern as a function of the crack orientation with respect to the applied uniaxial tensile stress, in agreement with the computed variation of the domains of compressive stress. The orientation of the folds of the buckling patterns are also shown to follow closely the isostatics calculated exactly for the unbuckled state. (Author abstract) [References: 36]
Properties and adhesion of thin films made by copper catalyzed cycloaddition
Polymer Preprints (American Chemical Society, Division of Polymer Chemistry)
46
1
456-457
2005
Copper iodide (CuI) catalyzed azide-alkyne cycloaddn. was used to form crosslinked polymeric triazoles from N,N-bis(2-azidoethyl)-4-methyl-benzenesulfonamide-N,N',N''-tri-2-propynyl-1,3,5-triazine-2,4,6-triamine copolymers. The polyacetylene-polytriazoles have glass transition temp. up to 50 Deg above the curing temp. The polyacetylene-polytriazoles were evaluated as thin film adhesives for copper and brass using fracture mechanics tests. The fracture toughness of cured polymer joints with brass strips increased with cure temp. but decreased with cure time, above 2 days, for room temp. and 50 Deg cure, probably due to water uptake. In all cases failure was cohesive in the polymer, probably because the polymers are brittle. [on SciFinder (R)]
Adhesives; Crosslinking (cycloaddn.; curing and performance of polyacetylene-polytriazo; Fracture toughness (curing and performance of poly; Glass transition temperature (of adhesive; Joints (adhesive; polyacetylene polytriazole copper curing catalyst; Polyacetylenes Role: CPS (Chemical process), PEP (
Effects of Varying the Tire Cap Ply, Sidewall Filler Height and Pavement Surface Texture on Tire/Pavement Noise Generation.
SQDH 2003-1, Final Report, Purdue University
90-
2003
In order to better understand the effect of tire carcass construction and pavement texture on tire/pavement noise generation, a measurement program was conducted on a group of four automobile tires on three pavement textures. The tires included all combinations of cap ply, no cap ply, sidewall filler height of 1.75 inches and sidewall filler height of 0.35 inches. The tires, General AmeriG4S, P205/65R15, were nominally identical in all other respects including tread pattern and rubber compound properties. During this investigation, other tire design variables such as tire pressure and rim size were held constant. The pavement samples were made of rigid Portland Cement Concrete (PCC) pavement sections with smooth, textured and porous surface textures. Tests were conducted at speeds of 10, 20 and 30 mph. The Tire/Pavement Test Apparatus (TPTA) at the Ray W. Herrick Laboratories at Purdue University was used for the tests. Five microphones were used to measure the sound generated by the tire/pavement interaction. Three microphones were located according to the specifications of the Close Proximity Method (ISO/CD 11819-2). The other two microphones were located such that one was in front of the tire 5 cm from the leading edge of the contact patch and one was behind the tire 5 cm from the trailing edge of the contact patch, along the centerline of the tire. The tires all produce similar overall sound pressure level and frequency spectra for a specific test surface. The three pavements produced significantly different spectra. The porous pavement produced higher levels below 1000 Hz but lower levels than the other two pavement types above 1000 Hz. The pavement surface textures investigated had a much more significant effect on sound generation and radiation of the tires than the variations investigated for cap ply and sidewall filler height.
Asphalt pavements; Tire noise; Tire pavement interfa
The fundamental concepts of classical equilibrium statistical mechanics
Physics Essays
17
2
223-244
2004
10.4006/1.3025677
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between physical and mathematical aspects, particularly regarding the role of probability theory. The focus is on the equilibrium case, which is currently better understood, serving also as a prelude for a further discussion of non-equilibrium statistical mechanics.
Ensembles; Equilibrium; Foundations; Phase transitions; Probability; Statistical mechanics
Lattice quantum mechanics: An application to Bose-Einstein condensation
International Journal of Modern Physics C
9
8
1577-1585
1998
10.1142/S0129183198001424
A lattice formulation of nonrelativistic quantum mechanics is presented, based on a formal analogy with discrete kinetic theory. The method is applied to the Gross-Pitaevski equation, a specific form of self-interacting nonlinear Schrodinger equation relevant to the study of Bose-Einstein condensation.
kinetic theory; lattice-boltzmann; quantum mechanics; schrodinger-equation
Mechanics Simulations in Second Life
International Journal of Virtual and Personal Learning Environments
1
2
31-44
2010
10.4018/jvple.2010040103
This paper examines the use of the 3-D virtual world Second Life to explore basic mechanics in physics. In Second Life, students can create scripts that take advantage of a virtual physics engine in order to conduct experiments that focus on specific phenomena. The paper explores two particular examples of this process: 1) the movement of an object under the influence of gravity, and 2) the movement of an object using simple forces. Findings suggest that Second Life offers a flexible and wide range of possibilities for simulations in mechanics; paradoxically, however, the environment also presents challenges for effective use by instructors and learners. Any implementation making use of the Second Life application requires technical knowledge of the system and a wide range of pedagogical and learner skills related to building, scripting, and educational design.
Kinematics; Linden Scripting Language; Mechanics; Physics Engine; Second Life; Simulations; Virtual Environment
Quantum Mechanics at the Planck Scale
arXiv
1995
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically. (Talk given at the Workshop on Physics at the Planck Scale, Puri, India, December12-21, 1994. This talk is a precis of the author's 1992 Les Houches Lectures: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime, gr-qc/9304006).
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Quantum Physics
Fluid mechanics of heart valves
Annu Rev Biomed Eng
6
331-62
2004
10.1146/annurev.bioeng.6.040803.140111
Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review.
Quantum Mechanics
American Journal of Physics
2
9
620
2007
10.1119/1.16631
Rapid advances in quantum optics, atomic physics, particle physics and other areas have been driven by fantastic progress in instrumentation (especially lasers) and computing technology as well as by the ever-increasing emphasis on symmetry and information concepts-requiring that all physicists receive a thorough grounding in quantum mechanics. This book provides a carefully structured and complete exposition of quantum mechanics and illustrates the common threads linking many different phenomena and subfields of physics.
Debonding of a thin rubberised and fibre-reinforced cement-based repairs: Analytical and experimental study
Materials and Design
49
90-95
2013
10.1016/j.matdes.2013.01.036
An analytical approach for the prediction of debonding initiation between a rubberised cement-based overlay and old concrete substrate under monotonous mechanical loading was applied. Based on the linear elastic fracture mechanics, a model has been developed taking into account the interlocking between two crack surfaces in the overlay. Assuming that the debonding initiation just occurs after the crack cutting the overlay layer reaches the overlay-substrate interface, the stress intensity factor of the debonding tip can be calculated, allowing prediction of stress fields near the interface debonding tip. Then with a criterion of debonding initiation and propagation depending on the interface tensile strength, the load associated could be determined and might be interesting for the design of thin bonded cement-based overlays. The adequateness of this analytical approach was verified by both experimental data and finite element calculations. It has been used to show the relevance of a cement-based material with low modulus of elasticity combined with a high residual post crack strength to achieve sustainable repairs. ?? 2013 Elsevier Ltd.
Bonded overlays; Debonding; Interface; Interlocking; Rubber
The dynamic process of the inflation of thin elastomeric shells under the action of an excess pressure
Journal of Applied Mathematics and Mechanics
78
2
163-171
2014
10.1016/j.jappmathmech.2014.07.009
Abstract A problem of the dynamic process of their deformation is formulated in the momentless approximation for thin shells made of rubber-like elastomers under the action of a time-varying excess hydrostatic pressure. A system of non-linear equations of motion is set up for the case of arbitrary displacements and deformations in which the true deformation of the transverse compression of the shell, corresponding to the use of the modified Kirchhoff–Love model proposed earlier, and the coordinates of the points of the middle surface with respect to a fixed Cartesian system of coordinates, are taken as the required unknown functions. Physical relations connecting the components of the true internal stresses with the elongation factors and the extent of the shear strain are constructed using relations proposed earlier by Chernykh. A finite-difference method is developed for solving the initial-boundary value problem and, on the basis of this, the dynamic process of the inflation of shells of revolution at different rates of pressure increase is investigated and the unstable stages of their deformation are established with a determination of the corresponding limiting (critical) pressure value. After this value has been reached, a further increase in the deformations occurs at decreasing values of the internal pressure.
Creep measurements in free-standing thin metal film micro-cantilever bending
Conference Proceedings of the Society for Experimental Mechanics Series
4
167-171
2011
10.1007/978-1-4614-0210-7_24
Creep is a time-dependent deformation mechanism that affects the reliability of metallic MEMS. Examples of metallic MEMS are RF-MEMS capacitors/switches, found in wireless/RF applications. Proper modeling of this mechanism is yet to be achieved, because size-effects that play a role in MEMS are not well understood. To understand this better, a methodology is setup to study creep in Al-Cu alloy thin film micro-cantilevers micro-fabricated in the same MEMS fabrication process as actual RF-MEMS devices. The methodology entails the measurement of time-dependent deflection recovery after maintaining cantilevers at a constant deflection for a prolonged period. Confocal profilometry and a simple mechanical setup with minimal sample handling are applied to control and measure the deformation. Digital image correlation, leveling and kinematics-based averaging algorithms are applied to the measured surface profiles to correct for various errors and improve the precision to yield a precision <7% of the surface roughness. A set of measurements is presented in which alloy microstructure length scales at the micrometer-level are varied to probe the nature of this creep behavior.
Analysis of the vibrationally induced dissipative heating of thin-wall structures containing piezoactive layers
International Journal of Non-Linear Mechanics
47
2
105-116
2012
http://dx.doi.org/10.1016/j.ijnonlinmec.2011.03.004
A strongly non-linear dynamic problem of thermomechanics for multilayer beams is formulated based on the Kirchhoff–Love hypotheses. In the case of harmonic loading, a simplified formulation is given using a single-frequency approximation and the concept of complex moduli to characterise the non-linear cyclic properties of the material. As an example, the problem of forced vibrations and dissipative heating of a roller-supported layered beam containing piezoactive layers is solved. Different aspects of thermal, mechanical and electric responses to the mechanical and electric excitations are addressed. Dissipative heating due to electromechanical losses in the three-layer beam with piezoelectric layers is studied. It is assumed that the structure fails if the temperature exceeds the Curie point for piezoceramics. Using this criterion, the fatigue life of the structure is estimated. Limitations of the approximate monoharmonic approach are also specified.
Complex moduli; Fatigue life; Forced vibrations; Layered thin-wall structure; Piezoelectric material; Roller-supported beam
Nosing thin-walled tubes into axisymmetric seamless reservoirs using recyclable mandrels
Journal of Cleaner Production
18
16–17
1740-1749
2010
http://dx.doi.org/10.1016/j.jclepro.2010.06.025
This paper is focused on novel utilizations of raw materials and technologies for manufacturing lightweight metallic reservoirs. The objective is to develop an environmental friendly technology for producing gas and liquid storage reservoirs that ensures a more efficient utilization of raw materials and a better end-of-life management of products than other technologies currently used to fabricate metallic reservoirs. The proposed technology utilizes previously engineered single-stage nosing of thin-walled tubes using sacrificial (expendable) mandrels to develop a multi-stage process that makes use of recyclable mandrels for producing lightweight, axisymmetric, seamless reservoirs. Recyclable mandrels are cast from low melting point alloys, possess the ability to continuously adapt its shape to that of the preforms and are easily removed by melting, while leaving the reservoir intact, at the end of the process. The prospects for eliminating the welding routes commonly used in the fabrication of reservoirs and for remelting and recycling the mandrels, results in significant economic and time savings and offers potential for opening new markets for the production of low-cost seamless reservoirs. The presentation is supported by experimentation and numerical modelling based on independently determined mechanical properties of the materials with the purpose of understanding the deformation mechanics and identifying the major operating parameters of the proposed technology.
Experimentation; Finite element method; Recyclable mandrel; Tube nosing
PT-symmetric Quantum Mechanics: A Precise and Consistent Formulation
Czechoslovak Journal of Physics
54
10
1125-1132
2004
10.1023/B:CJOP.0000044014.54626.c8
The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical equivalence of PT-symmetric and conventional quantum mechanics. The results reported in this paper apply to arbitrary PT-symmetric Hamiltonians with a real and discrete spectrum. They hold regardless of whether the boundary conditions defining the spectrum of the Hamiltonian are given on the real line or a complex contour.
Quantum Physics
Born – Jordan Quantization and the Equivalence of Matrix and Wave Mechanics
arXiv
3
1-11
2014
10.1007/s10701-014-9831-z
In a recent Note we showed that the equivalence of Heisenberg's matrix mechanics and Schr\"odinger's wave mechanics requires that one quantizes both theories in the same way, using the Born--Jordan correspondence, which is motivated by physical considerations. We present here in detail the definition and properties of Born--Jordan quantization for arbitrary variables, and discuss its fundamental differences with Weyl quantization.
Generalized stress variables in Continuum Damage mechanics
Mechanics Research Communications
60
81-84
2014
10.1016/j.mechrescom.2014.06.006
“Damage” in Continuum Mechanics is an internal variable used at the scale of a Representative Elementary Volume (REV) to model the decrease of stiffness due to the nucleation and propagation of crack tips in the bulk. Moreover, irreversible deformation can result from specific distributions of crack displacement vectors. This communication presents a work in progress on the thermodynamic consistency of Continuum Damage Mechanics (CDM) for quasi-brittle materials such as rock or concrete, in which “damage” actually lumps two effects: cohesive damage (i.e. propagation of crack tips) and adhesive damage (i.e. separation of crack faces). It is shown that state-of-the-art CDM models lumping cohesive and adhesive damage into the same internal variable are based on contradicting thermodynamic assumptions, and that the ambivalent definition of damage requires the use of generalized stress variables in a CDM framework. Corresponding work-conjugates of damage and crack-induced deformation are expressed for a general CDM model. Future work will investigate the conditions in which a hyper-elastic framework can be used in CDM.
continuum damage mechanics
Inverse problems in experimental solid mechanics
Experimental Mechanics
2008
This chapter browses the use of inverse procedures in experimental solid mechanics. After a general introduction on inverse problems including a description of the different fields of application in general solid mechanics, the topic is narrowed down to the important area of the identification of the mechanical properties of materials, with a specific view to the use of full-field measurements. For this particular case, a more dedicated definition of the inverse problem to solve is given and the main routes to solve it are described. Finally,exmaples of experimental applications of such procedures are presented.
1; biomaterials; damage; elasto-; field measurements; finite element model updating; full-; general introduction to inverse; high strain rate testing; identification of constitutive equations; inverse problem; inverse problem, finite element model updating, vi; linear elasticity; plasticity; problems in solid mechanics; virtual fields method
Preterm rabbit lung tissue mechanics: maturational changes and effect of antenatal steroids.
Pediatric pulmonology
45
4
349-55
2010
10.1002/ppul.21191
Describe lung tissue and central airway mechanics using forced oscillation in preterm rabbits at different gestational ages and after maternal administration of betamethasone (BM).
Animals; Betamethasone; Betamethasone: pharmacology; Gestational Age; Glucocorticoids; Glucocorticoids: pharmacology; Lung; Lung: drug effects; Lung: embryology; Models, Animal; Rabbits; Random Allocation; Reference Values; Respiration, Artificial; Respiratory Mechanics; Respiratory Mechanics: drug effects; Respiratory Mechanics: physiology
Improving students' understanding of quantum mechanics by using peer instruction tools
AIP Conference Proceedings
1413
77-80
2012
10.1063/1.3679998
Quantum mechanics is a challenging subject, even for advanced undergraduate and graduate students. Here, we discuss the development and evaluation of research-based concept tests for peer instruction as a formative assessment tool in quantum mechanics (QM) courses. The preliminary evaluations show that these tools are effective in helping students develop a good grasp of quantum mechanics.
formative assessment; peer instruction; quantum mechanics
Mechanics of Wood Deformation
Forest Products Journal
17
3
55-67
1967
Discusses in general terms the types of theoretical approach employed to predict mechanical behaviour of wood and related substances. Part I deals with classical continuum mechanics and its application to elastic and viscoelastic behaviour of wood. Part II, Strength and plastic behaviour of wood, includes strength at an angle to the natural axes and fracture-strength behaviour on the basis of classical continuum mechanics and advanced theories. Part III, Geometrical models, discusses models that incorporate the complex anatomical structural features of wood at both the cell and the cell-wall levels. Reviews some models in the literature.
Forest products and their utilisation; physical and mechanical properties; Strength; wood; Wood; wood deformation
Fatigue strength of laser beam welded automotive components made of thin steel sheets considering size effects
International Journal of Fatigue
34
1
65-75
2012
10.1016/j.ijfatigue.2011.01.022
The applicability of and the quality of assessment using the nominal stress, structural stress and notch stress approaches for calculating the fatigue strength of laserbeam welded components made of thin steel sheets has been investigated. For this purpose, the fatigue lives of a longitudinal carrier, an injector and two tube-flange specimens have been determined by tests under constant amplitude loading. Fatigue cracks initiated at sharp root notches on all of these components. While the nominal stress is derived by theory of structural mechanics, the determination of structural and notch stresses is performed using 3D finite element models and solid elements. The structural stress is derived by an extrapolation of surface stress to the fatigue critical notch and the notch stresses by rounding the sharp root notch with a reference radius of rref = 0.05 mm. For all of the concepts used, the endurable stresses have been compared to the design SN-curves recommended by the International Institute of Welding (IIW). On comparing the quality of assessment of the different concepts, the notch stress approach shows the highest scatter. The highest endurable notch stresses occur in specimens with crack initiation at weld ends. These specimens have a very small highly loaded weld length. The lowest endurable stresses are determined for specimens with a long, equally loaded weld. The reason for these findings can be explained by statistical size effects. For an improved fatigue assessment, an easily applicable method is introduced, which takes into account the highly stressed weld length. ?? 2011 Elsevier Ltd. All rights reserved.
Fatigue assessment concepts; Laserbeam welds; Notch stress approach; Size effects
Theoretical and Applied Mechanics
Theoretical and Applied Mechanics
407-426
1989
10.1016/B978-0-444-87302-6.50031-4
Problems using the continuum theory of solid mechanics to analyze the tectonic movements are reviewed. The difference between these problems and those of ordinary mechanics problems are discussed. The main difference is that the problems here are inverse ones, from the surficial manifestation of tectonic movements to model the interior processes, from the present information to trace their histories. Information gathered by Earth scientists are to be used to guide the inversion. The establishment of proper constitutive relation and rupture criterion is of paramount importance in the numerical simulation. Challenging problems in solid mechanics are mentioned.
Ensembles in Quantum Mechanics
Compendium of Quantum Physics
557
199-201
2009
10.1007/978-3-540-70626-7_63
The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which immediately become unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems. — Albert Einstein (1879–1955) [1], p. 671. This quotation is perhaps the most famous statement of the ensemble interpretation of quantum mechanics. The role of the ensemble in quantum mechanics ranges from innocuous to profound, and even controversial.
Relativistic quantum mechanics
New York
176
300
1964
In this text the authors develop a propagator theory of Dirac particles, photons, and Klein-Gordon mesons and per-form a series of calculations designed to illustrate varioususeful techniques and concepts in electromagnetic, weak, andstrong interactions. these include defining and implementingthe renormalization program and evaluating effects of radia-tive corrections, such as the Lamb shift, in low-ordercalculations. The necessary background for the book is pro-vided by a course in nonrelativistic quantum mechanics atthe general level of Schiff's text, QUANTUM MECHANICS.
Fluid Mechanics
Fluid Mechanics
421-472
2012
10.1016/B978-0-12-382100-3.10010-1
This chapter focuses on computational fluid dynamics. Computational fluid dynamics (CFD) is a science that, with the help of digital computers, produces quantitative predictions of fluid-flow phenomena based on the conservation laws (conservation of mass, momentum, and energy) governing fluid motion. CFD has increased in importance and in accuracy; however, its predictions are never completely exact. Because many potential sources of error may be involved, one has to be very careful when interpreting the results produced by CFD techniques. The most common sources of error are mentioned in the chapter. The key to various numerical methods is to convert the partial different equations that govern a physical phenomenon into a system of algebraic equations. Different techniques are available for this conversion. CFD is merely a tool for analyzing fluid-flow problems. If it is used correctly, it can provide useful information cheaply and quickly. This chapter presents the basics of the finite-difference and finite-element methods and their applications in CFD. There are other kinds of numerical methods, for example, the spectral method and the spectral element method, which are often used in CFD. They share the common approach that discretizes the Navier-Stokes equations into a system of algebraic equations.
Calcite twinning strains in Alpine orogen flysch: Implications for thrust-nappe mechanics and the geodynamics of Crete
Lithosphere
1
3
174-191
2009
10.1130/L31.1
Recent uplift in Crete, along the Hellenic trench, has exposed the internal portions of Alpine nappes that were transported south along north-dipping thrusts from the middle Cretaceous to the Oligocene (100-20 Ma). Flysch deposited along the leading, southern edge of the Alpine foreland basin dates the timing of nappe transport and contains twinned calcite in synorogenic limestones and calcite veins that record the stress-strain fields associated with nappe transport and stacking for a 17 Ma period between 35 and 18 Ma. The flysch ages young away from the craton thereby documenting thin-skin thrusting and nappe motion, for the first time, toward the trench. Fossiliferous marine limestones and calcareous shales were deposited in marginal basins on the leading edges of four thrust-nappes in Crete: the higher and older flysch deposits (Asteroussia, Pindos) are underlain by younger flysch deposits of the Tripolitza and Plattenkalk nappes. The ages of these flysch deposits are well constrained and the flysch sequences are now found deformed between nappes without visible signs of Alpine metamorphism, except the lowest Plattenkalk flysch. Field observations in the flysch deposits include variable bedding, vein, fold axis, and kinematic orientations. Twinned calcite in the flysch limestones (16 samples, n = 425) and veins (23 samples, n = 612) generally preserve subhorizontal, in-transport shortening and vertical extension; where there is a strain overprint (high negative expected values [NEV]), a vertical shortening strain with transport-parallel extension (similar to N-S) is preserved. Strain magnitudes are greater in the vein sample suite, and differential stress magnitudes responsible for twinning are -230 bars for the entire sample suite. The tectonic evolution of the region involved thin-skinned shortening with south-vergent nappe formation, from north to south, followed by thrust motion on the Cretan detachment. Today, metamorphosed rocks (i.e., Phyllite-Quartzite unit [PQU]) overlie the basal Plattenkalk nappe placing earlier exhumed rocks of the Asteroussia, Tripolitza, and Pindos nappes on top of high-pressure (HP)-metamorphic rocks of the PQU without the deposition of any flysch.
From molecular models to continuum mechanics
Archive for Rational Mechanics and Analysis
164
4
341–381
2002
10.1007/s00205-002-0218-5
We present here a limiting process allowing us to write some continuum mechanics models as a natural asymptotic of molecular models. The approach is based on the hypothesis that the macroscopic displacement is equal to the microscopic one. We carry out the corresponding calculations in the case of two-body energies, including higher order terms, and also in the case of Thomas-Fermi type models.
Finite Element Analysis for Platform of 3 DOF Spacecraft Simulator Based on the Theory of Deformable Body Mechanics
Mechanical Engineering
2010
According to the theory of the thin plate and beam bending of elastics mechanics and taking the hypothesis of G.kirchhoff into account, a finite element model of the platform is built. Based on the theory of deformable body mechanics and kinetics, the formulary for the mass-center elastics displacement of the platform caused by deforming was deduced. Depending on the theory of the spacecraft attitude kinetics, the gravity torque vector in the body frame was given as the boundary condition of the finite element model and the formulary for unbalance torque caused by the mass-center displacement was presented. The result and analysis have revealed the essential reason that platform deforming causes unbalance torque is the difference of stiffness of the platform structure in various directions. The unbalance torque cause by the shift between the deformable body mass-center of the platform and the center of rotation is a function of the loading condition and of the elevation angle. It varies with the sine of twice the elevation angle
- simulator
Quantum decoherence and classical correlation in quantum mechanics
Physical Review D
42
8
2929-2932
1990
We study two conditions for the quantum system to behave classically: decoherence in the quantum interference and the establishment of the classical trajectory in phase space. We show, despite the fact that these two conditions partially conflict with each other, the upside-down harmonic oscillator with a diffusion term satisfies them simultaneously. The implications for quantum cosmology and the measurement theory of quantum mechanics are given.
Survey of Engineering Mechanics in Civil Engineering Curricula
2008 American Society of Engineering Education Annual Conference & Exposition
AC2008 - 1139
2008
Newtonian mechanics provides most of the core concepts that enable civil engineering students to identify, formulate, and solve engineering problems. The Department of Civil and Environmental Engineering at Villanova University is investigating how to better present material in the core mechanics courses to better meet the educational needs of the students and improve learning. The core sequence in mechanics at Villanova University consists of five courses: Statics/Dynamics, Mechanics of Solids, Civil Engineering Materials, Fluid Mechanics and Fluid Mechanics Laboratory. To determine the current state of practice in mechanics education, the authors conducted a survey of civil engineering mechanics curricula at fifty universities. Civil engineering curricula present mechanics in a variety of courses and formats; the survey evaluated format (e.g. lecture, laboratory, recitation, or workshop), total credits in the curriculum, total credits devoted to mechanics courses, lecture hours, laboratory hours, whether the courses were required or elective, administrating department and the school's classification and profile. Additionally innovative practices and combined courses were noted. Survey information was acquired via the school's respective web sites to develop a database on engineering mechanics. The survey results show that while the mechanics courses and sequencing are generally similar, there exists some variation among programs. This paper presents the detailed results of the survey and describes the major similarities and differences identified. Innovative and unique practices among the programs surveyed are identified, and recommendations are provided to initiate mechanics curricula change. © American Society for Engineering Education, 2008.
Some applications of geometry is continuum mechanics
Reports on Mathematical Physics
12
1
35-44
1977
10.1016/0034-4877(77)90044-1
Some contemporary ideas from differential geometry are applied to continuum mechanics. The Lie derivative is used to clarify the notion of “objective rates”, an intrinsic treatment of Piola transformations is described, a simplified proof of Vainberg's theorem for potential operators is given by way of the Poincaré lemma on infinite dimensional manifolds, and a new derivation of the basic equations of continuum mechanics is presented which is valid in a general Riemannian manifold setting.
Fracture mechanics for the reconstruction of Noto Cathedral
Construction and Building Materials
17
8
579-593
2003
10.1016/S0950-0618(03)00055-2
The baroque buildings of Sicily should be ideal subjects of Fracture Mechanics, having heights up to 60 m, PGA up to 0.30×g, low strengths, few reinforcements, aggregate with irregular stones in the most vulnerable zones. Their analysis constitutes a severe test. The damages between the earthquake on 13.12.1990 and its collapse on 13.03.1996 are due to cracking development always. A monotonic static analysis by FE is performed here. Prestressing and lightening are examined.
Cathedral; Cracking; Finite element analysis; Fracture mechanics; Stone masonry
Statistical mechanics of the isothermal Lane-Emden equation
Journal of Statistical Physics
29
3
561-578
1982
10.1007/BF01342187
{{{For classical point particles in a box ? with potential energy H(N)=N-1(1/2) ?i?j=1NV(xi,xj) we investigate the canonical ensemble for largeN. We prove that asN?8 the correlation functions are determined by the global minima of a certain free energy functional. Locally the distribution of particles is given by a superposition of Poisson fields. We study the particular case ?=[-pL, pL] andV(x, y)=}-{\\ss} cos(x-y),L}>0, {\\ss}}>0.
Computational models of vascular mechanics
Computational Modeling in Biomechanics
99-170
2010
10.1007/978-90-481-3575-2_4
Many of the world’s leading causes of death involve pathology of the vasculature, both arterial and venous. In addition to the biochemical and genetic factors governing vascular health and disease, mechanics strongly modulates the form and function of the vessel wall. Biomechanical analysis is being increasingly used to not only elucidate key disease processes, but also to predict disease progression and response to therapeutic and surgical intervention on a patient-specific basis. This chapter reviews some of the recent advances in computational vascular mechanics, with references to key works in constitutive modeling, fluid-structure interaction, image-based modeling, and atherosclerotic plaque mechanics.
Magnetoelastic thin films and multilayers for high-frequency applications
Smart Structures and Materials 2002: Active Materials: Behavior and Mechanics
4699
542-552
2002
Doi 10.1117/12.475010
Magnetoelastic and magnetic high-frequency proper-ties of single and multilayer thin films are investigated with respect to applications in micro-inductors and as remote-interrogated sensors for mechanical quantities. The basic structure is a thin film inductor incorporating a magnetic material in order to enhance the inductance. In case of a sensor the inverse magnetostriction is used to change the permeability of the magnetic material and thus the inductance of the device. Materials properties like saturation magnetization, anisotropy field, resulting domain structures, electrical resistivity as well as the stress state of the films have to be adjusted carefully in order to meet certain requirements like high cut-off frequencies combined with low losses, and a high and controllable inverse magnetostrictive effect. In this paper (Fe-Co/Fe-Co-B-Si) multilayers are investigated in terms of their magnetic, high-frequency, and structural properties. (Fe50Co50/Co80B20) multilayers, e.g., have been fabricated which show ferromagnetic resonance frequencies up to 5 GHz while exhibiting a high inverse magnetostrictive effect up to the GHz frequency range. The obtained results for first LC circuits realized using (FC50Co50/Co80B20) multilayers are discussed.
high-frequency permeability; inductors; magnetic-properties; magnetoelastic thin films; permeability; sensors
Common Sense and a ``{Wigner--Dirac}'' Approach to Quantum Mechanics
The Monist
80
1
131-159
1997
This paper presents a case for the thesis that quantum mechanics is compatible with common sense. I make this case by exhibiting a Wignerian formulation of quantum mechanics (i.e., the phase space picture) and a neo-Dirackian interpretation of quantum mechanics thus formulated. Together these reconcile quantum mechanics with some commonsense theses, which might seem to be violated by quantum mechanics.(edited)
Resonance expansions in quantum mechanics
Czechoslovak Journal of Physics
55
9
1141-1150
2005
10.1007/s10582-005-0119-6
The goal of this contribution is to discuss various resonance expansions that have been proposed in the literature.
Quantum mechanics of black holes
arXiv preprint hep-th/9412138
1994
These lectures give a pedagogical review of dilaton gravity, Hawking radiation, the black hole information problem, and black hole pair creation.
Two problems in Classical Mechanics
ArXiv Physics eprints
2004
A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects.
general physics
Young's Modulus Measurement of Polysilicon Thin Film Using Thin Film Tensile Tester Equipped with Electrostatic Force Grip
Advanced Technology in Experimental Mechanics Conference
1-5
2003
Young's modulus of polysilicon thin film was measured by means of\na tensile tester equipped with an electrostatic force grip system.\nImages of gauge marks on a specimen were captured by a high-speed\ndigital CCD camera and the tensile strain was calculated from the\nimages. The linear stress-strain curve was obtained and Young's modulus\nmeasured. The polysilicon specimens were 1.7 æm thick, 20 and 50\næm wide, and 100 and 500 æm in gauge length. The mean Young's modulus\nranged from 163 ~ 174 GPa, which agreed with the theoretical and\nvalues measured using the bulge method. The resolution of the strain\nmeasurement was less than 50 nm, and the comparison to the differential\nmethods shows the image analysis system had smaller deviations.
CCD camera; Experimental; force; measurement; Mechanic; polysilicon; resolution; semiconductor; sensor; strain; Strain measurement; stress-strain curve; tensile strain; tensile tester; thin film; Young's modulus; Young's modulus measurement
Thermomechanical postbuckling of imperfect shear deformable laminated plates on elastic foundations
Computer Methods in Applied Mechanics and Engineering
189
761-784
2000
10.1016/S0045-7825(99)00328-X
Postbuckling analysis is presented for a simply supported, shear deformable composite laminated plate subjected to combined axial and thermal loads and resting on an elastic foundation. The two cases of thermal postbuckling of initially compressed plates and of compressive postbuckling of initially heated plates are considered. The initial geometric imperfection of the plate is taken into account. The formulations are based on Reddy's higher order shear deformation plate theory, including the plate-foundation interaction and thermal effects. The analysis uses a perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates resting on Pasternak-type or softening nonlinear elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation and initial geometric imperfections are studied.
combined loading; composite laminated thick plate; elastic foundation; higher order shear deformation; perturbation technique; plate theory; structural stability; thermomechanical postbuckling
Stiffness reduction of cracked solids
Engineering Fracture Mechanics
26
5
637-650
1987
10.1016/0013-7944(87)90129-9
A method for the determination of the effective moduli of elastic solids containing a doubly periodic rectangular array of cracks is given. The derivation is based on the analysis of a unit cell in which the displacement vector is expanded to a second order in the distances from centerlines. The equilibrium equations in conjunction with the continuity conditions for the displacements and tractions, give a system of equations for the elastic field variables. The determination of the elastic internal energy provides the requested effective moduli of the cracked body. The method is applied to predict the loss of stiffness of cracked isotropic solids and unidirectional composites, as well as cracked cross-ply laminates.
Measuring Strains through the Thickness of a Composite Structural Specimen Subjected to Bending
Experimental Mechanics
49
6
877-880
2009
10.1007/s11340-008-9209-2
This study concerns the central reinforced zone of a composite structural specimen. In order to estimate the strain distribution during a series of three and four-point bending tests, several optical fiber Bragg grating sensors have been embedded in various levels of the ply stack. Simultaneously, surface strain field measurements by 3-D digital image correlation are undertaken. Both techniques show a general linear distribution of longitudinal strains through the thickness of the thick zone but values are slightly different. A numerical model is developed and a test-calculation dialogue is carried out. The complementary information given by the two optical techniques for in-core and surface measurements reveals the importance of considering structural and edge effects.
Tuning scaffold mechanics by laminating native extracellular matrix membranes and effects on early cellular remodeling.
Journal of biomedical materials research. Part A
April
1-9
2013
10.1002/jbm.a.34791
At approximately 50 µm thin, the human amniotic membrane (hAM) has been shown to be a versatile biomaterial with applications ranging from ocular transplants to skin and nerve regeneration. These investigations describe laminating layers of the hAM into a multilayered, conformation creating a thicker, more robust biomaterial for applications requiring more supportive structures. Amniotic membranes were decellularized using 4 M NaCl and prepared as either flat single-layered sheets or rolled into concentric five-layered configurations. Constructs were seeded with human vascular smooth muscle cells and cultured over 40 days to quantify biological and mechanical changes that occurred during early remodeling events. By day 40 single-layered constructs displayed a decreasing trend in cellular densities and glycosaminoglycan (GAG) concentration, comparative to multilayered constructs with increasing cell densities (from 9.1 to 32 × 10(6) cells/g) and GAG concentrations (from 6.07 to 17.4 mg/g). Oxygen diffusion was calculated and found to be sufficient to maintain cell populations through the constructs full thickness. Although an overall decrease in the modulus of elasticity was noted, the modulus in the failure range of rolled constructs stabilized at values 25 times higher than single-layered constructs. Rolled constructs typically displayed an upregulation of contractile and matrix remodeling markers (α-actin, SM22 and type 1 collagen, MMP-2 respectively) indicating biological adaptation. Considerable design flexibility can be achieved by varying the number of scaffold layers, allowing the possibility of tuning the constructs physical dimensions, shape and tensile properties to suit specific targeted vascular locations. © 2013 Wiley Periodicals, Inc. J Biomed Mater Res Part A, 2013.
early; rolling approach; tissue engineering
Pure bending of curved beams of thin-walled rectangular box section
Journal of Applied Mechanics, Transactions ASME
58
1
154-156
1991
A closed-form solution of the subject problem is presented. The analytical method resembles that used by Bleich (1933) to study curved beams of I or T section. It is found that the circumferential stress may be smaller than a perpendicular stress that arises from flexing of parts of the box. Accuracy of the solution is verified by comparison with finite element analyses.
Dependence of Active Layer Thickness of Polymer Thin Film Transistors on Electrical Characteristics of Inverter Circuit
2009 Electronics Robotics and Automotive Mechanics Conference CERMA
1
259-262
2009
10.1109/CERMA.2009.63
Electrical simulations of a single inverter circuit have been done to analyze effects on them of the active layer thickness of PTFTs. Unified model and extraction method was introduced in Smash simulator using Verilog-A. We validate results with measured characteristics of PTFTs fabricated with PMMA on P3HT. Transfer characteristic of the inverter is strongly depending on the active layer thickness.
inverter; p3ht; tft; thickness
Local values in quantum mechanics
Physics Letters A
212
315-319
1996
An exact equation is derived for the uncertainty of an operator in terms of the real and imaginary parts of (A) over cap psi/psi. We show that the uncertainty always consists of two terms which are qualitatively different and that can be interpreted in terms of local values. Exact equations are given for the spread of momentum, energy, and squeezing operator in terms of the amplitude and phase of the wave function
8; amplitude; and; ENERGIES; energy; equation; Equations; exact; function; in; L; local; LOCAL VALUES; mechanic; mechanics; momentum; operator; phase; quantum; Quantum Mechanics; Quantum-Mechanics; TERM; Terms; two; uncertainty; value; VALUES; wave; WAVE-FUNCTION
Fractional Classical Mechanics
arXiv.org
math-ph
2013
Fractional classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented for the fractional classical mechanics. The Lagrangian of fractional classical mechanics has been introduced, and equation of motion has been obtained. Fractional oscillator model has been launched and solved in 1D case. A new equation for the period of oscillations of fractional classical oscillator has been found. The interplay between the energy dependency of the period of classical oscillations and the non-equidistant distribution of the energy levels for fractional quantum oscillator has been discussed. We discuss as well, the relationships between new equations of fractional classical mechanics and the well-known fundamental equations of classical mechanics.
Fluid Mechanics E1.2
Image Rochester NY
11
1
51-52
2005
One of the bestselling books in the field, Introduction to Fluid Mechanics continues to provide readers with a balanced and comprehensive approach to mastering critical concepts. The new seventh edition once again incorporates a proven problem-solving methodology that will help them develop an orderly plan to finding the right solution. It starts with basic equations, then clearly states assumptions, and finally, relates results to expected physical behavior. Many of the steps involved in analysis are simplified by using Excel.
Advances in computational mechanics
Nucl Eng Des
134
1
1-22
1992
10.1016/0029-5493(92)90004-F
Some of the major issues which have been addressed in finite element\nresearch are reviewed, including some issues which remain unresolved.\nThe focus is on topics related to problems of constrained media and\nfluid dynamics by finite elements. Two examples of constrained media\nare considered: isoparametric element approaches to incompressible\nmaterials and beam and shell elements. Pertinent issues include locking,\nspurious singular modes, and stress oscillations. In fluid mechanics,\nthe central themes are stable treatments of the convection or transport\nterms and arbitrary Lagrangian-Eulerian meshes.
Modulation of optical and electrical properties of sputtering-derived amorphous InGaZnO thin films by oxygen partial pressure
Journal of Alloys and Compounds
615
636-642
2014
10.1016/j.jallcom.2014.06.194
Sputtering-derived amorphous InGaZnO (a-IGZO) thin films were grown on Si and glass substrates in a mixed ambient of Ar and O2 at fixed 0.5Pa working pressure. The influence of O2/Ar flow ratio on the optical and electrical properties of a-IGZO thin films has been systematically investigated by means of characterization from spectroscopic ellipsometry (SE), X-ray diffraction (XRD), scan electron microscopy (SEM), atomic force microscope (AFM), UV–vis spectroscopy, and electrical measurements. Results have shown that the band gap of the as-deposited IGZO films increases from 3.45eV to 3.75eV as the O2/Ar flow ratio increases from 0% to 20%. Blue shift in band gap and reduction in reactive index with increasing the O2/Ar flow ratio have been detected. Electrical measurements have indicated the increase in resistivity at higher O2/Ar gas flow ratio. Related mechanics about the increase in band gap and resistivity have been discussed in detail.
Amorphous InGaZnO films; Band gap; Resistivity; Sputtering
Measurements of Interface Fracture Strength between Fiber-Reinforced Composite Laminates and Thin Surface Films Using the Blister Test
Key Engineering Materials
471-472
315-319
2011
10.4028/www.scientific.net/KEM.471-472.315
The blister test is a promising test method to determine the interface fracture toughness of thin films adhering to rigid fibre reinforced plastics. In this paper nonlinear finite element analysis is used to determine a suitable layout for both the shaft loaded and the pressurised blister test. On the example of a PET film adhering to a quasi-isotropic fibre reinforced plastic, it is shown that energy release rates in a range of 0-1500N/m can be obtained for a 0.5mm thick film if test parameters are carefully selected. The two main causes for deviations of the analytic solution from the FEA results is attributed to infringement of the membrane limit condition and plastic deformation in the film. © (2011) Trans Tech Publications.
abstract; a promising test method; blister; energy release rate; finite element analysis; fracture mechanics; fracture toughness; fracture toughness of; in this paper nonlinear; lister test; rigid fibre reinforced plastics; the blister test is; thin films adhering to; to determine the interface
Inverse method for detection and sizing of cracks in thin sections using a hybrid genetic algorithm based signal parametrisation
Theoretical and Applied Fracture Mechanics
49
2
185-198
2008
10.1016/j.tafmec.2007.11.004
A hybrid-GA method, based on signal parameterization, has been reported here for the improved detection and sizing of surface cracks of small sizes/depths in thin sections. The method relies on parameterizing the composite reference from the defect into its individual components i.e., the crack tip diffracted echo and the corner trap echo and subsequently use the relative arrival time technique (RATT). The phased array ultrasonic technique was employed in the investigation. Both experimental and simulated signals were used in the study. It is shown through both simulations and experiments that the hybrid-GA is successful in parameterizing both non-overlapping and overlapping echoes encountered in thin sections. It is additionally shown that the hybrid-GA improves the signal to noise ratio and correct for under-sampling of data. (c) 2007 Elsevier Ltd. All rights reserved.
Supersymmetric classical mechanics: free case
arXiv preprint hep-th/0201242
13
2002
We present a review work on Supersymmetric Classical Mechanics in the context of a Lagrangian formalism, with $N=1-$supersymmetry. We show that the N=1 supersymmetry does not allow the introduction of a potential energy term depending on a single commuting supercoordinate, $\phi (t;\Theta)$.
Black Holes and Superconformal Mechanics
Physical Review Letters
81
4553
1998
10.1103/PhysRevLett.81.4553
The dynamics of a (super)particle near the horizon of an extreme Reissner-Nordström black hole is shown to be governed by an action that reduces to a (super)conformal mechanics model in the limit of large black hole mass.
Assessment of plate elements on bending and vibrations of composite structures
Mechanics of Advanced Materials and Structures
September 2001
333-357
2002
10.1080/1537649029009698
This article assesses classical and refined finite plate elements on bending and vibrations of layered composites and sandwich structures. To this purpose, recent authors' findings have been extended to dynamics. About 20 plate finite elements have been implemented and compared: classical ones based on displacement assumptions are compared to advanced mixed elements which are formulated on the basis of Reissner's mixed variational theorem. Finite elements which preserve the independence of the number of independent variables from the numbers of the N<sub>1</sub> layers (equivalent single-layer models) as well as those elements in which the number of the unknown variables remains N<sub>1</sub>-dependent (layer-wise models) are both considered. Linear up to fourth-order expansions in the thickness direction are treated for the unknown stress and displacement variables. Sandwich beams and cross-ply as well as angle-ply composites plates have been analyzed. Simply supported as well as clamped edges have been considered. Finite-element results have been implemented and compared, where available, to analytical closed form solutions. Mostly the fundamental circular frequency has been used as a test bed to assess the whole implemented multilayered elements
Shear Correction Factors for Orthotropic Laminates Under Static Load
Journal of Applied Mechanics
40
1
302
1973
10.1115/1.3422950
In this Note the procedure of Chow is extended to orthotropic laminates of nonsymmetric construction, and the accuracy of the approach is demonstrated by comparing the static bending solution for various laminated plates to solutions obtained by satisfying exact theory of elasticy in each ply as well as the interface continuity conditions. Numerical results show the values of k//1**2, and k//2**2 depend on detailed laminate construction. Significant difference between k//1**2 and k//2**2 is also noted for symmetric laminates.
COMPOSITE MATERIALS - Elasticity; STRESSES - Analys
Nonlinear Analytical Approach for Preliminary Sizing of Discrete Composite Stringer Terminations
Aiaa Journal
47
3
606-617
2009
10.2514/1.37745
A recently developed nonlinear approach is adapted and used to predict\ncrack initiation in stringer terminations of discretely assembled\ncomposite panels made from skin and stiffeners. A linear elastic\nfracture mechanics based submodel is used to simulate the crack initiation\nin the critical regions and the influence of ply drop-off is captured.\nThe von Karman formulation for moderately large deflections in plates\nis used to capture the nonlinear structural behavior; three-dimensional\nassemblies are schematized and the effect of eccentricity is included\nin the simulation. An optimum design criterion is sought and basic\nguidelines for good design are provided. Furthermore, a method for\npreliminary assessment of structural strength is proposed and predictions\nare validated against detailed nonlinear finite element analysis.
Fluid Mechanics
Fluid Mechanics
1-37
2012
10.1016/B978-0-12-382100-3.10001-0
This chapter focuses on kinematics, the study of motion without reference to the forces or stresses that produce the motion. This chapter presents fluid kinematics in two and three dimensions starting with simple fluid-particle-path concepts and then proceeding to topics of greater complexity. These include: particle- and field-based descriptions for the time-dependent position, velocity, and acceleration of fluid particles; the relationship between the fluid velocity gradient tensor and the deformation and rotation of fluid elements; and the general mathematical relationships that govern arbitrary volumes that move and deform within flow fields. There are two ways to describe fluid motion: Lagrangian description and Eulerian description. These descriptions are described in the chapter.
Statistical mechanics model for protein folding
AIP Conference
1-24
2009
We present a novel statistical mechanics formalism for the theoretical\ndescription of the process of protein folding$\leftrightarrow$unfolding\ntransition in water environment. The formalism is based on the construction of\nthe partition function of a protein obeying two-stage-like folding kinetics.\nUsing the statistical mechanics model of solvation of hydrophobic hydrocarbons\nwe obtain the partition function of infinitely diluted solution of proteins in\nwater environment. The calculated dependencies of the protein heat capacities\nupon temperature are compared with the corresponding results of experimental\nmeasurements for staphylococcal nuclease and metmyoglobin.
FRACTAL DAMAGE MECHANICS OF GEOMATERIALS
TERRA NOVA
5
5
421-437
1993
10.1111/j.1365-3121.1993.tb00280.x
Recent progress in a new field of mechanics of diluted solids is\nreviewed -the fractal mechanics of geomaterials. It has become clear\nthat the mechanics of geomaterials should take into consideration the\ninfluence of the fracture delocalization process on fundamental fracture\ncharacteristics such as the strength, the fractal dimension of a network\nof cracks, the surface energy of fracture and the elastic properties of\nfragmented media.\nThe percolation model of fracture proposed by this author in 1979, in\naccordance with experimental data, treats the destruction process as a\nsequence of nucleation and coalescence of microcracks caused by their\ninteraction. This approach enables the mathematical description of the\nentire process of fracturing. Many aspects of the fracture of\nheterogeneous solids - the magnitude-frequency distribution of seismic\nactivity and acoustic emission, the high-surface energy of fracture in\ncomposite materials and rocks, the geometrical peculiarities of a crack\nnetwork, the appearance of forerunners of mechanical collapse, and the\nintermittency of the fracture process in the time domain - find\nquantitative explanation in the percolation model. The process of\ndetermining the elasticity of fractured media, which is the object of\nthe elastic percolation theory, also reveals some unusual features that\ncan affect the process of geophysical interpretation. For example, the\nelastic modulus M and the velocity of elastic waves v become\nscale-dependent in the fractal regime. It is shown that the fractal\ndimension of the elastic modulus of a depleted solid differs\nsignificantly for `refilled' and `hollow' voids.\nSeveral implications of fractal mechanics for seismology are considered,\nnamely the generalized form of the magnitude-frequency relationship, the\nphenomenon of anomalous tensosensitivity, the scale-dependence of the\nelastic moduli of massively faulted rocks and the possibility of\napparent seismic boundaries.
Electro-mechanics in biventricular models
Computers in Cardiology, 2004
537-540
2004
Cardiac electro-mechanical models are valuable tools to gain insights in physiology and pathophysiology of the heart. Progressive models can be created by fusion of various basic models. In this work biventricular models of cardiac electro-mechanics were developed by fusion of anatomical, electrical, and mechanical models. The importance of anatomical modeling was researched by inclusion of two different anatomical models, i.e. an analytical and a magnetic resonance diffusion tensor imaging based model. The fused models were applied in simulations of physiological behavior and results of these were analyzed. Significant difference of deformation were found, which can be attributed to the anatomical models. The analysis emphasized the importance of appropriate anatomical modeling for simulations of cardiac mechanics.
Statistical Mechanics on Isoradial Graphs
Springer Proceedings in Mathematics
11
491-512
2012
10.1007/978-3-642-23811-6_20
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs naturally arise in two approaches used by physicists: transfer matrices and conformal field theory. This leads us to the fact that isoradial graphs provide a natural setting for discrete complex analysis, to which we dedicate one section. Then, we give an overview of explicit results obtained for different models of statistical mechanics defined on such graphs: the critical dimer model when the underlying graph is bipartite, the 2-dimensional critical Ising model, random walk and spanning trees and the q-state Potts model.
Nonlinear responses of a symmetric cross-ply composite laminated cantilever rectangular plate under in-plane and moment excitations
Composite Structures
100
554-565
2013
10.1016/j.compstruct.2013.01.013
The nonlinear dynamic responses of a composite laminated cantilever rectangular plate under the in-plane and moment excitations are studied. The Reddy’s higher-order shear deformation theory and the von Karman type equations for the geometric nonlinearity are used to establish the governing equations of motion. The nonlinear governing partial differential equations of motion for the composite laminated cantilever rectangular plate are derived by using the Hamilton’s principle, which are transformed into a two-degree-of-freedom nonlinear system by using the Galerkin approach. A new kind of expression of the displacement functions is given. The case of 1:2 internal resonance and primary parametric resonance is taken into account. The influence of the in-plane and moment excitations on the nonlinear vibrations of the composite laminated cantilever rectangular plate is discussed by using numerical simulation. The numerical results demonstrate that there exist the bifurcation and chaotic motions of the composite laminated cantilever rectangular plate. The nonlinear frequency–response curves of this system under different excitations are investigated to show the relationships between the excitations and the amplitudes of the first two modes.
Composite laminated cantilever rectangular plate; High-order shear deformation theory; Nonlinear responses; Periodic and chaotic motions
Nerve regeneration through a two-ply biodegradable nerve guide in the rat and the influence of ACTH4-9 nerve growth factor
Microsurgery
12
6
412-419
1991
10.1002/micr.1920120608
Biodegradable polyurethane-based (PU) nerve guides, instilled with or without ACTH4-9 analog (a melanocortin) were used for bridging an 8 mm gap in the rat sciatic nerve and were evaluated for function and histological appearance after 16 weeks of implantation. Autologous nerve grafts functioned as controls. The guides successfully enabled the sciatic nerve to regenerate across the 8 mm gap, thus effectively reestablishing the contact between the proximal and distal nerve ends. The mean conduction velocity, motor latency, and muscle action potentials of all the nerve guides did not differ significantly from the autografts. The histological quality of the regeneration in the nerve guides was significantly better than in the autografts; in the nerve guides, a well-defined nerve cable of normal architecture had regenerated without extensive endoneural scarring as seen in the autografts. ACTH4-9 instilled in the nerve guides showed a slight, but significant, increase in the number of myelinated axons. It is concluded that biodegradable PU nerve guides result in similar functional recovery when compared with autografts, but their histological quality is significantly better. ACTH4-9 showed only slight, but significant, improved nerve growth promoting activity. Therefore biodegradable PU nerve guides with ACTH4-9 would appear to be promising alternatives to autografts for bridging nerve defects.
QBism AND LOCALITY IN QUANTUM MECHANICS
American Journal of Physics
83
197-198
2015
10.1119/1.4907264
A critique to the article by C.A. Fuchs, N.D. Mermin, and R.Schack, "An introduction to QBism with and application to the locality of quantum mechanics" that appeared in Am. J. Phys. 82 (8), 749-754 (2014)
The mechanics of fatigue crack growth in a medium with microdamage
Journal of Applied Mathematics and Mechanics
59
2
289-297
1995
10.1016/0021-8928(95)00032-K
Fatigue crack growth at a high stress level is considered using the\nmodel of a thin plastic zone taking microdamage accumulation in this\nzone into account. It is assumed that a crack grows when the stability\ncondition of the #cracked##body-loading# system is violated. This\ncondition is treated in the framework of the principle of virtual\nwork for systems with unilateral constraints. The damage accumulation\nprocess in the plastic zone and on its prolongation is assumed to\ndepend on the opening stress range. The process of crack growth is\nstudied by numerical simulation. Diagrams of the growth of fatigue\ncracks are obtained that describe all three stages of fatigue damage\nincluding the anomalous behaviour of short cracks and the accelerated\ngrowth near the final fracture. It is shown that the proposed theory\npredicts that the slope of the middle part of the diagram is close\nto two when the parameters of microdamage accumulation vary over\na wide range.
Fluid Mechanics
Image Rochester NY
6
1
539
1987
10.1007/b138775
Mjog god kennslubok. Agaet fyrir byrjendur sem og lengra komna
Fracture mechanics. II.
The Journal of bone and joint surgery British volume
43-B
9
162-166
1961
Fracture-toughness tests described to obtain fracture data for transformation into allowable design stresses
Molecular Mechanics.
Current pharmaceutical design
9
49-59
2013
Molecular Mechanics (MM) force fields are the methods of choice for protein simulations, which are essential in the study of conformational flexibility. Given the importance of protein flexibility in drug binding, MM is involved in most if not all Computational Structure-Based Drug Discovery (CSBDD) projects. This section introduces the reader to the fundamentals of MM, with a special emphasis on how the target data used in the parametrization of force fields determine their strengths and weaknesses. Variations and recent developments such as polarizable force fields are discussed. The section ends with a brief overview of common force fields in CSBDD.
Molecular mechanics.
Current pharmaceutical design
20
20
3281-92
2014
10.1016/j.biotechadv.2011.08.021.Secreted
Molecular Mechanics (MM) force fields are the methods of choice for protein simulations, which are essential in the study of conformational flexibility. Given the importance of protein flexibility in drug binding, MM is involved in most if not all Computational Structure-Based Drug Discovery (CSBDD) projects. This paper introduces the reader to the fundamentals of MM, with a special emphasis on how the target data used in the parametrization of force fields determine their strengths and weaknesses. Variations and recent developments such as polarizable force fields are discussed. The paper ends with a brief overview of common force fields in CSBDD.
Drug Discovery; Quantum Theory
A study of generating yarn thin places of murata vortex spinning
Textile Research Journal
79
2
129-137
2009
10.1177/0040517508092021
In Murata vortex spinning, fiber loss is an important cause of the generation of yarn thin areas. In this paper, based on the attenuation law of flow field inside the nozzle block, the force analysis of a separated fiber twined over the top exterior of a hollow spindle in a twisting chamber is carried out, and the movement of a separated fiber affected by a swirling current is discussed. We also present a simple analytical formation that determines the critical angular velocity of the open-end trailing fiber rotating around the hollow spindle, as a function of the length of the core fiber and fiber radius, as well as other parameters. The critical angular velocity can affect whether the leading end of the fiber is pulled out from the yarn trail or not, which can explain the generation of fiber loss and yarn. The critical angular velocity increases with increasing length of the core fiber and decreasing fiber radius. Above a certain nozzle pressure, the fiber radius is larger, there is greater fiber loss and there are a greater number of thin places in the vortex spun yarn. Increasing the nozzle pressure first enhances the yarn tenacity, and then generates more fiber loss and yarn thinning in places, and also causes a deterioration of the yarn properties when the nozzle pressure exceeds the critical point. 2009 SAGE Publications.
Agricultural products; Angular velocity; Equations of state; Fibers; Flow fields; Flow of fluids; Flow simulation; Mechanics; Nozzles; Spinning (fibers); Vortex flow; Wool; Yarn
Vibrational power flow analysis of thin cylindrical shell with a circumferential surface crack
Journal of Sound and Vibration
302
1-2
332-349
2007
DOI 10.1016/j.jsv.2006.12.001
In the view of structure-borne sound, the structural wave and power flow characteristics of infinite thin cylindrical in vacuo shell with a circumferential surface crack are investigated. In this paper, the equivalent distributed line spring is designed to model the surface crack in the shell. The local compliance matrix due to the presence of the crack is deduced from fracture mechanics and three modes of the crack stress intensity factors and their coupling are considered in the local compliance matrix. The vibration of the thin shell is described by the Flugge shell equations. Under the excitation of radial harmonic line force, the input power flow and transmitted power flow of uncracked and cracked shells are obtained. The results show that the vibrational power flow of cracked shell changes substantially due to the presence of crack, and the change is strongly related to the depth and location of crack. Contours of input power flow at different frequencies are constructed to identify the location and depth of the crack. It is revealed that the power flow in the cylindrical shell structures can be used as an alternative defect information carrier. This research provides theoretical basis for the crack detection by measuring the vibrational power flow in cracked shell structures. (c) 2006 Published by Elsevier Ltd.
beams; energy-flow; fluid; identification; pipes; plate structures; propagation
Finite element simulation of the axial collapse of thin-wall square frusta
International Journal of Crashworthiness
6
2
155-164
2001
10.1533/cras.2001.0169
In vehicle crashworthiness studies special effort has been spent on experimental research and in establishing safe theoretical design criteria on the mechanics of crumpling, providing, in this manner, to the engineers the ability to design safe vehicle structures, so that the maximum amount of the crash energy will dissipate while the material surrounding the passengers department is deformed. Generally, this energy absorbing capability depends upon the governing deformation phenomena of all or part of structural components of simple geometry, such as thin-walled tubes, cones, frames, sections etc. In particular, the crash analysis of plated structural components has been traditionally based on destructive prototype testing and requires analytical and/or numerical theoretical models to incorporate in detail the main crash phenomena, i.e. local buckling, post-buckling and maximum strength of each section and the various crumpling mechanisms expected. For this purpose, specialized finite element codes have been developed to establish efficient design of energy absorbing systems. The main objective of the present paper is to apply the explicit FE code LS-DYNA to the simulation of the crash behaviour of metallic thin-walled square frusta subjected to axial compression. The results taken from the simulation, in comparison to the actual experimental data on similar specimens, agree on many aspects and the concluding remarks pertaining to the design of the crushing process are drawn.
Continuum Mechanics in a Restructured Engineering Undergraduate Curriculum
International Journal of Engineering Education
16
4
301-314
2000
The framework of the revised undergraduate engineering curriculum at Texas A&M University consists of the basic conservation principles and their application to engineering science. The conservation principles are presented in a way consistent with the Kolb learning cycle and an active approach to teaching. Utilizing these principles, a unified pedagogical process is developed, which can be applied to cover topics traditionally taught under statics, dynamics, fluid mechanics, thermodynamics, heat transfer, solid mechanics, materials science and electrical circuits. Using this instructional framework, the students can analytically solve simple engineering problems, while they learn how to formulate complex problems at early stages of their undergraduate education. Since their technical ability to analyze such complex problems is limited during their second or even third year of the undergraduate curriculum, the utilization of computer software enables them to numerically solve advanced problems in the above engineering topics. In particular, the use of the finite-element method as an enhancement tool to solve solid mechanics and heat transfer problems in a sophomore year course on continuum mechanics and more advanced problems in stress analysis in a junior level course on solid mechanics is discussed in this paper. Students use computer software to formulate and solve boundary value problems in a variety of structures, to verify analytical solutions for simple structural problems, and finally to test the various assumptions that permit approximate analyses in solid mechanics.
Conformal Field Theory and Statistical Mechanics
ArXiv
July
2008
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
High Energy Physics - Theory; Statistical Mechanics
The Equivalence Myth of Quntum Mechanics (Addendum)
Studies in History and Philosophy of Science Part B: …
30
4
543-545
1999
This addendum strengthens one of the six claims of my two-part paper 'The Equivalence Myth of Quantum Mechanics'. (edited)
Properties of the trajectories in Bohmian mechanics
Physics Letters A
227
3-4
139-142
1997
10.1016/S0375-9601(97)00044-3
The three different types of flow that can occur in Bohmian mechanics are examined. The nodes of the guiding wave function are found to be crucial, both in providing a mixing like behaviour and as the main source of nonclassical motion.
On a New Form of Quantum Mechanics (II)
Quantum
2
1
3
2008
We propose a new form of nonrelativistic quantum mechanics which is based on a quantum version of the action principle.
Modern quantum mechanics, 1993 rev. ed.
Recherche
1993
This classic text sets the standard for the quantum mechanics physics market. It provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts for first year graduate students. The author was a noted theorist in particle theory, and was well ...
Monitoring mechanics during mechanical ventilation
Seminars in Respiratory and Critical Care Medicine
20
1
65-79
1999
Patients with acute respiratory failure necessitating mechanical ventilation have significant abnormalities in pulmonary mechanics, yet formal assessment of their nature is rarely included in clinical decision making. Because of our increased understanding of the pathophysiology, together with the rapid, technological advances, assessment of respiratory mechanics - resistance, compliance, and work of breathing - can be safely and rapidly performed in the intensive care unit (ICU). This chapter provides a review of abnormalities in respiratory mechanics that can be monitored during passive and spontaneous breathing, a description of the methods and techniques, and a summary of clinical observations and applications in critically ill patients.
acute respiratory failure; airway obstruction; airway resistance; artificial ventilation; breathing mechanics; human; intensive care unit; lung compliance; lung flow volume curve; lung function test; lung mechanics; lung resistance; lung ventilation; lung volume; medical decision making; patient satisfaction; positive end expiratory pressure; pressure measurement; pressure volume curve; priority journal; review; risk management; treatment planning
Fluid Mechanics
Image Rochester NY
6
1
539
1987
10.1007/b138775
Mjog god kennslubok. Agaet fyrir byrjendur sem og lengra komna
Subtalar Anatomy and Mechanics
Foot and Ankle Clinics
20
2
195-221
2015
10.1016/j.fcl.2015.02.001
Understanding subtalar joint biomechanics and pathomechanics provides a framework for understanding both common pathologic hindfoot and forefoot conditions and surgical planning. It is important to identify mechanical impairment and to define what mechanical effect is needed to change a pathologic condition. It is also important to know what the initial problem is and what the consequences are in terms of soft tissue or bony stress leading to peritalar injury. Whenever possible, one should try to operate to change pathomechanics and facilitate spontaneous repair of stressed structures
subtalar joint mechanics pathomechanics; talus calcaneus peritalar
Mechanics of Materials
Equals
964
2004
10.1016/j.mechmat.2009.08.001
Mechanics of materials is a basic engineering subject that must be understood by anyone concerned with the strength and physical performance of structures, whether those structures are man-made or natural. The subject matter includes such fundamental concepts as stresses and strains, deformations and displacements, elasticity and inelasticity, strain energy, and load-carrying capacity. These concepts underlie the design and analysis of a huge variety of mechanical and structural systems. At the college level, mechanics of materials is usually taught during the sophomore and junior years. The subject is required for most students majoring in mechanical, structural, civil, aeronautical, and aero- space engineering. Furthermore, many students from such diverse fields as materials science, industrial engineering, architecture, and agricul- tural engineering also find it useful to study this subject.
materials science; mechanics of materials
Elements of Hamiltonian mechanics
American Journal of Physics
1962
10.1119/1.1942070
Elements of . [American Journal of Physics 30, 474 (1962)]. D. ter Haar, Author, FW Van Name, Jr., Reviewer.
Statistical Mechanics
Advanced Books Classics
1998
Physics, rather than mathematics, is the focus in this classic graduate lecture note volume on statistical mechanics and the physics of condensed matter. This book provides a concise introduction to basic concepts and a clear presentation of difficult topics, while challenging the student to reflect upon as yet unanswered questions.
theory; thermodynamics
Optimization process for thin-walled high performance concrete sandwich panels
Research and Applications in Structural Engineering, Mechanics and Computation - Proceedings of the 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013
1655-1659
2013
A Nearly zero energy buildings are to become a requirement as part of the European energy policy. There are many ways of designing nearly zero energy buildings, but there is a lack of knowledge on optimization processes in the sense of structurally and thermally efficient design with an optimal economical solution. The present paper aims to provide multi-objective optimisation procedure addressed to structural precast thin-walled High Performance Concrete Sandwich Panels (HPCSP). The research aim is concerned with developing a tool that considers the cost of HPCSP materials along with the specifications of the design constrains and variables. The tool integrates the processes of HPCSP design, quantity take-off and cost estimation into a single system that would provide different costs for different HPCSP designs. The proposed multi-objective optimisation scheme results into derivation of basic design recommendations, regarding the material's strength and HPCSP's geometrical parameters that fulfil the objective of minimum cost. © 2013 Taylor & Francis Group, London, UK.
Applications of a constrained mechanics methodology in economics
European Journal of Physics
32
6
1443-1463
2011
10.1088/0143-0807/32/6/001
This paper presents instructive interdisciplinary applications of constrained mechanics calculus in economics on a level appropriate for undergraduate physics education. The aim of the paper is (i) tomeet the demand for illustrative examples suitable for presenting the background of the highly expanding research field of econophysics even at the undergraduate level and (ii) to enable the students to gain a deeper understanding of the principles and methods routinely used in mechanics by looking at the well-known methodology from the different perspective of economics. Two constrained dynamic economic problems are presented using the economic terminology in an intuitive way. First, the Phillips model of the business cycle is presented as a system of forced oscillations and the general problem of two interacting economies is solved by the nonholonomic dynamics approach. Second, the Cass-Koopmans-Ramsey model of economical growth is solved as a variational problem with a velocity-dependent constraint using the vakonomic approach. The specifics of the solution interpretation in economics compared to mechanics is discussed in detail, a discussion of the nonholonomic and vakonomic approaches to constrained problems in mechanics and economics is provided and an economic interpretation of the Lagrange multipliers (possibly surprising for the students of physics) is carefully explained. This paper can be used by the undergraduate students of physics interested in interdisciplinary physics applications to gain an understanding of the current scientific approach to economics based on a physical background, or by university teachers as an attractive supplement to classical mechanics lessons.
COUPLED ROLLING MOTION; DYNAMICS; ECONOPHYSICS; NONHOLONOMIC MECHANICS; SISTER DISCIPLINES
Developing a Theory of the Refining of Metal in Tundishes Based on Postulates of Fluid Mechanics
Metallurgist
53
9-10
613-622
2009
Results are presented from a theoretical evaluation of the extent to which metal is refined of alumina particles through their interaction with a covering slag in the tundish of a continuous caster. Mass exchange between the alumina particles and the refining slag is analyzed by simultaneously solving equations that describe the convective diffusion of the inclusions in the metallic melt and the flow of the melt inside the tundish. One key element of the problem's formulation is allowance for the turbulent character of the melt's flow by using the method proposed by Launder and Spalding and employing the finite-elements method to numerically solve the system of partial differential equations. Another method is proposed for theoretically evaluating the coefficient of mass transfer between the alumina particles and the refining flux at the interface between the metal and the covering slag. This method is based on a representation of the wave-driven flow of a thin film of liquid flux during the interaction of the film with the rough surface of sintered slag.
alumina; covering slag; inclusions; mass-transfer coefficients; turbulent flow
Coupled instabilities in thin-walled beams: A qualitative approach
European Journal of Mechanics, A/Solids
22
1
139-149
2003
10.1016/S0997-7538(02)00008-6
A direct one-dimensional beam model is adopted. Kinematics is described by axis displacement, rigid rotation of the cross-section and an average measure of warping. Mechanical power is introduced as a linear functional of the kinematic descriptors and their first derivatives, hence mechanical actions naturally result as their duals. In particular, the bi-shear and bi-moment turn out to be quantities spending power on the warping and on its first derivative, respectively. Assuming as basic postulate the balance between external and internal power, local equilibrium equations for the mechanical actions are obtained. In addition to the standard inner constraint of shear indeformability, a linear relationship between twist and warping is assumed. To obtain field equations in terms of displacements, non-linear hyperelastic constitutive relations are formulated. Two coupled bifurcations for axially loaded beams are examined: in the first case no coupling occurs, in the second the beam can be sensitive to initial imperfections. ?? 2002 ??ditions scientifiques et m??dicales Elsevier SAS. All rights reserved.
Bi-moment; Bi-shear; Coupled bifurcations; Non-linear constitutive relations; One-dimensional model
Use of thin polyparaxylene films to study the plastic deformation bismuth single crystals
Journal of Applied Mechanics and Technical Physics
47
4
596-599
2006
10.1007/s10808-006-0094-0
The effect of thin polyparaxylene films on the mechanical twinning of bismuth single crystals with the (111) surface subjected to local deformation. It is found that the number of twins formed near the stress concentrator increases in the presence of the film. Possible mechanisms are proposed to explain an increase in the mobility of twin dislocations in a deformable crystal whose surface is coated with a polyparaxylene film. Spalling of bismuth is found in the regions deformed by the indenter. © Springer Science+Business Media, Inc. 2006.
Bismuth single crystals; Polyparaxylene film; Twinning
NEW MIXED FORMULATION FOR FINITE ELEMENT ANALYSIS OF THIN SHELL STRUCTURES.
American Society of Mechanical Engineers, Applied Mechanics Division, AMD
73
25-37
1985
A nine node shell element is developed by a new and more efficient mixed formulation. The new shell element formulation is based on the Hellinger-Reissner principle with independent strain and the concept of degenerate solid shell. By dividing assumed strain fields into the lower order part and the higher order part, the new formulation can be made much more efficient in terms of computing time than the standard mixed formulation. Moreover, the present approach provides a rational way of introducing stabilization matrix to suppress undesirable kinematic modes. The numerical results indicate that the present nine node element is free of locking even for very thin plates and shells.
Screw dislocation in the two-phase isotropic thin film of an interfacial crack
Engineering Fracture Mechanics
36
6
979-986
1990
10.1016/0013-7944(90)90274-K
The screw dislocation in the two-phase isotropic thin film of an interfacial crack has been investigated. The stress field, stress intensity factors at the crack tip and for dislocation emission, crack extension force, strain energy and the image force on the dislocation are obtained and found to be related to the thickness and effective shear modulus. The effect of size on fracture is pronounced when the thickness is smaller than the distance between dislocation and crack tip by a factor of 1000. The effect of the second phase on fracture is pronounced when μ(2)/μ(1) is in the range from 0.01 to 100. Newton's third law is proved to be valid for any thickness and shear modulus ratio. This result can be reduced to three special cases.
On the axial crumpling of fibre-reinforced composite thin-walled conical shells
International Journal of Vehicle Design
12
4
450-467
1991
In this article we report on the axial compression and crush behaviour of conical frusta, made from chopped strand glass mat and polyester resin. The effect of specimen geometry, i.e. thickness, length of the shell and its apical angle, on the energy-absorbing capability are being studied both experimentally and analytically. Attention is directed towards the mechanics of the axial crumpling process from a macroscopic point of view for facilitating engineering design calculations of the amount of energy dissipated and the buckling loads exerted during quasi-static loading.
Analysis of aerodynamic drawing of a thin nonisothermal jet of a viscoelastic fluid
Journal of Applied Mechanics and Technical Physics
38
5
746-750
1998
The parameters of a thin nonisothermal jet are studied against various conditions of its motion, namely, to find the final velocity or diameter and temperature of the jet versus the conditions of its motion. Using an aerodynamic drawing of a jet model, the results obtained can find applications in the development of the technology of aerodynamic formation of chemical fibers. Using an injector in the production of nonwoven materials from a polymer melt, the fiber and the final product can produced in a single technological step.
Aerodynamic drawing; Aerodynamic jet; Aerodynamics; Boundary conditions; Calculations; Computer simulation; Drawing (forming); Equations of motion; Fluids; Friction; Jets; Mathematical models; Temperature distribution; Viscoelastic fluid
Modeling the Field Emission Current Fluctuation in Carbon Nanotube Thin Films
Nanotechnology
1
1-4
2007
Owing to their distinct properties, carbon nanotubes (CNTs) have emerged as\npromising candidate for field emission devices. It has been found\nexperimentally that the results related to the field emission performance show\nvariability. The design of an efficient field emitting device requires the\nanalysis of the variabilities with a systematic and multiphysics based modeling\napproach. In this paper, we develop a model of randomly oriented CNTs in a thin\nfilm by coupling the field emission phenomena, the electron-phonon transport\nand the mechanics of single isolated CNT. A computational scheme is developed\nby which the states of CNTs are updated in time incremental manner. The device\ncurrent is calculated by using Fowler-Nordheim equation for field emission to\nstudy the performance at the device scale.
carbon nanotube; current density; dynamics; eld emission; electro-
Propagation of normal waves through a fluid contained in a thin-walled cylinder
International applied mechanics
38
1
103-112
2002
The properties of normal axisymmetric waves propagating through a perfect compressible fluid contained in an elastic thin-walled cylinder are investigated. The problem is solved using the complete system of equations of the dynamic theory of elasticity. The effects of interaction between elastic and fluid waves are studied within a wide frequency range. The numerical results are classified on the basis of data on the properties of partial subsystems. Partial subsystems are those for which the interaction effects are insignificant. For special cases of compound waveguides, the dispersion spectra are constructed and the kinematic and energy characteristics of normal waves are analyzed. Particular attention is given to the lowest normal wave, which has specific properties and participates in the elastic–liquid interaction over a wide frequency range.
Flow past a thin axisymmetric body with a given velocity distribution along part of its surface
Journal of Applied Mechanics and Technical Physics
9
1
49-52
1972
10.1007/BF00923463
Longitudinal flow past a thin body of revolution, part of whose surface is not known a priori and is to be determined from the tangential velocity specified there (free-flow boundary), is considered. The flow is assumed to be vortex-free, and the fluid to be ideal and incompressible. An integral equation for the form of the free surface is derived and is solved by the method of successive approximations. Conditions for the existence and uniqueness of the solution are given. A constant velocity flow along the free boundary (cavitation flow) is considered as a particular example of the general theory. © 1972 Consultants Bureau.
A numerical study on motion of a sphere coated with a thin liquid film at intermediate Reynolds numbers
Journal of Fluids Engineering-Transactions of the Asme
119
2
397-403
1997
The steady viscous pow past a sphere coated with a thin liquid film at low and intermediate Reynolds numbers (Re less than or equal to 200) was investigated numerically. The influences of fluid physical properties, film thickness, and Reynolds number on the flow pattern were clarified. Temperature field around the compound drop was also analyzed. The strong dependence of flow pattern on the characteristics of heat transfer was recognized. The empirical equation of the drag coefficient for the compound drop was proposed. Furthermore, the explicit adaptability of the drag coefficient equation for a gas bubble, a liquid drop, and a rigid sphere in the range of Reynolds number Re less than or equal to 1000 was confirmed.
compound multiphase drops; flow past bubbles; fluid-mechanics; growth
Mechanical Characterization of Thin Films by Micromechanical Techniques
MRS Bulletin
17
07
34-45
2013
10.1557/S0883769400041646
This paper reports on the refinement of a mechanical model for the\nload-deflection of multilayer membranes under uniform differential\npressure and on its application to the experimental extraction of\nmaterial parameters. Going beyond previous results, the analytical\nmodel takes into account the mechanics of multilayers and elastic\nsupports covering all cases between rigidly clamped to simply supported\nstructures and enables the straightforward assessment of stress profiles\nwithin the deformed structures. A comprehensive set of long membranes\nmade of various multilayers of silicon nitride and oxide films are\nfabricated and characterized. The out-of-plane deflection profile\nunder pressure load is monitored by means of a laser profilometer.\nThe pressure is stepped up until fracture occurs. From the stress\nprofiles in the membrane at fracture, the brittle material strength\nis analyzed using Weibull statistics. The bulge setup has been fully\nautomated for the measurement of 80 membranes per wafer. This realizes,\nfor the first time, the high throughput-acquisition of mechanical\nthin film data with convincing statistical control.
On Marangoni drying: nonlinear kinematic waves in a thin film
Journal of Fluid Mechanics
254
649-670
1993
10.1017/S0022112093002290
In the field of industrial drying, a recent innovation has exploited the occurrence of Marangoni effects in such a way that the resultant free-surface flow enhances the drying process. To this end, alcohol vapour, soluble in water, is introduced above a drying film and as a result of diffusion through the air and water phases a favourable concentration gradient gives rise to the required shear flow. We consider here a simple process driven by this mechanism, and by means of asymptotic simplification and the concepts of singular perturbation theory a leading-order approximation is obtained in which the alcohol concentration in the water is a specified function of space and time. The evolution of the free surface thus reduces to a single nonlinear partial differential equation of a similar form to the Korteweg–de Vries and Burgers equations, higher-derivative terms corresponding to surface tension and gravity effects. Numerical solutions of this equation are obtained and are compared to the application of first order nonlinear kinematic wave theory with corresponding shock solutions.
Two-vector mechanics.
Progress in orthodontics
4
2
62-73
2003
The conventional orthodontic appliance is not without its limitations for certain types of tooth movements; in particular, if the appliance cannot access the area to elicit the type of force vector for a particular displacement. Examples of such movements are: space closure by translation, uprighting and intrusion of posterior teeth, intrusion with retraction and lingual root torque of anterior teeth. In this paper we describe a mathematical method to design an appliance system that overcomes these difficulties. This system includes two statically determined elements and allows for highly controlled force vector application point and direction. A clinical case of midline discrepancy is shown to demonstrate the clinical use and utility of this method.
biomechanics; two vector mechanics
Emergence And Quantum Mechanics
Philosophy of Science
69
2
324-347
2002
10.1086/341056
In a recentarticleHumphreyshas developedan intriguingproposalfor makingsense of emergence.The crucial notion for this purpose is what he calls "fusion"and his paradigmfor it is quantumnonseparability.In what follows, we will develop this po- sitioninmoredetail,andthendiscussitsramificationsandlimitations.Itsramifications are quite radical;its limitationsare substantial.An alternativeapproachto emergence that involvesquantumphysicsis then proposed
Analysis of contact mechanics for composite cushion knee joint replacements.
Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine
212
1
1-10
1998
10.1243/0954411981533773
Recent research in the area of cushion form bearings for total joint replacements has primarily used thin, soft, elastomeric layers with similar elastic modulus to articular cartilage, bonded to rigid substrates. These are designed to promote the body's natural lubricants to separate the articulating surfaces and prevent wear. Applications to joint replacements have revealed that the abrupt change in stiffness between the soft layer and the rigid substrate and the relatively low strength of the interface resulted in high shear stresses and debonding of the soft layer from the substrate. The approach adopted in this study is to use components with a graded modulus or composite construction. The composite construction consists of a soft compliant layer of polyurethane and a second stiffer polyurethane layer thought to be rigid enough to mechanically interlock to a metallic tibial tray. In this composite structure the deformation of the more rigid polyurethane underlay may generally influence the stress distribution and deformation in the softer upper layer and at the interface between the two materials. A simple analysis technique is presented in the present study where the composite double layer was approximated as an equivalent modulus single layer. Single layer theory, which is readily available in the literature, can then be used to determine the contact parameters, including the maximum contact pressure and the contact radius, for the composite structure. By varying the layer thicknesses and material properties of both the soft surface layer and the stiffer structural support layer, the magnitudes and locations of stresses can be controlled. Results of a parametric stress analysis are presented to assist in the selection of the most appropriate composite layers for cushion knee designs. A 4 mm thick surface layer with an elastic modulus of 20 MPa and a 4 mm thick structural support layer with an elastic modulus of 1000 MPa were considered suitable for this application.
Biomechanical Phenomena; Elasticity; Humans; Knee Joint; Knee Prosthesis; Models, Biological; physiology; Polyurethanes; Prosthesis Design; Stress, Mechanical; Surface Properties
Analogies and differences between quasi-static indentation and hypervelocity impact morphologies on thin solar cells
International Journal of Impact Engineering
26
1-10
321-331
2001
10.1016/S0734-743X(01)00101-4
Morphologies produced by quasi-static indentation on thin Hubble Space Telescope (HST) solar cells show remarkable similarities to much of the hypervelocity damage sustained by the HST solar array whilst in orbit. Quasi-static indentation tests carried out with blunt and sharp indentors reveal analogies between static and dynamic (hypervelocity) indentation indicating similar fracture mechanics processes over the energy range evaluated. Understanding the static case assists to characterise better the dynamic process and bridge the intervening gap.
Debris; Hypervelocity; Impact; Indentation; Meteoroid; Solar Cell
Structure and magnetic properties of Mn_4N thin films synthesized by plasma-based ion implantation
Physica A: Statistical Mechanics and its Applications
358
1
136-141
2005
DOI: 10.1016/j.physa.2005.06.014
Plasma-based ion implantation was used to synthesize the manganese\nnitride Mn4N by implanting nitrogen in manganese layers first deposited\nby sputtering assisted by multi-dipolar microwave plasma. The structural\ncharacterization of the layer has been performed using X-ray diffraction\nat grazing incidence and XPS. The magnetic properties have been measured\nusing a SQUID susceptometer. In parallel, a FLAPW method has been\nused to calculate the theoretical magnetic state of Mn4N. The modeling\nresults are compared with neutron diffraction and magnetization saturation\nmeasurements.
Magnetic; Manganese; Mn4N; Nitride; Thin film
Equations of higher order of accuracy describing the vibrations of thin plates
Pmm Journal of Applied Mathematics and Mechanics
69
4
593-610
2005
Methods developed in the mathematical theory of the averaging of processes in periodic media are used to derive two-dimensional equations describing the propagation of waves in non-uniform anisotropic plates with a periodic structure. Equations of higher order of accuracy in a small parameter - the ratio of the typical thickness of the plate to the typical wavelength, are derived. The case of uniform isotropic thin plates is considered in detail. Equations of different order of accuracy, derived in this paper, are analysed and compared with the equations proposed by others. Some corrections for the coefficients in Timoshenko-type equations, which increase the accuracy of these equations, are proposed. (c) 2005 Elsevier Ltd. All rights reserved
Lowered Interdiffusivity In Thin Amorphous Ni-Zr Films With Large Composition Gradients
Philosophical Magazine B-Physics Of Condensed Matter Statistical Mechanics Electronic Optical And Magnetic Properties
69
6
1083-1091
1994
Using Rutherford backscattering spectrometry, the interdiffusion in amorphous Ni-Zr thin films with large concentration gradients has been studied. The interdiffusion coefficient is found to depend on the concentration gradient. In the thinner films with steeper gradients, lowered interdiffusivities are observed. These experimental findings appear to be in accordance with predictions from Stephenson's model, in which stresses can lower the interdiffusion over short distances in alloys with high viscosity.
alloys; amorphization; diffusion; metallic glasses; Solid-state reaction; strain; structural-relaxation
Using the perturbation method to solve the problem of separated incompressible flow past thin airfoils
Journal of Applied Mechanics and Technical Physics
47
3
346-358
2006
10.1007/s10808-006-0062-8
A model for separated incompressible flow past thin airfoils in the neighborhood of the "shockless entrance" condition is constructed based on the averaging of the vortex shedding flow past the airfoil edges. By approximation of the vortex shedding by two vortex curves, determination of the average hydrodynamic parameters is reduced to a twofold solution of an integral singular equation equivalent to the equation describing steady-state nonseparated airfoil flow. In this case, the calculation time is two orders of magnitude smaller than the time required for the solution of the corresponding evolution problem. The results of a test calculation using the proposed method are in fair agreement with available results of calculations and experiments. © Springer Science+Business Media, Inc. 2006.
Airfoil; Incompressible fluid; Separation; Vortex shedding
Based on the Theory of Thin-Walled Bar Flexure-Torsion Analysis of the Oblique Combined Structure
Applied Mechanics and Materials
55-57
2122-2125
2011
10.4028/www.scientific.net/AMM.55-57.2122
This paper assumes that a row of the frame, shear wall structure as affected by lateral bending and torsion modules coupling effect of thin-walled members, through the floor to work together to establish a collaborative analysis of structural bias of the Hamiltonian on the dual system, with precise integration method for the numerical solution of high-precision systems, analysis of bias is given a set of construction the structure of collaborative work. The results make the structure more in line with the actual deformation. © (2011) Trans Tech Publications.
Coupling of flexure-torsion; Hamilton duality solution system; Oblique combined structure
Effects of mode interaction on collapse of short, imperfect, thin-walled columns
Transactions of the ASME. Journal of Applied Mechanics
51
3
566-573
1984
Deals with the design of beneficial geometric imperfections of short, thin-walled columns in order to maximize their energy absorption. The investigation was motivated by the experimental finding that under axial compressive load, the symmetric mode (which has a higher buckling load than the antisymmetric mode) actually has a much higher energy absorption than the antisymmetric mode as measured by the area under the curve of applied load versus end-shortening curve. Thus, an attempt is made to introduce imperfections in the beneficial symmetric mode so that the mode shapes of extremely large deflection in plastic collapse will also be of the symmetric type. The two-mode stability problem is studied using Koiter's theory of elastic stability
buckling; mechanical stability; plastic deformation
Statistical Mechanics of Dictionary Learning
Arxiv preprint arXiv12036178
28008
2-5
2012
10.1209/0295-5075/103/28008
Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.
Solitary waves and Bohmian mechanics.
Proceedings of the National Academy of Sciences of the United States of America
99
24
15257-15261
2002
10.1073/pnas.222494299
We study a Schr dinger-like equation with a nonlinear term. This nonlinearity has the effect of allowing the existence of highly concentrated stable solitary waves of a topological nature. Such solitary waves tend to move according to Bohmian mechanics. Therefore our model can be considered a nonsingular realization of de Broglie pilot wave theory.
Fractional supersymmetry and quantum mechanics
Physics Letters B
312
1-2
115-120
1993
10.1016/0370-2693(93)90496-5
We present a set of quantum-mechanical Hamiltonians which can be written as the $F^{\,\rm th}$ power of a conserved charge: $H=Q^F$ with $[H,Q]=0$ and $F=2,3,...\, .$ This new construction, which we call {\it fractional}\/ supersymmetric quantum mechanics, is realized in terms of \pg\ variables satisfying $\t^F=0$. Furthermore, in a pseudo-classical context, we describe {\it fractional}\/ supersymmetry transformations as the $F^{\,\rm th}$ roots of time translations, and provide an action invariant under such transformations.
Effects of the top-electrode size on the piezoelectric properties (d(33) and S) of lead zirconate titanate thin films
Journal of Applied Physics
96
5
2800-2804
2004
10.1063/1.1775306
The effects of a decreasing top electrode size on the electric and piezoelectric properties of tetragonal Pb(Zr-X, Ti1-X)O-3 thin films are investigated. The effective piezoelectric small-signal coefficient d(33,eff) and the piezoelectric large signal-strain S are measured using a double-beam laser interferometer. Both properties are found to decrease rapidly with decreasing size of the used Pt top electrode for the investigated dimensions of 5 mm to 100 mum edge length (square pads). While the loss of d(33,eff) is as high as 75%, the influence on the relative permittivity is only small. The source of the pad size effect on the measured piezoelectric properties is found to be the mechanics of the layered structure commonly used for piezoelectric measurements (Pt/PZT/Pt/TiO/SiO2/Si), PZT, Pb(Zr-x, Ti1-x)O-3 which is verified by finite element simulations. (C) 2004 American Institute of Physics.
integration; phase
DEVELOPMENT OF AGRICULTURAL MECHANICS
11th International Scientific Conference on Engineering for Rural Development, Vol 11
67-73
2012
A brief review is given on the research carried out in the field of agricultural mechanics. Agricultural mechanics is a subdivision of science about the functional relations of agricultural technological processes and machinery, which provides the possibility to improve the motivation, productivity and effectiveness of the mechanisation of agricultural production. Their cognition provides a possibility to improve the mechanisation issues of agricultural production in a more motivated, economical and faster way. A considerable development in agricultural mechanics was achieved in soil tillage (terra mechanics), field crop growing, beet harvesting, the design of broad-grip machines and aggregates by finding new relations between technological processes and functioning of machines and their working parts. The obtained correlations allow to apply a method of simulation and modelling technological processes and function of machine working parts, and to determine the optimal parameters of the operating parts for machines and the draft resistance in connection with the technological properties of soil and working mode. A study has been carried out of probable plant spacing in the field crop and vegetable plantations and their corresponding yields by sowing seeds at exact intervals and growing them without thinning. Mathematical coherences for the determination of the plant spacing density and their distribution were obtained. It is stated that the plant spacing density is a function of the seed germinating power in the field.
agricultural mechanics terra mechanics mechanics o
A continuum damage model for linear viscoelastic composite materials
Mechanics of Materials
35
3-6
463-480
2003
This paper presents a constitutive model for linear viscoelastic orthotropic solids containing a fixed level of distributed cracks. The model is formulated in a continuum damage mechanics framework using internal variables taken as second rank tensors. Use is made of the correspondence principle for linear viscoelastic solids to define a pseudo strain energy function in the Laplace domain. This function is then expressed as a polynomial in transformed strain and tensorial damage variables using the integrity bases restricted by the initial orthotropic symmetry of the material. The constitutive relationships derived in the Laplace domain are then converted to the time domain by using the inverse Laplace transform. The model is applied to the specific case of cross-ply laminates with transverse matrix cracks. The material coefficient functions appearing in the model are determined by a numerical (finite element) method for one cross-ply laminate configuration at one damage level. Predictions of the viscoelastic response are then made for the same laminate at other damage levels and for other cross-ply laminate configurations at different damage levels. These predictions agree well with independently determined time variations of properties by an analytic method (Kumar and Talreja, 2001, Linear viscoclastic behavior of matrix cracked cross-ply laminates. Mechanics of Materials 33 (3), 139154) as well as with the numerically calculated values. Extension of the model to incorporate effects of transient temperature. physical aging and moisture is outlined. (C) 2002 Elsevier Science Ltd. All rights reserved.
behavior; composite materials; constitutive modeling; continuum damage mechanics; correspondence principle; crack initiation; damage; deformation; formulation; growing damage; growth; internal variables; media; pseudo strain energy function; viscoelasticity
On phase-space representations of quantum mechanics
PHYSICS LETTERS A
286
2-3
97-101
2001
We discuss a class of representations of quantum mechanics which uses\nfunctions defined on a parameter space to represent observable\nquantities. We show that infinitesimal canonical transformations could\nbe used to introduce a phase-space-like structure consistent with the\nrequirements of quantum mechanics. The resulting family of phase-space\nrepresentations of quantum mechanics contains many well-known\nrepresentations as special cases, e.g., the Weyl-Wigner-Moyal, normal\nand antinormal one. It is also flexible enough to represent, e.g.,\nPT-symmetric theories, introduced recently within the context of\nnon-Hermitian quantum mechanics. (C) 2001 Elsevier Science B.V. All\nrights reserved.
Search for violations of quantum mechanics
Nuclear Physics B
241
2
381-405
1984
10.1016/0550-3213(84)90053-1
The treatment of quantum effects in gravitational fields indicates that pure states may evolve into mixed states, and Hawking has proposed modification of the axioms of field theory which incorporate the corresponding violation of quantum mechanics. In this paper we propose a modified hamiltonian equation of motion for density matrices and use it to interpret upper bounds on the violation of quantum mechanics in different phenomenological situations. We apply our formalism to the system and to long baseline neutron interferometry experiments. In both cases we find upper bounds of about 2 × 10−21 GeV on contributions to the single particle “hamiltonian” which violate quantum mechanical coherence. We discuss how these limits might be improved in the future, and consider the relative significance of other successful tests of quantum mechanics. An appendix contains model estimates of the magnitude of effects violating quantum mechanics.
International Journal of Rock Mechanics & Mining Sciences A composite sphere assemblage model for porous oolitic rocks
International Journal of Rock Mechanics and Mining Sciences
48
6
909-921
2011
10.1016/j.ijrmms.2011.05.003
International Journal of Rock Mechanics and Mining Sciences, 48 + (2011) 909-921. doi:10.1016/j.ijrmms.2011.05.003
Composite sphere assemblage model; Effective properties; Four phase model; Limestone; Micromechanics; Multistep homogenization; Poroelasticity
Revised Proof of the Uniqueness Theorem for 9No Collapse : Interpretations of Quantum Mechanics
Science
31
1
95-98
2000
We show that the Bub-Clifton uniqueness theorem for 'no collapse' interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the 'weak separability' assumption.
interpretations of quantum mechanics; no collapse
A new appraisal of old formulations of mechanics
American Journal of Physics
72
3
407
2004
10.1119/1.1625924
Lazare Carnot’s formulation of mechanics (1783) is re-evaluated in relation to other formulations of classical mechanics and modern theories.
On the theory of quantum mechanics
Proceedings of the Royal Society of …
1926
Downloaded from rspa.royalsocietypublishing.org on December 15, 2010 G61 On the Theory of Quantum Mechanics . By PAM Dirac, St. John's College, Cambridge. (Communicated by RH Fowler, FRS—Received August 26, 1926.) § 1. Introduction and Summary. The new ...
Conformal Mechanics and the Virasoro Algebra
Journal of High Energy Physics
1999
006
1999
10.1088/1126-6708/1999/04/006
We demonstrate that any scale-invariant mechanics of one variable exhibits not only 0+1 conformal symmetry, but also the symmetries of a full Virasoro algebra. We discuss the implications for the adS/CFT correspondence.
The Meaning of Wave Mechanics
Dublin Seminar, July 1952 Colloquium
1952
An non-mathematical explanation of Shcrodinger's view that that waves are indeed primary/real and particles are just an interpretation.
Copenhagen interpretation; quantum mechanics
Development and prospect of 'engineering mechanics'
Gongcheng Lixue/Engineering Mechanics
26
10
1-13
2009
'Engineering Mechanics' reports the application of mechanics in engineering practice and the latest research observations. The goal of this journal is to promote the combination of mechanics and engineering, thus to lead the advancement of engineering technology; to strengthen the mutual propelling of mechanics and engineering technology, thus to achieve mutual improvements. Engineering Mechanics is an academic journal with high theoretical level, and is one of the most popular journals in the field of mechanics. In the past 25 years since its start publication, great advancement has been achieved in academic quality, editorial quality, published paper amount, impact factor and circulation. These advancements were summarized in this paper, and a prospect was given.
Direction of scientific journals; Editing procedure; Engineering Mechanics; Engineering technology; Evaluation of scientific journals; Mechanics; Publication quality; Publishing
Fluid mechanics and continuum mechanics
Heat and Mass Transfer
44
5
625-633
2008
DOI 10.1007/s00231-007-0284-1
The symmetry of the tensor of the viscous stresses, based on the assumption of the deformation of a continuum fails in the appropriate description already in the cases of extremely simple flow fields. From these observations we must conclude that the Navier-Stokes equations provide only necessary, but not sufficient conditions. This conclusion might provide a first step towards a logically based understanding of turbulent flows.
Anatomical and physiological simulation for respiratory mechanics.
Journal of image guided surgery
1
3
164-71
1995
10.1002/(SICI)1522-712X(1995)1:3<164::AID-IGS6>3.0.CO;2-8
Injuries in trauma affect anatomical structures, indirectly affecting physiological systems through mechanical behavior and physical proximity. This paper describes the theory for and preliminary results from our approach to couple a three-dimensional (3-D) anatomical model of the chest with a physiological model of respiratory mechanics. In particular, we investigated behavior in quiet, normal breathing and in an open, sucking chest wound. We envision that our integrated simulation of respiratory anatomy and respiratory mechanics could assist students in visualizing and predicting relationships between structural-anatomical and functional-physiological changes in an interactive, 3-D environment.
Computer-Assisted; Computer-Assisted Instruction; Computer Simulation; Education; Humans; Image Processing; Lung; Lung: physiopathology; Medical; Penetrating; Penetrating: physiopathology; Pneumothorax; Pneumothorax: etiology; Pneumothorax: physiopathology; Respiratory Mechanics; Thoracic Injuries; Thoracic Injuries: complications; Thoracic Injuries: physiopathology; Thorax; Thorax: physiopathology; Wounds
Some inverse problems in penetration mechanics
Mechanics Based Design of Structures and Machines
38
4
468-480
2010
10.1080/15397734.2010.501274
Many empirical and semi-empirical models that are widely used in impact dynamics employ the dependencies between the impact (initial) velocity and the depth of penetration (DOP). These dependencies are often obtained by statistical processing of experimental results and are not based on the theoretical models of penetration. In this study we develop an approach that allows using such phenomenological correlations for determining the dependencies of forces acting on a penetrator versus the instantaneous DOP and the instantaneous velocity. The developed approach can be also useful in other fields of mechanics. Copyright Taylor Francis Group, LLC.
Kant’s third law of mechanics: The long shadow of Leibniz
Studies in History and Philosophy of Science Part A
44
3
493-504
2013
10.1016/j.shpsa.2012.10.014
This paper examines the origin, range and meaning of the Principle of Action and Reaction in Kant’s mechanics. On the received view, it is a version of Newton’s Third Law. I argue that Kant meant his principle as foundation for a Leibnizian mechanics. To find a ‘Newtonian’ law of action and reaction, we must look to Kant’s ‘dynamics,’ or theory of matter. I begin, in part I, by noting marked differences between Newton’s and Kant’s laws of action and reaction. I argue that these are explainable by Kant’s allegiance to a Leibnizian mechanics. I show (in part II) that Leibniz too had a model of action and reaction, at odds with Newton’s. Then I reconstruct how Jakob Hermann and Christian Wolff received Leibniz’s model. I present (in Part III) Kant’s early law of action and reaction for mechanics. I show that he devised it so as to solve extant problems in the Hermann-Wolff account. I reconstruct Kant’s views on ‘mechanical’ action and reaction in the 1780s, and highlight strong continuities with his earlier, pre-Critical stance. I use these continuities, and Kant’s earlier engagement with post-Leibnizians, to explain the un-Newtonian features of his law of action and reaction.
Dynamical laws; Interaction; Kant; Leibniz; Mechanics; Newton
Analysis of various thick-walled cross-ply composite cylindrical shells subjected to lateral pressures
Composites Part B: Engineering
27
95
651-655
1996
10.1016/1359-8368(95)00049-6
A simple and accurate finite cylindrical element method was formulated by the authors to determine stresses and deformations in laminated thick-walled cylindrical composite shells. This method reduces the overall problem to a one-dimensional one. In the previous study it was found that significant tensile radial strains occur near the inner shell surface, when the shell is subjected to external pressures. These radial tensile strains are of the same magnitude as the failure strains for the composite shells for shell dimensions and pressures of practical use. In the present study various stacking sequences are investigated to determine the one resulting in the lowest radial tensile strains. Using this optimum stacking sequence, results are obtained for shells composed of E-glass/epoxy, T300/SP-286 graphite/epoxy, and Kevlar 49/epoxy. In addition, two hybrid composite systems consisting of graphite/epoxy and glass/epoxy are studied. Copyright ?? 1996 Elsevier Science Limited.
Composites; Deep submergence; Optimum stacking sequence; Shells
Strength degradation during fatigue of unidirectional and cross-ply SCS-6/Ti-15-3 composites
International Journal of Fatigue
21
3
215-223
1999
10.1016/S0142-1123(98)00068-1
The majority of previous fatigue studies on Titanium Matrix Composites (TMCs) have investigated fatigue life where specimens are cycled until failure. Although fatigue life is very important to designers, it is not the only cycle-dependent criterion used to characterize the material. Another behavior required to evaluate the material is the residual strength degradation due to cyclic loading. To date, very few investigations have been completed to determine this behavior in TMCs. Of those investigations, none has explicitly determined the dependence of residual strength reduction on laminate orientation. To study this, the residual strength behaviors of SCS-6/Ti-15-3 with laminate orientations of [0]8 and [0/90]2s were investigated after being fatigued at 427°C with different frequencies, R-ratios and control modes. Results show that residual strength degradation is primarily dependent on laminate orientation and percent of cyclic life. Different test parameters mainly affect residual strength degradation through the corresponding changes in cyclic life. Micromechanical analysis reveals that the laminate dependence is due to differences in damage morphologies and there is no single parameter, such as axial fiber stress, that can correlate all the residual strength data from the different fatigue conditions.
An image-based computational model of ovine lung mechanics and ventilation distribution
Proceedings of SPIE
5746
84-91
2005
10.1117/12.600723
A computational model of soft tissue mechanics and air flow has been developed with the aim of linking computed tomography measures of ventilation distribution to subject-specific predictions in image-based geometric (finite element)
airflow; continuum mechanics; finite deformation elasticity; keywords
Realism and quantum mechanics
Studies in Logic and the Foundations of Mathematics
134
609-631
1995
10.1016/S0049-237X(06)80066-2
We consider realism as a purely metaphysical regulative principle, not subject to scientific proof. In this sense, realism can be maintained in quantum mechanics, provided one does not claim that matter is made out of elementary particles. The epistemological dualism of subject versus object is achieved by a Cartesian cut between object and subject. Once the cut is made, we speak of an exophysical description, as opposed to the concept of an endosystem, a strictly closed physical system without any concept of an observer. The cut resulting in the notion of the object always singles out the object's environment, with which the object interacts. Objects appear not in spite of but because they interact with their environment. In the intrinsically nonprobabilistic individual ontic interpretation, a quantum endosystem's intrinsic properties are represented by the commutative C*-subalgebras of a C*-algebra A. The exophysical description of the quantum system is generated by a context dependent fixing of a representation of A. The resulting von Neumann algebra refers to the contextual observables. The context dependence of the objects and the fact that they are entangled with their environment means that it is not realism that is refuted by quantum mechanics but atomism and the idea of context-independent objects.\nKeywords:\tRealism. Atomism. Cartesian Cut. Environment. Contextual objects. Ontic descriptions. Epistemic descriptions.
Quantum Mechanics without Nonlocality
Aristotelian. Society Supplementary
May
8
2006
We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states. The same concerns the entangled states of compound quantum systems. In the it existing quantum mechanics, introducing Bell's inequalities is fully legal. However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation. Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm. They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.
The mechanics of mobile robots
Robotics
2
2
113-121
1986
10.1016/0167-8493(86)90048-3
The interaction of the mechanics of a mobile platform with control and sensing hardware and software is important to performance in robotic applications. In this paper the basic principles involved will be reviewed, and new material on comparative characterizations will be presented. The application of those principles to a specific example: the Adaptive Suspension Vehicle, will be presented.
Legged locomotion; Mobile robots; Sensor fusion; System design
Many-fingered time Bohmian mechanics
Physics
i
7
2006
The many-fingered time (MFT) formulation of many-particle quantum mechanics and quantum field theory is a natural framework that overcomes the problem of "instantaneous collapse" in entangled systems that exhibit nonlocalities. The corresponding Bohmian interpretation can also be formulated in terms of MFT beables, which alleviates the problem of instantaneous action at a distance by using an ontology that differs from that in the standard Bohmian interpretation. The appearance of usual single-time particle-positions and fields is recovered by quantum measurements.
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Quantum Physics
Recent work in rock mechanics
Géotechnique
13
2
99-120
1963
10.1680/geot.1963.13.2.99
Recent laboratory studies on rock alteration such as changes brought about in rock by action of water, by variation in water-vapor content of atmosphere ambient to rock, and by changes in temperature; techniques for in situ measurement of modulus of rock deformation are illustrated by case study of dam site in southern France; artificial improvement of rocks in situ by grouting.
Rock mechanics
Structural mechanics for electromagnetic railguns
IEEE Transactions on Magnetics
41
1
246-250
2005
10.1109/TMAG.2004.839828
The objective of this investigation is to explore potential designs and appropriate materials for a lightweight fieldable electromagnetic railgun. Lessons learned from the previous launcher designs are reviewed and discussed from a mechanical point of view. Analyses are performed with a conceptually workable gun bore to illustrate the requirement of a fieldable gun construction. Both static and dynamic responses of the railgun are discussed. The study provides a fundamental understanding for developing a fieldable railgun in terms of mechanics and material requirement.
Composite material; Electromagnetics; Large caliber; Pulsed-power; Railgun; Tactical gun
Modelization and numerical approximation of piezoelectric thin shells Part I: The continuous problems
Computer Methods in Applied Mechanics and Engineering
192
4003-4043
2003
10.1016/S0045-7825(03)00364-5
This paper comprises three parts mainly directed to the obtention of a two-dimensional formulation (Part I), to the analysis of an approximation by finite element methods and to some numerical experiments (Part II) and to the use of piezoelectric components in order to realize active structures (Part III). In this first part, the general three-dimensional equations of piezoelectricity are recalled; they use a representation of the three-dimensional body by a system of three curvilinear coordinates. An existence and uniqueness result is proved. Next, under appropriate assumptions on the mechanical and on the electrical behaviour of the shell during the deformation, the integration of the three-dimensional equations through the thickness leads to a set of two-dimensional equations which are themselves simplified by using an energy criterion. Finally, it is proved that these reduced two-dimensional equations have one and only one solution. ?? 2003 Elsevier B.V. All rights reserved.
Thermomechanical finite element analysis of slider-disk impact in magnetic storage thin film disks
Tribology International
43
737-745
2010
10.1016/j.triboint.2009.10.014
Oblique impact of a slider with a rotating disk in a hard disk drive was analyzed using the finite element method. A three dimensional, thermomechanical, impact model was developed to study the mechanical and thermal response during the impact of a spherical slider corner with a rotating disk. The model was validated by comparing the finite element results with analytical solutions for a homogeneous glass substrate disk. Impact penetration, stress and incurred flash temperature were obtained for various normal impact velocities. The effects of material layers on the disk were also investigated by introducing layers with different material properties and thicknesses. It was found that for a rounded slider corner and a critical normal impact velocity of 0.03 m/s studied in this work, the layers have insignificant effects on the mechanical response and small but predictable effects on the flash temperature. ?? 2009 Elsevier Ltd. All rights reserved.
Contact mechanics; Frictional heating; Impact; Magnetic storage
Identification of the Elastic Properties of Isotropic and Orthotropic Thin-Plate Materials with the Pulsed Ultrasonic Polar Scan
Experimental Mechanics
54
6
1121-1132
2014
10.1007/s11340-014-9861-7
Already in the early 1980’s, it has been conjectured that the pulsed ultrasonic polar scan (P-UPS) provides a unique fingerprint of the underlying mechanical elasticity tensor at the insonified material spot. Until now, that premise has not been thoroughly investigated, nor validated, despite the opportunities this would create for NDT and materials science in general. In this paper, we report on the first-ever implementation of an inverse modeling technique on the basis of a genetic optimization scheme in order to extract quantitative information from a P-UPS. We validate the optimization approach for synthetic data, and apply it to experimentally obtained polar scans for annealed aluminum, cold rolled DC-06 steel as well as for carbon fiber reinforced plastics. The investigated samples are plate-like and do not require specific preparation. The inverted material characteristics show good agreement with literature, micro-mechanical models as well as with results obtained through conventional testing procedures.
Characterization; Elastic properties; Metals and composites; Polar scan; Ultrasound
Momentum in stochastic quantum mechanics
Letters in Mathematical Physics
5
6
523-529
1981
10.1007/BF00408134
Momentum is analyzed as a random variable in stochastic quantum mechanics. Arbitrary potential energy functions are considered. The oscillator is presented as an example.
Mechanics of Microstructured Solids 2
Lecture Notes in Applied and Computational Mechanics
50
1-8
2010
10.1007/978-3-642-05171-5
The linear couple-stress theory of Mindlin and Tiersten is reformulated allowing also for dislocations and disclinations. The governing equations are compiled in form of a Tonti diagram.
Fatigue dissipation and failure in unidirectional and angle-ply glass fibre/carbon fibre hybrid laminates
Experimental Techniques and Design in Composite Materials 5
221-2
35-47
2002
10.4028/www.scientific.net/KEM.221-222.35
The tensile fatigue behaviour of unidirectional 0degrees, [+/-10](4S) and [+/-45](4S) carbon fibre/glass fibre hybrid composite has been investigated. The dissipation was measured by the stiffness, hysteresis loss and temperature field of the specimen surface in an insulated testing chamber. The hysteresis loss correlates well with the increase temperature. Microscopic studies show frictional sliding of longitudinal crack faces between carbon and glass fibre bundles to be the main source of dissipation for on-axis specimens. With increasing off-axis angle the primary loss mechanism became cyclic shear deformation of the polymer matrix. With a finer dispersion of the constituents of the hybrid, the growth of these longitudinal cracks or of zones of inelastic matrix shear deformation. would be suppressed, which would result in a more fatigue resistant material. A localisation of heat generation sets in just prior to final failure. Damage and heat localisation lead to impending failure. If the parameters that control localisation were better understood, it would be possible to improve the fatigue resistance of the material by sensible microstructural design.
From Classical to Quantum Mechanics through Optics
arXiv:0909.3258
2009
10.1088/0143-0807/31/1/016
In this paper we revise the main aspects of the Hamiltonian analogy: the fact that optical paths are completely analogous to mechanical trajectories. We follow Schr\textbackslash"odinger's original idea and go beyond this analogy by changing over from the Hamilton's principal function \$S\$ to the wave function $\textbackslashPsi\$. We thus travel from classical to quantum mechanics through optics.
Inserting Group Variables into Fluid Mechanics
arXiv
hep-th
2004
A fluid, like a quark-gluon plasma, may possess degrees of freedom indexed by a group variable, which retains its identity even in the fluid/continuum description. Conventional Eulerian fluid mechanics is extended to encompass this possibility.
Possibilities for a Causal Interpretation of Wave Mechanics
arXiv preprint quant-ph/0401105
1-14
2004
The basic physical problems that necessitated the emergence of quantum physics are summarized, along with the elements of wave mechanics and its traditional statistical interpretation. Alternative interpretations to the statistical one, such as the hydrodynamical and optical interpretations, nonlinear waves and nonlinear electrodynamics, and the conception of spacetime as an ordered medium are reviewed.
Geometrisation of Statistical Mechanics
Quantum
31
1997
Classical and quantum statistical mechanics are cast here in the language of projective geometry to provide a unified geometrical framework for statistical physics. After reviewing the Hilbert space formulation of classical statistical thermodynamics, we introduce projective geometry as a basis for analysing probabilistic aspects of statistical physics. In particular, the specification of a canonical polarity on $RP^{n}$ induces a Riemannian metric on the state space of statistical mechanics. In the case of the canonical ensemble, we show that equilibrium thermal states are determined by the Hamiltonian gradient flow with respect to this metric. This flow is concisely characterised by the fact that it induces a projective automorphism on the state manifold. The measurement problem for thermal systems is studied by the introduction of the concept of a random state. The general methodology is then extended to include the quantum mechanical dynamics of equilibrium thermal states. In this case the relevant state space is complex projective space, here regarded as a real manifold endowed with the natural Fubini-Study metric. A distinguishing feature of quantum thermal dynamics is the inherent multiplicity of thermal trajectories in the state space, associated with the nonuniqueness of the infinite temperature state. We are then led to formulate a geometric characterisation of the standard KMS-relation often considered in the context of $C^{*}$-algebras. The example of a quantum spin one-half particle in heat bath is studied in detail.
General Relativity and Quantum Cosmology
A Modified Hole-drilling Technique for Determining Residual Stresses in Thin Plates
Experimental Mechanics
June
226-232
1976
This paper presents a modified hole-drilling technique for measuring residual stresses in sheet and thinplate materials. The primary advantage of the modification is that it eliminates the necessity for calibration of each experimental hole-gage assembly. The relaxation coefficients are calculated from theory, and the strain components which are extraneous to the true relaxation strains are determined and separated from the measured relaxation strains. Experiments were conducted on 0.050-in. (l.27-mm) and 0.125-in. (3.175-mm)-thickness aluminum-alloy specimens. Sources of extraneous strain components ore analyzed and values for these strain components resulting from machining residual stresses and localized plastic yielding are determined. Finally, the recommended range of the nondimensional ratio of hole diameter to distance between hole center and strain-gage center is determined by the maximum permissible error in residual-stress estimates. The modified technique appears to be accurate within percent or better and is, therefore, comparable in precision with the X-ray technique.
residual stress
Comparison of two dynamic contact line models for driven thin liquid films
European Journal of Applied Mathematics
15
625-642
2004
Doi 10.1017/S0956792504005741
The modeling of the motion of a contact line, the triple point at which solid, liquid and air meet, is a major outstanding problem in the fluid mechanics of thin films [2, 9]. In this paper, we compare two well-known models in the specific context of Marangoni driven films. The precursor model replaces the contact line by a sharp transition between the bulk fluid and a thin layer of fluid, effectively pre-wetting the solid; the Navier slip model replaces the usual no-slip boundary condition by a singular slip condition that is effective only very near the contact line. We restrict attention to traveling wave solutions of the thin film PDE for a film driven up an inclined planar solid surface by a thermally induced surface tension gradient. This involves analyzing third order ODE that depend on several parameters. The two models considered here have subtle differences in their description, requiring a careful treatment when comparing traveling waves and effective contact angles. Numerical results exhibit broad agreement between the two models, but the closest comparison can be done only for a rather restricted range of parameters. The driven film context gives contact angle results quite different from the case of a film moving under the action of gravity alone. The numerical technique for exploring phase portraits for the third order ODE is also used to tabulate the kinetic relation and nucleation condition, information that can be used with the underlying hyperbolic conservation law to explain the rich combination of wave structures observed in simulations of the PDE and in experiments [3, 15].
equations; flows; fluid interface; gradients; motion; surface; traveling-waves
Comparison of Two Approaches to Model Cure-Induced Microcracking in Three-Dimensional Woven Composites
ASME 2012 …
1-6
2012
Finite element models of 3D woven composites are developed to predict possible microcracking of the matrix during curing. A specific ply-to-ply weave architecture for carbon fiber reinforced epoxy is chosen as a benchmark case. Two approaches to defining the geometry of reinforcement are considered. One is based on the nominal description of composite, and the second involves fabric mechanics simulations. Finite element models utilizing these approaches are used to calculate the overall elastic properties of the composite, and predict residual stresses due to resin curing. It is shown that for the same volume fraction of reinforcement, the difference in the predicted overall in-plane stiffness is on the order of 10%. Numerical model utilizing the fabric mechanics simulations predicts lower level of residual stresses due to curing, as compared to nominal geometry models.
Open questions in the teaching of mechanics
Journal of Engineering Education
19
4
398-403
1928
Consideration of following questions; reason for there being so much diversity in different institutions in amount of time allotted to subject; purposes and objects of teaching mechanics to engineering students; general method of treatment of subject matter of mechanics; matter of correlation of mechanics with other subjects both before and after it in course.
Engineering education; Mechanics
Thermocapillary effects on a thin viscous rivulet draining steadily down a uniformly heated or cooled slowly varying substrate
Journal of Fluid Mechanics
441
195-221
2001
10.1017/S0022112001004797
We use the lubrication approximation to investigate the steady flow of a thin rivulet of viscous fluid with prescribed volume flux draining down a planar or slowly varying substrate that is either uniformly hotter or uniformly colder than the surrounding atmosphere, when the surface tension of the fluid varies linearly with temperature. Utilizing the (implicit) solution of the governing ordinary differential equation that emerges, we undertake a comprehensive asymptotic and numerical analysis of the flow. In particular it is shown that the variation in surface tension drives a transverse flow that causes the fluid particles to spiral down the rivulet in helical vortices (which are absent in the corresponding isothermal problem). We find that a single continuous rivulet can run from the top to the bottom of a large horizontal circular cylinder provided that the cylinder is either warmer or significantly cooler than the surrounding atmosphere, but if it is only slightly cooler then a continuous rivulet is possible only for a sufficiently small flux (though a rivulet with a discontinuity in the free surface is possible for larger values of the flux). Moreover, near the top of the cylinder the rivulet has finite depth but infinite width, whereas near the bottom of the cylinder it has finite width and infinite depth if the cylinder is heated or slightly cooled, but has infinite width and finite depth if the cylinder is significantly cooled.
Mathematics
Mechanics of Materials and Structures
Materials and Structures
4
February
2009
This paper describes an experimental procedure for the simultaneous determination of heat sources and mechanical energy involved locally during a heterogeneous tensile test. This procedure involves two complementary imaging techniques: digital image correlation (DIC) and infrared thermography (IRT). The first technique gives displacement fields from which strains are derived while the second provides temperature fields with which the heat sources are estimated using a local form of the heat equation. Moreover, a method based on integration of equilibrium equations under the plane stress assumption is used to determine the stress distribution during the test. The distribution of the local deformation energy developed by the material is then assessed using stress and strain-rate fields. Tensile tests were performed on thin flat steel samples. The results revealed early and gradual devel- opment of strain localization within the gauge part of the specimen. Energy balances were performed inside and outside the necking zone based on the assumption that the thermoelastic part of the behaviour remains linear and isotropic. Finally, indirect estimate of the stored energy led us to compute the time course of the local Taylor–Quinney coefficient.
digitial image correlation; dissipation; infrared thermography; localization.; plasticity; stored energy
Comparison Of Two Dynamic Contact Line Models For Driven Thin Liquid Films
European Journal Of Applied Mathematics
15
6
625-642
2004
10.1017/S0956792504005741
The modeling of the motion of a contact line, the triple point at\nwhich solid, liquid and air meet, is a major outstanding problem\nin the fluid mechanics of thin films [2, 9]. In this paper, we compare\ntwo well-known models in the specific context of Marangoni driven\nfilms. The precursor model replaces the contact line by a sharp transition\nbetween the bulk fluid and a thin layer of fluid, effectively pre-wetting\nthe solid; the Navier slip model replaces the usual no-slip boundary\ncondition by a singular slip condition that is effective only very\nnear the contact line. We restrict attention to traveling wave solutions\nof the thin film PDE for a film driven up an inclined planar solid\nsurface by a thermally induced surface tension gradient. This involves\nanalyzing third order ODE that depend on several parameters. The\ntwo models considered here have subtle differences in their description,\nrequiring a careful treatment when comparing traveling waves and\neffective contact angles. Numerical results exhibit broad agreement\nbetween the two models, but the closest comparison can be done only\nfor a rather restricted range of parameters. The driven film context\ngives contact angle results quite different from the case of a film\nmoving under the action of gravity alone. The numerical technique\nfor exploring phase portraits for the third order ODE is also used\nto tabulate the kinetic relation and nucleation condition, information\nthat can be used with the underlying hyperbolic conservation law\nto explain the rich combination of wave structures observed in simulations\nof the PDE and in experiments [3, 15].
Solitons and Bohmian mechanics
Discrete and Continuous Dynamical Systems
8
2
303-317
2002
10.3934/dcds.2002.8.303
This article proposes a set of ideas concerning the introduction of\nnonlinear analysis, particularly nonlinear PDE, in the theory of\nparticles. The Quantum Mechanics theory is essentially a linear theory,\nduo mainly to the fact that there was a the lack of nonlinear mathematics\nat the time of the discoveries in particle physics. The main idea\nis to perturb the Schroedinger equation by a nonlinear term. This\nnonlinear term has two main parts, a second order quasilinear differential\noperator responsible for the smoothing of the solutions and a nonlinear\n0-order term with a singularity providing topology to the space.\nBy minimizing the energy functional, solutions to the equation are\nobtained in each topological class. Then the qualitative properties\nof the soliton is analyzed. By resealing arguments, the asymptotic\nbehavior of the static solutions is studied, Next the evolution is\nstudied, deriving stability of the soliton and the guidance formula,\nIn this way the equations of Bohmian Mechanics are obtained. Most\nproofs arc omitted, but in all cases a proper reference is given.
nonlinear schroedinger equation solitary waves pil
Advances in Damage Mechanics
Advances in Damage Mechanics
159-179
2006
10.1016/B978-008044688-2/50008-4
This chapter deals with an overall approach to metal–matrix composites. It uses the concepts of damage mechanics with a micromechanical composite model to analyze damage and elasto-plastic deformation in fibrous composite materials with a ductile matrix. The main objective is to introduce appropriate expressions for the yield function and hardening rule in the damaged state in terms of an overall damage tensor M. The damage tensor M is assumed to represent all types of damage that the composite system undergoes such as nucleation and growth of voids in the matrix, fracture of fibers, debonding, and delamination. The end result of this approach is to introduce a new class of yield criteria, flow and hardening rules for the damaged composite system that can be used directly in the expression of the stiffness tensor to be used in numerical applications of the model proposed in the chapter. An anisotropic yield function is derived for the composite system based on using a von Mises type yield criterion for the undamaged matrix material.
Microscopic characterization of modified phenol-formaldehyde resin penetration of bamboo surfaces and its effect on some properties of two-ply bamboo bonding interface.
BioResources
9
1953-1963
2014
The bonding interface between bamboo elements and adhesives is presumed to be significantly influenced by the degree of adhesive penetration into the porous network of interconnected cells of bamboo surfaces. In the study presented here, the average depth and effective depth of phenol-formaldehyde resin (PF) modified by different contents of lower-molecular weight (LMW) PF on bamboo surface were evaluated, making use of fluorescent microscopy characterization. The shear distribution at the bonding interface was measured by means of electronic speckle pattern interferometry (ESPI), along with tensile strength measurements, to determine the shear strain distribution on a macroscopic scale. This research combined macroscopic mechanical properties with microscopic interfacial mechanical properties, and it was found that PF modified with 10% LMW PF performed better than other modified PF. Moreover, it was assumed that the results of this study would influence the choice of bamboo-specific adhesives under different strain conditions.\n
adhesives; angiosperms; bamboo; bamboos; characterization; Cyperales; eukaryotes; glues; measurement; mechanical properties; metrology; monocotyledons; penetration; physical properties; plants; Poaceae; Spermatophyta; tensile strength
Free flexural vibration of symmetric angle-ply triangular composite laminates
Journal of Sound and Vibration
169
5
633-654
1994
10.1006/jsvi.1994.1038
This paper reports an extension of previous work [1] to the study of the free flexural vibration analysis of symmetrically laminated triangular plates. The analysis is performed by using a simple and straightforward pb-2 Rayleigh-Ritz method. A governing frequency equation for the laminated triangular plates with different combinations of free, simply supported or clamped edge conditions is derived. Although only the vibration frequencies for cantilevered right-angled and isosceles triangular plates are reported, the method is readily applied to general triangular laminated plates. In the present analysis, the effects of material properties, the number of layers and different fibre stacking sequences of various composites on the vibration frequencies are investigated. Convergence tests have been carried out for selected plate examples to demonstrate the accuracy of the solutions.
Flexural vibrations; Laminated composites; Numerical analysis; Plates (structural components); Rayleigh-Ritz method; Triangular plates; Vibrations (mechanical)
Do Intellegent Observers Exist in Quantum Mechanics?
Physics Letters A
103
A
3-5
1984
10.1016/0375-9601(84)90042-2
The purpose of this letter is to argue that despite claims in a recent article in this journal, the reality addressed in the classic paper of Einstein, Podolsky and Rosen is not completely described by quantum mechanics no matter what interpre- tation is adopted.
Quantum mechanics of the dynamic Kingdon trap
Physical Review A - Atomic, Molecular, and Optical Physics
73
2
1-5
2006
10.1103/PhysRevA.73.023411
Classical mechanics is not sufficient to describe ion confinement in the dynamic Kingdon trap. We compute quantum corrections to the classical pseudopotential and supplement classical stability criteria with quantum stability criteria. Considering a realistic experimental scenario we show that it is possible to operate the dynamic Kingdon trap in the quantum regime.
Gradual introduction of some aspects of quantum mechanics in a high school curriculum
Physics Education
32
302-308
1997
10.1088/0031-9120/32/5/012
The basic concepts of quantum mechanics can be introduced at a high school level by considering the action of classical mechanics and then introducing Planck’s constant as the granularity of that action. A practical example of the periodic motion of a spring allows students to investigate the limits of classical mechanics, and concepts such as the Uncertainty Principle can be discussed.
Smooth quantum mechanics
PhilSci Archive
37
2
1-32
2008
10.1007/s10701-006-9089-1
I show that the contradiction between the unitary evolution and the con- dition to obtain, as a result of the measurement, an eigenstate of the observable, can be resolved without making use of discontinuities. The apparent state vector reduction can be replaced with a delayed initial condition, imposed to the unitary evolution of the observed system entangled with the measurement device used for the preparation. Since the quantum state of this device is not available entirely to the observer, its unknown degrees of freedom inject, by the means of entanglement, an apparent ran- domness in the observed system, leading to a probabilistic behavior. The condition imposed by the observable combined with the condition of minimal disturbance lead to the Born rule. Thus, we can construct a Smooth Quantum Mechanics, without the need of discontinuities in time evolution, and the probabilities appear from the lack of knowledge of the quantum states of all the systems involved. As a consequence, the evolution is deterministic, but there is no way for an observer to make complete use of this determinism. For such an observer, and for an open quantum system, the evolution will still be indeterministic. The possibility to choose the initial conditions with a delaymakes the determinismto be compatible with the free will at the same extent as the indeterministic version of Quantum Mechanics is. The apparent indeterminism at the observer’s level also leaves room for a smooth version of the Many Worlds Interpretation.
Excited-States in Stochastic Mechanics
Physics Letters A
155
6-7
348-350
1991
Doi 10.1016/0375-9601(91)91037-E
A procedure is proposed to construct the excited states in stochastic mechanics which eliminates singular drifts.
Incompatibility of the Copenhagen interpretation with quantum mechanics formalism
Physics
4
2006
It is proved the mathematical theorem, that the wave function describes the statistical ensemble of particles, but not a single particle. Supposition, that the wave function describes a single particle appears to be incompatible with formalism of quantum mechanics.
Fluid Mechanics - An Introduction to the Theory of Fluid Flows
Springer
723
2008
10.1007/978-3-540-71343-2
This is a modern book on fluid mechanics that is written in a way needed these days to teach the subject to students in engineering and science at higher ...
On the uniqueness of quantum equilibrium in Bohmian mechanics
Journal of Statistical Physics
128
1197-1209
2007
10.1007/s10955-007-9354-5
In Bohmian mechanics the distribution $|\psi|^2$ is regarded as the equilibrium distribution. We consider its uniqueness, finding that it is the unique equivariant distribution that is also a local functional of the wave function $\psi$.
Powerful respiratory stimulation by thin muscle afferents
Respir Physiol
117
1
1-12
1999
The ventilatory responses to electrical stimulation of phrenic afferents were examined in spontaneously breathing dogs at different levels of sodium pentobarbital anesthesia. High intensity stimulation (activation of all the afferents, including thin fibers) increased ventilation (V(E)). The increase in V(E) was comparable to that of breathing 10% CO2 and was inversely related to anesthesia level. Under light anesthesia, V(E) increased to 282+/-36% of the control value when the phrenic nerve was stimulated at 130 times the twitch threshold (n = 15; P < 0.01). The increase in V(E) was due to increases in breathing rate (193+/-19%) and tidal volume (V(T)) (143+/-8%). On the other hand, inspiratory time (T(I)) decreased. Thus, average airflow rate (V(T)/T(I)) increased to 204+/-23%. After administration of 20 and 40% of the initial dose of pentobarbital, V(E) response was attenuated to 157+/-21 and 121+/-4%, respectively. We conclude that thin muscle afferents are capable of eliciting pronounced ventilatory stimulation. The small responses observed earlier were likely due to depth of anesthesia.
Anesthesia; Animal; Anoxia/metabolism; Blood Pressure/physiology; Carbon Dioxide/metabolism; Dogs; Electric Stimulation; Female; Male; Muscle, Skeletal/innervation/physiology; Neurons, Afferent/*physiology; Phrenic Nerve/physiology; Respiratory Mechanics/*physiology; Respiratory Muscles/*innervation/*physiology; Support, Non-U.S. Gov't; Vagotomy
Invertebrate swimming: integrating internal and external mechanics
Symp Soc Exp Biol
49
61-89
1995
Challenges in understanding design for locomotion in any swimming animal revolve around the complex interactions between the mechanics of fluid motions around an animal and the mechanics of internal force production. The former is governed by force-velocity relationships that arise from fluid motion, whereas the latter is governed by force-velocity relationships of both active (e.g. muscle) and passive tissues. In reality, all such relationships must be satisfied simultaneously in any swimming creature. Towards this end, I combine traditional analyses of muscle contractility, soft tissue mechanics and hydrodynamic models to examine how organism morphology, muscle physiology and mode of propulsion interact to affect swimming performance. This combination involves a solution to a set of equations that describe the relevant internal and external mechanics. The solution has the unique benefit of providing predictions for both body and propulsor kinematics. Such predictions are examined for a variety swimming animals and are compared with existing kinematic data. Armed with such an approach, I re-examine traditional scaling arguments to show that classical approaches that neglect internal mechanics predict swimming performance relationships that may not be physiologically feasible.
Animals; Biomechanics; Invertebrates/ physiology; Kinetics; Models, Biological; Muscle Contraction/physiology; Swimming/ physiology
Foundations of gravity dams: Rock mechanics requirements
12th International Congress on Rock Mechanics of the International Society for Rock Mechanics, ISRM 2011
Beijing
1985-1990
2012
The requirements for the foundation of concrete (CVC, RCC, hardfill) dams are usually expressed in qualitative terms: "sound rock", "fresh rock", "below the decompressed surface strata". That lefts a big margin to the engineering judgment of the dam construction responsible. On the other hand the requirements depend on the dam class, and material (CVC concrete has bigger deformation modulus than RCC and hardfill, and therefore requires a less deformable foundation). In this paper the minimum requirements for the rock mass in the foundation of concrete gravity dams (CVC, RCC, hardfill) are expressed in terms of rock mechanics parameters: rock mass longitudinal velocity (celerity), measured by geophysical methods; ISRM weathering degree; unconfined compressive strength; rock mass deformation modulus; geomechanics classifications classes. © 2012 Taylor & Francis Group, London.
Concrete gravity dams; Dam construction; Deformable foundations; Deformation; Deformation modulus; Foundations; Geomechanics; Geophysical methods; Gravity dams; Hydraulic structures; Longitudinal velocity; Rock mass; Rock mass deformation modulus; Rock mechanics; Rock mechanics parameters; Rocks; Rock slopes and foundations; Teaching; Unconfined compressive strength; Weathering degree
Agricultural Mechanics Laboratory Management Professional Development Needs of Wyoming Secondary Agriculture Teachers
Journal of Agricultural Education
52
3
75-86
2011
10.5032/jae.2011.03075
Accidents happen; however, the likelihood of accidents occurring in the agricultural mechanics laboratory is greatly reduced when agricultural mechanics laboratory facilities are managed by secondary agriculture teachers who are competent and knowledgeable. This study investigated the agricultural mechanics laboratory management in-service needs of Wyoming secondary agriculture teachers who are responsible for managing agricultural mechanics laboratories. Data were collected with a Web-based questionnaire designed to determine teachers' perceptions of the importance of 70 selected agricultural mechanics laboratory management competencies and their self-assessed ability to perform those competencies. The Borich (1980) needs assessment model was used to assess and evaluate the in-service needs of the teachers. This study found that Wyoming secondary agriculture teachers were in need of agricultural mechanics laboratory management in-service education in the areas of: first aid, correcting hazardous laboratory conditions, and general laboratory safety. Wyoming teacher educators, state agricultural education supervisory personnel, and local professional development coordinators should provide pertinent and continuous in-service education for Wyoming secondary agriculture teachers in the area of agricultural mechanics laboratory management through technical workshops, summer professional development conferences, and university instructed agricultural mechanics courses. (Contains 5 tables.)
Agricultural Education; Secondary School Teachers;; Wyoming; Needs Assessment Model
Quantum mechanics of inflation
Nuclear Physics B
259
4
730-744
1985
10.1016/0550-3213(85)90011-2
We derive the Harrison-Zeldovich spectrum by perturbatively solving the Wheeller-DeWitt equations for an inflating universe coupled to a scalar field in 2 + 1 and 3 + 1 dimensions.
On a Non-Linear Theory of Thin Jets. Part 1
Journal of Fluid Mechanics
31
03
583-601
1968
The injection of a two-dimensional jet into a uniform stream is considered, the fluids being assumed inviscid and incompressible. When the total head of the jet is much larger than that of the uniform flow, the motion is characterized by two disparate length scales, and uniformly valid asymptotic solutions can be found by the method of matched expansions. Inner and outer expansions are developed for the jet and the external flow. The first-order outer solution in the jet is the usual thin jet approximation which fails in the neighbourhood of the jet exit except for 90° injection, when it is uniformly valid. The basic non-linearity introduced by the pressure condition along the vortex sheet separating the jet from the external flow appears as a non-linear boundary condition for the first-order outer solution in the external flow. A novel feature of the analysis is the necessity of imposing a logarithmic singularity as an ‘inner’ boundary condition for the outer solution in the external flow. The first-order fluid speed and streamline deflection angle are shown to be given correctly to O(1) uniformly in the external flow (for all injection angles) by the first-order outer solution.
Not printed
The Effect of Compressibility on the Stress Distributions in Thin Elastomeric Blocks and Annular Bushings
Journal of Applied Mechanics-Transactions of the Asme
59
4
902-908
1992
The effect of the bulk compressibility of elastomers on the response of rubber blocks and bushings bonded to platens is investigated. Closed-form solutions for the stresses and deformations within the elastomer are presented for the case of rigid adherends. It is shown that even with relatively small shape factors, the compressibility can significantly affect the apparent stiffness. A finite element analysis shows that the closed-form solution accurately predicts the stress distribution for rigid adherends, but also reveals that platen deformations in realistic systems may significantly alter the distributions.
Experimental and Finite Element Investigation of Fracture in Aluminium Thin Plates.
Journal of the Mechanics and Physics of Solids
28
167-189
1980
10.1016/0022-5096(80)90002-2
Detailed strain and crack-opening measurements have been made on center crack and double edge crack specimens of aluminum alloys L70 and L71 in plates 1. 6 mm thick, using the Moire technique to measure strains in front of the instantaneous crack tip during stable crack growth. The specimen load-displacement curves were also monitored during stable crack growth, using a displacement-controlled loading machine, and fracture resistance (R-) curves calculated. A two-dimensional elastic-plastic finite element program was used in a numerical model of the experiments. A simple energy balance proved adequate in explaining the main features of stable and unstable crack growth.
Trends in the applied mechanics literature
Technological Forecasting and Social Change
10
3
309-318
1977
Generalizations about the field and literature of applied mechanics are made on the basis of the growth of the Journal of Applied Mechanics (JAM) and Applied Mechanics Reviews (AMR) through 1975. The data show that the field is currently doubling its size about once every 10 years and that there is a definite increase in multiple-author papers.
Theory of thin thermoelastic rods made of porous materials
Archive of Applied Mechanics
81
10
1365-1391
2010
10.1007/s00419-010-0490-z
In this paper, we consider thin rods modeled by the direct approach, in which the rod-like body is regarded as a one-dimensional continuum (i.e., a deformable curve) with a triad of rigidly rotating orthonormal vectors attached to each material point. In this context, we present a model for porous thermoelastic curved rods, having natural twisting and arbitrary shape of cross-section. To describe the porosity, we employ the theory of elastic materials with voids. The basic laws of thermodynamics are applied directly to the one-dimensional continuum, and the nonlinear governing equations are established. We formulate the constitutive equations and determine the structure of constitutive tensors. We prove the uniqueness of solution to the boundary-initial-value problem associated with the deformation of porous thermoelastic rods in the framework of linear theory. Then, we show the decoupling of the bending-shear and extension-torsion problems for straight porous rods. Using a comparison with three-dimensional equations, we identify and give interpretations to the relevant fields introduced in the direct approach. Finally, we consider the case of orthotropic materials and determine the constitutive coefficients for deformable curves in terms of three-dimensional constitutive constants by means of comparison between simple solutions obtained in the two approaches for porous thermoelastic rods. © 2010 Springer-Verlag.
Effective stiffness; Materials with pores; Orthotropic behavior; Theory of rods; Thermoelasticity; Uniqueness of solution
Regular and chaotic forced vibration of thin rotating rings
International Journal of Non-Linear Mechanics
33
5
843-855
1998
10.1016/S0020-7462(97)00056-5
Dynamics of thin rings rotating with constant spin speed is investigated. The rings rotate with respect to their axis of rotational symmetry and they are under the influence of external forcing which leads to conditions of two-frequency or single-frequency primary resonance. First, a two-degree-of-freedom weakly non-linear model is employed, governing the amplitude of two in-plane bending modes of the ring with the same wave number. Then, a perturbation procedure is applied and modulation equations are derived for the amplitudes and phases of approximate analytical solutions of this model. For two-frequency quasiperiodic forcing, constant solutions of the modulation equations are shown to correspond to structural response involving combinations of forward and backward traveling waves, while for single-frequency resonant Forcing the ring response is dominated by a forward or backward traveling wave. Characteristic effects of system parameters on the ring dynamics are then illustrated by representative series of response diagrams. Finally, direct integration of the modulation equations reveals rich dynamic behavior, involving coexistence and interaction of constant solutions with periodic and chaotic solutions. (C) 1998 Elsevier Science Ltd. All rights reserved.
bifurcations; chaos; dynamics; inplane vibrations; quasiperiodic forcing; rotating ring; traveling waves
Thickness Measurement for Thin Films and Coatings Using Millimeter Waves
Research in Nondestructive Evaluation
9
2
97-118
1997
10.1007/PL00003892
An accurate technique for measuring the thickness of dielectric thin films and coatings is presented in this paper. Millimeter-wave sensors operated at 80 GHz are placed near the sample surface. A better than 1∘/μ1^{\circ}/\mu m sensitivity of the phase of the received signal with respect to sample thickness can be achieved. A theoretical model consisting of a vertical electric dipole over a two-layer structure is used to generate calibration information and to guide the optimization of sensor placement. To facilitate the theoretical study, we devise an efficient and reliable numerical algorithm for evaluating Sommerfeld integrals. This algorithm surpasses the performance of conventional numerical methods and renders fast convergence even in the worst-case scenario, when the transmitter and the receiver have the same elevation and the materials are lossless.
On the buckling of thin tensioned sheets with cracks and slots
Engineering Fracture Mechanics
4
4
939-950
1972
10.1016/0013-7944(72)90027-6
The problem of local buckling in tensioned sheets with holes is discussed in relation to its effect on fracture and fatigue characteristics. The results of an experimental investigation designed to determine the tensile buckling stress are presented. The results indicate that for the range of the parameters investigated, the sheet thickness to hole length ratio and a nondimensional hole shape parameter are the dominant geometric variables. It is shown that the results obtained in the investigation described and the results obtained by other investigators can be described by a single formula. The physical significance of local buckling is discussed and particular emphasis is placed on the importance of accounting for buckling in residual strength analyses of thin cracked sheets. Recommendations are made for the standardization of the buckling stress determination in terms of its relationship to the effect of middle-surface stretching due to the bending. Finally, the influence of the buckling process on plane stress fracture toughness values, Kc, obtained from center cracked sheet specimens is discussed.
Effective critical exponents of magnetization in transverse Ising thin films
Physica a-Statistical Mechanics and Its Applications
332
367-379
2004
10.1016/j.physa.2003.10.016
The characteristic influence of exchange interaction and transverse field at the surface on the critical behavior of a ferromagnetic transverse Ising thin film is examined by the use of the standard mean-field theory and the effective-field theory with correlations. The exchange interaction and transverse field at the surface take values different from those in the bulk. Depending on the ratios of these properties between the surface and the bulk, many characteristic behaviors are obtained in the magnetic properties, as discussed in the previous works (Physica A 319 (2003) 355; J. Magn. Magn. Mater. 264 (2003) 30; Phys. Stat. Sol. (B) 237 (2003) 592; Physica A (2003), published online). In particular, the critical effective exponent beta(eff) of magnetization in the film with a thickness L is studied by the use of the two theoretical frameworks. We find some new phenomena of beta(eff), depending on the values of L and the ratios. (C) 2003 Elsevier B.V. All rights reserved.
critical properties; effective-field; ferroelectric-films; magnetization; model; phase-diagrams; transitions; transverse ising film
Thermal buckling of clamped symmetric laminated plates
Thin-Walled Structures
13
4
259-273
1992
10.1016/0263-8231(92)90024-Q
The buckling behavior of moderately thick symmetric angle-ply laminates having clamped edges and subject to a uniform temperature rise is investigated. Transverse shear deformation is accounted for by employing the Reissner-Mindlin theory. The exact solution to the coupled differential equations is obtained using the general double Fourier series approach. Calculated values of the critical temperature are compared with corresponding finite element results.
Hygrothermal effects on the postbuckling of axially loaded shear deformable laminated cylindrical panels
Composite Structures
56
1
73-85
2002
10.1016/S0263-8223(01)00187-8
The effect of hygrothermal conditions on the buckling and postbuckling of shear deformable laminated cylindrical panels subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling is extended to the case of shear deformable laminated cylindrical panels under hygrothermal environments and a singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, moderately thick and thin, cross-ply laminated cylindrical panels under different sets of environmental conditions. The results show that the hygrothermal environment has a significant effect on the buckling load as well as postbuckling response of the panel. In contrast, it has a small effect on the imperfection sensitivity of symmetric cross-ply laminated cylindrical thin panels.
Boundary layer theory of shell buckling; Hygrothermal effect; Postbuckling; Shear deformable laminated cylindrical panel; Singular perturbation technique
Adaptive implicit-explicit finite element algorithms for fluid mechanics problems
Computer Methods in Applied Mechanics and Engineering
78
2
165-179
1988
10.1016/0045-7825(90)90099-8
The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.
Quantum mechanics with respect to different reference frames
J. Math. Phys.
48
082104
2007
10.1063/1.2769147
Geometric (Schrodinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space fibered over a time axis R. Under quantization, it yields a connection on the quantum algebra of Schrodinger operators. The operators of energy with respect to different reference frames are examined.
Austere quantum mechanics as a reductive basis for chemistry
Foundations of Chemistry
15
3
311
2013
10.1007/s10698-012-9173-x
This paper analyses Richard Bader{\rq}s {\lq}operational{\rq} view of quantum mechanics and the role it plays in the the explanation of chemistry. I argue that QTAIM can partially be reconstructed as an {\lq}austere{\rq} form of quantum mechanics, which is in turn committed to an eliminative concept of reduction that stems from Kemeny and Oppenheim. As a reductive theory in this sense, the theory fails. I conclude that QTAIM has both a regulatory and constructive function in the theories of chemistry.
Mechanics and mechanisms of fracture of thermosetting epoxy polymers
Advances in Polymer Science
72
45-46
1985
Thermosetting epoxy polymers are widely employed in structural engineering applications and thus a knowledge of the mechanics and mechanisms of the fracture of such materials is of vital importance. The present Chapter discusses the fracture of epoxy polymers, concentrating on the use of a continuum fracture mechanics approach for elucidating the micromechanisms of crack growth and identifying pertinent failure criteria.
Chern-Simons Reduction and non-Abelian Fluid Mechanics
Physical Review D
hep-th
April
12
2000
10.1103/PhysRevD.62.085018
We propose a non-Abelian generalization of the Clebsch parameterization for a vector in three dimensions. The construction is based on a group-theoretical reduction of the Chern-Simons form on a symmetric space. The formalism is then used to give a canonical (symplectic) discussion of non-Abelian fluid mechanics, analogous to the way the Abelian Clebsch parameterization allows a canonical description of conventional fluid mechanics.
Jeans' criterion in nonextensive statistical mechanics
Physica A: Statistical Mechanics and its Applications
335
107-114
2004
10.1016/j.physa.2003.11.027
The Jeans' gravitational instability in nonextensive statistical mechanics is studied and a general form of the generalized Jeans' criterion is obtained that is related to the q-function cq = ∑ip i\nq. In this approach, the nonextensive model of classical ideal gas is applied to the Jeans' problem instead of the ordinary one in extensive statistical mechanics and the generalized critical wavelength to describe the gravitational instability is deduced. This nonextensive modification of the Jeans' criterion leads to a new critical length that depends not only on the nonextensive parameter q but also on the dimension D and the total particle numbers N of the system. When q → 1 - , the Jeans' length is perfectly recovered. We also give the nonextensive parameter q a physical interpretation that q = 1 represents an isothermal process of the gas, corresponding to the state of complete mixing, but 0 < q < 1 is nonisothermal, corresponding to the state of incomplete mixing, it measures the degree of mixing. © 2003 Elsevier B.V. All rights reserved.
Jeans' criterion; Nonextensive statistical mechanics
Statistical microdamage mechanics and damage field evolution
Theoretical and Applied Fracture Mechanics
37
1–3
1-10
2001
10.1016/S0167-8442(01)00087-8
Discussed are the underlying background of statistical microdamage mechanics, the fundamental partial differential equation of evolution of microdamage number density, two basic solutions, and the saturation of microdamage number density evolution. Knowledge of microdamage number density evolution is applied to engineering practice by using the field equations of microdamage number density and continuum damage. The addition of continuum equations renders a complete system of field equations of deformation and damage. However, they are open-ended in character at the continuum level although the dynamic damage function is completed from the meso- to the macro-scale level. Once decoupling of the function is made, the system of equations can be connected in an approximate manner. This provides a reasonable approximation to the continuum field of deformation and damage. The open literature prediction based on damage evolution relies on assuming arbitrary critical damage states. In this work, use is made of the criterion for damage localization. Several applications of statistical microdamage mechanics are made. This includes damage evolution in a heterogeneous medium and failure forecast under impact. The results show that statistical microdamage mechanics and the derived closed approximate continuum formulations are physically sound and practically effective.
Thin Airfoil Theory
School of Mechanical and Aerospace Engineering, Oklahoma State, USA
Project On
March
15
2000
The thin airfoil theory for calculation of section flight properties is reviewed. Lift and moment coefficient and center of pressupre calculations are made for cambered and flapped wing sections. Effects of camber flaps are discussed. The thin wing thoery results are compared to experimental airfoil data.
thin airfoil theory
Turbulent Flow.(Book Reviews: Statistical Fluid Mechanics. Mechanics of Turbulence. Vol. 1) Book
Science
1972
Title: . (Book Reviews: Statistical Fluid Mechanics. Mechanics of Turbulence. Vol. 1). Book Authors: Monin, AS; Lumley, John L.
Nonlinear wave mechanics from classical dynamics and scale covariance
Physics Letters A
370
5-6
374-378
2007
10.1016/j.physleta.2007.06.011
Nonlinear Schrodinger equations proposed by Kostin and by Doebner\nand Goldin are rederived from Nottale's prescription for obtaining\nquantum mechanics from classical mechanics in nondifferentiable spaces;\ni.e., from hydrodynantical concepts and scale covariance. Some soliton\nand plane wave solutions are discussed. (C) 2007 Elsevier B.V. All\nrights reserved.
hydrodynamics; nonlinear wave mechanics; scale covariance; soliton wave solutions
A continuum damage mechanics model for high cycle fatigue
International journal of fatigue
20
7
503–508
1998
The paper presents a continuum damage mechanics model, which is based on the general thermodynamic framework advocated by Lemaitre and Chaboche, etc., for high cycle fatigue. It can give a good clarification for
continuum damage mechanics; fatigue; fatigue life
Free vibration analysis of stiffened laminated plates using layered finite element method
STRUCTURAL ENGINEERING AND MECHANICS
14
3
245-262
2002
The free vibration analysis of stiffened laminated composite plates has\nbeen performed using the layered (zigzag) finite element method based on\nthe first order shear deformation theory. The layers of the laminated\nplate is modeled using nine-node isoparametric degenerated flat shell\nelement. The stiffeners are modeled as three-node isoparametric beam\nelements based on Timoshenko beam theory. Bilinear in-plane displacement\nconstraints are used to maintain the inter-layer continuity. A special\nlumping technique is used in deriving the lumped mass matrices. The\nnatural frequencies are extracted using the subspace iteration method.\nNumerical results are presented for unstiffened laminated plates,\nstiffened isotropic plates, stiffened symmetric angle-ply laminates,\nstiffened skew-symmetric angle-ply laminates and stiffened\nskew-symmetric cross-ply laminates. The effects of fiber orientations\n(ply angles), number of layers, stiffener depths and degrees of\northotropy are examined.
A model for crystal plasticity based on micro-slip descriptors
Continuum Mechanics and Thermodynamics
14
5
425-435
2002
Within the framework of multi-field theories of damage mechanics we address the problem of crystal plasticity without introducing either the usual decomposition of the deformation gradient into elastic and plastic parts, or the associated concept of intermediate (or lattice) configuration. In comparison with the standard presentations of crystal plasticity we use a more refined kinematical description able to assess the effects of any dislocation on the macro-motion of the body. We ap ply the principle of virtual working to obtain the balance equations; the first and the second principles of thermodynamics to get suitable restrictions for the constitutive relations. A numerical simulation is worked out to illustrate the main features of the model.
Relativistic viscoelastic fluid mechanics
ReCALL
2011
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski spacetime become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Fluid Dynamics; High Energy Physics - Theory; Statistical Mechanics
Thermoelastic fracture mechanics with regularized hypersingular boundary integral equations
Engineering Analysis with Boundary Elements
23
1
89-96
1999
10.1016/S0955-7997(98)00064-2
This paper is concerned with thermoelastic fracture mechanics, in three-dimensional linear elasticity, using hypersingular boundary integral equations (HBIEs). The HBIEs are regularized by employing modes of deformation (or “simple solutions”). In addition to rigid-body and linear displacement modes, which have been used before for isothermal linear elastic fracture mechanics (LEFM), a new mode is employed here. This new mode is a thermal one in which the body is elevated to a uniform temperature but fully constrained (i.e., zero prescribed displacements) on its bounding surface. An existing isothermal LEFM computer code called BES is extended in this work to include thermoelastic terms. Some numerical results are presented from this new code.
Computational mechanics; Computer code; Hypersingular boundary intergral equations; Thermoelastic fracture mechanics
Following Weyl on quantum mechanics: The contribution of Ettore Majorana
Foundations of Physics
34
5
871-887
2004
10.1023/B:FOOP.0000022190.47446.f3
After a quick historical account of the introduction of the group-theoretical description of quantum mechanics in terms of symmetries, as proposed by Weyl, we examine some unpublished papers by Ettore Majorana. Remarkable results achieved by him in frontier research topics as well as in physics teaching point out that the Italian physicist can be well considered as a follower of Weyl in his reformulation of quantum mechanics.
Measurements of airway mechanics in spontaneously breathing young children
Paediatric Respiratory Reviews
5
1
77-84
2004
10.1016/j.prrv.2003.09.004
This paper gives an overview of the general principles of airway mechanics and methods to measure lung fuction in non-sedated, spontaneously breathing young children. Although lower airway obstruction is probably best evaluated using FEV1, other techniques can be applied when such measurement is impossible, as in young children. These techniques include measurement of resistance using the interrupter or impulse oscillation techniques. © 2004 Elsevier Ltd. All rights reserved.
Airway mechanics; Pulmonary function; Young children
The EPR Argument in a Relational Interpretation of Quantum Mechanics
Arxiv Preprints
1-21
2000
It is shown that in the Rovelli relational interpretation of quantum mechanics, in which the notion of absolute or observer independent state is rejected, the conclusion of the ordinary EPR argument turns out to be frame-dependent, provided the conditions of the original argument are suitably adapted to the new interpretation. The consequences of this result for the `peaceful coexistence' of quantum mechanics and special relativity are briefly discussed.
Footnotes to the history of statistical mechanics: In Boltzmann’s words
Physica A: Statistical Mechanics and its Applications
389
15
2898-2901
2010
10.1016/j.physa.2010.01.023
Although Ludwig Boltzmann was one of the primary founders of the field of statistical mechanics, very few contemporary physicists have actually read his papers. As a result, some of his ideas have been distorted or even lost over the course of time. In this paper, I will discuss some of the reasons for the neglect of Boltzmann’s writings and try to reintroduce one of his most important ideas, the definition of entropy.
A new two-dimensional cracked finite element for fracture mechanics
Engineering Fracture Mechanics
135
17-33
2015
10.1016/j.engfracmech.2015.01.013
A novel finite element with a central crack is proposed for fracture applications. The introduced element is applicable in 2D problems. The crack is modeled by an additional flexibility matrix based on fracture mechanics. Among the topics discussed in this paper, the deficiencies of previous works related to cracked elements are modified. Furthermore, a method for calculating stress intensity factor (SIF) by applying cracked elements is suggested. To show the capability of the suggested element and proposed procedure, several numerical samples are performed.
Numerical analysis of hydraulic fracturing test by fracture mechanics and continuum mechanics
Contribution of Rock Mechanics to the New Century, Vols 1 and 2
457-462
2004
Under the condition which is expected to be realized at the pit wall of high level radioactive waste repository, a hydraulic fracturing test was carried out by using 1m cube of mortar block. Fracture toughness of mortar for tension and shear modes is obtained by laboratory experiments. It is found from the tests that the mortar has a property like a soft rock such that the shear toughness is smaller than toughness in tension. To understand the mechanism of the hydraulic fracturing, the 2-D analysis with fracture mechanics and 3-D analysis with continuum mechanics are carried out. It is found that the crack propagation from fracture tip of soft rock may occur by shear fracturing and the failure at the bottom of the borehole is a result of tension failure. The fracturing mechanism can be estimated by applying both fracture and continuum mechanics models.
continuum; fracture mechanics; fracture toughness; hydraulic fracturing; mechanics
Middle ear mechanics of Type III tympanoplasty (stapes columella): II. Clinical studies
Otol Neurotol
24
2
186-194
2003
OBJECTIVES: To determine the structural features that are responsible for the large variation in postoperative hearing results after Type III stapes columella tympanoplasty, to compare the clinical results after Type III tympanoplasty with predictions based on experimental investigations using a temporal bone model, and to investigate the effectiveness of a modification in surgical technique for Type III reconstruction. STUDY DESIGN: Retrospective case review. SETTING: Tertiary referral center. INCLUSION CRITERIA: The ear was healed with an intact tympanic membrane graft; the status of the stapes was known, whether mobile or fixed; and the postoperative status of aeration of the middle ear was known, whether aerated or not. MAIN OUTCOME MEASURE: Air-bone gap at frequencies 250, 500, 1,000, 2,000 and 4,000 Hz. RESULTS: In ears with temporalis fascia graft onto stapes head: mobile stapes and aerated middle ear (n = 34), mean air-bone gaps at audiometric frequencies were 15 to 30 dB, consistent with predictions of the experimental model; mobile stapes and nonaerated middle ear (n = 16), large air-bone gaps of 35 to 55 dB; fixed stapes and aerated middle ear (n = 4), large air-bone gaps of 30 to 50 dB; fixed stapes and nonaerated middle ear (n = 2), large air-bone gaps of 30 to 70 dB. In ears with a fascia-cartilage graft onto stapes head, where a thin disc of meatal cartilage, 0.3 to 0.5 mm thick and 4 to 6 mm in diameter was interposed between the fascia graft and the stapes head: mobile stapes and aerated middle ear (n = 9), mean air-bone gaps at audiometric frequencies were 10 to 25 dB, about 5 dB better at 250, 500, and 2,000 Hz than in ears with only a fascia graft ( <0.05), improvement consistent with that observed experimentally when a thin cartilage disc was used in the temporal bone model, hypothesis that the cartilage increased the effective vibrating area of the graft; mobile stapes and nonaerated middle ear (n = 2), air-bone gaps were 40 to 50 dB. CONCLUSIONS: Large air-bone gaps of 30 to 70 dB occurred as a result of stapes fixation, nonaeration of the middle ear, or both. When the stapes was mobile and the middle ear was aerated, a fascia graft resulted in air-bone gaps of 15 to 30 dB. Interposing a thin disc of cartilage between the fascia graft and stapes head to improve the effective vibrating graft area gave better hearing, with air-bone gaps of 10 to 25 dB. The clinical Type III results were consistent with predictions based on experimental investigations of mechanics of the Type III procedure in a temporal bone model.
Acoustic Impedance Tests/methods; Adolescent; Adult; Aged; Biomechanics; Bone Conduction/physiology; Cartilage/transplantation; Clinical Trials as Topic; Ear, Middle/*physiology; Fascia/transplantation; Female; Humans; Male; Middle Aged; Middle Ear Ventilation/methods; Otologic Surgical Procedures/methods; Postoperative Care; Retrospective Studies; *Stapes Surgery; Surgical Flaps; Tympanic Membrane/surgery; Tympanoplasty/*methods
Geometric Structure for Quantum Mechanics
International Journal of Theoretical Physics
42
4
775-781
2003
10.1023/A:1024454431280
A geometric connection between quantum mechanics and classical mechanics is described and an operator version of the Poisson bracket is developed.
On resonance in celestial mechanics
Celestial mechanics
1982
Abstract This brief survey of the author's contribution to the theory of resonance in celestial mechanics begins with the genesis of the Small Divisor. The fundamental distinction between theshallow anddeep resonance is illustrated by the 5∶ 2 Jupiter-Saturn and the ... \n
Numerical analysis of intralaminar failure mechanisms in composite structures. Part II: Applications
Composite Structures
93
2
1047-1053
2011
10.1016/j.compstruct.2010.06.022
A three-dimensional continuum damage mechanics-based material model was implemented in an implicit Finite Element code to simulate the progressive intralaminar degradation of fibre reinforced laminates based on ply failure mechanisms. This paper presents some structural applications of the progressive failure model implemented. The focus is on the non-linear response of the shear failure mode and its interaction with other failure modes. Structural applications of the damage model show that the proposed model is able to reproduce failure loads and patterns observed experimentally. ?? 2010.
Damage mechanics; Finite element analysis (FEA); Modelling; Non-linear behaviour
Possible connection between probability, spacetime geometry and quantum mechanics
Physica A: Statistical Mechanics and its Applications
385
1
185-190
2007
10.1016/j.physa.2007.06.006
Following our discussion [E. Canessa, Physica A 375 (2007) 123] to associate an analogous probabilistic description with spacetime geometry in the Schwarzschild metric from the macro- to the micro-domain, we argue that there is a possible connection among normalized probabilities P, spacetime geometry (in the form of Schwarzschild radii rs) and quantum mechanics (in the form of complex wave functions ??), namely sqrt(P??, ??, t\n(n)) ??? Rs\n(n) / rs = | ??n\n(n) (X(n)) |2 / | ??n (x) |2. We show how this association along different (n)-nested surfaces-representing curve space due to an inhomogeneous density of matter-preserves the postulates of quantum mechanics at different geometrical scales. ?? 2007 Elsevier B.V. All rights reserved.
Probability; Quantum mechanics; Spacetime geometry
FRACTAL DIMENSION OF THIN-FILM SURFACES OF GOLD SPUTTER DEPOSITED ON MICA - A SCANNING TUNNELING MICROSCOPIC STUDY
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
182
4
532-541
1992
10.1016/0378-4371(92)90019-M
STM images on four gold thin films sputter deposited on mica at four\ndifferent substrate temperatures have been acquired. From these images\nthe fractal dimension of the surfaces is determined by using a modified\n``slit island{''} technique, wherein the obtained log(Perimeter) versus\nlog(Area) plots showed linearity over seven decades. The fractal\ndimensions, in good agreement with the expected surface morphology,\neventually reduce to two at higher substrate temperatures. The fractal\ndescription is found to apply down to areas of about 30 angstrom 2 in\nagreement with the proposed lower dimensional limit for fractal objects.
Measuring the damage factor of materials with the thin-walled cylinder torsion test and the low-cycle fatigue test
Engineering Fracture Mechanics
44
2
267-273
1993
10.1016/0013-7944(93)90051-S
We have derived the expression of the damage factor, D = 1−(G̃/G), by applying Lemaitre's strain equivalent hypothesis to the pure shear case, and used it as the theoretical basis for measuring D with the thin-walled cylinder torsion test. According to the damage strain energy release rate Y and the Mises criterion, we have obtained the relation between D1c and D2c, 1−D1c1−D2c = √[32(1 + v)] Here, we have performed the torsion test on steel No. 35 and steel No. 45, and measured the value of D2c; D2c is then converted into D1c. We also have measured Dc of steel No. 45 in the low-cycle fatigue test with controlled strain amplitude, and compared the test result of steel No. 45.
Modelling cross-ply laminated elastic shells by a higher-order theory and multiquadrics
Computers & Structures
84
19-20
1288-1299
2006
The higher-order shear-deformation theory of laminated orthotropic elastic shells of Vlasov-Reddy is a modification of Sanders' theory and accounts for parabolic distribution of the transverse shear strains through the thickness of the shell. The Vlasov-Reddy shell theory allows the fulfillment of homogeneous conditions (zero values) at the top and bottom surfaces of the shell. This paper deals with a meshless solution of the Vlasov-Reddy higher-order shell theory. The meshless technique is based on the asymmetric global multiquadric radial basis function method proposed by Hardy and Kansa. This paper demonstrates that this truly meshless method is successful in the analysis of laminated composite shells.
Composite shells; Multiquadrics; Shear-deformation theories
The embryo teacher of mechanics
Journal of Engineering Education
19
9
884-891
1929
Author makes plea for teacher of mechanics, who, he claims deserves greater consideration than is usually given him; he suggests plan, according to which new instructor would have light schedule and not be expected to teach three or more subjects.
Engineering education; Mechanics
PT-symmetrized supersymmetric quantum mechanics
CZECHOSLOVAK JOURNAL OF PHYSICS
51
4
420-428
2001
Supersymmetry between bosons and fermions is modelled within\nPT-symmetric quantum mechanics. a non-Hermitian alternative to the\nWitten's supersymmetric quantum mechanics is obtained.
Applied and computational fluid mechanics
Choice: Current Reviews for Academic Libraries
48
1
128
2010
The article reviews the book "Applied and computational fluid mechanics," by Scott Post.
APPLIED & Computational Fluid Mechanics (Book); BOOKS -- Reviews; NONFICTION; POST, Scott
An energy approach to the link-up of multiple cracks in thin aluminum alloy sheets
Theoretical and Applied Fracture Mechanics
35
2
111-127
2001
10.1016/S0167-8442(00)00053-7
An energy approach has been used in the study of the coalescence or linkage of multiple cracks in aluminum alloy sheets. The study was motivated by concern for the structural integrity of aging aircraft. Forty reported tests for 2024-T3 aluminum panels with a major crack and several multiple-site damage (MSD) cracks have been analyzed via a simple computational model with a Dugdale–Barenblatt [D.S. Dugdale, J. Mech. Phys. Solids 8 (1960) 100–104; G.I. Barenblatt, in: H.L. Dryden, Th. VonKarman (Eds.), Advances in Applied Mechanics, vol. II, 1962, pp. 55–130] type of plastic or inelastic deformation. For simplicity, the computational model considers only the plastic interaction between the major crack and two symmetrically adjacent MSD cracks in an infinite sheet under remote tensile stress. By following the approach given in [B. Cotterell, J. K. Reddel, Int. J. Fract. 13 (1977) 267–277], the specific work to cause ligament failure is found to be a linear function of the normal extent of the confined plastic region for most tests considered. A few exceptions to this linear relation are attributed to the limitation of the employed computational model. A new criterion and an engineering method to predict crack link-up in an MSD sheet are proposed based on this specific work concept, and they have been demonstrated through application to stiffened panels.
A material nonlinear finite element model of spatial thin-walled beams
Gongcheng Lixue/Engineering Mechanics
26
8
138-142
2009
Based on the theories of Bernoulli-Euler beams and Vlasov's thin-walled members, a new material nonlinear finite element model is developed by adding an interior node to the element and applying the independent interpolation to bending angles and warp. Factors such as shear deformation, coupling of flexure and torsion and warp induced by non-uniform torsion and second shear stress are all considered in this model. Material of the element is assumed to be perfectly plastic, complying with Von Mises' yielding rule and the incremental relationship of Prandtle-Reuss. With the aid of the finite segment method, a certain amount of Guass points are distributed along the length of the element and in its cross section, thus the elastoplastic stiffness matrix being derived by numeric integration. Examples testify to the precision and validity of the model. It concludes that the model is applicable to the analysis of thin-walled structures.
Element stiffness matrix; Finite element; Material nonlinear; Spatial beams; Thin-walled structures
New development in welding thin-shell aluminum alloy structures with high strength
CHINA WELDING
13
1
27–30
2004
From the viewpoint of welding mechanics, two new welding methods - welding with trailing peening and welding with trailing impactive rolling were introduced. For aluminum alloy thin-shell structures with high strength, welding will lead to hot cracking, poor joint and distortion. In order to solve them, trailing impactive device was used behind welding torch to impact the different positions of welded joints, thus realizing the welding with free-hot cracking, low distortion and joint strengthening. By use of impactive rolling wheels instead of peening heads, the outlook of welded specimen can be improved and stress concentration at weld toes can be reduced. Equipment of this technology is simple and portable. It can used to weld sheets, longitudinal and ring-like beams of tube-like structures, as well as the thin-shell structures with closed welds such as flanges and hatches. So the technology has the wide application foreground in the fields of aviation and aerospace.
Aluminum alloys; impactive rolling; joint strengthening; Rolling; Shells (structures); Shot peening; Stress concentration; Thin shell aluminum alloy structures; Trailing peening; Welding; welding distortion; welding with trailing peening
Determination of the elastic moduli of thin samples and adherent cells using conical atomic force microscope tips.
Nature nanotechnology
7
11
733-6
2012
10.1038/nnano.2012.163
The atomic force microscope can detect the mechanical fingerprints of normal and diseased cells at the single-cell level under physiological conditions. However, atomic force microscopy studies of cell mechanics are limited by the 'bottom effect' artefact that arises from the stiff substrates used to culture cells. Because cells adhered to substrates are very thin, this artefact makes cells appear stiffer than they really are. Here, we show an analytical correction that accounts for this artefact when conical tips are used for atomic force microscope measurements of thin samples. Our bottom effect cone correction (BECC) corrects the Sneddon's model, which is widely used to measure Young's modulus, E. Comparing the performance of BECC and Sneddon's model on thin polyacrylamide gels, we find that although Sneddon's model overestimates E, BECC yields E values that are thickness-independent and similar to those obtained on thick regions of the gel. The application of BECC to measurements on live adherent fibroblasts demonstrates a significant improvement on the estimation of their local mechanical properties.
Algorithms; Animals; Atomic Force; Atomic Force: methods; Elastic Modulus; Fibroblasts; Fibroblasts: chemistry; Fibroblasts: cytology; Mice; Microscopy; NIH 3T3 Cells
Deposition and Characterization of Boron Doped ZnO Thin Films by Ultrasonic Spray Pyrolysis Method
Applied Mechanics and Materials
475-476
1280-1283
2013
10.4028/www.scientific.net/AMM.475-476.1280
Boron doped ZnO (BZO) thin films were deposited on glass substrate by ultrasonic spray pyrolysis method using zinc acetylacetonate and boric acid. The structural, morphological, optical and electrical properties of BZO thin films under various doping level of boron and substrate temperature were investigated. The results show that zinc acetylacetonate is helpful to deposit BZO thin films at low temperature. The morphology of grains at low and high substrate temperature is circular and flake-like. The preferred orientation along (101) plane is obvious at 360 °C. The doping level and substrate temperature have remarkable influence on sheet resistance, but little impact on visible transmittance. The optimal sheet resistance of 173 Ω/sq and average visible transmittance of above 80% can be achieved at doping level of 5 at% and growth temperature of 340 °C. © (2014) Trans Tech Publications, Switzerland.
BZO; Transparent and conducting; Ultrasonic spray pyrolysis; Zinc acetylacetonate
A new nonlinear finite element model for spatial thin-walled beams
Gongcheng Lixue/Engineering Mechanics
28
6
1-5
2011
Based on the theories of Timoshenko's beams and Vlasov's thin-walled members, a new nonlinear beam element model is developed by placing an interior node in the element and applying independent interpolation on bending angles and warping angles, in which factors such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and second shear stress are all considered. According to nonlinear strain in Updated Lagrangian formulation, geometrical stiffness matrix is deduced. In the aspect of physical nonlinearity, the perfectly plastic model is applied and the yield rule of Von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration on the basis of the finite segment method. Examples show that the developed model is accurate and can be applied to the analysis of thin-walled structures.
Finite element; Geometrical nonlinearity; Material nonlinearity; Spatial beams; Thin-walled section
A new spatial thin-walled beam element including transverse and torsional shear deformation
Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics
45
2
293-296
2013
10.6052/0459-1879-12-218
Based on the Timoshenko and Benscoter's theory, a new spatial thin-walled beam element with an arbitrary open or closed cross section is proposed in this paper, accounting for the influences of shear deformation, flexural and torsional coupling and warping shear stress. With introduction of an interior node to the element, three-node interpolation functions are adopted for bending angles and warping angle to consider shear deformation and warping shear stress, and to avoid shear locking simultaneously. Through a kinematic description of the cross section of a deformed thin-walled beam under loads, the flexural-torsional coupling is included in the displacement and strain equations. In order to verify its accuracy and convergence, some numerical examples are analyzed and their results obtained from the present element are compared with theoretical solutions and numerical solutions of the commercial finite element software and other literatures. Comparisons indicate that the present element is free of shear locking and more accurate than those beam elements presented in other documents.
Arbitrary open or closed cross section; Benscoter's theory; Spatial beam element; Stiffness matrix; Thin-walled beam
Shear locking-free earthquake analysis of thick and thin plates using Mindlin's theory
Structural Engineering and Mechanics
33
3
373-385
2009
The purpose of this paper is to study shear locking-free parametric earthquake analysis of thick and thin plates using Mindlin's theory, to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick and thin plates subjected to earthquake excitations. In the analysis, finite element method is used for spatial integration and the Newmark-beta method is used for the time integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the earthquake analysis of thick and thin plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.
17-noded finite element; aspect ratio; boundary; elastic foundations; finite-element-analysis; forced vibrations; orthotropic rectangular-plates; reissner plate; shear locking-free parametric earthquake analysis; thickness/span ratio; thick plate, mindlin's theory
MISUNDERSTANDING MODELLING IN MECHANICS: A REVIEW OF THE A-LEVEL TEXTBOOK LITERATURE
Research in Mathematics Education
5
1
97-120
2003
10.1080/14794800008520117
All A-level boards have included a modelling approach in the syllabus of their respective mechanics modules and the plethora of textbooks during the past decade is structured according to this approach. This review will attempt to show that these books have confused modelling that is specific to mechanics with mathematical modelling in general. To place the recent textbooks in perspective, this review outlines the logical structure of mechanics, how this relates to the specificity of modelling in mechanics, the philosophical assumptions underlying the traditional textbook, how these assumptions have influenced the modern textbook and how history has been rewritten to justify these assumptions. The conclusion drawn is that the modular scheme has made this confusion unsustainable.
The mechanics of timbrel vaults: a historical outline
Essays on the History of Mechanics: In Memory of Clifford Ambrose Truesdell and Eduardo Benvenuto
89-133
2003
10.1007/978-3-0348-8091-6_5
S. Huerta, The mechanics of timbrel vaults: a historical outline, Basel: Berkhäuser, 2003.
Characterization of the Pt-Hf-Zr-Ni Thin Film Amorphous Alloys for Precise Optical Glass Lens Mold
Journal of Solid Mechanics and Materials Engineering
3
8
1022-1032
2009
10.1299/jmmp.3.1022
We researched the characteristics of the Pt-Hf-Zr-Ni thin film amorphous alloys for precise optical glass lens mold. The five Pt-Hf-Zr-Ni thin film amorphous alloys having various alloy composition were prepared. Desired characteristics for the glass lens mold were researched. Thus, the Pt51Hf20Zr17Ni12 sample was found as the candidate material for the glass crystallization temperature of 994 K, lens mold. This sample showed the the fractured stress of 1.01 GPa and anti-sticking properties to molten glass. However, since the Pt51Hf20Zr17Ni12 sample exhibited insufficient oxidation resistance, it is necessary to inhibit oxidation with protective coating in order to apply this sample to glass lens mold. Moreover, the Pt51Hf20Zr17Ni12 sample fabricated using alloy target could be cut to taperd shape by the single crystal diamond tools without tool wear.
amorphous alloy; optical glass lens mold; thin film
Size effect on tensile strength of surface-micromachined Al-3%Ti thin films
Experimental Mechanics in Nano and Biotechnology, Pts 1 and 2
326-328
Part 1-2
313-316
2006
A new tensile tester using an electromagnetic-force actuator (voice\ncoil) was developed to measure the mechanical characteristics of\nsurface-micromachined thin film materials. The tester has a load cell\nwith maximum capacity of 0.5 N and a non-contact position measuring\nsystem based on the principle of capacitance micrometry with 0.1 nm\nresolution for displacement measurement. The tester was applied for\ntensile testing of Al-3%Ti thin films with dimensions of 1000 mu m\nlong, 50-480 mu m wide and 1.0 and 1.1 mu m thick. The Al-3%Ti is\ncommonly used in RF(radio frequency) microelectromechanical\nsystems(MEMS) switch. The specimen with holes and bridges was designed\nfor easy tensile test. The holes at center of grip end are able to make\nalignment and gripping easy. The bridges are to remove the side supports\neasily and extract specimen from wafer without sawing. It was found that\nthe mean tensile strengths of Al-3%Ti are 140-380 MPa, depending on the\nwidth of specimens and converging to a certain tensile strength as the\nwidth decreases.
tensile loading; thin film; mechanical properties;
Optimization of texturing process via sensor feedback in manufacturing of thin-film rigid disks
Proceedings of the 1992 Japan - USA Symposium on Flexible Automation Part 2 (of 2)
San Franci
1591-1597
1992
This paper investigates the feasibility of using acoustic emission (AE) feedback as a means to monitor and control the tape texturing and burnishing process. Experiments have been conducted in an attempt to use AE and force sensors to monitor the extent of texturization in a thin-film rigid disk manufacturing process. A fluid-coupled acoustic emission sensing device was built to measure the AE signals from a rotating disk. Normal and frictional forces were measured simultaneously to be compared with the AE signals. A strong correlation was found between characteristics of the disk texture and the parameters of AE signals, such as RMS value, mean frequency, zero crossing rate, and spectral density. It is also found that AE sensing method is a sensitive tool for investigation of tribological fundamentals in the texturing processes. Based on the experimental results, the mechanics of the texturing process was qualitatively described.
Artificial intelligence; Artificial intelligence (AE) sensing techniques; Optimization; Rotating disks; Sensor feedback manufacturing; Texturing process optimization; Thin film rigid disks; Thin films
Consideration of deformation of TiN thin films with preferred orientation prepared by ion-beam-assisted deposition
JSME International Journal, Series A: Solid Mechanics and Material Engineering
44
1
94-99
2001
Plastic deformation of TiN thin films with (111) and (200) preferred orientation was determined based on their hardness anisotropy. Hardness was measured by means of the nano-indentation technique. Plastic deformation of TiN films was caused by the indentation of the trigonal diamond tip, and evidence of this phenomenon was provided by cross-sectional scanning electron microscopy (SEM) observation and transmission electron diffraction (TED) analysis. The influence of the differences in residual stress and grain size on hardness anisotropy was restrictive, and hardness anisotropy can be explained by the anisotropy of yield stress as calculated using Schmid's law. This relationship suggests the existence of a {100}<110> slip system in the TiN crystal. Transmission electron microscopy (TEM) observation of brettle cracks in TiN films confirmed that these cracks are caused not by cleavage fractures but by intergranular fractures.
Anisotropy; coating; corrosion resistance; deformation; Deposition; Electron diffraction; film; Fracture; Hardness; Indentation; Intergranular fractures; Ion-beam-assisted deposition; Plastic deformation; Plasticity; Preferred orientation; Scanning electron microscopy; Slip system; Thin film; Thin films; Tin; titanium nitride; Transmission electron microscopy; wear resistance
Maximum-Likelihood Parameter Estimation for the Thin-Shell Quasi-Newtonian Model for a Laboratory Blown Film Extruder
Industrial & Engineering Chemistry Research
49
17
8007-8015
2010
10.1021/ie100188g
While most plastic films are manufactured by blown film extrusion, their first-principles modeling has remained substantially more challenging than for most other chemical engineering unit operations due to its combination of heat transfer, crystallization, and non-Newtonian fluid mechanics. This paper applies maximum-likelihood parameter estimation to characterize the convective heat transfer characteristics from measured spatial radii and temperature profiles for a laboratory-scale blown film process extruding a linear low density polyethylene (LLDPE) polymer. The Pearson and Petrie thin-film extrusion model incorporates (i) a quasi-Newtonian constitutive relation for the effect of temperature and crystallization on the viscosity of the polymer and (ii) a spatial variation of the heat transfer coefficient that is qualitatively consistent with turbulent flow simulations reported in the literature. A single heat transfer expression fit the experimental conditions for a cooling air flow rate of 1.5 m/s, whereas the variation of two parameters was able to fit all but one experimental condition for a cooling air flow rate of 1.0 m/s. The experimental condition that was poorly fit by the model had the highest takeup ratio, which was the operating condition closest to film instability and likely the condition most sensitive to the heat transfer relation. The experimental conditions corresponding to observed stable operations were investigated by linearized stability analysis. © 2010 American Chemical Society.
Granite Genesis and the Mechanics of Convergent Orogenic Belts with Application to the Southern Adelaide Fold Belt
Transactions of the Royal Society of Edinburgh-Earth Sciences
83
83-93
1992
10.1017/S026359330000777X
Two models for the heating responsible for granite generation during convergent deformation may be distinguished on the basis of the length- and time-scales associated with the thermal perturbation, namely: (1) long-lived, lithospheric-scale heating as a conductive response to the deformation, and (2) transient, localised heating as a response to advective heat sources such as mantle-derived melts. The strong temperature dependence of lithospheric rheology implies that the heat advected within rising granites may affect the distribution and rates of deformation within the developing orogen in a way that reflects the thermal regime attendant on granite formation; this contention is supported by numerical models of lithospheric deformation based on the thin-sheet approximation. The model results are compared with geological and isotopic constraints on granite genesis in the southern Adelaide Fold Belt where intrusion spans a 25 Ma convergent deformation cycle, from about 516 to 490 Ma, resulting in crustal thickening to 50-55 km. High-T metamorphism in this belt is spatially restricted to an axis of magmatic activity where the intensity and complexity of deformation is significantly greater, and may have started earlier, than in adjacent low-grade areas, The implication is that granite generation and emplacement is a causative factor in localising deformation, and on the basis of the results of the mechanical models suggests that granite formation occurred in response to localised, transient crustal heating by mantle melts. This is consistent with the Nd- and Sr-isotopic composition of the granites which seems to reflect mixed sources with components derived both from the depleted contemporary mantle and the older crust.
deformation; granite; mechanics; metamorphism
Middle-ear mechanics of Type III tympanoplasty (stapes columella): I. Experimental studies
Otol Neurotol
24
2
176-185
2003
OBJECTIVE: To investigate the mechanics of Type III tympanoplasty by developing a cadaveric temporal bone model. BACKGROUND: Type III stapes columella tympanoplasty involves the placement of a tympanic membrane graft, usually made of temporalis fascia, directly onto the stapes head. The procedure is usually done in conjunction with a canal wall down mastoidectomy. Postoperative hearing results vary widely, with air-bone gaps of 10 to 60 dB. The structural features responsible for the wide range in hearing results have not been systematically investigated. METHODS: Canal wall down Type III procedures were performed in eight cadaveric temporal bones. Acoustic stimuli were presented in the ear canal, and round window velocity VRW (used as an index of hearing) was measured, while systematically varying stapes mobility, mechanical properties of tympanic membrane graft, and tightness of connection between tympanic membrane graft and stapes. The effect of interposing a thin cartilage disc between the tympanic membrane graft and stapes head was also assessed. RESULTS: When the middle ear was aerated and the stapes was mobile, VRW was 15 to 30 dB lower than in an intact, normal ear. Stapes fixation led to a significant reduction in VRW; reduction was greatest at low frequencies. There was little effect of varying the tightness of connection between the tympanic membrane graft and stapes head. Sound energy was transmitted from the graft to the stapes as long as the graft was in physical contact with the stapes head. Different tympanic membrane graft materials with a range of mechanical properties (stiffness and mass) resulted in little variation in VRW. Interposing a thin cartilage disc between the tympanic membrane graft and stapes improved VRW in the lower frequencies by 5 to 10 dB. The authors hypothesize that the disc acted to increase the effective vibrating area of the graft. CONCLUSIONS: The feasibility of using a cadaveric temporal bone model to study the mechanics of Type III tympanoplasty was demonstrated. A mobile stapes and aerated middle ear were essential for a successful Type III tympanoplasty. There was little effect of varying the mechanical properties of the tympanic membrane graft or changing the tightness of connection between the graft and stapes head. Improved results were achieved by interposing a thin cartilage disc between the graft and stapes head to increase the effective vibrating area of the graft.
Aged; Aged, 80 and over; Biomechanics; Culture Techniques; Ear Canal/surgery; Ear, Middle/*physiology; Feasibility Studies; Female; Humans; Laser-Doppler Flowmetry/methods; Male; Mastoid/surgery; Middle Aged; Otologic Surgical Procedures/methods; *Stapes Surgery; Temporal Bone/*transplantation; Tympanoplasty/*methods
A simple atomic force microscopy calibration method for direct measurement of surface energy on nanostructured surfaces covered with molecularly thin liquid films.
Review of Scientific Instruments
80
5
055109
2009
10.1063/1.3136908
A simple calibration method is described for the determination of surface energy by atomic force microscopy (AFM) pull-off force measurements on nanostructured surfaces covered with molecularly thin liquid films. The method is based on correlating pull-off forces measured in arbitrary units on a nanostructured surface with pull-off forces measured on macroscopically smooth dip-coated gauge surfaces with known surface energy. The method avoids the need for complex calibration of the AFM cantilever stiffness and the determination of the radius of curvature of the AFM tip. Both of the latter measurements are associated with indirect and less accurate measurements of surface energy based on various contact mechanics adhesion models.
Atomic Force; Atomic Force: methods; Atomic Force: standards; Calibration; Lubricants; Microscopy; Nanostructures; Nanostructures: chemistry; Surface Properties
Damage in composite laminates: Effects of transverse cracks
Mechanics of Materials
7
2
91-107
1988
10.1016/0167-6636(88)90008-7
Two different methods of solution are used to study the effects of transverse cracks in cross-ply composite laminates. The results of an approximate analytical solution are compared with those obtained using a finite element analysis in order to study the effects of transverse cracks on the degradation of elastic and thermal coefficients as well as stress distributions. In particular, it is shown that transverse cracks cause significant degradation of the Poisson's ratio and shear modulus of the laminates, and also affect some stress distributions in a peculiar manner. Theoretical results are compared with existing experimental results where appropriate.
Multiaxial fatigue life prediction of composite bolted joint under constant amplitude cycle loading
Composites Part B: Engineering
74
131-137
2015
10.1016/j.compositesb.2015.01.013
In this paper, a fatigue model of composite is established to predict multiaxial fatigue life of composite bolted joint under constant amplitude cycle loading. Firstly, finite element model is adopted to investigate stress state of composite bolted joint under constant amplitude cycle loading. Secondly, Tsai–Hill criterion is used to calculate equivalent stress of joint. At last, modified S–N fatigue life curve fitted by unidirectional laminate S–N curve which takes ply angle and stress ratio into consideration is adopted to determine fatigue life of composite. Calculation results of equivalent stress model show excellent agreement with experiments of composite bolted joint.
A. Laminate; B. Fatigue; C. Damage mechanics
Invariant Hermitian finite elements for thin Kirchhoff rods. I: The linear plane case
Computer Methods in Applied Mechanics and Engineering
213-216
427-457
2012
10.1016/j.cma.2011.05.009
The objective of this work is to develop finite elements for the simulation of thin Kirchhoff rods, that is, rods where the influence of transverse shear strain can be neglected leading to governing equations that require C1-continuous finite element interpolations. We start in this paper with the formulation of new finite elements for the infinitesimal plane deformations of otherwise generally curved rods, addressing in particular the lack of invariance observed in related traditional treatments of plane arches. By non-invariance we mean that the classical rigid-body modes of translations and infinitesimal rotations of the underlying structural theory lead to non-zero strains in the element, an effect sometimes referred to as self-straining. This phenomenon occurs in curved configurations of the elements and, in the infinitesimal setting of interest in this paper, it results in the elements stiffness matrix not to exhibit the correct zero-energy modes associated with these physical rigid-body motions. As a consequence, the basic equilibrium relations of balance of forces and moments are not satisfied for the associated nodal forces and moments in non-invariant finite elements. In this context, we propose a new framework for the formulation of C1-continuous finite elements based on Hermitian shape functions that do lead to the satisfaction of this fundamental invariance property, accounting fully for the rod’s curvature and associated Kirchhoff’s kinematics in contrast to common straight (framework) element approximations based on the simplified Euler–Bernoulli beam kinematics. The formulation relies crucially on a consistent treatment of the kinematics and the assumed interpolation of the rods geometry. An additional assumed strain treatment is considered to avoid limitations of membrane locking. Complete rigorous analyses and several numerical simulations are presented to prove and illustrate the properties and performance of the newly proposed finite element methods.
Hydroelastic interaction between water waves and a thin elastic plate of arbitrary geometry
Science China: Physics, Mechanics and Astronomy
54
1
59-66
2011
10.1007/s11433-010-4199-3
An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow. Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system. According to the surface boundary conditions, the fluid domain is divided into two regions, namely, an open water region and a plate-covered region. With the assumption that all the motion is time-harmonic, the series solutions for the spatial velocity potentials are derived by the method of eigenfunction expansion. The matching conditions for the continuities of the velocity and pressure are transformed by taking the inner products successively with respect to the vertical eigenfunction for the free surface and the angular eigenfunction. A system of simultaneous equations, including two edge conditions and two matching conditions, is set up for deriving the expansion coefficients. As an example, numerical computation for the expansion coefficients of truncated series is performed for an elliptic plate. The results show that the method suggested here is useful to revealing the physical features of the gravity wave scattering in the open water and the hydroelastic response in the plate. © 2010 Science China Press and Springer-Verlag Berlin Heidelberg.
arbitrary geometry; elastic plate; hydroelastic response; method of matched eigenfunction expansions; wave scattering
Approximate method for determining the momentum in a wedge-shaped notch with the instantaneous dispersion of a thin layer of matter from its surface
Journal of Applied Mechanics and Technical Physics
15
5
722-725
1976
10.1007/BF00851540
The article proposes a geometric method, based on the superposition of elementary momenta with the repeated reflection of particles scattered from the surface of the notch. The results of the calculation are in good agreement with experiment. © 1976 Plenum Publishing Corporation.
Textiles for composites. Virtual reality and fabric mechanics
Textile Horizons
15
2
12-15
1995
Computer simulation of how fabrics will drape is discussed, with reference to the underlying fabric mechanics. Improved computers and programs are expected to enhance simulation capabilities. The basic underlying mechanics are related to the ability of textiles to buckle into domes of double curvature.
Quantum mechanics does not require the continuity of space
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
34
2
319-328
2003
10.1016/S1355-2198(03)00003-0
We argue that the experimental verification of Newtonian mechanics and of non-relativistic quantum mechanics do not imply that space is continuous. This provides evidence against the realist interpretation of the most mathematical parts of physics.
■
Minimum Energy Cross-Well Actuation of Bistable Piezocomposite Unsymmetric Cross-Ply Plates
Proceedings of ICAST 2014
1-12
2014
A hybrid unstable-then-stable positive position feedback (PPF) control scheme applied to a bistable unsymmetric cross-ply composite plate with surface-bonded piezoelectric actuators is presented. The plate is clamped on one end for the purpose of forming a low aspect-ratio wing for small UAVs and MAVs. The PPF controller, a simple second-order single-degree-of-freedom system in nature, takes advantage of the first bending mode of the plate about different stable equilibrium positions, and dynamically induces snap-through between the two equilibrium states. Compared to quasi-static actuation, driving the bistable plate dynamically using surface bonded piezoelectric materials requires, theoretically, a lower peak excitation voltage to achieve snap-through. In practice and in most situations, dynamic actuation is the only way to achieve snap-through because of the power density limitation of surface-bonded piezoelectric actuators. The energy consumption to achieve snap-through is automatically minimized by the hybrid feedback control scheme, and undesirable cross-well oscillations are inherently avoided. The proposed control scheme is an improvement over previous strategies where the bistable system was forced at resonance to achieve snap through, where energy consumption is not minimized and chaotic cross-well oscillation may be induced if the actuation amplitude is not precisely determined and controlled. The proposed hybrid PPF controller could be, potentially, applied to any bistable structure where the dynamic stiffness can be minimized on-demand. This is in contrast to permanent mechanical reduction of stiffness techniques where the actuation device loses its passive load carrying capacity for the purpose of increasing its stroke.
Off-Axis Properties of Cross-Ply Metal Matrix Composites at Quasi-Static and High Strain Rates
11th International Conference on the Mechanical Behavior of Materials (Icm11)
10
1532-1537
2011
DOI 10.1016/j.proeng.2011.04.256
Cylindrical samples of a 0/90 degrees cross-ply Nextel 610 (TM)/Al-6061 (similar to 55V(f)%) metal matrix composite have been subjected to compression testing at quasi-static and high strain rates over a range of angles between 0 and 45 with respect to the principal fiber directions. The results, combined with testing in the longitudinal, transverse and through thickness directions, provide a detailed description of the response of such composites over a wide range of orientations. In addition, metallographic and fractographic studies along with high-speed camera records provide detailed information about the sequence of deformation events leading to fracture. Results confirm not only the strong dependence of mechanical properties upon orientation but also the critical importance of precise fiber alignment and processing in obtaining the desired theoretical properties. A misalignment of 10 was sufficient to cause an similar to 40% decrease in maximum stress and the properties were found to vary by >70% over the orientations investigated. The high strain rate properties were generally significantly greater than those measured quasi-statically. A numerical model based on the commercial explicit finite element code LS-DYNA was used to investigate the compressive deformation and fracture of the composite. Experimental results are compared with those of the numerical model. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of ICM11.
compression; compressive strength; fiber-composites; metal matrix composite; numerical model; off-axis properties
Performance of polyvinyl acetate and phenol resorcinol formaldehyde as binding materials for laminated bamboo and composite-ply from tropical bamboo species.
International Journal of Agricultural Research
1
2
108-112
2006
Polyvinyl Acetate (PVAc) and Phenol Resorcinol Formaldehyde (PRF) were used to bind together three-layers laminated bamboo and composite-ply consisting of a single-layer bamboo strips and two layers of wood veneers. Tropical bamboo species Gigantochloa scortechinii were used in the study. Both panels were tested for their physical, mechanical and gluing properties. The results shows that both panels possess about the same values in density, MoE and MoR. These panels possess almost the same values in density about 780 (kg m-3), Modulus of Elasticity (MoE) between 15, 000 to 16, 210 N mm-2, Modulus of Rupture (MoR) in bending tests between 98 to 126 N mm-2 and means compression strength of 63 N mm-2 at 12% moisture content. Both panel were found to possess good gluing strength. The overall strength of this laminates passed the requirements of standard studies. These results are equivalent with some of the structural strength groups, which comparative with some high density commercial solid wood.\n
adhesion; adhesives; angiosperms; APEC countries; ASEAN Countries; Asia; bamboo; bamboos; bond strength; Commonwealth of Nations; composite boards; compression strength; compressive strength; crushing strength; Cyperales; Developing Countries; eukaryotes; formaldehyde; Gigantochloa; Gigantochloa scortechinii; glues; laminated wood; Malaysia; modulus of elasticity; modulus of rupture; moisture content; monocotyledons; plants; Poaceae; polyvinyl acetate; South East Asia; Spermatophyta; strength; Threshold Countries; veneers; Young's modulus
Quantum Mechanics/Molecular Mechanics Calculations of the Vanadium Dependent Chloroperoxidase
Journal of Chemical Theory and Computation
1
6
1265-1274
2005
10.1021/ct050132o
Large quantum mechanics/molecular mechanics (QM/MM) calculations are used to probe the resting and initial protonated states of the vanadium dependent chloroperoxidase from the pathogenic fungus Curvularia inaequalis. QSite was used to model 433 residues and 24 structural waters with molecular mechanics, while 8 active-site residues and the vanadate cofactor (161 atoms) were represented at the B3LYP/lacvp* level of theory. Our previous study of small model systems implied that the resting state of the enzyme contains a trigonal bipyramidal vanadate with one hydroxyl group in the equatorial plane and another in the axial position. This study uses a much larger model of the biological system at a higher level of theory to identify the location of the equatorial hydroxo group with respect to the enzyme active site. We also identify a second resting-state configuration with an axial water and three equatorial oxo moieties that is nearly isoenergetic with the previously identified state. We propose that the resting state is a hybrid of these two configurations, stabilized by the long-range electrostatic field of the protein environment. The first step in catalysis is believed to be protonation of the vanadate. Our previous small models indicated that there were two protonated configurations, but this study shows that the configuration containing an axial water and one hydroxo group in the equatorial plane is significantly lower in energy than any other configuration. Additionally, we can now assign an important role for lysine 353 in the catalytic cycle. Based on our calculations and other model studies, we provide an updated catalytic cycle for vanadium dependent haloperoxidase activity. Further, we demonstrate the importance of system set up. In particular, maintaining the proper electrostatic field at the active site is crucial for identifying the correct minima in a truncated protein model. Large quantum mechanics/molecular mechanics (QM/MM) calculations are used to probe the resting and initial protonated states of the vanadium dependent chloroperoxidase from the pathogenic fungus Curvularia inaequalis. QSite was used to model 433 residues and 24 structural waters with molecular mechanics, while 8 active-site residues and the vanadate cofactor (161 atoms) were represented at the B3LYP/lacvp* level of theory. Our previous study of small model systems implied that the resting state of the enzyme contains a trigonal bipyramidal vanadate with one hydroxyl group in the equatorial plane and another in the axial position. This study uses a much larger model of the biological system at a higher level of theory to identify the location of the equatorial hydroxo group with respect to the enzyme active site. We also identify a second resting-state configuration with an axial water and three equatorial oxo moieties that is nearly isoenergetic with the previously identified state. We propose that the resting state is a hybrid of these two configurations, stabilized by the long-range electrostatic field of the protein environment. The first step in catalysis is believed to be protonation of the vanadate. Our previous small models indicated that there were two protonated configurations, but this study shows that the configuration containing an axial water and one hydroxo group in the equatorial plane is significantly lower in energy than any other configuration. Additionally, we can now assign an important role for lysine 353 in the catalytic cycle. Based on our calculations and other model studies, we provide an updated catalytic cycle for vanadium dependent haloperoxidase activity. Further, we demonstrate the importance of system set up. In particular, maintaining the proper electrostatic field at the active site is crucial for identifying the correct minima in a truncated protein model.
Hand eczema in car mechanics.
Contact dermatitis
30
3
129-134
1994
To estimate the prevalence of hand eczema, a questionnaire was distributed to 901 male car mechanics. Of the 801 persons who responded, 15% reported hand eczema on some occasion in the previous 12 months, and 57% admitted dry skin on the hands. In a 2nd part of the study, those who reported hand eczema were examined and patch tested with a standard series and a special "car mechanics' series". The most common diagnosis was irritant contact dermatitis, 55%, and 2nd was allergic contact dermatitis, 19%. 35/105 (33%) had a total of 51 positive patch test reactions, all to substances in the standard series, except for 2 persons who reacted to oxidized d-limonene. The most frequent reactions were to thimerosal (9%), nickel (8%) and colophony (5%). One plausible explanation for the high prevalence of nickel allergy was the common use of nickel-plated tools. 5 individuals had a history of contact urticaria, but scratch tests were negative. It was concluded that car mechanics are at high risk for contact dermatitis on the hands, irritant as well as allergic.
Modeling Modal Talk in Quantum Mechanics
International Journal of Theoretical Physics
44
4
375-383
2005
10.1007/s10773-005-3853-4
In this paper, modal and counterfactual logical connectives are defined in an extended framework of branching space-time (Belnap, N. D. (1992). Branching space-time. Synthese 92, 385–434). It is shown that a variety of definitions of the counterfactual can be given. The validity of certain modal statements occurring in quantum mechanics depends on the choice of definition. These considerations can be applied to an analysis of Stapp’s premises LOC1 and LOC2 from his purported proof of non-locality (Stapp, H. P. (1997). Nonlocal character of quantum theory. American Journal of Physics 65, 300–304). It is shown that while the validity of LOC1 depends on the choice of the definition of the counterfactual, LOC2 is absolutely invalid.
branching space-times; counterfactuals; locality; modality; quantum mechanics
Asbestos-associated lung effects in car mechanics
Scandinavian Journal of Work, Environment and Health
13
3
252-254
1987
10.5271/sjweh.2055
In a study of the possible impact of asbestos exposure on car mechanics, 925 car mechanics and 109 referents (office workers in car-repair firms) were examined. They took part in a health screening in 1977-1981. The forced expiratory volumes in 1 s and the forced vital capacities of the car mechanics were close to the predicted values and did not differ from the findings of the referents. Pleural plaques were found in 41 of the mechanics but in none of the referents. Only minor changes were detected in the chest radiographs ie, 1/1 or less according to the ILO-U/C classification. It is concluded that asbestos exposure can generally cause pleural plaques in car mechanics but no substantial impairment of lung function.
Effects of different loading methods on thermal expansion behaviors of 2D cross-ply carbon/carbon composites from 850°C to 2300°C
Ceramics International
40
8
12545-12551
2014
10.1016/j.ceramint.2014.03.098
2D cross-ply carbon/carbon (C/C) composites were prepared by isothermal chemical vapor infiltration (ICVI) process. Thermal expansion behaviors of 2D cross-ply C/C composites and effects of static loading and fatigue loading conditions on coefficient of thermal expansion (CTE) of the C/C composites from 850°C to 2300°C were studied. In static test cases, different damage levels were produced inside samples by displacement-controlled three-point bending loading. Meanwhile, flexural fatigue experiments were conducted under stress level of 70%, cycling numbers (N) of 105 and 106 at a sinusoidal loading frequency of 15Hz. Afterwards, the thermal expansion behaviors were investigated. It showed that CTE of the C/C composites after static loading and fatigue loading had a decrease compared with CTE of the as-prepared C/C composites. After static loading, there was a larger decrease in CTE for the C/C composites with more severe damage levels. Moreover, the influence of damage on CTE reached to the greatest at around 1550°C. The largest decline percentage of the C/C composites after static loading and fatigue loading was 30% and 85% in contrast to the as-prepared C/C composites, respectively. In addition, weakening interfacial strength of the C/C composites was the main effect on the large decrease of CTE after the fatigue loading.
C/C composites; C. Fatigue; C. Thermal expansion; Damage
Explicit dynamics simulation of blade cutting of thin elastoplastic shells using “directional” cohesive elements in solid-shell finite element models
Computer Methods in Applied Mechanics and Engineering
285
515-541
2015
10.1016/j.cma.2014.11.027
The intentional or accidental cutting of thin shell structures by means of a sharp object is of interest in many engineering applications. The process of cutting involves several types of nonlinearities, such as large deformations, contact, crack propagation and, in the case of laminated shells, delamination. In addition to these, a special difficulty is represented by the blade sharpness, whose accurate geometric resolution would require meshes with characteristic size of the order of the blade curvature radius. A computational finite element approach for the simulation of blade cutting of thin shells is proposed and discussed. The approach is developed in an explicit dynamics framework. Solid-shell elements are used for the discretization, in view of possible future inclusion in the model of delamination processes. Since a sharp blade can interfere with the transmission of cohesive forces between the crack flanks in the cohesive process zone, standard cohesive interface elements are not suited for the simulation of this type of problems unless extremely fine meshes, with characteristic size comparable to the blade curvature radius, are used. To circumvent the problem, the use of a new type of directional cohesive interface element, previously proposed for the simulation of crack propagation in elastic shells, is further developed and reformulated for application to the cutting of elastoplastic thin structures, discretized by solid-shell elements. The proposed approach is validated by means of application to several cutting problems of engineering interest.
blade cutting; cohesive model; crack propagation; explicit dynamics; solid-shell elements
An object-oriented framework for multidisciplinary, multi-physics, computational mechanics
Engineering with Computers
15
1
105–125
1999
This paper presents the design and development of an object-oriented framework for computational mechanics. The framework has been designed to address some of the major deficiencies in existing computational mechanics software packages. The framework addresses the deficiencies of existing computational mechanics software packages by (a) having a sound design using the stare of the art in software engineering, and (b) providing model manipulation features that are common to a large set of computational mechanics problems.The framework provides features that are essential to a large set of computational mechanics problems. The domain-specific features provided by the framework are a geometry sub-system specifically designed for computational mechanics, an interpreted Computational Mechanics Language (CML), a structure for management of analysis projects, a comprehensive data model, model development, model query and analysis management. The domain independent features provided by the framework are a drawing sub-system for data visualization, a database server; a quantity sub-system, a simple GUI and an online help serverIt is demonstrated that the framework, can be used to develop applications that can: (a) extend or modify important parts of the framework to suit their own needs; (b) use CML for rapid prototyping and extending the functionality of the framework; (c) significantly ease the task of conducting parametric studies; (d) significantly ease the task of modeling evolutionary problems; (e) be easily interfaced with existing analysis programs; and (f) be used to carry out basic computational, mechanics research. It is hope that the the framework will substantially ease the task of ct-earing families of software applications that apply existing and upcoming theories of computational mechanics to solve bath academic and real world interdisciplinary simulation problems
albuquerque; analysis management; computational; computational mechanics language; correspondence and offprint requests; mechanics; r; sahu; to
Reception of an acausal quantum mechanics
Reception of unconventional science
3
12-22
1979
the classic statement of the argument that the postwar crisis was entangled with the collapse of classical physics
20. Jahrhundert; Quantenmechanik; Wissenssoziologie
Fluid mechanics and mathematical structures
Introduction to the Geometry and Topology of Fluid Flows
47
105-134
2001
This paper provides an informal survey of the various mathematical structures that appear in the most basic models of fluid motion.
Numerical simulations in stochastic mechanics
Physical Review A
37
9
3479-3492
1988
10.1103/PhysRevA.37.3479
The stochastic differential equation of Nelson’s stochastic mechanics is integrated numerically for several simple quantum systems. The calculations are performed with use of Helfand and Greenside’s method and pseudorandom numbers. The resulting trajectories are analyzed both individually and collectively to yield insight into momentum, uncertainty principles, interference, tunneling, quantum chaos, and common models of diatomic molecules from the stochastic quantization point of view. In addition to confirming Shucker’s momentum theorem, these simulations illustrate, within the context of stochastic mechanics, the position-momentum and time-energy uncertainty relations, the two-slit diffraction pattern, exponential decay of an unstable system, and the greater degree of anticorrelation in a valence-bond model as compared with a molecular-orbital model of H2. The attempt to find exponential divergence of initially nearby trajectories, potentially useful as a criterion for quantum chaos, in a periodically forced oscillator is inconclusive. A way of computing excited energies from the ground-state motion is presented. In all of these studies the use of particle trajectories allows a more insightful interpretation of physical phenomena than is possible within traditional wave mechanics.
Progressive fracture of laminated composite stiffened plate
Theoretical and Applied Fracture Mechanics
51
2
144-147
2009
DOI: 10.1016/j.tafmec.2009.04.008
Laminated fiber-reinforced composite stiffened plate with [0/90/±45]S plies made of S-Glass/epoxy are evaluated via computational simulation to study damage and fracture progression. The loads are pressure and temperature which varies from 21 to 65.5 °C (case I) and from 143.3 to 21 °C (case II). An integrated computer code is used for the simulation of the damage progression. Results show that damage initiation begins at low load level, with matrix cracking at the 0° (bottom and top) plies, fiber fracture at the bottom (0°) ply and interply delamination at the top (0°) ply. Increasing the applied pressure, the damage growth is expended resulting in fracture through the thickness of the structure. At this stage, 90% of the plies damage at applied pressure 15.306 MPa for the case I and 15.036 MPa for the case II. After this stage, the cracks propagate rapidly and the structure collapses.
Composites; Degradation; Fracture; Laminates; Simulation; Stiffened panel
Blood flow mechanics in cardiovascular development.
Cellular and molecular life sciences : CMLS
72
13
2545-59
2015
10.1007/s00018-015-1885-3
Hemodynamic forces are fundamental to development. Indeed, much of cardiovascular morphogenesis reflects a two-way interaction between mechanical forces and the gene network activated in endothelial cells via mechanotransduction feedback loops. As these interactions are becoming better understood in different model organisms, it is possible to identify common mechanogenetic rules, which are strikingly conserved and shared in many tissues and species. Here, we discuss recent findings showing how hemodynamic forces potentially modulate cardiovascular development as well as the underlying fluid and tissue mechanics, with special attention given to the flow characteristics that are unique to the small scales of embryos.
Angiogenesis; Atherosclerosis; Biomechanics; Cardiomyopathy; Fluid mechanics; Klf2; Valvulopathie
Chest wall mechanics during pressure support ventilation.
Critical care
10
2
R54
2006
10.1186/cc4867
During pressure support ventilation (PSV) a part of the breathing pattern is controlled by the patient, and synchronization of respiratory muscle action and the resulting chest wall kinematics is a valid indicator of the patient's adaptation to the ventilator. The aim of the present study was to analyze the effects of different PSV settings on ventilatory pattern, total and compartmental chest wall kinematics and dynamics, muscle pressures and work of breathing in patients with acute lung injury.
Adult; Aged; Female; Humans; Male; Middle Aged; Positive-Pressure Respiration; Positive-Pressure Respiration: methods; Positive-Pressure Respiration: statistics & numeri; Respiratory Insufficiency; Respiratory Insufficiency: physiopathology; Respiratory Insufficiency: therapy; Respiratory Mechanics; Respiratory Mechanics: physiology; Respiratory Muscles; Respiratory Muscles: physiology; Thoracic Wall; Thoracic Wall: physiology
Quantum Mechanics and First-Principles Molecular Dynamics Selection of Polymer Sensing Materials
Computational Methods for Sensor Material Selection
71-92
2010
10.1007/978-0-387-73715-7
We present two first-principles methods, density functional theory (DFT) and a molecular dynamics (MD) computer simulation protocol, as computational means for the selection of polymer sensing materials. The DFT methods can yield binding energies of polymer moieties to specific vapor bound compounds, quantities that were found useful in materials selection for sensing of organic and inorganic compounds for designing sensors for the electronic nose (ENose) that flew on the International Space Station (ISS) in 2008–2009. Similarly, we present an MD protocol that offers high consistency in the estimation of Hildebrand and Hansen solubility parameters (HSP) for vapor bound compounds and amorphous polymers. HSP are useful for fitting measured polymer sensor responses with physically rooted analytical models. We apply the method to the JPL electronic nose (ENose), an array of sensors with conducting leads connected through thin film polymers loaded with carbon black. Detection relies on a change in electric resistivity of the polymer film as function of the amount of swelling caused by the presence of the analyte chemical compound. The amount of swelling depends upon the chemical composition of the polymer and the analyte molecule. The pattern is unique and it unambiguously identifies the compound. Experimentally determined changes in relative resistivity of fifteen polymer sensor materials upon exposure to ten vapors were modeled with the first-principles HSP model.
Second postural mechanics seminar.
Podiatry Now
11
7
44
2008
The second postural mechanics seminar was held in London in April. This international two-day multidisciplinary event brought together podiatrists, orthotists, chiropractors and remedial therapists, to hear Prof. Brian Rothbart's theories on the involvement of abnormal foot motion in chronic pain patterns.
Equipment and Supplies; Foot; Gait; Mechanics; Motion; Pain; Pelvis; Posture; Pronation; Seminars and Workshops -- United Kingdom; Spine; Theory; United Kingdom
Infinite-range Ising ferromagnet: Thermodynamic limit within Generalized Statistical Mechanics
Physica A: Statistical Mechanics and its Applications
213
3
337-356
1995
doi: 10.1016/0378-4371(94)00231-H
We first discuss, for a variety of similar systems, the physical need for departure from Boltzmann-Gibbs statistical mechanics and thermodynamics. Then, we numerically discuss the infinite-range spin-1/2 Ising ferromagnet within the recently generalized statistical mechanics (canonical ensemble). Through the specific heat, we exhibit (for the first time, as far as we know, for an interacting system) that the thermodynamic limit is well defined.
_cleaned_10012013; hardcopyluding
Computational Fracture Mechanics Analysis of Truck Tire Durability
Journal of Applied Mechanics
73
5
799
2006
10.1115/1.2069983
A three-dimensional fracture mechanics model is formulated to study fatigue crack growth and durability in tires. The application of this model in a radial medium truck tire reveals fracture characteristics of belt edge cracks and helps to explain mechanical and material changes in the tire subject to indoor accelerated durability tests. Along with a proprietary fatigue crack growth law, a fracture mechanics based durability analysis methodology is developed and successfully applied to rank durability of tires with different constructions or different rubber materials.
Singular Lagrangian systems and variational constrained mechanics on Lie algebroids
Dynamical Systems
23
3
351-397
2008
10.1080/14689360802294220
The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard tangent bundles...). In particular, we are interested in two cases: singular Lagrangian systems and vakonomic mechanics (variational constrained mechanics). Several examples illustrate the interest of these developments.
On obtaining classical mechanics from quantum mechanics
Classical and Quantum Gravity
24
3
24
2006
10.1088/0264-9381/24/3/002
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of coarser observations. The Hilbert space of any quantum mechanical system naturally has the structure of an infinite dimensional symplectic manifold (`quantum phase space'). There is also a systematic, quotienting procedure which imparts a bundle structure to the quantum phase space and extracts a classical phase space as the base space. This works straight forwardly when the Hilbert space carries weakly continuous representation of the Heisenberg group and recovers the linear classical phase space mathbbR mathrm2N. We report on how the procedure also allows extraction of non-linear classical phase spaces and illustrate it for Hilbert spaces being finite dimensional (spin-j systems), infinite dimensional but separable (particle on a circle) and infinite dimensional but non-separable (Polymer quantization). To construct a corresponding classical dynamics, one needs to choose a suitable section and identify an effective Hamiltonian. The effective dynamics mirrors the quantum dynamics provided the section satisfies conditions of semiclassicality and tangentiality.
Analyses of buckling and stable tearing in thin-sheet materials
Fatigue and Fracture Mechanics: Twenty-Ninth Volume
1332
114-134
1999
Doi 10.1520/Stp14946s
The purpose of this paper was to verify the capability of the STAGS (general shell, geometric and material nonlinear) code and the critical crack-tip-opening angle (CTOA) fracture criterion to predict stable tearing in cracked panels that fail with severe out-of-plane buckling. Materials considered in the analyses ranged from brittle to ductile behavior. Experimental test data used in this study are reported elsewhere. The STAGS code was used to model stable tearing using a critical CTOA value that was determined from a cracked panel that was "restrained" from buckling. The STAGS code and the critical CTOA were then used to predict the influence of buckling on stable tearing and failure loads. Parameters like crack-length-to-specimen-width ratio, crack configuration, thickness, and material tensile properties had a significant influence on the buckling behavior of cracked thin-sheet materials. Experimental and predicted results showed a varied buckling response for different crack-length-to-sheet-thickness ratios because different buckling modes were activated. The effects of material tensile properties and fracture toughness on buckling response were presented and discussed. The STAGS code and the CTOA fracture criterion were able to predict the influence of buckling on stable tearing behavior and failure loads on a variety of materials and crack configurations.
buckling; crack growth; cracks; crack-tip-opening angle (ctoa); multiple-site damage cracking; stags shell code
Failure probability of laminated architectural glazing due to combined loading of wind and debris impact
Engineering Failure Analysis
36
226-242
2014
10.1016/j.engfailanal.2013.10.005
Building fa??ades are vulnerable to wind and wind-borne debris during extreme weather conditions like hurricanes. Laminated glazing is widely used as window glazing material to ensure the integrity of the building interiors. Wind-borne debris has been classified as small-hard and large soft missiles representing small gravel to large wooden bars that constitute the debris impacting the glazing during severe storms. Failure of laminated window glazing due to combined effect of wind and debris is studied. Stress analysis is done using finite element code ABAQUS. This is used in conjunction with a mechanics based statistical model to predict the cumulative probability of inner glass ply breakage in laminated glazing. A parametric study involving failure probability of inner glass ply for different geometry of laminated glazing is also performed. ?? 2013 Elsevier Ltd.
Failure probability; Laminated architectural glazing; Wind; Wind-borne debris
Analysis of thick walled composite pipes with metal liner subjected to simultaneous matrix cracking and plastic flow
Composites Science and Technology
68
2705-2716
2008
10.1016/j.compscitech.2008.04.032
Filament wound thick walled composite pipes designed for withstanding high-pressures and axial loads are designed using angle ply layers for obtaining sufficient strength and a metallic liner for obtaining a barrier against diffusion or leakage of gas and/or liquid media. The analysis presented goes beyond the formation of first ply failure and at the same time allows for plastic flow in the liner. The progressive matrix cracking is modelled using a postulated shape function of the displacement field and crack surface geometry. The effective elastic parameters, the stress and strain fields in the cracked composite layers were obtained from an approximate closed form analytical solution, deduced by variational principles. Various failure criteria can be used in order to simulate the progressive evolution of matrix cracks. The plastic flow of the liner was modelled using the method of successive elastic solutions. The analysis of matrix cracking and the plastic flow are based on incremental loading and the two failure mechanisms were modelled in a coupled and simultaneous scheme. ?? 2008 Elsevier Ltd. All rights reserved.
B. Plastic deformation; C. Computational simulation; C. Damage mechanics; C. Elastic properties; C. Transverse cracking
Single-molecule magnetic tweezer tests on DNA: bounds on topoisomerase relaxation
Proc. Roy. Soc. {A}
464
2099
2811-2829
2008
doi:10.1098/rspa.2008.0132
Biomedical researchers regularly stretch and twist single DNA molecules in magnetic tweezer experiments. By making the molecule writhe into a plectoneme (ply) and plotting its load-extension curves, key DNA parameters, such as effective radius, can be estimated. Adding untangling enzymes (topoisomerases) to the DNA's environment, their individual cuts are detected as jumps in extension. Sufficient information is now known about the topoisomerases for us to make good idealizations about their kinematics and mechanics. The novelty of this paper is to study their actions in the context of accurate ply solutions from the theory of elastic rods. To do this, we define an extended rod-plus-tension system that allows us to determine the stored energies from areas in the conventional link versus writhe plane. After a cut, the molecule relaxes dynamically to a new equilibrium state, and often there will be two or more alternative stable configurations onto which it might settle. Knowing the energy levels allows us to identify which states can and cannot be reached over the unstable mountain passes, and which of the accessible states offer the greatest energy relaxation. Strict energy bounds on behaviour are established. This knowledge has medical value because topoisomerase inhibitors, lethal for cells, are used as antibiotics and in chemotherapy for cancer.
Low-energy impact response of composite and sandwich composite plates with piezoelectric sensory layers
International Journal of Solids and Structures
51
14
2713-2727
2014
http://dx.doi.org/10.1016/j.ijsolstr.2014.04.005
Abstract An efficient model reduction based methodology is presented for predicting the global (impact force, plate deflection and electric potential) and through-thickness local (interfacial strains and stresses) dynamic response of pristine simply-supported cross-ply composite and sandwich composite plates with piezoelectric sensory layers subjected to low-energy impact. The through-thickness response of the laminate is modelled using coupled higher-order layerwise displacement-based piezoelectric laminate theories. Linearized contact laws are implemented for simulating the impactor–target interaction during impact. The stiffness, mass, piezoelectric and permittivity matrices of the plate are formulated from ply to structural level and reduced by applying a Guyan reduction technique to yield the structural system in state space. This reduction technique enables the formulation of a plate–impactor structural system of minimum size (1 term per vibration mode for composite plates – 2 terms for sandwich plates) and reduces computational cost, thus facilitating applicability for real-time impact and vibration control.
Composite; Interfacial stress; Layerwise mechanics; Low-energy impact; Piezoelectric; Plates; Sandwich
Finite element modelling of composite structures under crushing load
Composite Structures
131
215-228
2015
10.1016/j.compstruct.2015.05.008
This paper details the theory and implementation of a composite damage model, addressing damage within a ply (intralaminar) and delamination (interlaminar), for the simulation of crushing of laminated composite structures. It includes a more accurate determination of the characteristic length to achieve mesh objectivity in capturing intralaminar damage consisting of matrix cracking and fibre failure, a load-history dependent material response, an isotropic hardening nonlinear matrix response, as well as a more physically-based interactive matrix-dominated damage mechanism. The developed damage model requires a set of material parameters obtained from a combination of standard and non-standard material characterisation tests. The fidelity of the model mitigates the need to manipulate, or “calibrate”, the input data to achieve good agreement with experimental results. The intralaminar damage model was implemented as a VUMAT subroutine, and used in conjunction with an existing interlaminar damage model, in Abaqus/Explicit. This approach was validated through the simulation of the crushing of a cross-ply composite tube with a tulip-shaped trigger, loaded in uniaxial compression. Despite the complexity of the chosen geometry, excellent correlation was achieved with experimental results.
Crushing response; Damage mechanics; Energy absorption; Finite element analysis; Non-linear behaviour; Structure failure
Teaching fluid mechanics from an interactive book
1999 National Civil Engineering Education Congress
17-32
1999
Interactive text is becoming very advantageous in the field of fluid mechanics. This text has more flexibility in teaching. The student can concentrate on fluid mechanics with the total exclusion of methods of calculation and can study the material without doing tedious calculations with the help of computer aids.
Quaternionic Formulation of Supersymmetric Quantum Mechanics
International Journal of Theoretical Physics
48
2
305-314
2008
10.1007/s10773-008-9803-1
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.
Formulation of statistical mechanics for chaotic systems
Pramana Journal of Physics
72
2
315-323
2009
We formulate the statistical mechanics of chaotic system with few degrees of freedom and investigated the quartic oscillator system using microcanonical and canonical ensembles. Results of statistical mechanics are numerically verified by considering the dynamical evolution of quartic oscillator system with two degrees of freedom.
Effects of convection during the photodeposition of polydiacetylene thin films
Journal of Crystal Growth
173
1-2
172-181
1997
In this work, we describe a preliminary investigation of buoyancy-driven heat transfer during the growth of thin films from solution following exposure to ultraviolet (UV) light. Irradiation of the growth cell occurs at various directions relative to gravitational acceleration. Through numerical computations, the steady-state flow and temperature profiles are simulated during the course of light exposure. Light-induced polymerization accompanies a heat transfer process through a fairly complicated recirculating flow pattern. A scaling analysis shows that buoyancy-driven velocities only reduce by a factor of 10 for gravity levels as low as 10(-2)g(0). Paley et al. observe what appears to be gravitationally sensitive particle development and inclusion in thin films using a photodeposition process. From this study, it is clear that production of homogeneous thin films would have to occur in the environment of a complicated flow pattern of recirculation with a nonuniform temperature distribution. Indeed, even when irradiation occurs from the top of the cell, the most stable stratified cell orientation, defects remain in our films due to the persistence of buoyancy-driven convection. To achieve homogeneity, minimal scattering centers, and possible molecular order, photodeposition of polymer films by UV light exposure must proceed in a reduced-convection environment. Fluid mechanics simulations are useful for establishing gravitational sensitivity to this recently discovered process (patent # 5,451,433) for preparing thin films having quite promising nonlinear optical characteristics.
derivatives; diacetylene; gravity; growth; microgravity; optical-properties; poly(diacetylenes); single-crystals
Global structural behaviour of thin and moderately thick monoclinic spherical shells using a mixed shear deformation model
Archive of Applied Mechanics
74
3-4
262-276
2004
10.1007/s00419-004-0348-3
The static and dynamic responses of anisotropic spherical shells under a uniformly distributed transverse load are investigated. Analytical solutions using the mixed variational formulation are presented for spherical shells subjected to various boundary conditions. Numerical results of a refined mixed first-order shear deformation theory for natural frequencies, critical buckling, center deflections and stresses are compared with those obtained using the classical shell theory. A variety of simply-supported and clamped boundary conditions are considered and comparisons with the existing literature are made. The sample numerical results presented herein for global structural behaviour of monoclinic spherical shells should serve as references for future comparisons.
Extensive generalization of statistical mechanics based on incomplete information theory
Entropy
5
2
15
2000
10.3390/e5020220
Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization sumi=1 wpi q=1 is used to obtain generalized entropy S=-ksumi=1 wpi qln pi. The concomitant incomplete statistical mechanics is applied to some physical systems in order to show the effect of the incompleteness of information. It is shown that this extensive generalized statistics can be useful for the correlated electron systems in weak coupling regime.
generalized statistics; incomplete information; statistical mechanics
Fracture Mechanics of Composite Materials
Journal of Engineering Materials and Technology
100
233-247
1978
10.1115/1.3443485
The applicability of fracture mechanics to conventional isotropic materials has been well demonstrated. For fiber-reinforced materials, however, fracture mechanics investigations have met with mixed results. For collinear crack extension of a crack on a plane of symmetry in orthotropic materials, fracture behavior has been successfully predicted using linear elastic fracture mechanics concept; however, extrapolation to other fiber orientation combinations has been less successful. This is because fracture in anisotropic materials is more complex than in isotropic materials and is governed by additional parameters such as fiber orientation, lamination order and the constitutive relations that describe the mechanical responses of the fiber, the matrix and the interface. This paper reviews the fundamentals of fracture mechanics for isotropic materials and discusses its extension to orthotropic materials. This is followed by a discussion of the variety of failure modes observed in composites and review of the predominant fracture mechanics theories that attempt to predict fracture using semiempirical state and to demonstrate the approach taken by each investigator. The paper concludes with two examples where linear elastic fracture mechanics concept have been satisfactorily employed for composite materials.
Metamaterials with unusual mechanics
Chemical & Engineering News
93
14
28-29
2015
Internal structuring gives ceramics and other materials ability to absorb shocks, dampen vibrations
String statistical mechanics
Physica A: Statistical Mechanics and its Applications
158
1
516-535
1989
A review of the statistical mechanics of free string networks is given. This provides an interesting example of a system with canonical thermodynamics and in particular the notion of temperature break down. The results are applied to cosmic strings where they show good agreement with numerical results. They may also have important implications for the behaviour of fundamental strings at high density. Various erroneous recent claims regarding the statistical mechanics of fundamental strings are also discussed, in particular regarding duality, the role of winding modes, and the notion of negative specific heats. © 1989.
International Journal of Rock Mechanics & Mining Sciences Experimental investigation of borehole ballooning due to flow of non-Newtonian fluids into fractured rocks
International Journal of Rock Mechanics and Mining Sciences
47
7
1200-1206
2010
10.1016/j.ijrmms.2010.07.002
International Journal of Rock Mechanics and Mining Sciences, 1 + (2010) 1200-1206. doi:10.1016/j.ijrmms.2010.07.002
Fracture mechanics model for subthreshold indentation flaws
Journal of Materials Science
26
8
2157-2168
1991
10.1007/bf00549183
A fracture mechanics model for subthreshold indentation flaws is. described. The model describes the initiation and extension of a microcrack from a discrete deformation-induced shear “fault” (shear crack) within the contact zone. A stress-intensity factor analysis for the microcrack extension in residual-contact and applied-stress fields is used in conjunction with appropriate fracture conditions, equilibrium in Part I and non-equilibrium in Part II, to determine critical instability configurations.
fracture-mechanics; indentation; kratzer; spannungsverteilung
Quantum Mechanics of the Einstein-Hopf Model
American Journal of Physics
49
2
177-184
1981
10.1119/1.12552
The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)
College Science; Connecticut; Dipole Oscillator; Electromagnetic Field; Higher Education; Interaction; Kinetics; Light; Nuclear Physics; Physics; Quantum Mechanics; Radiation; Relativity; Science Education; Thermodynamics
Mechanics (including force, mass, and acceleration)
Anaesthesia & Intensive Care Medicine
15
7
336-339
2014
10.1016/j.mpaic.2014.04.009
A knowledge of classical (Newtonian) mechanics is fundamental to understanding anaesthetic equipment and the world around us. This article introduces essential concepts and illustrates them with practical examples. Topics include: Newton's Laws of Motion; instantaneous and average quantities; the relationships between distance, speed, displacement, velocity and acceleration; gravity, mass and weight; inertia and momentum; energy and power; and translational and rotational motion.
Acceleration; energy; force; mass; mechanics; Newton's Laws of Motion; power; work
Mechanics of a free-surface liquid film flow
Journal of Applied Mechanics
54
4
951-954
1987
10.1115/1.3173144
The mechanics of a free surface viscous liquid curtain flowing steadily between two vertical guide wires under the influence of gravity is investigated. The Navier-Stokes equation is integrated over the film thickness and an integro-differential equation is derived for the average film velocity. An approximate nonlinear differential equation, attributed to G. I. Taylor, is obtained by neglecting the higher order terms. An analytical solution is obtained for a similar equation which neglects the surface tension effects and the results are compared with the experimental measurements of Brown (1961).
The molecular mechanics of eukaryotic translation
Annual Review of Biochemistry
73
657-704
2004
Great advances have been made in the past three decades in understanding the molecular mechanics underlying protein synthesis in bacteria, but our understanding of the corresponding events in eukaryotic organisms is only beginning to catch up. In this review we describe the current state of our knowledge and ignorance of the molecular mechanics underlying eukaryotic translation. We discuss the mechanisms conserved across the three kingdoms of life as well as the important divergences that have taken place in the pathway.
Nonlinear Response of Imperfect Eccentrically Stiffened Ceramic-Metal-Ceramic Sigmoid Functionally Graded Material (S-FGM) Thin Circular Cylindrical Shells Surrounded on Elastic Foundations Under Uniform Radial Load
Mechanics of Advanced Materials and Structures
22
12
1031-1038
2015
10.1080/15376494.2014.910320
This article researches nonlinear response of imperfect eccentrically stiffened symmetric FGM thin circular cylindrical shells with ceramic-metal-ceramic layers, which are symmetric through the middle surface by Sigmoid-law distribution (S-FGM) and have stiffeners surrounded on elastic foundations under uniform radial load. The Donnell classical shell theory, stress function, and Galerkin method are used for investigation of the nonlinear stability of the S-FGM shell. The obtained results show the effects of the stiffeners, elastic foundations, mechanical load, and material parameters on the nonlinear buckling response of symmetric S-FGM circular cylindrical shells.
Seven Principles of Quantum Mechanics
Quantum
7
2002
The list of basic axioms of quantum mechanics as it was formulated by von Neumann includes only the mathematical formalism of the Hilbert space and its statistical interpretation. We point out that such an approach is too general to be considered as the foundation of quantum mechanics. In particular in this approach any finite-dimensional Hilbert space describes a quantum system. Though such a treatment might be a convenient approximation it can not be considered as a fundamental description of a quantum system and moreover it leads to some paradoxes like Bell's theorem. I present a list from seven basic postulates of axiomatic quantum mechanics. In particular the list includes the axiom describing spatial properties of quantum system. These axioms do not admit a nontrivial realization in the finite-dimensional Hilbert space. One suggests that the axiomatic quantum mechanics is consistent with local realism.
Fluid mechanics of heart valves
Annual Review of Biomedical Engineering
6
331-362
2004
DOI 10.1146/annurev.bioeng.6.040803.140111
Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review.
3-dimensional computational method; aortic-valve; bioprosthetic valves; blood-flow; computational fluid dynamics; doppler-echocardiography; functional mitral regurgitation; in-vitro; laser doppler velocimetry; mechanical heart valves; native heart valves; numerical-simulation; steady axisymmetric flow; tilting-disk; velocity profiles
Sections along a map applied to higher-order Lagrangian mechanics. Noether's theorem
Acta Applicandae Mathematicae
25
2
127-151
1991
10.1007/BF00047147
We show that the concept of a section along a map is a fundamental concept within the framework of the geometrical description of classical mechanics. We review the higher-order Lagrangian mechanics formulation, and simpler redefinitions of basic objects appear in a natural way. As an application, Noether's theorem for higher-order Lagrangian mechanics admitting a converse is developed. © 1991 Kluwer Academic Publishers.
AMS subject classification (1991): 58F05; derivations; Higher-order Lagrangian mechanics; Higher-order tangent bundles; sections along a map
A Philosophy of Quantum Mechanics
Philosophy in Science (Tucson)
1
139-148
1983
Observables in quantum mechanics may be divided into two classes of different ontological and epistemological character: undeterminate (undecided) like position, and predeterminate as e.g., momentum, helicity, isospin and other conserved quantities for free particles. the existence of predetermined quantities prior to their possible measurement secures a realistic character of quantum mechanics. the state in quantum mechanics means an optimal information, but not an immanent property of the physical system.
Physics; Quantum Mechanics; Science
001-2012on anisotropic elasticity damage mechanics
International Journal of Damage Mechanics
2013
The anisotropic elasticity damage mechanics is considered within the framework of the classical theory of elasticity. Starting from the principle of strain equivalence and notion of isotropic group, damage tensor components are derived in terms of elastic parameters of undamaged (virgin) material in closed-form solution. The procedure was applied for several symmetries that are important for applications
anisotropic damage mechanics; crystal classes; damage tensor; elasticity; isotropy group
Nambu quantum mechanics: A nonlinear generalization of geometric quantum mechanics
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
536
305-314
2002
10.1016/S0370-2693(02)01865-8
We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a nonlinear temporal evolution given by Jacobi elliptic functions. In the limit where latter's moduli parameters are set to zero, the usual geometric formulation of quantum mechanics, based on the Kahler structure of a complex projective Hilbert space, is recovered. We point out various novel features of this extended quantum mechanics, including its geometric aspects. Our approach sheds a new light on the problem of quantization of Nambu dynamics. Finally, we argue that the structure of this nonlinear quantum mechanics is natural from the point of view of string theory. ?? 2002 Published by Elsevier Science B.V.
A simple atomic force microscopy calibration method for direct measurement of surface energy on nanostructured surfaces covered with molecularly thin liquid films
Rev Sci Instrum
80
5
55109
2009
10.1063/1.3136908
A simple calibration method is described for the determination of surface energy by atomic force microscopy (AFM) pull-off force measurements on nanostructured surfaces covered with molecularly thin liquid films. The method is based on correlating pull-off forces measured in arbitrary units on a nanostructured surface with pull-off forces measured on macroscopically smooth dip-coated gauge surfaces with known surface energy. The method avoids the need for complex calibration of the AFM cantilever stiffness and the determination of the radius of curvature of the AFM tip. Both of the latter measurements are associated with indirect and less accurate measurements of surface energy based on various contact mechanics adhesion models.
Calibration; Lubricants; Microscopy, Atomic Force/*methods/standards; Nanostructures/*chemistry; Surface Properties
Probability in Orthodox Quantum Mechanics: Probability as a Postulate Versus Probability as an Emergent Phenomenon
Arxiv Preprints
1
1-12
2000
The role of probability in quantum mechanics is reviewed, with a discussion of the "orthodox'' versus the statistical interpretive frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum mechanics, a survey is given of attempts either to give a new interpretive framework assuming quantum mechanics is exact, or to modify quantum mechanics assuming it is a very accurate approximation to a more fundamental theory. This survey focuses particularly on the issues of whether probabilities in quantum mechanics are postulated or emergent.
quantum mechanics.
Philosophical Transactions of the Royal Society A: Mathematical, Physical, & Engineering Sciences
371
1989
20120523
2013
10.1098/rsta.2012.0523
-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics.
quantum mechanics.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
371
1989
20120523
2013
10.1098/rsta.2012.0523
-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics.
Time reversal in classical and quantum mechanics
International Journal of Theoretical Physics
18
3
213-230
1979
10.1007/BF00670397
A review of Wigner's time reversal is presented and some important aspects are emphasized. The subject is introduced via classical mechanics. Non-physical statements as "time running backwards" are avoided. Comments are made on the roles of time and of the operator ih(d/dt) in quantum mechanics. The role of symmetries and conservation laws and some properties of the time-reversed states are discussed.
Joint mechanics measurement using magnetic resonance imaging
Top Magn Reson Imaging
21
5
325-334
2010
10.1097/RMR.0b013e31823fb2b9 00002142-201009000-00006 [pii]
Magnetic resonance imaging-based methods for measuring the mechanics of human joints have been successfully applied to quanti- tatively evaluate biomechanics in a wide variety of joints, pathologies, and interventions. The objective of this review was to provide a detailed overview of methods in the literature for measuring joint kinematics, me- niscal and ligament movement, and cartilage strain usingMRI.
2010; 21; 325y334; biomechanics; cartilage; hip; imaging; joint; kinematics; knee; mechanics; mri; shoulder; strain; stress; top magn reson imaging
General noncommuting curvilinear coordinates and fluid mechanics
Chinese Physics Letters
23
10
2637-2639
2006
10.1088/0256-307X/23/10/004
We show that restricting the states of a charged particle to the lowest Landau level introduces noncommutativity between general curvilinear coordinate operators. The Cartesian, circular cylindrical and spherical polar coordinates are three special cases of our quite general method. The connection between U(1) gauge fields defined on a general noncommuting curvilinear coordinates and fluid mechanics is explained. We also recognize the Seiberg-Witten map from general noncommuting to commuting variables as the quantum correspondence of the Lagrange-to-Euler map in fluid mechanics.
scattering; spaces
Fracture toughness of unidirectional graphite fibre reinforced/epoxy composite in mode ii (forward shear), using a thin tubular specimen
Engineering Fracture Mechanics
30
4
531-545
1988
The fracture toughness of graphite fibre reinforced unidirectional composite in mode II has been determined using a thin tubular specimen, by the method developed by Giare and Campbell, accepted for publication in Engng Fracture Mech. The crack growth resistance at instability and the corresponding initial strain energy release rates were independent of the initial crack in the range of the crack length investigated. GIIC obtained by thin tubular torsion specimen is 42% greater as compared to end-cracked beam method. The end-cracked beam method underestimated the GIIC as reported by J. W. Gillespie Jr, L. A. Carlson and R. B. Pipes [Compos. Sci. Technol.27, 177-197 (1986)]. They presented a finite element analysis of the End-Notched Flexure test specimen for mode II interlaminar fracture testing of composite materials. They predicted, using finite elements, that data reduction schemes based upon beam theory underestimate GIIC by approximately 20-40% for typical graphite fibre composite test specimen. It is very encouraging that our results follow very close to their prediction. It is concluded that the thin tubular torsion specimen method is accurate as compared to the end cracked beam method. GIIC of graphite fibre reinforced epoxy composite is found to be half of the glass fibre reinforced/epoxy composites, for practically the same Vt of fibres.
Squeeze flows of apparently lubricated thin films
Journal of Non-Newtonian Fluid Mechanics
124
1-3
115-127
2004
10.1016/j.jnnfm.2004.07.011
In many systems the use of traditional shear rheometry suffers from slip related issues which can lead to large errors in the measurement of apparent rheological properties. For this reason for a long time there has been considerable interest in alternative methods for the measurement of many ‘difficult’ materials such as suspensions. One such alternative method is to use a squeezing flow between a pair of parallel discs. In the current work a fully coupled pair of non-linear ordinary differential equations are derived describing the evolution of the flow of a sample film sandwiched between a pair of lubricant films and a pair of plates. Here the flow fields are derived from the radially symmetric stream function solution in contrast to previously published approaches which invoke the lubrication approximation. Three clear flow regimes are identified: ‘super-lubricated’, apparent slip, and lubrication failure. Which of these regimes is observed in a particular experiment depends on the viscosity ratio, relative thicknesses of the films and the applied stress or strain, respectively. Finally, the possibility of pumping an additional amount of lubricant fluid through the top plate in order to ensure pure bi-axial stretching of the sample film is investigated. It seems that it is possible to achieve this, at least from a theoretical perspective, although the control of the lubricant flow through the top plate must be carefully adjusted as a function of the system evolution.
Bi-axial; Extension; Lubrication; Rheometry; Squeeze flow; Squeezing flow; Stream function
The spacetime approach to quantum mechanics
Vistas in Astronomy
1-22
1993
10.1016/0083-6656(93)90097-4
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schr\"odinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. Sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not "at definite moments of time". An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics is the set of the alternatives defined by whether a particle never crosses a fixed spacetime region or crosses it at least once. The general notion of a set of spacetime alternatives is a partition (coarse-graining) of the histories into an exhaustive set of exclusive classes. With this generalization the sum-over-histories formulation can be said to be in fully spacetime form with dynamics represented by path integrals over spacetime histories and alternatives defined as spacetime partitions of these histories. When restricted to alternatives at definite moments of times this generalization is equivalent to Schr\"odinger-Heisenberg quantum mechanics. However, the quantum mechanics of more general spacetime alternatives does not have an equivalent Schr\"odinger-Heisenberg formulation. We suggest that, in the quantum theory of gravity, the general notion of "observable" is supplied by diffeomorphism invariant partitions of spacetime metrics and matter field configurations. By generalizing the usual alternatives so as to put quantum theory in fully spacetime form we may be led to a covariant generalized quantum mechanics of spacetime free from the problem of time.
Springer Handbook on Experimental Mechanics Chapter 21 Mechanical Testing at the Micro / Nano Scale
Evolution
814
1-49
2008
Mechanical testing of micro and nanoscale materials such as thin films, nanotubes and nanowires, cellular and sub-cellular biomaterials is a significant step towards the realization of nanoscale devices and essential for the commercialization of microscale integrated systems. The challenges in mechanical testing at the smaller length scales emanate from the very basic (specimen preparation and manipulation, high-resolution force and displacement sensing) to complex (enhanced multi-physics coupling, specimen-environment interaction) experimental issues. In this chapter, we attempt to focus on these issues in light of the existing and potential solutions as we review the state of the art in micro and nanoscale mechanical testing as well as our understanding in materials behavior at these length scales.
ATTACK MECHANICS.
Coaching Volleyball
30
4
13-15
2013
The article provides a summary of the training methods of Jim Miret, head girls' volleyball coach at Front Range Volleyball, Englewood, Colorado and Billy Glisan, founder and owner of Powercore 360 in Fort Collins, Colorado proven to increase swing power and decrease inherent injuries. It suggests the use of pictures or slow-motion video as sport movements are best taught and learned faster when hitters see and feel their body doing correct movements. It notes that sport is trial and error.
*SPORTS injuries -- Prevention; TRAINING of; *VOLLEYBALL coaches; *VOLLEYBALL for women; *VOLLEYBALL players
Statistical Mechanics
Biopolymers
6
1
512
1987
10.1146/annurev.pc.06.100155.002325
Unlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition.
Equilibrium and nonequilibrium statistical mechanics
Research supported by EURATOM. New York
1975
The general concepts of statistical mechanics are examined, taking into account Hamiltonian dynamics, statistical ensembles, and reduced distribution functions. Equilibrium statistical mechanics are considered, giving attention to equilibrium ensembles and thermodynamics, equilibrium properties of ideal systems, slightly nonideal systems in equilibrium, reduced distribution functions in equilibrium, dense fluids in equilibrium, phase transitions, and modern theories of critical phenomena. Discussed subjects of nonequilibrium statistical mechanics include an intuitive treatment of nonequilibrium phenomena, kinetic equations and hydrodynamics, eigenvalues of the kinetic equations and the theory of transport coefficients, and the evolution in time of weakly coupled gases.
Classical Mechanics; Distribution Functions; Dynamic Characteristics; Eigenvalues; Equilibrium Equations; Hamiltonian Functions; Hydrodynamics; Kinetic Equations; Kinetic Theory; Nonequilibrium Conditions; Phase Transformations; Quantum Mechanics; Statistical Distributions; Statistical Mechanics; Steady State; Thermodynamic Equilibrium; Transport Theory
A new kind of energy transfer from high frequency mode to low frequency mode in a composite laminated plate.
Acta Mechanica
224
12
2937-2953
2013
This paper brings to light a new type of nonlinear resonant motion in a fiber-reinforced composite laminated rectangular thin plate, which is not reported in other literature. The investigated system is a simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitation whose frequency is near to the first-order natural frequency of the plate. This new phenomenon demonstrates that the responses of a low-order frequency mode can be excited by those of a high-order frequency mode. The high-order frequency is the first-order natural frequency of the test plate, and the low-order frequency here is lower than the first-order nature frequency. Experimental research works on the nonlinear vibrations of the composite laminated rectangular thin plate have been carried out for the first time. It is found from the experimental results that the nonlinear dynamic responses consist of four modes, whose frequencies include a lower frequency than the first-order natural frequency, 1/3 sub-harmonic, 2/3 sub-harmonic and the first-order natural frequencies. In this case, the amplitude of the mode for lower frequency is larger than those of modes for the aforementioned frequencies. Moreover, the theoretical job goes to analyze this new phenomenon. An analytical mode is given to explain the interactions between the first-order mode and the lower-frequency mode observed in the experiment. Based on Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion are formulated for the test plate under parametric excitation. Galerkin’s method is utilized to discretize the partial differential governing equations of motion for the composite laminated rectangular thin plate to a two-degree-of-freedom nonlinear system. The results of numerical simulations qualitatively agree very well with the experimental results. In addition, the multi-pulse chaotic motions are also found in numerical simulations. [ABSTRACT FROM AUTHOR]
COMPOSITE materials; ENERGY transfer; LAMINATED materials; PLATES (Engineering); THIN films; VIBRATION (Mechanics)
Soil mechanics in engineering practice
Engineering Geology
48
149-150
1996
10.1016/S0013-7952(97)81919-9
One of the best-known and most respected books on geotechnical engineering, this updated version features expanded coverage of vibration problems, mechanics of drainage, passive earth pressure and consolidation. In the years since publication of the past editions there has been a proliferation of soil mechanics research, much of it irrelevant to engineering practice. It is the aim of the authors to bring order out of this confusion.
Integrated mechanics for the passive damping of polymer-matrix composites and composite structures
ASME Journal of Applied Mechanics
61
375-383
1991
10.1016/0010-4361(91)90379-U
Some recent developments on integrated damping mechanics for unidirectional composites, laminates, and composite structures are reviewed.
ASPECT RATIO; COMPOSITE STRUCTURES; DYNAMIC STRUCTURAL ANALYSIS; FIBER ORIENTATION; LAMINATES; MICROMECHANICS; MOISTURE; PLATES (STRUCTURAL MEMBERS); POLYMER MATRIX COMPOSITES; STRUCTURAL VIBRATION; VIBRATION DAMPING
A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks
Engineering Fracture Mechanics
35
l
587-598
1990
10.1016/0013-7944(90)90233-7
New models for the efficient simulation of discrete crack closure, and fracture mechanics based model for crack propagation, both under transient dynamic conditions, are developed. Following simple validation problems, those two models are integrated into an interactive graphics program which was used to analyse Koyna dam.
Car Mechanics in the Lab - Investigating the Real Experts on Experimental Markets for Credence Goods
Journal of Economics
108
11
2009
10.1016/j.jebo.2014.09.008
We compare the behavior of car mechanics and college students as sellers in experimental credence goods markets. Finding largely similar behavior, we note much more overtreatment by car mechanics, probably due to decision heuristics they learned in their professional training.
artefactual field experiment
Mathematical Foundations of Quantum Mechanics
The Mathematical Foundations of Quantum Mechanics
8
10
96
1955
10.2307/2313034
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.
Fracture Mechanics
Manufacturing Systems
71
Mode I
12-14, 18
2004
10.1007/b118073
Summary Ceramic materials fail due to the extension of processing defects such as pores, inclusions or cracks. Under rapid loading, unstable extension of these defects causes failure of the component. Under constant or cyclic loading, the defects may extend slowly until a critical size is reached, where unstable extension occurs. The subcritical extension of the defects under constant loading is called static fatigue, subcritical extension under cyclic loading is called cyclic fatigue. The defects can be described as cracks with a sharp tip and, therefore, the methods of fracture mechanics-in most cases of linear fracture mechanics-can be applied. This concept of sharp cracks has been applied successfully to describe the failure behaviour of ceramics, even in cases where the flaws are three-dimensional, e.g. pores.
Molecular Mechanics
Current Pharmaceutical Design
20
2014
Molecular Mechanics (MM) force fields are the methods of choice for protein simulations, which are essential in the study of conformational flexibility. Given the importance of protein flexibility in drug binding, MM is involved in most if not all Computational Structure-Based Drug Discovery (CSBDD) projects. This paper introduces the reader to the fundamentals of MM, with a special empha- sis on how the target data used in the parametrization of force fields determine their strengths and weaknesses. Variations and recent de- velopments such as polarizable force fields are discussed. The paper ends with a brief overview of common force fields in CSBDD.
force fields; molecular mechanics; structure-based drug design
MULTIVARIABLE MECHANICS OF THE NEUROMUSCULAR SYSTEM.
IEEE/Engineering in Medicine and Biology Society Annual Conference
New York, NY, USA
594-598
1986
An analysis of neuromuscular system mechanics shows that the spring-like behavior of single muscles can be extended to the multivariable case only if the curl of the net force-displacement relation is zero. Further, nonzero curl can only be due to intersegment feedback. Experimental measurements in humans show that curl is in fact zero.
BIOMECHANICS; BIOMEDICAL ENGINEERING - Neurophysiology; INTRAMUSCULAR FEEDBACK; KINEMATICS; MULTIVARIABLE MECHANICS; NEUROMUSCULAR SYSTEM; SPRING-LIKE BEHAVIOR OF SINGLE MUSCLES
Non-local variational mechanics—IX
International Journal of Engineering Science
13
9-10
861-867
1975
10.1016/0020-7225(75)90086-5
The nonlocal variational calculus is extended to include Lagrangian functions that depend on functionals of the state variables that represent multiple interactions, in distinction to our previous results in which only two point interactions were included. It is also shown that, under rather mild differentiability conditions, arbitrary functional dependence can be approximated by finite multiple interaction functional dependence.
Fractal fracture mechanics - a review
Engineering Fracture Mechanics
51
6
997-1033
1995
The revolution in geometry, which has recently created the notion of the fractional dimension of real world bodies and has formed fractal geometry, has substantially influenced fracture science. An experimentally measured crack in real materials has appeared to be substantially a fractal, that is, a geometrical object of fractional dimension. In the present paper, an attempt has been undertaken to provide an account of some achievements in this area, herein called "Fractal Fracture Mechanics".
Quantum mechanics is a relativity theory
Armenian Journal of Physics
2006
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the Heisenberg inequalities invariant and form a group. They are related to dilatations of space variables provided the quantum potential is added to the classical Hamiltonian functional. The Schr"odinger equation appears to have a nonunitary and nonlinear companion acting in another time variable. Evolution in this time seems related to the state vector reduction.
Soil mechanics in engineering practice
Engineering Geology
48
1996
10.1016/S0013-7952(97)81919-9
One of the best-known and most respected books on geotechnical engineering, this updated version features expanded coverage of vibration problems, mechanics of drainage, passive earth pressure and consolidation. In the years since publication of the past editions there has been a proliferation of soil mechanics research, much of it irrelevant to engineering practice. It is the aim of the authors to bring order out of this confusion.
Foundation; geotechnical
Beyond “Inop”: Logbook Communication Between Airline Mechanics and Pilots
The International Journal of Aviation Psychology
18
1
86-103
2008
10.1080/10508410701749563
When mechanical discrepancies occur on an aircraft, effective communication between pilots and mechanics can facilitate identification of the problem. A survey of pilots and mechanics was conducted to determine how often they were able to discuss discrepancies directly and to identify factors that influenced the detail they provided about discrepancies in the aircraft logbook. Logistical factors such as short turn times between flights and crew schedules appeared to present barriers to face-to-face meetings between pilots and mechanics. Guidelines for pilot logbook entries appeared to be less clearly defined than for mechanic entries. Pilots reported receiving significantly less training on writing logbook entries and spent significantly less time making individual entries than mechanics. Mechanics indicated greater concern about the Federal Aviation Administration reading their entries than pilots. Mechanics indicated they had little opportunity to follow upwith pilots to clarify a logbook entry once pilots departed the aircraft.[ABSTRACT FROM AUTHOR]
Extension of Fracture Mechanics Principles to Viscoelastic Continuum Media
Journal of Engineering Mechanics
138
4
317-326
2012
10.1061/(ASCE)EM.1943-7889.0000335
The fracturing of materials is well known on the basis of the theory of fracture mechanics. An important concept in fracture mechanics theory is that crack propagation is governed by the fundamental material properties of energy dissipation and energy threshold. However, to apply the fracture mechanics approach and measure these properties, a notch needs to be introduced into a continuum body. This requires additional effort to make the notch, which is often sensitive to the formation of materials surrounding the area near the crack tip. These effects become more complex for a material that exhibits time, rate, and temperature dependency. To overcome these complexities and problems regarding fracture testing, this study used the analogy between the material’s behaviors with and without a notch. A transfer of the fracture mechanics principle to continuum viscoelastic media was the key to the model developed in this study. For this purpose, the energy release rate (G) which is theoretically derived from a v...
Effects of pneumoperitoneal pressure and position changes on respiratory mechanics during laparoscopic colectomy
Korean Journal of Anesthesiology
63
5
419-424
2012
10.4097/kjae.2012.63.5.419
This study was designed to assess the effects of pneumoperitoneal pressure (PP) and positional changes on the respiratory mechanics during laparoscopy assisted colectomy.
Laparocolectomy; Pneumoperitoneum; Position; Respiratory mechanics
Changes in breathing control and mechanics after laparoscopic vs open cholecystectomy.
Archives of surgery (Chicago, Ill. : 1960)
141
1
16-22
2006
10.1001/archsurg.141.1.16
We hypothesized that there might be different effects on breathing control and respiratory mechanics after laparoscopic vs open cholecystectomy.
Adult; Aged; Airway Resistance; Anesthesia, General; Cholecystectomy; Cholecystectomy, Laparoscopic; Humans; Middle Aged; Respiration; Respiratory Mechanics; Spirometry
Boltzmann's Approach to Statistical Mechanics
Physics
16
2001
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann's analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann's later work on the subject have little merit. Most twentieth century innovations -- such as the identification of the state of a physical system with a probability distribution $\varrho$ on its phase space, of its thermodynamic entropy with the Gibbs entropy of $\varrho$, and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics -- are thoroughly misguided.
History of Physics; Mathematical Physics; Quantum Physics; Statistical Mechanics
Thin film drainage between pre-inflated capsules or vesicles
Bulletin of the American Physical Society
58
18
M18.7
2013
Capsules and vesicles are often used as vehicles to carry active ingredients or fragrance in drug delivery and consumer products and oftentimes in these applications the particles may be pre-inflated due to the existence of a small osmotic pressure difference between the interior and exterior fluid. We study the dynamics of thin film drainage between capsules and vesicles in flow as it is crucial to fusion and deposition of the particles and, therefore, the stability and effectiveness of the products. Simulations are conducted using a numerical model coupling the boundary integral method for the motion of the fluids and a finite element method for the membrane mechanics. For low capillary numbers, the drainage behavior of vesicles and capsules are approximately the same, and also similar to that of drops as the flow-independent and uniform tension due to pre-inflation dominates. The tension due to deformation caused by flow will become more important as the strength of the external flow (i.e. the capillary number) increases. In this case, the shapes of the thin film region are fundamentally different for capsules and vesicles, and the drainage behavior in both cases differs from a drop.
Thermoelastic analysis of periodic thin lines deposited on a substrate
Journal of the Mechanics and Physics of Solids
47
5
1113-1130
1999
10.1016/S0022-5096(98)00092-1
Thermoelastic stresses and curvatures arising from patterned thin lines on initially flat isotropic substrates are analyzed. A connection is made between substrates with patterned lines and laminated anisotropic composites containing transverse matrix cracks. Using this analogy along with anisotropic plate theories, approximate analytical expressions are derived for volume-averaged stresses as well as curvatures along and normal to the lines, for any thickness, width and spacing of the lines. The predictions of the analysis are shown to compare favorably with finite element simulations of stresses and curvatures for Si substrates with Al, Cu or SiO2 lines. The predictions also match prior experimental measurements of curvatures along and normal to patterned SiO2 lines on Si wafers, and further capture the general experimental trends reported previously for curvature evolutions in Si wafers with Al lines. The model presented here thus provides a very convenient and simple analytical tool for extracting stresses in thin lines on substrates from a knowledge of experimentally determined film stress, thereby circumventing the need for detailed computations for a wide range of unpassivated line geometries of interest in microelectronic applications.
a; b; constitutive behavior principles; plates; thermal stress; thermomechanical processes
Adhesive failure of a thin epoxy film on an aluminized substrate
Materials Research Society Symposium - Proceedings
649
Q6.3.1-Q6.3.6
2001
In this study we used nanoindentation to determine mechanical properties and combined nanoindentation with stressed overlayers to determine interfacial fracture energy of a 164 nm thick film of Epon 828/T403 on an aluminized glass substrate. The combination of nanoindentation and a tungsten overlayer was required to trigger delamination of the epoxy film from the aluminized substrate. Mechanics-based models for circular blister formation were then used to determine residual stresses and interfacial fracture energies. This approach showed that the tungsten overlayer had a compressive residual stress of 1.9 GPa which drove blister formation at a fracture energy of 1.9 J/m2 with a phase angle of loading equal to -62°.
Adhesive failure; Aluminized substrate; Aluminum; Circular blister formation; Epoxy resins; Glass; Interfaces (materials); Mathematical models; Mechanical properties; Nanoindentation; Plastic adhesives; Plastic films; Residual stresses; Substrates; Thin epoxy film; Thin films; Tungsten
Grown crystalline Ni-Ti shape memory alloy thin films
Smart Structures and Materials 2003: Active Materials: Behavior and Mechanics
5053
212-218
2003
10.1117/12.484742
Crystallization of sputter deposited Ni-Ti thin film is commonly achieved with high temperature annealing to induce the shape memory effect. High temperature annealing has several disadvantages such as formation of precipitates, exclusion of unstable substrates, increases residual stress. An attempt has been made to obtain as grown crystallized film by using hot target as a process parameter so that those disadvantages can be overcome. In this paper it will be shown that the transformation properties of sputter deposited as grown NiTi thin films from a hot Ti-rich target on single crystal. Si substrate is crystalline in nature and shape memory above room temperature. X-ray diffraction reveals that as grown film is crystalline and shows a mixture of martensite and rhombohedral phases. Transformation temperatures of the sputtered films are determined by using both differential scanning calorimetry and four point probe techniques. Film microstructure has been studied using transmission electron microscope. The as deposited films have large grain sizes with well defined twinned structure. We attribute film crystallinity to target composition and the high kinetic energy of the sputtered species creating a favorable condition to form crystalline film.
deposition; hot target; Magnetron Sputtering; martensite; shape memory; target
Convective inertia effects in wall-bounded thin film flows
Meccanica
41
5
473-482
2006
DOI 10.1007/s11012-006-0006-7
We apply the boundary layer equations to inertial flow in wall bounded films that might be characterized as `thin', say epsilon <= 0.1 where epsilon is the ratio of the characteristic lengths, yet to which the lubrication approximation of Reynolds no longer applies. Two particular flow geometries are investigated, nominally parallel plates and nominally inclined plates, both with and without spatially periodic perturbation of the stationary plate. A Galerkin-B spline formulation of the governing equations is employed, and we rely on parametric continuation to obtain solutions at higher values of the Reynolds number. In particular, we are able to demonstrate that the boundary layer equations yield accurate results for a wide range of Reynolds numbers when the aspect ratio is less than 1/10. We also find that in both nominally parallel and nominally inclined geometries the sign of the inertial force correction is determined by the film contour in the neighborhood of the exit, this result might have implications in the design of MEMS devices.
bearings; boundary-layer equations; channel flow; elastohydrodynamic lubrication; fluid inertia; fluid mechanics; thin-film approximation
Quantum mechanics
Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming
21-87
2009
The charge carriers in semiconductor devices—electrons and holes—are quantum particles. Any researcher in device modelling must have a thorough grounding in the theory of quantum mechanics, because there is no point in finding solutions to the quantum equations without being able to sensibly interpret these solutions in the quantum context. This chapter presents the basic theory of quantum mechanics, including a discussion of the derivation and structure of the Schrödinger equation, its solutions for one-dimensional problems, operators, spin, the hydrogen atom, and identical particles.
Appl.Mathematics/Computational Methods of Engineer; Mathematical Methods in Physics; Mathematical Modeling and Industrial Mathematics
Quantum Mechanics
QMBook
2009
Why yet another book on quantum mechanics? Quantum mechanics was born in the first quarter of the twentieth century and has received an enormous number of theoretical and experimental confirmations over the years. It is considered to be the fundamental physical paradigm, and has a wide range of applications, from cosmology to chemistry, and from biology to information sciences. It is one of the greatest intellectual achievements of the past century. As an effect of its invention, the very concept of physical realitywas changed, and “observation,” “measurement,” “prediction,” and “state of the system” acquired a new and deeper meaning.
Predicting intact rock properties of selected sandstones using petrographic thin-section data
International Journal of Rock Mechanics and Mining Sciences
41
1
93-98
2004
10.1016/j.ijrmms.2004.03.025
The determination of strength and deformability of intact rock material is one of the major requirements and/or input parameters in rock engineering. However, preparation of high quality specimens for these determinations are not always possible particularly from fractured and weathered rocks. Due to this limitation, indirect tests and predictive models can be considered as alternative methods. In this study, an attempt was made to suggest practical and inexpensive predictive models based on statistical techniques for estimation of strength and some engineering properties of the five selected sandstones from their petrographic characteristics. The study revealed that the influence of the textural characteristics, such as angular grains, packing density and packing proximity appear to be more important than mineralogy for predicting engineering properties. The results of the study were presented in the form of correlation coefficient models and predictive models, and performance of the models with highest correlation coefficient were also checked by comparing predicting and measured values.
Petrographic characteristics; Predictive models; Regression; Uniaxial compressive strength; Young’s modulus
Modeling of ductile crack propagation in expanded thin-walled 6063-T5 aluminum tubes
International Journal of Mechanical Sciences
80
160-168
2014
10.1016/j.ijmecsci.2014.01.012
In this paper the ductile failure behavior of mechanically expanded 6063-T5 aluminum tubes was studied experimentally and numerically. The expansion of the tubes was performed mechanically by using a conical mandrel with the objective to study the failure mode that governs the expansion process of this material. To localize the failure the tubes were drilled with circular holes. The fractured surfaces of failed expanded tubes were examined and revealed a flat ductile dimple rupture characteristic. A finite element model, which is based on continuum damage mechanics, is developed to mimic the experiments. The model also predicts ductile crack propagation and failure in the expanded tubes with embedded holes very well making it a suitable tool for studying the tubular expansion process and for optimizing the expansion tools. ?? 2014 Elsevier Ltd.
Aluminum; Continuum damage model; Ductile failure; Oil and gas; Tubular expansion
Long waves on a thin layer of conducting fluid flowing down an inclined plane in an electromagnetic field
European Journal of Mechanics, B/Fluids
18
1975
295-313
1999
10.1016/S0997-7546(99)80028-4
Wave formation on film flow is an intriguing hydrodynamic phenomenon with a variety of practical consequences, especially in heat and mass transfer. In this paper the propagation of weakly nonlinear waves over a flow of an electrically conducting viscous film flowing down an inclined plane under simultaneous action of electrical and magnetic fields is studied. The set of Navier-Stokes equations with electromagnetic force in the limit of low magnetic Reynolds number and subject to corresponding boundary conditions serves as a mathematical description of the problem. Long-wave expansions are carried out and an evolution equation of the Kuramoto-Sivashinsky type governing propagation of weak surface perturbations is derived. The critical values of the Reynolds number are determined explicitly and linear stability is investigated. It is shown that the electrical field provides a destabilizing effect on the film flow while the magnetic field stabilizes it. The strongest stabilizing effect of the magnetic field in the presence of the electrical one can be achieved if it is purely longitudinal. The Karman-Polhausen integral boundary-layer theory is considered for the MHD-approach and main results are discussed.
Discerned and non-discerned particles in classical mechanics and convergence of quantum mechanics to classical mechanics
Annales de la Fondation Louis de Broglie
36
2011
We introduce into classical mechanics the concept of nondiscerned particles for particles that are identical, non-interacting and prepared in the same way. The non-discerned particles correspond to an action and a density which satisfy the statistical Hamilton-Jacobi equations and allow to explain the Gibbs paradox. On the other hand, a discerned particle corresponds to a particular action that satisfies the special Hamilton-Jacobi equations. We then study the convergence of quantum mechanics to classical mechanics when ~ tends to 0 by considering two cases : the convergence to non-discerned classical particles and the convergence to a classical discerned particle. Based on these convergences, we propose an updated interpretation of quantum mechanics.
A one field full discontinuous Galerkin method for Kirchhoff Love shells applied to fracture mechanics
Computer Methods in Applied Mechanics and Engineering
200
45-46
3223-3241
2011
10.1016/j.cma.2011.07.008
In order to model fracture, the cohesive zone method can be coupled in a very efficient way with the finite element method. Nevertheless, there are some drawbacks with the classical insertion of cohesive elements. It is well known that, on one the hand, if these elements are present before fracture there is a modification of the structure stiffness, and that, on the other hand, their insertion during the simulation requires very complex implementation, especially with parallel codes. These drawbacks can be avoided by combining the cohesive method with the use of a discontinuous Galerkin formulation. In such a formulation, all the elements are discontinuous and the continuity is weakly ensured in a stable and consistent way by inserting extra terms on the boundary of elements. The recourse to interface elements allows to substitute them by cohesive elements at the onset of fracture.The purpose of this paper is to develop this formulation for Kirchhoff-Love plates and shells. It is achieved by the establishment of a full DG formulation of shell combined with a cohesive model, which is adapted to the special thickness discretization of the shell formulation. In fact, this cohesive model is applied on resulting reduced stresses which are the basis of thin structures formulations. Finally, numerical examples demonstrate the efficiency of the method. © 2011 Elsevier B.V.
Cohesive element; Discontinuous Galerkin method; Finite-elements; Fracture mechanics; Kirchhoff-Love; Shells
On nonlinear oscillations of a thin bar
Archive of Applied Mechanics
66
3
168-176
1996
Based on one of the simplest mathematical model of a solid, nonlinear\ninteractions between waves in a rectilinear bar are investigated,\nin order to reveal and display a number of dynamic properties inherent\nnot only to the bar, but also to most weakly nonlinear mechanical\nsystems with internal resonances. The presence of internal resonances\nin the bar is twofold. Firstly, there exists a slow periodic energy\nexchange between the longitudinal and the two quasi-harmonic bending\nwaves involved in the resonant triad due to the phase matching, secondly,\ntriple-frequency envelope solitons can be created from the resonant\ntriad with the same modal state. The paper investigates the evolution\nof waves in the bar with the aim to classify the elementary types\nof wave triplet resonant interactions and define their existence\nand coexistence areas.
nonlinear oscillations internal resonance slow per
Visualization techniques for engineering mechanics
Computing Systems in Engineering
1
1
37-50
1990
10.1016/0956-0521(90)90046-N
Scientific visualization is an emerging computational technology that helps scientists and engineers to investigate physical systems through a process of geometric abstraction. Visualization is an interdisciplinary subject, drawing on numerical simulation, perceptual psychology, graphic arts, computer graphics, image processing, data management, parallel processing, distributed computing and various disciplinary specialities of science and engineering. Recent developments in the field are surveyed, with emphasis on the role of visualization in engineering mechanics. Visualization is described as a structured process of data preprocessing, geometric abstraction and image rendering. After a discussion of the role of human perception in visualization, various techniques for displaying scalar, vector, and higher-order tensor fields are presented. An application of visualization to elastodynamic fracture mechanics demonstrates the benefits of combining visualization with numerical simulation.
Visualization techniques for engineering mechanics
Computing Systems in Engineering
1
37-50
1990
DOI: 10.1016/0956-0521(90)90046-N
Scientific visualization is an emerging computational technology that helps scientists and engineers to investigate physical systems through a process of geometric abstraction. Visualization is an interdisciplinary subject, drawing on numerical simulation, perceptual psychology, graphic arts, computer graphics, image processing, data management, parallel processing, distributed computing and various disciplinary specialities of science and engineering. Recent developments in the field are surveyed, with emphasis on the role of visualization in engineering mechanics. Visualization is described as a structured process of data preprocessing, geometric abstraction and image rendering. After a discussion of the role of human perception in visualization, various techniques for displaying scalar, vector, and higher-order tensor fields are presented. An application of visualization to elastodynamic fracture mechanics demonstrates the benefits of combining visualization with numerical simulation.
Mirror potentials in classical mechanics
Rev. Mex. Fis. E
52
2
5
2006
It is shown that for a central potential that is an injective function of the radial coordinate, a second central potential can be found that leads to trajectories in the configuration space and the momentum space coinciding, respectively, with the trajectories in the momentum space and the configuration space produced by the original potential.
classical mechanics; configuraci; coordenada radial; en el espacio de; hamiltonian mechanics; on inyectiva de la; para un potencial central; que lleva a trayectorias; que sea una funci; segundo potencial central; se muestra que; se puede hallar un
Foundations of anisotropic relativistic mechanics
Journal of Mathematical Physics
50
4
2009
10.1063/1.3104065
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such mechanics allow for the presence of anisotropy, both conventional (due to non-standard synchronisation protocols) and real (leading to detectable chronogeometrical effects, independent of the choice of synchronisation). We give a general method for finding the fundamental dynamical quantities (Lagrangian, energy and momentum), and write their explicit expression in all the kinematics compatible with the basic requirements. We also write the corresponding dispersion relations and outline a formulation of these theories in terms of a pseudo-Finslerian spacetime geometry. Although the treatment is restricted to the case of one spatial dimension, an extension to three dimensions is almost straightforward.
Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics
Applied Mathematics and Computation
205
1
212-230
2008
DOI 10.1016/j.amc.2008.06.042
The conservation laws for second order scalar partial differential equations and systems of partial differential equations which occur in fluid mechanics are constructed using different approaches. The direct method, Noether's theorem, the characteristic method, the variational approach (multiplier approach) for arbitrary functions as well as on the solution space, symmetry conditions on the conserved quantities, the direct construction formula approach, the partial Noether approach and the Noether approach for the equation and its adjoint are discussed and explained with the help of an illustrative example on a non-linear field equation describing the relaxation to a Maxwellian distribution. The conservation laws for the non-linear diffusion equation for the spreading of an axisymmetric thin liquid drop, the system of two partial differential equations governing flow in a laminar two-dimensional jet and the system of two partial differential equations governing flow in a laminar radial jet are discussed via these approaches. (C) 2008 Elsevier Inc. All rights reserved.
characteristic method; conservation laws; direct construction formula approach; direct construction method; direct method; noether approach for the system and its adjoint; noether's theorem; partial noether approach; symmetries; symmetry conditions; variational approach for arbitrary functions and o
Nonequilibrium statistical mechanics
Summer school Les Houches
1
2-4
238
2001
This is a presentation of the main ideas and methods of modern nonequilibrium statistical mechanics. It is the perfect introduction for anyone in chemistry or physics who needs an update or background in this time-dependent field. Topics covered include fluctuation-dissipation theorem; linear response theory; time correlation functions, and projection operators. Theoretical models are illustrated by real-world examples and numerous applications such as chemical reaction rates and spectral line shapes are covered. The mathematical treatments are detailed and easily understandable and the appendices include useful mathematical methods like the Laplace transforms, Gaussian random variables and phenomenological transport equations.
New Modal Quantum Mechanics
Arxiv Preprints
1
1-4
2013
We describe an interpretation of quantum mechanics based on reduced density matrices of subsystems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not suffer from the range of problems that plague other modal interpretations. The key feature is that quantum states carry an additional property assignment in the form of one the eigenvectors of the reduced density matrix which evolves according to a stochastic process driven by the unmodified Schroedinger equation, but it is usually hidden from the emergent classical description due to the ergodic nature of its dynamics. However, during a quantummeasurement, ergodicity is broken by decoherence and definite outcomes occur with probabilities that agree with the Born rule.
Hydraulics and Fluid Mechanics
Hydraulics and Fluid Mechanics
133-147
1964
10.1016/B978-0-08-010291-7.50013-6
In order to extend the prediction of butterfly valve characteristics to compressible flows and unusual geometries capable of giving a low self-closing torque, a simplified analysis of butterfly valve behaviour is necessary. In the paper an analysis based upon regarding the butterfly valve as two non-interacting jets is presented and compared with an orthodox “exact” solution for a plane butterfly in a parallel channel. It appears that the jet-flow analysis gives results closer to available experimental values, at least when the valve approaches closure, than does the “exact” analysis. It is concluded that the jet-flow analysis will be useful for designing unusual butterflies. However, more careful experiments are needed, both with plane channels and pipes to give reliable data for comparison with theory.
9.1 Fracture Mechanics
Handbook of Advanced Ceramics
647-705
2003
Summary Ceramic materials fail due to the extension of processing defects such as pores, inclusions or cracks. Under rapid loading, unstable extension of these defects causes failure of the component. Under constant or cyclic loading, the defects may extend slowly until a critical size is reached, where unstable extension occurs. The subcritical extension of the defects under constant loading is called static fatigue, subcritical extension under cyclic loading is called cyclic fatigue. The defects can be described as cracks with a sharp tip and, therefore, the methods of fracture mechanics--in most cases of linear fracture mechanics--can be applied. This concept of sharp cracks has been applied successfully to describe the failure behaviour of ceramics, even in cases where the flaws are three-dimensional, e.g. pores.
Teaching unsaturated soil mechanics as part of the undergraduate civil engineering curriculum
Pan american Conference on Geotechnical Engineering Education
26-27
2002
Soil mechanics for unsaturated soils has been slower to develop than soil mechanics for satu rated soils. Likewise, the teaching of unsaturated soil mechanics has been slow to become a part of the uni versity curriculum in civil engineering. Generally, unsaturated soil mechanics is briefly covered at the gradu ate level, if it is even taught at all in the university. This paper suggests that unsaturated soil mechanics concepts should be introduced and taught at the undergraduate leve!. The paper illustrates how the basic con cepts of both saturated and unsaturated soil mechanics can be introduced simultaneously during the initial presentation of soil mechanics to undergraduate students. The concepts that need to be introduced are related to the stress state and the constitutive relationships for the soil; namely, seepage, shear strength and volurne mass changes. The concepts are introduced through the use of a pictorial, elliptical world of soil mechanics.
Flexuralwave filtering and platonic polarisers in thin elastic plates
Quarterly Journal of Mechanics and Applied Mathematics
66
4
437-463
2013
10.1093/qjmam/hbt013
A solution method is given to the problem of plane wave propagation through one- and two-dimensional platonic arrays. The problem is formulated in terms of boundary integral equations and a solution is constructed using boundary element methods. Previous work has been restricted to simple geometries such as circles, pins and squares, and here the framework is extended to consider scatterers of arbitrary shape subject to clamped-edge boundary conditions at the edge. This is done by constructing scattering matrices for a single grating and using Bloch's theorem to form an eigenvalue problem which connects the grating problem to the array problem. The associated eigenvalues then permit the construction of band surfaces which reveal the flexural wave filtering capabilities of different geometries, as well as the behaviour of Bloch waves within the array. Multiple geometries are investigated and the first band surfaces are computed for these specific cases.
Experimental and theoretical characterization of structure in thin disordered films
Acta Crystallographica Section A Foundations of Crystallography
55
2
178-187
1999
10.1107/S0108767398008769
The electron microscope provides an ideal environment for the structural analysis of small volumes of amorphous and polycrystalline materials by enabling the collection of scattering information as a function of energy loss and momentum transfer. The scattered intensity at zero energy loss can be readily processed to a reduced density function, providing information on nearest-neighbour distances and bond angles. A method for collecting and processing the scattered intensity, which allows for the collection of an energy-loss spectrum for a range of momentum transfers, is discussed. A detailed structural determination from a reduced density function alone is difficult and it is shown that a more detailed structural model can be obtained by combining the experimental reduced density function with model structures obtained from molecular dynamics based on first-principles quantum mechanics. This method is applied to tetrahedral amorphous carbon, as an example of a monatomic network, and to aluminium nitride, as a prototype for a binary amorphous alloy.
Buckling behavior of a central cracked thin plate under tension
Engineering Fracture Mechanics
35
6
1019-1027
1990
10.1016/0013-7944(90)90129-5
The buckling characteristics of cracked plates subject to uniaxial tensile loads are analysed by the aid of the finite element method. Owing to the fact that crack buckling behavior is affected by the in-plane stress distribution around a crack, to get more accurate results, pre-buckling in-plane stress fields are analysed by the finite element method. For the critical loads calculation, the finite element approach adopted is based on Von Karman's linearize theory for buckling of plates subjected to pre-buckling state of plane stress. Several singular elements based on the Willian series are used in this plate bending approach. In this study, the effect of crack length, the effect of boundary condition, the effect of Poison's ratio and the effect of biaxial force on critical loads are analysed and discussed. Furthermore, the effect of initial imperfection is also discussed. There is a good agreement between other researcher's work and present results.
Tensile Membrane Action of Thin Slabs Exposed to Thermal Gradients
Journal of Engineering Mechanics
139
November
1497 - 1507
2013
10.1061/(ASCE)EM.1943-7889.0000597
AbstractA number of simplified design methods have been developed to predict composite slab capacities in fire. Most of these extend ambient-temperature large-deflection slab behavior to the elevated-temperature phase by reducing the strengths of fire-exposed concrete and reinforcement while neglecting the effects of thermal expansion and thermal bowing of the slab. Experiments have shown that there are significant differences between the predictions from these methods and the actual behavior and failure modes of ambient- and elevated-temperature concrete slabs in tensile membrane action. Therefore, this paper describes the development of a new analytical method that incorporates both thermal and mechanical effects into the prediction of slab behavior in fire conditions. It uses the variational Rayleigh-Ritz approach to classical large-deflection plate theory. The method is found to produce accurate predictions of deflections and membrane tractions; however, it requires further refinement for accuracy of ...
Fluid mechanics
PloS one
6
3
e18068
2011
10.1371/journal.pone.0018068
Dental thermal pain is a significant health problem in daily life and dentistry. There is a long-standing question regarding the phenomenon that cold stimulation evokes sharper and more shooting pain sensations than hot stimulation. This phenomenon, however, outlives the well-known hydrodynamic theory used to explain dental thermal pain mechanism. Here, we present a mathematical model based on the hypothesis that hot or cold stimulation-induced different directions of dentinal fluid flow and the corresponding odontoblast movements in dentinal microtubules contribute to different dental pain responses. We coupled a computational fluid dynamics model, describing the fluid mechanics in dentinal microtubules, with a modified Hodgkin-Huxley model, describing the discharge behavior of intradental neuron. The simulated results agreed well with existing experimental measurements. We thence demonstrated theoretically that intradental mechano-sensitive nociceptors are not "equally sensitive" to inward (into the pulp) and outward (away from the pulp) fluid flows, providing mechanistic insights into the difference between hot and cold dental pain. The model developed here could enable better diagnosis in endodontics which requires an understanding of pulpal histology, neurology and physiology, as well as their dynamic response to the thermal stimulation used in dental practices.
Animals; Biological; Biomechanics; Biomechanics: physiology; Cats; Cold Temperature; Computer Simulation; Dentinal Fluid; Dentinal Fluid: physiology; Dogs; Hot Temperature; Membrane Potentials; Microtubules; Microtubules: physiology; Models; Nociceptors; Nociceptors: metabolism; Rheology; Toothache; Toothache: physiopathology
Induced electric fields and plasmonic interactions between a metallic nanotube and a thin metallic film
Science China-physics Mechanics & Astronomy
53
1
38-43
2010
10.1007/s11433-010-0094-1
We have numerically simulated the induced electric fields and the\nplasmonic interactions of a metallic nanotube near a thin metallic\nfilm. Our study shows that the energies and intensities of the plasmon\nresonances depend strongly on the aspect ratio (the ratio of the\ninner to outer radius) of the nanotube as well as the separation\nbetween the center of the nanotube and the upper surface of the metallic\nfilm and the thickness of the film. The enhancement of the induced\nelectric field of this system reaches as high as 10(4) orders of\nmagnitude and its field distribution is characterized by waveguide-mode\nresonance. The report proposes that these phenomena can be applied\nto designing surface enhanced spectroscopies such as surface enhanced\nRaman spectroscopy for efficient chemical and biological sensing.
Behavior of extensional modes in a thin rod immersed in a viscous medium
The Journal of the Acoustical Society of America
99
2
706-712
1996
10.1121/1.414647
Aviscoelastic model is established for the coupled motion in a thin solid rod and an infinite viscous medium surrounding it, starting from the basic laws of elastic and fluid mechanics. The effect of various material parameters of the surrounding medium on the propagation of acoustic waves along the rod is investigated using numerical calculations. It is demonstrated that, at low frequencies, the fundamental radial–axial mode R01 responds most to changes in the material parameters of the surrounding medium related to shear motion in a manner similar to that of the fundamental torsional mode T00. Based on this effect, a model miniature viscosity and density sensor is proposed and tested in viscous liquids. The attenuation in the device agrees well with the theoretical model and exhibits an approximately linear dependence on the square root of the product of the density and the shear viscosity of the surrounding medium. This work shows that simple traditional acoustic technology can be used to develop small size, low-cost sensors for liquid viscosity and density measurement with the possibility of on-line applications.
Strain evolution and morphological transition of magnetron-sputtered CeO2 thin films induced by deposition parameters.
Current Applied Physics
14
3
275-281
2014
10.1016/j.cap.2013.11.018
Abstract: Cerium dioxide (CeO2) films were fabricated on yttria-stabilized zirconia (YSZ) single crystals using unbalanced radio frequency (RF) magnetron sputtering. X-ray diffraction measurements revealed film strain discrepancies under different deposition parameters. Strain evolution was induced by varying sputtering pressure, RF power, and sputtering gas. A distinct morphological transition from a granular surface to an interwoven surface was also realized by varying the above parameters. On the basis of the “atomic peening” mechanism, the influence of different parameters on film strain was discussed. The film surface characteristics were revealed to be highly correlated with film strain. YBa2Cu3O7−δ (YBCO) films were post-deposited on the as-grown CeO2/YSZ(001) stack by using the trifluoroacetate metal-organic deposition (TFA-MOD) method. The superconducting property of the YBCO layer varied significantly with the morphology of the CeO2 buffer films. [Copyright &y& Elsevier]
CERIUM oxides; MAGNETRON sputtering; METALLIC surfaces; METALLIC thin films; PARAMETER estimation; STRAINS & stresses (Mechanics)
Relativistic continuum mechanics part I—mechanics and thermodynamics
International Journal of Engineering Science
4
6
611-638
1966
10.1016/0020-7225(66)90008-5
The basic laws of a special relativistic theory of continuous media suitable for the treatment of electromagnetic interactions with materials are formulated. The kinematics, dynamics and thermodynamics of a continuum are discussed from a relativistic viewpoint. Constitutive equations are deduced for thermoelastic solids, thermoviscous fluids and electromagnetic materials. Part I considers the mechanical and thermodynamical aspects of the theory of continuous media from a relativistic viewpoint. Part II considers the electromagnetic interaction with matter. © 1966.
Copenhagen Interpretation of Quantum Mechanics Is Incorrect
Foundations
852
1-15
2005
(A point-by-point response to a comment (quant-ph/0509130) on our paper (quant-ph/0509089) is added as Appendix C. We find the comment incorrect.) Einstein's criticism of the Copenhagen interpretation of quantum mechanics is an important part of his legacy. Although most physicists consider Einstein's criticism technically unfounded, we show that the Copenhagen interpretation is actually incorrect, since Born's probability explanation of the wave function is incorrect due to a false assumption on "continuous probabilities" in modern probability theory. "Continuous probability" means a "probability measure" that can take every value in a subinterval of the unit interval (0, 1). We prove that such "continuous probabilities" are invalid. Since Bell's inequality also assumes "continuous probabilities", the result of the experimental test of Bell's inequality is not evidence supporting the Copenhagen interpretation. Although successful applications of quantum mechanics and explanation of quantum phenomena do not necessarily rely on the Copenhagen interpretation, the question asked by Einstein 70 years ago, i.e., whether a complete description of reality exists, still remains open.
bell; born; copenhagen interpretation quantum; foundations quantum mechanics; function; mechanics; probability explanation wave; s; s inequality
Generalized continuum mechanics : what do we mean by that ?
Mechanics of Generalized Continua
3-13
2010
10.1007/978-1-4419-5695-8
Discursive historical perspective on the developments and ramifications of generalized continuum mechanics from its inception by the Cosserat brothers (Théorie des corps déformables. Hermann, 1909) with their seminal work of 1909 to the most current developments and applications is presented. The point of view adopted is that generalization occurs through the successive abandonment of the basic working hypotheses of standard continuum mechanics of Cauchy, that is, the introduction of a rigidly rotating microstructure and couple stresses (Cosserat con- tinua or micropolar bodies, nonsymmetric stresses), the introduction of a truly de- formable microstructure (micromorphic bodies), “weak” nonlocalization with gra- dient theories and the notion of hyperstresses, and the introduction of characteristic lengths, “strong nonlocalization” with space functional constitutive equations and the loss of the Cauchy notion of stress, and finally giving up the Euclidean and even Riemannian material background. This evolution is paved by landmark papers and timely scientific gatherings (e.g., Freudenstadt, 1967; Udine, 1970,Warsaw, 1977)
Continuum Mechanics
Bio-Chemo-Mechanical Models of Vascular Mechanics.
Annals of biomedical engineering
2014
10.1007/s10439-014-1201-7
Models of vascular mechanics are necessary to predict the response of an artery under a variety of loads, for complex geometries, and in pathological adaptation. Classic constitutive models for arteries are phenomenological and the fitted parameters are not associated with physical components of the wall. Recently, microstructurally-linked models have been developed that associate structural information about the wall components with tissue-level mechanics. Microstructurally-linked models are useful for correlating changes in specific components with pathological outcomes, so that targeted treatments may be developed to prevent or reverse the physical changes. However, most treatments, and many causes, of vascular disease have chemical components. Chemical signaling within cells, between cells, and between cells and matrix constituents affects the biology and mechanics of the arterial wall in the short- and long-term. Hence, bio-chemo-mechanical models that include chemical signaling are critical for robust models of vascular mechanics. This review summarizes bio-mechanical and bio-chemo-mechanical models with a focus on large elastic arteries. We provide applications of these models and challenges for future work.
Heinrich hertz, posthumous book on mechanics (1894)
Landmark Writings in Western Mathematics 1640-1940
1894
677-689
2005
10.1016/B978-044450871-3/50133-9
Offering a mechanical foundation of physics that avoided force as a basic concept, Heinrich Hertz's Posthumous Book on Mechanics was the first book on mechanics to make use of Riemannian geometry in configuration space. One of the main problems that were up for debate was the role of unobservable atoms and molecules and the forces at a distance assumed to act between them. A group of positivist and phenomenologically oriented physicists and chemists believed that if physics was based on a concept of energy, it could be possible to avoid making appeal to unobservables and forces at a distance. Hertz referred to many logical problems encountered in usual mechanics, and he concluded that the concept of force was to blame for most of them. Most reviews listed the following merits: its philosophical sophistication, its rigorous mathematical structure, its avoidance of forces, and its intuitively pleasing formulation of the fundamental law of motion. As its main weakness most reviews mentioned, it is the complete neglect of the problem of how to account for the actual motion of even simple systems in nature, such as those that the usual image of mechanics describes by way of forces. © 2005 Elsevier B.V. All rights reserved.
Particle Interactions in Diffusiophoresis and Electrophoresis of Colloidal Spheres with Thin but Polarized Double Layers.
Journal of colloid and interface science
231
2
265-282
2000
10.1006/jcis.2000.7145
The diffusiophoretic and electrophoretic motions of two colloidal spheres in the solution of a symmetrically charged electrolyte are analyzed using a method of reflections. The particles are oriented arbitrarily with respect to the electrolyte gradient or the electric field, and they are allowed to differ in radius and in zeta potential. The thickness of the electric double layers surrounding the particles is assumed to be small relative to the radius of each particle and to the gap width between the particles, but the effect of polarization of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of solute ions at the outer edge of the thin double layer are used as the boundary conditions for the fluid phase outside the double layers. The method of reflections is based on an analysis of the electrochemical potential and fluid velocity disturbances produced by a single dielectric sphere placed in an arbitrarily varying electrolyte gradient or electric field. The solution for two-sphere interactions is obtained in expansion form correct to O(r(12)(-7)), where r(12) is the distance between the particle centers. Our analytical results are found to be in good agreement with the available numerical solutions obtained using a boundary collocation method. On the basis of a model of statistical mechanics, the results of two-sphere interactions are used to analytically determine the first-order effect of the volume fraction of particles of each type on the mean diffusiophoretic and eletrophoretic velocities in a bounded suspension. For a suspension of identical spheres, the mean diffusiophoretic velocity can be decreased or increased as the volume fraction of the particles is increased, while the mean electrophoretic velocity is reduced with the increase in the particle concentration. Generally speaking, the particle interaction effects can be quite significant in typical situations. Copyright 2000 Academic Press.
and gravitational or centrifugal; convection; diffusiophoresis; electrophoresis; fields; layer; particle concentration effect; problems of the colloidal; sedimen-; tation; thin but polarized double; tion; transport induced by these; two-sphere interac-
Characterization of hole-diameter in thin metallic plates perforated by spherical projectiles using genetic algorithms
Archive of Applied Mechanics
81
7
907-924
2010
10.1007/s00419-010-0459-y
The empirical and semi-empirical models available in literature for the estimation of hole-diameter in thin metallic plates by the strike of spherical projectile are mostly valid for the data for which these have been developed. This may be partly attributed to the form of the model employed for their development. The behavioural constraints and the limiting conditions are not satisfied by these models. In the present paper, some of the non-dimensionalmodels have been developed that satisfy the behavioural constraints and limiting conditions. The data used in the development of earlier statistical models has been reanalyzed for the devel- opment of new models for the characterization of hole-diameter with a view towards seeing whether better characterization is possible. The genetic algorithm coupled with the penalty functionmethod has been used for the constrained optimization of model parameters that result in low errors and high correlation coefficients.
genetic algorithm; hole-diameter; hypervelocity impact; projectile; spherical projectile
Mechanical response of thin SMAW arc welded structures: Experimental and numerical investigation
Theoretical and Applied Fracture Mechanics
51
2
87-94
2009
10.1016/j.tafmec.2009.04.004
The mechanical response of thin welded plates made of Ck45 steel during shielded metal arc welding (SMAW) is investigated by employing data from numerical results using the finite element method and laboratory experimental measurements. The aim of this paper is to investigate the effect of the thermal uncertainty encountered during the thermal numerical analysis on the out-of-plane angular distortion of the welded panels. For this purpose a comparison between the numerical mechanical response (using the calibrated and as-predicted thermal history) and the experimental results is carried out. The effect of the microstructural transformations on the angular out-of-plane distortion is also investigated by introducing the material transformation within the numerical analysis by the simplest means in order to clearly demonstrate its influence. The same strategy is followed in order to investigate the effect of low-temperature martensitic transformation on the longitudinal residual stress field by properly combining experimental and numerical results and analyzing an idealized welding fabrication. Discussion is, finally, carried out regarding the design process of welded marine structures. ?? 2009 Elsevier Ltd. All rights reserved.
On the use of thin wafers to study dynamic properties of metals
Journal of the Mechanics and Physics of Solids
13
5
311-327
1965
10.1016/0022-5096(65)90034-7
Many different impact test arrangements have been utilized to investigate the dynamic properties of metals. This paper discusses the applications and limitations of a one-dimensional theory of bar impact, particularly as it relates to a specific experimental configuration known as the ‘thin wafer’ or ‘split Hopkinson pressure-bar’ technique. An analysis of this experiment, which utilized a bilinear approximation for the stress-strain curve of the aluminium being tested, led previous investigators to demand the incorporation of strain rate effects in the constitutive relation of metals. However, the present nonlinear analysis of the same test demonstrates that the experimental data for this particular metal can be predicted from a strain rate independent theory. This new analysis indicates the influence of assumptions which neglect certain stress wave propagation phenomena. These mechanical effects are shown to be an important contribution to dynamic observations which had been attributed only to intrinsic material properties, such as strain rate dependence.
Series solutions for spatially coupled buckling anlaysis of thin-walled Timoshenko curved beam on elastic foundation
Structural Engineering & Mechanics
33
4
447-484
2009
The spatially coupled buckling, in-plane, and lateral bucking analyses of thin-walled Timoshenko curved beam with non-symmetric, double-, and mono-symmetric cross-sections resting on elastic foundation are performed based on series solutions. The stiffness matrices are derived rigorously using the homogeneous form of the simultaneous ordinary differential equations. The present beam formulation includes the mechanical characteristics such as the non-symmetric cross-section, the thicknesscurvature effect, the shear effects due to bending and restrained warping, the second-order terms of semitangential rotation, the Wagner effect, and the foundation effects. The equilibrium equations and are derived from the energy principle and expressions for displacement parameters are derived based on power series expansions of displacement components. Finally the element stiffness matrix is determined using force-deformation relationships. In order to verify the accuracy and validity of this study, the numerical solutions by the proposed method are presented and compared with the finite element solutions using the classical isoparametric curved beam elements and other researchers analytical solutions.
Advances in Computational Mechanics
Nuclear Engineering and Design
134
1
1-22
1992
10.1016/0029-5493(92)90004-F
Some of the major issues which have been addressed in finite element research are reviewed, including some issues which remain unresolved. The focus is on topics related to problems of constrained media and fluid dynamics by finite elements. Two examples of constrained media are considered: isoparametric element approaches to incompressible materials and beam and shell elements. Pertinent issues include locking, spurious singular modes, and stress oscillations. In fluid mechanics, the central themes are stable treatments of the convection or transport terms and arbitrary Lagrangian-Eulerian meshes.
diffusion-problems; equations; finite-element methods; flow; formulation; generalized galerkin methods; hyperbolic problems; quadrilateral plate elements; shell element; transverse-shear
Quantum mechanics and Yoga
Research Journal of Philosophy and Social Sciences
1
84-91
1964
The physical probabilities that occur in quantum theory can be given a metaphysical frequency interpretation in terms of the branching-universe theory; since the probability of an event can be interpreted as the proportion of branches in which the event occurs. It is possible, but fantastically improbable according to statistical mechanics that the molecules in the air surrounding a man might move in such a manner that the air pressure above him became appreciable less than the pressure below him, so that he would levitate. If by a mental act, a Yogi could affect the physical probabilities in the space around himself, not merely those in his own nervous system as in an ordinary decision, then, among other things, he might be able to cause himself to levitate. ((c) 1997 APA/PsycINFO, all rights reserved)
Affect; Hi; Yoga
Nonlinear continuum mechanics for finite element analysis
Book
248
1997
Bonet and Wood present a unified treatment of nonlinear continuum analysis and finite element techniques.
Statistical Algebraic Approach to Quantum Mechanics
Theoretical and Mathematical Physics
129
1
1385-1397
2001
10.1023/A:1012419528129
A scheme for constructing quantum mechanics not based on the Hilbert space and linear operators as primary elements of the theory is proposed. A particular variant of the algebraic approach is discussed. The elements of a noncommutative algebra (i.e., the observables) and the nonlinear functionals on this algebra (i.e., the physical states) serve as the primary components of the theory. The functionals are associated with the results of a single measurement. The ensembles of physical states are suggested for the role of quantum states in the standard quantum mechanics. It is shown that the mathematical formalism of the standard quantum mechanics can be fully recovered within this scheme.
Mechanics of reinforced soil
Canadian Geotechnical Journal
38
6
1366
2001
10.1139/cgj-38-6-1366
This text presents the mechanical aspects of reinforced soil (RS) behaviour. Beginning with simple reinforced soil models, it discusses various aspects of this material, such as properties of its constituents, and stresses and strains in reinforced soil, up to the more complex analysis of RS structures. Its scope and level ensures it will be a valuable resource for students, academics and geotechnical engineering professionals alike.
Lie algebroids and Mechanics
AIP Conference Proceedings
1130
3-33
2009
10.1063/1.3146237
The category of Lie algebroids has proved useful in the formulation of problems in applied mathematics, algebraic topology, and differential geometry. In the context of Mechanics, Alan Weinstein proposed a program for the formulation of Lagrangian and Hamiltonian systems on Lie algebroids. In this course, I will review recent results about such formalism, including a symplectic and a variational description, and several extensions developed in recent years by many authors. Applications to the reduction of such systems will be presented. © 2009 American Institute of Physics.
Lagrange-poincaré equations; Lagrangian and Hamiltonian mechanics; Lie algebroids; Optimal control; Reduction of dynamical systems; Variational calculus
Mechanics of parallel fibre bundles
Fibres and Textiles in Eastern Europe
14
23-28
2006
his theoretical work deals with the mechanics of parallel fibre bundles, on the basis of the fact that each fibre in the bundle possesses different tensile behaviours. As a consequence of this, the tensile behaviour of a blended fibre bundle is found to be different than that obtained from Hamburger theory [3]. It is also observed that the average force per fibre in the bundle, the breaking force utilisation coefficient, and the breaking strain ulilisation coefficient depend only on the coefficient of variation of the fibre breaking strain.
Nilpotent quantum mechanics and SUSY
Physics of Particles and Nuclei Letters
8
3
279-281
2011
10.1134/S154747711103006X
Formalism where fundamental variables are nilpotent, but in contrast to the super-mathematics, not anticommutative but commutative gives another version of realization of the Pauli exclusion principle. We discuss some aspects of nilpotent quantum mechanics realized in generalized Hilbert space of functions of nilpotent commuting variables. The qubits are natural objects described by such a formalism. Supersymmetric system of qubit and fermion is presented.
Hermeneutics, underdetermination and quantum mechanics
Science & Education
4
2
137-146
1995
10.1007/BF00486581
There exists an essential underdetermination in the interpretation of the formalism of quantum mechanics and this extends even to the question of whether or not physical phenomena at the most fundamental level are irreducibly and ineliminably indeterministic or absolutely deterministic. This is true in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics. This lends support to Martin Eger's analysis of a role for hermeneutics in science education.
Mechanics of type IV tympanoplasty: experimental findings and surgical implications
Ann Otol Rhinol Laryngol
106
1
49-60
1997
In a type IV tympanoplasty, the stapes footplate is directly exposed to incoming sound while the round window is "shielded," usually with a fascia graft. Postoperative hearing results are quite variable, with air-bone gaps ranging from 10 to 60 dB. A cadaveric human temporal bone preparation was developed to investigate the middle ear mechanics of this operation to identify causes of variable results and to test predictions of a recently described theoretic model of type IV tympanoplasty. The ear canal, tympanic membrane, malleus, and incus were removed so as to expose the stapes and round window to the sound stimulus. A "cavum minor" chamber (air space adjacent to the round window) was constructed around the round window niche. The round window could be isolated from sound by placing an acoustic shield over this chamber. The mechanical properties of the shield, cavum minor, annular ligament, and round window membrane were varied experimentally. Stapes velocity as determined by an optical motion sensor was used as a measure of hearing level. The largest stapes velocity occurred with a mobile stapes and round window, a stiff shield, and a well-aerated cavum minor. Partial fixation of the stapes or round window caused a decrease in stapes velocity. Acoustic shields of conchal cartilage or Silastic silicone rubber sheeting (approximately 1 mm thick) provided near-optimal shielding. A temporalis fascia shield resulted in a stapes velocity 10 to 20 dB less than that seen with a cartilage or Silastic silicone rubber shield at low frequencies. A cavum minor air space as small as 16 microL was sufficient for unrestricted stapes motion, provided the air was in contact with the round window membrane. These results qualitatively matched predictions of our model, but there were some quantitative differences. The clinical implications of our results are that in order to optimize postoperative hearing, the surgeon should 1) preserve normal stapes mobility, preferably by covering the footplate with a very thin split-thickness skin graft, not a fascia graft; 2) reinforce a fascia shield with cartilage or Silastic silicone rubber; 3) create conditions that promote aeration of the round window niche; and 4) preserve the mobility of the round window membrane.
Adult; Aged; Biomechanics; Ear, Middle/anatomy & histology/physiology/*surger; Electric Impedance; Humans; Ligaments/physiology; Materials Testing; Middle Aged; Models, Biological; Oval Window, Ear/physiology; Pressure; Reference Values; Round Window, Ear/physiology; Silicone Elastomers; Stapes/physiology; Tympanoplasty/instrumentation/*methods
Generalized Stosszahlansatz and associated H-theorem in nonextensive statistical mechanics
Mathematics and Computers in Simulation
72
2-6
72-78
2006
10.1016/j.matcom.2006.05.004
Nonextensive statistical mechanics based on the maximum Tsallis entropy principle and its physical backgrounds are summarized. The Boltzmann equation with a generalized form of Stosszahlansatz and the associated H-theorem are proposed and analyzed in order to examine if relaxation of a nonextensive system to the maximum Tsallis entropy state can be kinetically described. ?? 2006 IMACS.
Generalized H-theorem; Generalized Stosszahlansatz; Nonextensive statistical mechanics
Econophysics: from game theory and information theory to quantum mechanics
Physica A: Statistical Mechanics and its Applications
348
505-543
2005
10.1016/j.physa.2004.09.029
Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the Quantum Mechanics principles. using Information and Game Theory. (C) 2004 Elsevier B.V. All rights reserved.
energy; information; optimal laws; quantum mechanic laws; rationality
Canonical transformations and the Hamilton-Jacobi theory in quantum mechanics
Canadian Journal of Physics
77
6
411-425
1999
10.1139/p99-048
We investigate two methods of constructing a solution of the Schr\"{o}dinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"{o}dinger equation from linear canonical transformations, the other focuses on the generating function which satisfies the Hamilton-Jacobi equation in classical mechanics. We also show that these two methods lead to the same solution of the Schr\"{o}dinger equation.
Is pseudo-Hermitian quantum mechanics an indefinite-metric quantum theory?
Czechoslovak Journal of Physics
53
11
1079-1084
2003
10.1023/B:CJOP.0000010537.23790.8c
With a view to eliminate an important misconception in some recent publications, we give a brief review of the notion of a pseudo-Hermitian operator, outline pseudo-Hermitian quantum mechanics, and discuss its basic difference with the indefinite-metric quantum mechanics. In particular, we show that the answer to the question posed in the title is a definite No.
Indefinite metric; Klein-Gordon field; Pseudo-Hermitian; PT-symmetry
Three Essential Reasons Why Nature Chose Quantum Mechanics
Organization
1-5
2012
We discuss the reason why quantum mechanics is chosen as the most basic law of nature. Probability amplitude, which becomes a probability density after square it, is considered as one of the most essential ingredient of quantum mechanics. Code transfer experiments based on the probability amplitude is proved to be i) error of code transfer is minimum, ii) that error is independent of coding parameters and iii) non-trivial and non-local correlation is possible.
3D Integration of electronics and mechanics
Proceedings of the International Symposium and Exhibition on Advanced Packaging Materials Processes, Properties and Interfaces
2005
5-8
2005
10.1109/ISAPM.2005.1432035
Nowadays, the design is one of the key features for all consumer products. All the novel functions must be available inside fashionable covers. However, the most interesting product shapes are not always possible due the restriction of the traditional rigid printed wiring board (PWB). To achieve a real design freedom, a formable multilayer PWB structure is needed. This paper introduces the three-dimensional printed wiring board and the 3D integration of electronics and mechanics. The 3D integration of electronics and mechanics increases design freedom and space utilization efficiency e.g. in portable devices. The 3D integration technology is enabled by thermoplastic PWB material innovations and a new kind of system integration process. Thermoplastics are formable and they are widely used in many fields, but as a substrate for a multilayer PWB, they are rather new. Furthermore, this paper discusses the benefits and challenges of the 3D integration of electronics and mechanics and the special characteristics of its system design process. Integration of electronics and mechanics has an effect on the design process management. Design phases must be coherent and teamwork needs to be well organized. In addition, special requirements for testing are presented.
Retrocausal quantum mechanics: Maudlin's challenge revisited
Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
44
4
442-449
2013
10.1016/j.shpsb.2013.09.004
In 1994, Maudlin proposed an objection to retrocausal approaches to quantum mechanics in general, and to the transactional interpretation (TI) in particular, involving an absorber that changes location depending on the trajectory of the particle. Maudlin considered this objection fatal. However, the TI did not die; rather, a number of responses were developed, some attempting to accommodate Maudlin's example within the existing TI, and others modifying the TI. I argue that none of these responses is fully adequate. The reason, I submit, is that there are two aspects to Maudlin's objection; the more readily soluble aspect has received all the attention, but the more problematic aspect has gone unnoticed. I consider the prospects for developing a successful retrocausal quantum theory in light of this second aspect of the objection. ?? 2013 Elsevier Ltd.
Advanced action; Quantum mechanics; Retrocausal quantum mechanics; Time-symmetric quantum mechanics; Transactional interpretation
Fluid Mechanics
Refrigeration And Air Conditioning
6
e18068
2010
http://dx.doi.org/10.1016/j.rser.2004.09.010
Dental thermal pain is a significant health problem in daily life and dentistry. There is a long-standing question regarding the phenomenon that cold stimulation evokes sharper and more shooting pain sensations than hot stimulation. This phenomenon, however, outlives the well-known hydrodynamic theory used to explain dental thermal pain mechanism. Here, we present a mathematical model based on the hypothesis that hot or cold stimulation-induced different directions of dentinal fluid flow and the corresponding odontoblast movements in dentinal microtubules contribute to different dental pain responses. We coupled a computational fluid dynamics model, describing the fluid mechanics in dentinal microtubules, with a modified Hodgkin-Huxley model, describing the discharge behavior of intradental neuron. The simulated results agreed well with existing experimental measurements. We thence demonstrated theoretically that intradental mechano-sensitive nociceptors are not "equally sensitive" to inward (into the pulp) and outward (away from the pulp) fluid flows, providing mechanistic insights into the difference between hot and cold dental pain. The model developed here could enable better diagnosis in endodontics which requires an understanding of pulpal histology, neurology and physiology, as well as their dynamic response to the thermal stimulation used in dental practices.
An Analysis of the System Effects in Woven Fabrics Under Ballistic Impact
Textile Research Journal\rText. Res. J.
62
9
1992
Article
Following a brief review of prior work on fabric-based armor systems, the system effects that occur during the ballistic impact of woven fabric body armor materials are discussed from a conceptual framework developed to relate single yam impact mechanics to fabric impact mechanics. The consequence of assembling yams into single-ply fabric structures is discussed from this perspective. A steep strain gradient along yams in the region of the transverse deflection of the fabric is related to the constraint imposed on them by neighboring yams. Striking and residual velocity data, collected for single-ply fabric systems of Spectra(R), Kevlar(R) 29, and nylon with various different yam deniers and weave types, are used to establish the response of spaced armor systems. The system effects of assembling fabric plies into body armor systems are determined by comparing the response of spaced armor systems to actual multiple-ply systems. There is a pronounced decrease in energy absorption capacity for the Spectra and nylon systems; this deleterious effect is ascribed to increased transverse stresses and possible interference of the deflection characteristics of fabric plies by subsequent plies.
Mechanics of swimming in water-beetles
Society for Experimental Biology Seminar Series
107-124
1980
Drag generated systems and thrust generating mechanisms in the swimming movements of water beetles are discussed.
Kinetic approach to lattice quantum mechanics
Cellular Automata, Proceedings
2493
114-122
2002
We discuss some lattice discretizations of the Klein-Gordon equation inspired by analogies with discrete kinetic theory.
boltzmann-equation
Contextual deterministic quantum mechanics
International Journal of Modern Physics B
1-7
2000
We present a simple proof of quantum contextuality for a spinless particle with a one dimensional configuration space. We then discuss how the maximally realistic determin- istic quantum mechanics recently constructed by this author and V. Singh can be applied to different contexts.
Fluid mechanics, Volume 10
Boston: McGraw-Hill Book Company
872
2008
2001086884
Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situationswhether in the liquid or gaseous state or ...
Fracture Mechanics in Switzerland
Material und Technik
1
17-20
1982
Research and appiication o/fracture mechanics in Switzerland are briefly discussed; the proper re/cTences, including the addresses 0/ the concerned laboratories are given.
Fracture; Mechanic; research
Mechanics not on a manifold
J. Phys. A: Math. Gen
42
4
45302
2009
10.1088/1751-8113/42/4/045302
The free scalar field is studied on the Y-junction of three semi-infinite axes which is the simplest example of a non-manifold space. It is shown that the transition rules for this system uniquely follow from conservation of energy and charge. A discrete version of the model gives the same result.
Classical Extensions, Classical Representations and Bayesian Updating in Quantum Mechanics
Arxiv preprint quantph0403055
Section 5
14
2004
I review the formalism of classical extensions of quantum mechanics introduced by Beltrametti and Bugajski, and compare it to the classical representations discussed e.g. by Busch, Hellwig and Stulpe and recently used by Fuchs in his discussion of quantum mechanics in terms of standard quantum measurements. I treat the problem of finding Bayesian analogues of the state transition associated with measurement in the canonical classical extension as well as in the related 'uniform' classical representation. In the classical extension, the analogy is extremely good.
Statistical mechanics of dictionary learning
EPL (Europhysics Letters)
103
2
28008
2013
10.1209/0295-5075/103/28008
Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.
Dynamical Symmetries and Nambu Mechanics
Lett. Math. Phys.
36
2
117-126
1996
10.1007/BF00714375
It is shown that several Hamiltonian systems possessing dynamical or hidden symmetries can be realized within the framework of Nambu's generalized mechanics. Among such systems are the SU(n)-isotropic harmonic oscillator and the SO(4)-Kepler problem. As required by the formulation of Nambu dynamics, the integrals of motion for these systems necessarily become the so-called generalized Hamiltonians. Furthermore, in most of these problems, the definition of these generalized Hamiltonians is not unique.
Introduction to Modern Statistical Mechanics
New York
1
288
1987
Leading physical chemist David Chandler takes a new approach to statistical mechanics to provide the only introductory-level work on the modern topics of renormalization group theory, Monte Carlo simulations, time correlation functions, and liquid structure. The author provides compact summaries of the fundamentals of this branch of physics and discussions of many of its traditional elementary applications, interspersed with over 150 exercises and microcomputer programs.
The mechanics of human walking
Advances in Psychology
78
167-186
1991
10.1016/S0166-4115(08)60742-6
This chapter illustrates the general principles on which the mechanics of walking are based. Using an analysis of the energy variations of the total body center of gravity, an interpretation key of the animal locomotion strategy associated with different gaits is presented. The discussion proceeds by tackling the problem of the identification of the objective functions which the locomotor strategy is required to optimize. A more detailed analysis leading to the description and interpretation of individual musculo-skeletal functions is then presented.
Biofluid mechanics and the circulatory system
Technology and Health Care
19
3
205-215
2011
10.3233/THC-2011-0623
A fluid is a medium which deforms, or undergoes motion, continuously under the action of a shearing stress and includes liquids and gases. Applying biofluid mechanics to the cardiovascular system requires knowledge of anatomy and geometry, pressure data and blood flow, volume and velocity measurements. A good example is the assessment of the haemodynamics of biological and mechanical heart valves.
Bernoulli; Doppler measurement; effective orifice area and performance index; heart valve; laminar flow; Pressure gradient; regurgitation; Reynolds number; turbulent flow
The Mechanics of the counterpart relation
Studies in health technology and informatics
152
13-26
1992
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
An Experimental Study on the Effect of Curvature-Rate at Preloading Stage on Subsequent Creep or Relaxation of Thin-Walled Tubes under Pure Bending
JSME International Journal, Series A: Mechanics and Material Engineering
41
4
525-531
1998
Pure bending with a constant curvature-rate followed by creep (hold constant moment for a period of time) or relaxation (hold constant curvature for a period of time) tests were conducted to investigate the effect of prior curvature-rate at preloading stage on the subsequent creep or relaxation behavior. Thin-walled tubes of 304 stainless steel were used in this investigation. The curvature-ovalization measurement apparatus, designed by Pan et al.(1), was used for conducting the present experiments. It has been found that the curvature-rate at the preloading stage has a strong influence on the subsequent creep or relaxation deformation under pure bending.
Bending (deformation); Creep; Curvature rate; Curvature-Rate; Load testing; Pure Bending; Relaxation; Stress relaxation; Thin-Walled Tube; Thin-walled tubes; Tubes (components)
[Class II mechanics and overbite].
L' Orthodontie française
71
3
249-54
2000
Class II mechanics are supposed to affect the vertical balance of the face when they are used in hyperdivergent patterns. We carried out a study about class II mechanics effects on 100 patients; 50 of them are hyperdivergent (GoGn/SN > or = 37), and 50 non-hyperdivergent. They all were treated with an Edgewise appliance without any high pull head gear. The authors showed that GoGn/SN angles and Occ/SN tend to be lessened in a skeletal open-bite population. Thus, Class II mechanics can be prescribed in any vertical facial pattern.
Cephalometry; Humans; Malocclusion; Malocclusion, Angle Class II; Malocclusion, Angle Class II: therapy; Malocclusion: therapy; Orthodontic Appliances; Orthodontic Appliances: contraindications; Orthodontic Appliances: utilization; Vertical Dimension
Quantum Mechanics and Black Holes
Scientific American
236
1
7
2005
The motion of a particle near the RN black hole horizon is described by conformal mechanics. Models of this type have no ground state with vanishing energy. This problem was resolved in past by a redefinition of the Hamiltonian which breaks translational time invariance but gives a normalizable ground state. We show that this change of the Hamiltonian is a quantum mechanical equivalent of the change of coordinates near the black hole horizon removing the singularity. The new Hamiltonian of quantum mechanics is identified as an operator of a rotation between 2 time-like coordinates of the adS hypersurface which translates global time. Therefore conformal quantum mechanics may eventually help to resolve the puzzles of the classical black hole physics.
CAUSALITY, SYMMETRIES AND QUANTUM MECHANICS
arXiv
15
5
415-438
2001
10.1023/A:1023918429687
It is argued that there is no evidence for causality as a metaphysical\nrelation in quantum phenomena. The assumption that there are no causal laws,\nbut only probabilities for physical processes constrained by symmetries, leads\nnaturally to quantum mechanics. In particular, an argument is made for why\nthere are probability amplitudes that are complex numbers, which obey the Born\nrule for quantum probabilities. This argument generalizes the Feynman path\nintegral formulation of quantum mechanics to include all possible actions that\nare allowed by symmetries, but only the lowest order terms are observable at\nthe presently accessible energy scales. The notion of relational reality is\nintroduced in order to give physical meaning to probabilities. This appears to\ngive rise to a new interpretation of quantum mechanics.
General Physics
Macroscopic Fracture MEchanics of Advanced Composite Materials
Journal of Composite Materials
5
446-455
1971
10.1177/002199837100500402
The application of classical fracture mechanics to laminated composites is discussed. A convenient method is presented for predicting the static strength of a flawed specimen. Theoretical predictions are compared with experimental data for specimens containing two types of ftaws.
Erwin Schrödinger and the rise of wave mechanics. II. The creation of wave mechanics
Foundations of Physics
17
12
1141-1188
1987
10.1007/BF01889592
Abstract This article (Part II) deals with the creation of the theory of wave mechanics by Erwin Schrödinger in Zurich during the early months of 1926; he laid the foundations of this theory in his first two communications toAnnalen der Physik. The background of Schrödinger's work on, and his actual creation of, wave mechanics are analyzed.
MECHANICS OF MATERIALS 2
Studies in health technology and informatics
152
1997
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
Biocompatible Materials; Biocompatible Materials: chemistry; Biological; Biomechanics; Biomedical Engineering; Chemical; Models; Physics
Theoretical and Applied Mechanics
Theoretical and Applied Mechanics
387-398
1985
10.1016/B978-0-444-87707-9.50030-0
The dynamical analysis of vehicles results in complex systems including the excitation process due to the guideway, the vehicle itself and the evaluation of the passenger response to mechanical motion. The vehicle is modeled as a linear or nonlinear multibody system, the road represents a stochastic process of white or colored noise and the passenger's frequency response follows from biomechanics. The resulting dynamical system is investigated by the covariance analysis.
Quantum Mechanics without amplitudes
Quantum
11
2004
Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities capable of give full account to quantum phenomena. Advanteges of this formulation are the evidence of physical processes not described by the orotodox formulation using amplitudes and the possibility of a full algoritimization of Quantum Mechanics.
quantum physics
MECHANICS AND VIBRATIONAL
Journal of Molecular Structure
144
215-223
1986
Structural and vibrational been determined by combined properties molecular for the high energy s-trans conformers of CH3COCl, CH3COOH and CH3COOCH3 mechanics and vibrational of CH3COOH and CH3COOCH3 have studies. New data are reported and the torsional mode of CH3COCl is identified.
Relativistic Quantum Mechanics
Proceedings of the Royal Society of London. Series A
1932
Relativistic Quantum Mechanics. 455 the wave equation of quantum theory. This suggests deep-lying connections and possibilities for simplification and unification which are entirely lacking in the Heisenberg-Pauli theory. In
Fatigue damage accumulation in notched woven-ply thermoplastic and thermoset laminates at high-temperature: influence of matrix ductility and fatigue life prediction
International Journal of Fatigue
80
1-9
2015
10.1016/j.ijfatigue.2015.04.019
This work was aimed at investigating the influence of matrix ductility on the high-temperature tensile fatigue behaviour in notched and unnotched C/PPS (thermoplastic) and C/Epoxy (thermoset) laminates. Damage mechanisms and overstress accommodation near the hole have been discussed by means of X-rays observations and fractography analysis. In order to quantitatively evaluate the fatigue damage within notched and unnotched laminates as a function of the cycles, a damage variable based on a mean strain calculated on each cycle from the experimental stress–strain loops has been used. Finally, a simple analytical model was applied to test its predictive capabilities to evaluate the fatigue damage accumulation in both materials. This model proved to be relevant to predict the evolution of fatigue damage in notched C/PPS composites but not in C/Epoxy laminates.
Fatigue; High temperature; Stress concentrator; Thermoplastic; Thermoset
Universal quantum mechanics
Physical Review D
78
8
15
2008
10.1103/PhysRevD.78.084004
If gravity respects quantum mechanics, it is important to identify the essential postulates of a quantum framework capable of incorporating gravitational phenomena. Such a construct likely requires elimination or modification of some of the "standard" postulates of quantum mechanics, in particular those involving time and measurement. This paper proposes a framework that appears sufficiently general to incorporate some expected features of quantum gravity. These include the statement that space and time may only emerge approximately and relationally. One perspective on such a framework is as a sort of generalization of the S-matrix approach to dynamics. Within this framework, more dynamical structure is required to fully specify a theory; this structure is expected to lack some of the elements of local quantum field theory. Some aspects of this structure are discussed, both in the context of scattering of perturbations about a flat background, and in the context of cosmology.
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Quantum Physics
Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid mechanics
Journal of the Physical …
2011
... 113703 : μSR Evidence of Nonmagnetic Order and 141Pr Hyperfine-Enhanced Nuclear Magnetism in the Cubic Γ3 Ground Doublet System PrTi2Al20 Takashi U. Ito, Wataru Higemoto, Kazuhiko Ninomiya, Hubertus Luetkens, Christopher Baines, Akito Sakai, and Satoru ... \n
Mechanics of single peptide hydrogelator fibrils
Nanoscale
2015
10.1039/C4NR07657E
The rigidity of peptide fibers is essential for their chemical and biological functions, despite that it remains largely unexplored. Here, we present the first direct measurement of the mechanics of individual fibers in peptide hydrogels by AFM imaging and statistical analysis and find that the intermolecular interactions play a considerable role.
Quasi-hermitian Quantum Mechanics in Phase Space
Journal of Mathematical Physics
48
10
1-42
2007
We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.
Concepts of hyperbolicity and relativistic continuum mechanics
Lect.Notes Phys.
692
101-116
2006
10.1007/11550259_5
After a short introduction to the characteristic geometry underlying weakly hyperbolic systems of partial differential equations we review the notion of symmetric hyperbolicity of first-order systems and that of regular hyperbolicity of second-order systems. Numerous examples are provided, mainly taken from nonrelativistic and relativistic continuum mechanics.
Noether’s theorem in discrete classical mechanics
American Journal of Physics
56
2
174
1988
10.1119/1.15700
A derivation of Noether’s theorem in discrete classical mechanics from the invariance properties of the action is given. This derivation closely parallels the one given in classical field theory and emphasizes the fact that the involved symmetry transformations act on paths rather than on space and time points. Several illustrative examples are also presented.
03 - Society from the Statistical Mechanics Perspective
Applications of Mathematics in Models, Artificial Neural Networks and Arts
89-98
2010
10.1007/978-90-481-8581-8_3
This chapter presents an introduction to social modeling with statistical mechanics. An elementary description of spin systems is given first, then we explain how this description has been applied to binary models of the social sciences that have implications for public policies. Next we suggest other applications to research in the social sciences.
Bohmian mechanics with discrete operators
Journal of Physics A: Mathematical and General
37
44
L547
2004
A deterministic and time reversible Bohmian mechanics for operators with continuous and discrete spectra is presented. Randomness enters only through initial conditions. Operators with discrete spectra are incorporated into Bohmian mechanics by associating with each operator a continuous variable in which a finite range of the continuous variable corresponds to the same discrete eigenvalue. In this way a deterministic and time reversible Bohmian mechanics can handle the creation and annihilation of particles. The formalism does not depend on the details of the Hamiltonian. Furthermore, many consistent choices are available for the dynamics. Examples are given and generalizations are discussed.
Engineering Rock Mechanics Part II
Engineering Rock Mechanics Part II
231-245
2000
10.1016/B978-008043010-2/50015-0
When designing a structure to be built on or in a rock mass, it is necessary not only to consider individual factors, such as the intact rock, fractures, rock stress, permeability, excavation and support, but also how these all interact together. As a means of linking the rock mechanics principles to the rock engineering applications, it is appropriate to consider how such interactions can be characterized. For rock mechanics modeling and rock engineering design for a specific project, one needs to be able to identify the relevant physical variables and the linking mechanisms, and then consider their combined operation.
Fluid mechanics and intestinal transit
Gastroenterology
88
3
858
1985
Applies model for particle flow which takes into account the fluid machanics.
flow rate; GI transit; intestinal transit; particle size; viscosity
Quantum mechanics: principles and formalism
The International encyclopedia of physical chemistry and chemical physics Topic 2: Classical and quantum mechanics,
1
xii, 155 p.
1972
Concerned strictly with the principles and formalism of quantum mechanics, this graduate student-oriented volume develops the subject as a fundamental discipline. Opening chapters review the origins of Schrdinger's equations and the nature of the solutions in certain simple and well-known cases, advancing to the ideas associated with vector spaces. Having provided students with the appropriate mathematical language, the author proceeds to the formulation of the main principles of quantum mechanics and their immediate consequences. The book concludes with final generalizations in which alternative "languages" or representations are discussed (each with reference to its specific advantages and applications), and the Dirac transformation theory is developed and explained. 1972 ed. 15 Figures.
Quantum theory.
Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory
Journal of Physics: Conference Series
67
1
012035
2007
10.1088/1742-6596/67/1/012035
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic\r quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant\r Bohmian equations for particle trajectories, the problem of particle creation and destruction, the\r Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and\r strings based on the De Donder-Weyl covariant canonical formalism.
Mechanics of capsulorhexis.
Journal of cataract and refractive surgery
18
6
623-628
1992
10.1016/S0886-3350(13)80456-7
Continuous (central, circular) curvilinear capsulorhexis (CCC), first introduced by Gimbel and Neuhann, has become increasingly popular, especially for endolenticular phacoemulsification with intracapsular intraocular lens implantation. The principles of simple mechanics are used to facilitate teaching the procedure and to reduce the incidence of complications. A safe and simple method of performing CCC based on these principles is described.
a; bi; c; d; f; hanics of capsulorhexis; iq; iriech; lj; m; r; s; steve arshinoff; t; tr; ulat
Statistical Mechanics, 2nd Edition
Statistical Mechanics
512
1987
Unlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition.
Strain-energy release rate analysis of delamination in a tapered laminate subjected to a tension load
Journal of Composite Materials
25
118-41
1991
10.1177/002199839102500201
Finite element method was used to analyze a tapered glass/epoxy composite laminate subjected to a tension load, in order to determine the interlaminar stress distributions the strain-energy release rate for the delamination growth that may occur due to ply drops. In a laminate having a typical configuration of a helicopter hub, the (+/- 45)3 plies were dropped in three distinct steps, each 20-ply thickness apart, with the resulting taper angle of 5.71 deg. Delaminations were assumed to initiate at the bottom of the taper on the -45/+45 interface, and the delamination growth was simulated along the taper and into the thin region. The results of the analysis indicated that a delamination initiating at the end of the taper will grow unstably along the taper and the thin laminate simultaneously.
Hydrodynamic Model of Quantum Mechanics
Physical Review D
1
8
2278-2285
1970
10.1103/PhysRevD.1.2278
An analysis of typical microphysical systems is presented in the hydrodynamic formulation of quantum mechanics. The emphasis is on the physical peculiarities appearing in the hydrodynamic picture, and on the mathematical treatment of the nonlinear quantum-hydrodynamic field equations. Further, quantum-hydro-dynamic uncertainty relations are derived, which relate the minimum uncertainty products to the interior quantum stresses.
Numerical techniques in matrix mechanics
Journal of Computational Physics
2
2
90-113
1967
10.1016/0021-9991(67)90028-9
We present, with numerical examples, several approximation techniques for solving some model problems in quantum mechanics. The emphasis is on matrix representations rather than differential or integral equations. Some of the methods are already known (extensions of the variational principle) and others are believed to be novel.
Non-equilibrium in Stochastic Mechanics
Journal of Physics: Conference Series
361
012017
2012
10.1088/1742-6596/361/1/012017
The notion of non-equilibrium, in the sense of a particle distribution other than ρ=|Ψ|^2, is imported into Nelson's stochastic mechanics, and described in terms of e ective wavefunctions obeying non-linear equations. These techniques are applied to the discussion of non-locality in non-linear Schrodinger equations.
Statistical mechanics of optimization problems
Physica A
365
1
2006
Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the presentation I will describe in details the problems related to the coloring of a random graph.
ALEKSANDRAS ČYRAS AND OPTIMIZATION IN STRUCTURAL MECHANICS
Journal of Civil Engineering and Management
8
1
4-33
2002
10.1080/13923730.2002.10531246
Abstract The study describes how in Lithuania (mostly in Vilnius) during some past decades a new trend of investigations in structural mechanics thanks to Aleksandras ?yras' (1927?2001) research and organisational activities has been developed. The main distinguished features of the trend are: application of mathematical programming, and especially the duality theory, to the optimization of elastic-plastic and other structures, formulation of mathematical models of structural mechanics problems, elaborating algorithms and programmes for their solution. The advantages of the research results are shown, a large information concerning the publication of the results and the evolution of investigations initiated by A. ?yras are presented. Abstract The study describes how in Lithuania (mostly in Vilnius) during some past decades a new trend of investigations in structural mechanics thanks to Aleksandras ?yras' (1927?2001) research and organisational activities has been developed. The main distinguished features of the trend are: application of mathematical programming, and especially the duality theory, to the optimization of elastic-plastic and other structures, formulation of mathematical models of structural mechanics problems, elaborating algorithms and programmes for their solution. The advantages of the research results are shown, a large information concerning the publication of the results and the evolution of investigations initiated by A. ?yras are presented.
elastic-plastic structures; mathematical programming; shake- down; strain hardening; structural mechanics in Lithuania; structural optimization
Differential Structures - the Geometrization of Quantum Mechanics
arXiv
13
2005
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor understanding of the geometrical character of quantum mechanics. In Einstein's theory gravitation is expressed by geometry of space-time, and the solutions of the field equation are invariant w.r.t. a certain equivalence class of reference frames. This class can be characterized by the differential structure of space-time. We will show that matter is the transition between reference frames that belong to different differential structures, that the set of transitions of the differential structure is given by a Temperley-Lieb algebra which is extensible to a $C^{*}$-algebra comprising the field operator algebra of quantum mechanics and that the state space of quantum mechanics is the linear space of the differential structures. Furthermore we are able to explain the appearance of the complex numbers in quantum theory. The strong relation to Loop Quantum Gravity is discussed in conclusion.
Application of mechanics to machine design
Journal of Engineering Education
20
5
563-570
1930
Methods of application of analytical mechanics and strength of materials in course at University of Illinois.
Education; Machine design
Development of some concepts of mechanics
Journal of Engineering Education
28
8
563-570
1938
Development of two concepts, those of equilibrium and those of motion of bodies, presented. Before Soc Promotion Eng Education.
Mechanics
Generalized stochastic mechanics on Riemannian manifolds
Letters in Mathematical Physics
4
3
475-483
1980
10.1007/BF00943434
Dankel's stochastic mechanics on Riemannian manifolds is generalized such that the diffusion constant becomes a free parameter in the theory.
Refining the comparison theorem of quantum mechanics
Journal of Physics A: Mathematical and General
25
16
4459-4469
1992
10.1088/0305-4470/25/16/021
Options for access to Refining the comparison theorem of quantum mechanics
{Distribution Functions in Classical and Quantum Mechanics}
rogress of Theoretical Physics Supplement
98
109-156
1989
{The correspondence between classical and quantum mechanics is an important subject for the better understandings of â? quantum chaosâ?. In particular, it is very important to investigate the correspondence between distribution functions in classical mechanics and in phase space representation of quantum mechanics. This is the review of our recent progresses in the study of distribution functions in classical and quantum mechanics, namely distribution functions in classical mechanics and in coarse-grained classical mechanics as well as the Wigner function and the Husimi function. Topics dealt with include formulations of the Wigner representation, the Husimi representation and coarse-grained classical mechanics, and their applications to the analyses of the eigenstates and time developments of the distribution functions.}
Non-linear progressive failure analysis of laminated composite plates
International Journal of Non-Linear Mechanics
30
5
629-649
1995
10.1016/0020-7462(94)00041-8
A progressive failure algorithm is developed where the Generalized Layerwise Plate Theory (GLPT) of Reddy is used for the kinematic description and the material is modeled as a stable progressively fracturing solid. The geometric non-linearity is taken into account in the von Kármán sense, and the extensibility of transverse normals is included in the finite element formulation. The progressive failure algorithm is used to study the effect of the geometric non-linearity, span-to-depth ratio, lamination sequence and the boundary conditions at the supports on the first-ply and the ultimate failure loads of composite laminates in bending. In addition, a new stiffness reduction scheme is proposed, in which stiffness properties of the failed element is reduced gradually, resulting in partial unloading depending on the amount of damage it accumulates.
Delamination and debonding of materials
ASTM Stp
189
1985
10.1016/0010-4361(87)90014-0
The general topics consist of stress analysis, mechanical behavior, and fractography/NDI of composite laminates. Papers are presented on a dynamic hybrid finite-element analysis for interfacial cracks in composites, energy release rate during delamination crack growth in composite laminates, matrix deformation and fracture in graphite-reinforced epoxies, and the role of delamination and damage development on the strength of thick notched laminates. In addition, consideration is given to a new ply model for interlaminar stress analysis, a fracture mechanics approach for designing adhesively bonded joints, the analysis of local delaminations and their influence on composite laminate behavior, and moisture and temperature effects on the mixed-mode delamination fracture of unidirectional graphite/epoxy.
Wind-driven ocean circulation and equilibrium statistical mechanics
Journal of Marine Research
1989
10.1357/002224089785076235
Abstract: In this paper, we show that numerical solutions of the single-layer quasigeostrophic equation in a beta-plane basin approach the state predicted by equilibrium statistical mechanics when the forcing and dissipation are (unrealistically) zero. This equilibrium ... \n
THE MECHANICS OF HUMAN SMOOTH PURSUIT EYE MOVEMENT
The Journal of physiology
180
3
569-591
1965
10.1113/jphysiol.1965.sp007718
Page 1. ;180;569-591 . . DA movement. The mechanics of human smooth pursuit eye This information is current as of March 10, 2008
Engineering mechanics : statics
Topic report / European Environment Agency
no 157
v.
1999
Table of contents, abstracts and full-text articles (PDF only), 1999-
1819-1891; 1939-1945 Engineering and construction; 1939-1945 Pictor; Accident Prevention Periodicals.; Accidents; Agriculture Sciences Soil Chemistry; Airplanes Design and construction Drawings.; Airplanes Design and construction Drawings History; Airplanes Motors Design and construction Drawings; Airplanes Motors Design and construction Drawings.; Air pollutants European Union countries.; Air Pollution.; Air Pollution Environmental aspects European Union; Air pollution European Union countries.; Air Pollution Great Britain Measurement.; Air Pollution Health aspects.; Air Pollution Mathematical models Congresses.; Air Pollution Meteorological aspects.; Air Pollution Physiological effects.; Air Pollution United States History.; Air Purification.; Air quality Evaluation.; Air quality management.; Air quality management European Union countries.; Air quality management Standards United States.; Atmospheric diffusion Mathematical models Congress; Bazalgette; Biomechanics Periodicals.; Buildings Environmental engineering.; Chemistry; Chemistry Biochemistry; Chemistry Chemical Engineering; Chemistry Environmental Chemistry; Chemistry General and Others; Civil engineering.; Clinical medicine Periodicals.; Construction contracts Great Britain.; Construction industry Law and legislation Great Br; Diagnostic imaging.; Dynamics Congresses.; Earth Sciences Geochemistry; Earth Sciences Geographic Information Systems & Re; Eastern Cong; Ecology Periodicals.; Electronic journals.; Engineering Aerospace and Aeronautics; Engineering Automobile and Transportation; Engineering Chemical Engineering; Engineering Civil Engineering; Engineering drawings.; Engineering drawings History.; Engineering drawings Standards.; Engineering Electronics; Engineering Environmental Engineering; Engineering Fire Fighting and Safety Engineering; Engineering General and Others; Engineering Industrial Engineering; Engineering Mechanical Engineering; Engineering Satellites; Engineers Great Britain Biography.; Environmental chemistry Periodicals.; Environmental Exposure.; Environmental geochemistry.; Environmental Illness.; Environmental impact analysis Europe; Environmental impact analysis European Union count; Environmental management Handbooks; Environmental Microbiology Periodicals.; Environmental Monitoring Periodicals.; Environmental policy European Union countries.; Environmental policy Europe Periodicals.; Environmental policy Periodicals.; Environmental Pollutants Periodicals.; Environmental Pollution adverse effects Periodical; Environmental Pollution Periodicals.; Environmental risk assessment.; Environmental risk assessment Europe; Environmental risk assessment European Union count; Environmental risk assessment Handbooks; Environmental Sciences Ecosystems & Ecology; Environmental Sciences Ecotoxicology; Environmental Sciences Environmental laws; Environmental Sciences Environmental Planning & St; Environmental Sciences General and Others; Environmental Sciences Pollution (Air; Environmental Sciences Sustainable Development; Environmental toxicology.; Environmental toxicology Periodicals.; Environment Periodicals.; etc.; Ethics; Evidence-based medicine Moral and ethical aspects.; Frank.; Germany. Heer. History World War; Global environmental change Periodicals.; Hazardous Substances toxicity.; Hazardous Waste adverse effects.; Hazardous wastes Health aspects.; Hazardous waste site remediation.; Hazardous waste sites Evaluation.; Hazardous waste sites Health aspects.; Hazardous wastes Risk assessment.; Health risk assessment.; Health Sciences General and Others; Heat Transmission Periodicals.; Heavy metals Toxicology.; Immune system Effect of heavy metals on.; Immunotoxicology.; Indoor air pollution.; Indoor air pollution Health aspects.; Indoor air pollution Standards United States.; Information Technology Computational Biosciences; Information Technology Modelling & Simulation; Joseph William; Kinematics Congresses.; Life Sciences Biochemistry; Life Sciences Biology; Life Sciences General and Others; Life Sciences Toxicology; London (England) Social conditions 19th century.; manuals; Material Science and Metallurgy Ceramics; Material Science and Metallurgy Composites; Material Science and Metallurgy Metals; Materials Periodicals.; Medical.; Medical ethics.; Medical ethics Periodicals.; Medical Periodicals.; Medical physics.; Medicine Practice Periodicals.; Microbial ecology Periodicals.; Microbiological assay Periodicals.; Microbiology; Military engineering Germany History 20th century.; Minerals; Motor vehicles Motors Exhaust gas Environmental as; Motor vehicles Motors Exhaust gas Health aspects.; Munger; Municipal water supply Periodicals.; Noise; Occupational Health.; Ocean waves Congresses.; Offshore gas industry Environmental aspects.; Offshore oil industry Environmental aspects.; Périodique électronique (Descripteur de forme); Physical and theoretical Periodicals.; Physicians (General practice) Professional ethics.; Physics; Physics Condensed Matter Physics; Physics General and Others; Physics Mechanics; Physics Thermodynamics and Heat Transfer; Pollutants.; Pollution Environmental aspects.; Pollution Environmental aspects Great Britain.; Pollution Law and legislation Great Britain.; Pollution Measurement.; Pollution Physiological effect Periodicals.; Primary care (Medicine) Moral and ethical aspects.; Professional Practice Periodicals.; Public Health.; Public Policy.; Radiography; Radiology; Refuse and refuse disposal.; Ressource Internet (Descripteur de forme); Risk assessment.; Rock mechanics.; Sanitary engineering England London History 19th c; Sir; Smoke prevention United States History.; Soil; Soil mechanics.; Space Probes & Technology; Toxicity testing Periodicals.; Traffic accidents Periodicals.; Traffic prevention and control Periodic; Traffic safety Periodicals.; Transportation engineering.; Urban hydrology Periodicals.; Urban pollution.; Urban runoff Management Congresses.; Ventilation Health aspects.; Water Pollution Toxicology Periodicals.; Water quality bioassay Periodicals.; Water quality management Congresses.; Water quality management Periodicals.; World War; Wounds and Injuries prevention & control Periodica; Wounds and injuries Prevention Periodicals.
Probing Weinberg's nonlinear quantum mechanics
Physics Letters A
151
5
215-217
1990
10.1016/0375-9601(90)90758-G
A search for nonlinear representations of propositions is made by assuming that the multiplication rule Weinberg uses to express the Lie bracket as a commutator can also be used to calculate functions representing squares of propositions. For systems described by two-component wave functions, the result is negative: the functions representing nontrivial propositions are all the same as in ordinary quantum mechanics.
Molecular Mechanics of Cytoskeletal Components
Mechanics of the 21st Century
355–364
2005
Summary Semiflexible polymers are of great biological importance in determining the mechanical properties of cells. We have used laser interferometry to passively trap and detect the motions of pairs of micron sized silica spheres in solutions of semiflexible polymer. The single-
cytoskeleton; laser; microrheology; optical tweezers; semiflexible polymers
Introduction to Modern Statistical Mechanics
Physics Today
1
12
288
1987
10.1063/1.2811680
Leading physical chemist David Chandler takes a new approach to statistical mechanics to provide the only introductory-level work on the modern topics of renormalization group theory, Monte Carlo simulations, time correlation functions, and liquid structure. The author provides compact summaries of the fundamentals of this branch of physics and discussions of many of its traditional elementary applications, interspersed with over 150 exercises and microcomputer programs.
Stochastic mechanics and dissipative forces
Journal of Mathematical Physics
18
2
308
1977
10.1063/1.523253
We analyze a simple velocity dependent potential in the framework of stochastic mechanics. A nonlinear Schrödinger–Langevin equation is obtained. This equation turns out to have solutions with the remarkable property of giving an approach to stationary quantum states. Informationtheoretical aspects on the irreversible behavior of the model is also briefly discussed.
Statistical mechanics of random graphs
Physica A: Statistical Mechanics and its Applications
344
1-2
6
2003
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
agents; backbone a; clustering; complex networks; describe ensemble; example; generic complex system can; graph; links represent interactions; monte carlo method; nodes refer; representation can used; represented a; such a; system subunits
Advances in Three-Dimensional Fracture Mechanics
Key Engineering Materials
312
27-34
2006
10.4028/www.scientific.net/KEM.312.27
The historical developments of the fracture mechanics from planar theory to three-dimensional (3D) theory are reviewed. The two-dimensional (2D) theories of fracture mechanics have been developed perfectly in the past 80 years, and are suitable for some specific cases of engineering applications. However, in the complicated 3D world, the limitation of the 2D fracture theory has become evident with development of the structure toward complication and micromation. In the 1990's, Guo has proposed the 3D fracture theory with a 3D constraint factor based on the deformation theory and energy theory. The proposed 3D theory can predict accurately the fracture problems for practical and complicated engineering structures with defects, by integrating the 3D theory of fatigue, which has been developed to unify fatigue and fracture. Our efforts to develop the 3D fracture mechanics and the unified theory of 3D fatigue and fracture are summarized, and perspectives for future efforts are outlined.
2d; 3d; abstract; and are suitable for; dimensional; fatigue life; fracture criterion; have been developed perfectly; in the past 80; out-of-plane constraint; planar theory to three-; some specific cases of; the fracture mechanics from; the historical developments of; theories of fracture mechanics; theory are reviewed; the two-dimensional; three-dimensional fracture; years
Hematopoietic and lymphatic malignancies in vehicle mechanics
Critical Reviews in Toxicology
27
5
443-494
1997
Although it is generally acknowledged that benzene causes leukemia, especially acute myeloid leukemia, considerable divergences persist in the assessment of the leukemia risk due to occupational low-level benzene exposure. Specifically, the risk for vehicle mechanics is considered by some authors as being nondetectable with epidemiologic methods, whereas others calculated that the incidence rate of leukemia (all types) in vehicle mechanics is increased more than 60 times. The purpose of this review is to examine the publications on this topic in light of criteria for causal inference and to discuss the possible role of bias, confounding factors, and chance. The results of this analysis reveal that there are surprisingly few epidemiologic observations supporting an increased incidence of leukemia in vehicle mechanics. Apparently, publications suggesting a leukemogenic effect of low-level benzene exposure in garage mechanics are more often quoted than their negative counterparts, although they are not better designed.
Benzene; Garages; Gasoline; Hodgkin's disease; Leukemia; Multiple myeloma; Myelodysplastic syndrome; non-Hodgkin's lymphoma; Vehicle mechanics
ANALISI DEI MODI DI DANNO A TRAZIONE DI LAMINATI CFRP UNIDIREZIONALI E CROSS-PLY MEDIANTE TECNICHE ESTENSIMETRICHE E DI EMISSIONE ACUSTICA
Convegno IGF 14
1998
La conoscenza dei meccanismi di danno e del comportamento a rottura di laminati in composito CFRP � di fondamentale importanza per la\nprogettazione e verifica di elementi strutturali, in particolare per il calcolo della resistenza residua post-danno. In condizioni di servizio, le\nstrutture in composito possono, infatti, manifestare: crack della matrice, debond fibra-matrice, rottura di fibre e delaminazioni. Questi fenomeni\ncausano una riduzione permanente dell�integrit� del laminato, degradando le caratteristiche di rigidezza e di resistenza del materiale stesso.\nIn questo lavoro vengono presentate diverse campagne di prova a trazione statica su laminati: unidirezionali a 0�, a 90� e cross-ply. Viene inoltre\ndiscussa una nuova metodologia per il monitoraggio dello stato di danneggiamento e l�individuazione dei modi di danno basata su tecniche\nestensimetriche e sull�Emissione Acustica. Le sequenze di laminazione considerate hanno generato preferenziali modi di danno. L�uso congiunto\ndi estensimetri elettrici e l�acquisizione degli eventi di EA hanno permesso il riconoscimento dei seguenti modi di danno: crack della matrice e\ndebond fibra-matrice, rottura di fibre e genesi e propagazione di delaminazioni.
Hand dermatitis in auto mechanics and machinists
Dermatitis
18
3
143-149
2007
Doi 10.2310/6620.2007.06039
Background. Auto mechanics and machinists presenting with suspected allergic contact dermatitis (ACD) have traditionally been patch-tested with a standard screening tray and a specialty tray such as the Oil and Cooling Fluid Series. While this has proven useful for patch-testing the machinist, there is a need for the development of a more specific allergen testing tray for the auto mechanic. Objective: The objective of the study was to compare clinical features and patch-test results of auto mechanics and machinists with hand dermatitis to evaluate differences in allergen profiles. Methods: We performed a chart review of 33 auto mechanics and 24 machinists referred to our Occupational Contact Dermatitis Clinic from 2002 to 2005 for evaluation of hand dermatitis. Results: With a panel of 84 allergens, 52 positive reactions were detected in 17 cases of ACD in mechanics. The profiles were different from the cases of ACD diagnosed in 10 of 24 machinists. Conclusions: Mechanics and machinists differ in the spectrum of occupational exposures. Patch testing with greater numbers of allergens likely identifies a larger proportion of mechanics with occupationally relevant ACD. Further study is needed to determine the most appropriate allergens to include in a clinically useful "mechanic's tray."
car mechanics
Further Developments in Generalized Classical Mechanics
American Journal of Physics
38
5
557
1970
10.1119/1.1976405
Transformation theory for mechanics with higher derivatives is investigated. Poisson brackets previously introduced are proved not to be invariant under canonical transformations. A new definition of Poisson brackets is proposed and it is found to be invariant. Hamilton-Jacobi theory is established.
On a New Form of Quantum Mechanics
Foundations
1
29-31
2008
We propose a new form of nonrelativistic quantum mechanics which is based on\na quantum version of the action principle.
Quantum Physics
Analysis of space flight mechanics problems
Acta Astronautica
52
8
663-670
2003
10.1016/S0094-5765(02)00134-0
The subject, place in astronautics, formation and evolution of space flight mechanics as a science are discussed in this paper. The main problems and connections with other sciences are analyzed. A view on some modern projects is given.
Pseudoanti-Hermitian operators in quaternionic quantum mechanics
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
35
34
7493-7505
2002
We introduce the concept of pseudoanti-Hermitian operators in\nquaternionic quantum mechanics and give a complete characterization of\ntheir spectra. We highlight some physical properties related to\ntime-reversal symmetry of the pseudoanti-Hermitian quaternionic\nHamiltonians.
Development of a concept inventory for fluid mechanics
33rd Annual Frontiers in Education Conference
1
T3D-23-T3D-28 Vol.1
2003
10.1109/FIE.2003.1263340
Concept inventories are assessment tools designed to determine the degree to which students understand the concepts of a subject and to identify the misconceptions that students hold. The results of a concept inventory can be used to change the methods of instruction to overcome student misconceptions. A cooperative effort between mechanical engineering faculty at the Universities of Wisconsin-Madison and Illinois, Champaign-Urbana has been directed toward development of a fluid mechanics concept inventory (FMCI). Fluid mechanics typically follows thermodynamics in the sequence of courses in thermal sciences, involves both the mechanics and dynamics of fluids, and builds on basic physics and Newtonian mechanics. This paper describes the process used for development of the FMCI, the details of how we determined the content, and examples of actual content of the instrument itself.
assessment tools; concept-based instruction methods; educational courses; engineering education; fluid mechanics; fluid mechanics concept inventory; student misconceptions; thermodynamics
A mechanistic model for fatigue damage evolution in composite laminates
Mechanics of Materials
29
2
123-140
1998
We propose a mechanistic model which is capable of describing the evolution of transverse cracking in cross ply laminates subjected to cyclic tension in the longitudinal direction. The key feature of the model is that it incorporates delamination associated with transverse cracks in a manner that induces further formation of transverse cracks as delamination grows in fatigue. A variational approach is taken to estimate the stresses in the region between transverse cracks, and these are found to be accurate away from the crack planes when comparison is made with finite element computations. The evolution of transverse crack density and the associated overall elastic moduli changes predicted by the model are in agreement with experimental results. (C) 1998 Elsevier Science Ltd. All rights reserved.
cross ply laminates; delamination; TRANSVERSE CRACKING; transverse cracks; VARIATIONAL APPROACH
Madhyamika Buddhism and Quantum Mechanics: Beginning a Dialogue
International Philosophical Quarterly
29
371
1989
A philosophic analysis of the middle way buddhist conception of emptiness is first presented. Then the philosophic foundations of quantum mechanics are explored through a nontechnical derivation of bell's inequality and a discussion of its experimental refutation. The paper shows the intimate relationship between the middle way buddhist conception of emptiness, The experimental refutation of bell's inequality, And the fundamental principles of quantum mechanics. It is hoped that these comparisons, Contrasts, And applications spark a dialogue between those concerned with the philosophic ramifications of quantum mechanics and those interested in an ancient path to liberation.
buddhism; madhyamika; quantum mechanics; science;
Stochastic Quantisation and Non-Equilibrium Statistical Mechanics
Writing
4
2005
The stochastic quantisation technique of Parisi and Wu is extended to study non-equilibrium statistical mechanics. We show that this scheme is capable of handling white as well as coloured noises. PACS numbers: 64.60.-i; 64.60.Ak; 64.60.Fr; 64.60.Ht
Noether's theorem in time-dependent lagrangian mechanics
Reports on Mathematical Physics
31
2
189-203
1992
10.1016/0034-4877(92)90014-R
We use the concepts of differential forms and vector fields along maps and g*-derivations for giving a generalized version of the Noether's theorem admitting a converse, in the setting of time-dependent regular Lagrangian systems. © 1992.
Statistical mechanics of dissipative particle dynamics
EPL (Europhysics Letters)
1995
Home Search Collections Journals About Contact us My IOPscience Page 2. EUROPHYSICS LETTERS Europhys. Lett., 30 (4), pp. 191-196 (1995) 1 May 1995 Statistical Mechanics of . P. EsP&oL(*)($ and P. (**)
Soil Mechanics A
Faraday Discussions
365
June
2-6
2011
In soil mechanics, student's models are classified as simple models that teach us unexplained elements of behaviour; an example is the Cam clay constitutive models of critical state soil mechanics (CSSM). 'Engineer's models' are models that elaborate the theory to fit more behavioural trends; this is usually done by adding fitting parameters to the student's models. Can currently unexplained behavioural trends of soil be explained without adding fitting parameters to CSSM models, by developing alternative student's models based on modern theories?Here I apply an alternative theory to CSSM, called 'breakage mechanics', and develop a simple student's model for sand. Its unique and distinctive feature is the use of an energy balance equation that connects grain size reduction to consumption of energy, which enables us to predict how grain size distribution (gsd) evolves-an unprecedented capability in constitutive modelling. With only four parameters, the model is physically clarifying what CSSM cannot for sand: the dependency of yielding and critical state on the initial gsd and void ratio.
Viscoelastic analysis of von Kármán laminated plates under in-plane compression with initial deflection
International Journal of Non-Linear Mechanics
32
6
1065-1075
1997
10.1016/S0020-7462(96)00133-3
The creep responses of simply-supported cross-ply and angle-ply viscoelastic laminates, having various magnitudes of imperfections, under in-plane compression are examined. The non-linear strain-displacement relation is based on the von Kármán assumption. The stress function is obtained by solving the compatibility equation by the use of the Laplace transform, and the deflection is calculated from the moment equation by the Galerkin method and a numerical integration scheme. The numerical results of deflection history and edge shortening for the glass/epoxy laminates are presented for illustrating the effect of imperfections and viscoelastic properties on the creep behavior. The solutions based on the quasi-elastic approach are also presented for comparison.
imperfection; laminate; quasi-elastic; viscoelastic
Experimental and Analytical Modeling of Scarf Repaired Composite Panels.
Mechanics of Advanced Materials & Structures
21
3
207-212
2014
Experiments and finite element analysis (FEA) were performed on scarf-patch repaired composite panels. Tensile static tests were performed on pristine and repaired panels to evaluate their tensile strength. The obtained results showed that the repaired panels restored tensile strength by 95% of the pristine value. Subsequently, a verification finite element (FE) model was established. Two additional models, one with homogenized mechanical properties of the laminate and one that considered that the ply-by-ply properties were built to simulate the experimental repairs. The predictions of the two models agreed reasonably well with the experimental results and the optimum scarf angle was found at 2.5°. [ABSTRACT FROM AUTHOR]
3D-FEA; composite laminate; COMPOSITE materials; failure analysis; FINITE element method; LAMINATED materials; MATERIALS -- Mechanical properties; patch repair; PHYSICS -- Experiments; scarf angle; scarf repair; TENSILE strength
Constrained quantum mechanics and a coordinate independent theory of the collective path
Nuclear Physics A
391
2
307-326
1982
10.1016/0375-9474(82)90612-1
The settings for two formulations of quantum mechanics are, respectively, Hilbert spaces and symplectic manifolds. The former leads naturally to matrix mechanics and, for example, the shell model while the latter leads to hamiltonian mechanics, of which the time-dependent Hartree-Fock theory is a standard example. In order to obtain practical approximate theories one needs to restrict the dynamics in both cases to suitable finite-dimensional subspaces. This paper addresses the problem of constructing subspaces of the projective Hilbert space, the fundamental symplectic manifold of quantum mechanics. The collective paths of Villars, Goeke and Reinhard, the valley path and the collective path and submanifold of Rowe and Basserman are examined and phrased in a coordinate independent manner. In this way we expose the dynamical foundations and the essential geometrical structures upon which they are based.
Topics in quantum statistical mechanics and operator algebras
arXiv preprint math-ph/0107009
36
2001
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications in mind. In Chapter 2 we study some questions related to the quantum statistical mechanics of spin systems, with particular attention to the time evolution of infinite systems. The basic reference for these two chapters is Bratteli-Robinson: Operator algebras and quantum statistical mechanics I, II. In Chapter 3 we discuss the nonequilibrium statistical mechanics of quantum spin systems, as it is currently being developped.
Curricular emphasis in mechanics: a national update
Engineering Education
76
7
664-669
1986
Reports results of a nationwide survey on undergraduate mechanics education. These results are compared with previous surveys to document trends in mechanics education. Areas addressed include degrees granted, courses required, teaching responsibility, quality of teachers and students, subject matter taught, evaluation methods, and teaching methods.
Course Content; Educational Trends; Engineering Curriculum; Engineering Education; Higher Education; Mechanics (Physics); Surveys; Teaching Methods
Instrumented indentation microscope applied to the elastoplastic indentation contact mechanics of coating/substrate composites
Journal of Materials Research
24
Compendex
1950-1959
2009
In instrumented indentation tests for a thin film coated on a substrate (film/substrate composite), it is well known that the substrate-affected contact area estimated through conventional approximations includes significant uncertainties, leading to a crucial difficulty in determining the elastic modulus and the contact hardness. To overcome this difficulty, an instrumented indentation microscope that enables researchers to make an in situ determination of the contact area is applied to an elastoplastic film on substrates having various values of their elastic moduli. Using the indentation microscope, the substrate-affected indentation contact parameters including contact hardness of the film/substrate composites are determined directly as well as quantitatively without any undesirable assumptions and approximations associated with the contact area estimate. The effect of a stiffer substrate on the contact profile of impression is significant, switching the profile from sinking in to piling up during penetration, and resulting in the substrate-affected contact hardness being highly enhanced at deeper penetrations. Through the present experimental study, it is demonstrated that the instrumented indentation microscopy is highly efficient in determining the substrate-affected elastoplastic contact parameters of film/substrate composite systems. 2009 Materials Research Society.
Elastic moduli; Elastoplasticity; Hardness; Microscopes; Substrates; Uncertainty analysis
The Mechanics of Friction Fatigue in Jacked Piles Installed in Sand
From Soil Behavior Fundamentals to Innovations in Geotechnical Engineering
233
546-557
2014
10.1061/9780784413265.044
The limit shaft resistance of displacement piles decreases with the number of axial loading cycles applied during pile installation (e.g., jacking, driving) or due to the nature of superstructure loading. This study examines the mechanisms governing the phenomenon of friction fatigue along piles jacked in sandy soils. Finite element analysis (FEA) of a thin disk of soil surrounding the pile shaft is performed. The pile installation process is modeled as a sequential combination of cylindrical cavity expansion and vertical shearing along the pile-soil interface. The soil disk is subjected to several vertical shearing cycles to simulate the successive application and removal of jacking loads. An advanced soil constitutive model based on two-surface plasticity and critical state theory is used in the FE simulations. FEAs examine the development and evolution of the normal stress acting on the pile shaft, which multiplied by an appropriate friction coefficient yields the value of mobilized shaft resistance. Results show that, in the absence of loading cycles, the normal stress attains values considerably larger than the in situ vertical stress. However, with subsequent application of loading cycles, the normal stress decreases at rates that increase with decreasing relative density and in situ vertical stress. © 2014 American Society of Civil Engineers.
Fracture mechanics of plastic-fiber composites
Engineering Fracture Mechanics
6
2 PG - 343
-359
1974
The concept of fracture mechanics is introduced to characterize the toughness of fiber-reinforced composites which should be distinguished from tensile strength. A material may have a high tensile strength but a low toughness meaning that...
International Journal ofRock Mechanics & Mining Sciences
International Journal of Rock Mechanics and Mining Sciences
48
1
141-145
2011
International Journal of Rock Mechanics and Mining Sciences, 48 + (2010) 141-145. doi:10.1016/j.ijrmms.2010.09.015
Classical and Quantum Mechanics via Lie algebras
Arxiv preprint
502
2008
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
Classical and Quantum Mechanics via Lie algebras
arXiv.org
quant-ph
2008
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
Quantum mechanics and stochastic control theory
Journal of Mathematical Physics
22
5
1010
1981
10.1063/1.525006
A time‐symmetric stochastic control theory is proposed as one of the representatives of quantum mechanics. The main idea is based on Nelson’s probability theoretical approach to quantum mechanics. His approach is reformulated as a time‐symmetric stochastic control problem. Several different control constraints equivalent to Nelson’s are obtained. One of them has a close connection to the Lagrangian formalism of classical mechanics. This suggests to us the use of stochastic calculus of variations. Within the realm of this time‐symmetric stochastic control theory it is shown why Schrödinger’s original variational method of quantization was successful. Several advantageous points of the stochastic control theoretical approach to quantum mechanics, including the analysis of the classical limit, are also discussed.
Effect of imperfections on buckling of thin cylinders and columns under axial compression
Journal of Applied Mechanics
17
73-83
1950
Von Karman and Tsien have shown that under elastic conditions the resistance of perfect thin cylinders sub jeeted to axial com.pression drops pl 'edpitously after buck%7E ling. It is considered that this indicates that this type of budding is very sensitive to imperfections or disturbances. In this paper the effects of certain im.perfections of shape (assum.ed to be equivalent to all the actual defects or distm: hances cmnbined) are studied by the large-deflection shell theOl 'y developed in a previous paper (2). ' It is found that two types of buckling failure lllay occur. One is of a purely elastic type which occurs when the peak of the average stress versus average strain curve is reached, while the other type is precipitated by yielding, which for thicker cylinders or lower-yield lllateriallllay occur before such a peak is reached. Curves are derived giving the dependence of each type of failure upon the diInensions and elastic and yield properties of the spedlllen and also upon an unevenness factor U which deterlllines the xnagni. tude of the initial and is assumed to depend on the m.ethod of fabrication. The relations derived are in Hne with test results, and shnilar studies of the buckling of struts indicate that the magnitude of the initial imperfections which have to be assumed to test strengths are reasonable.
Buckling; Defect; defects; Properties; resistance; shell; Strain; strength; Stress; stresses
Computational Mechanics Today
International Journal for Numerical Methods in Engineering
34
1
9-33
1992
10.1002/nme.1620340104
Computational Mechanics or Computational Applied Science is today the base on which most of the achievements of engineering and physics are built. Its concern is the solution of complex mathematical theories in numerical terms, without which the translation of these into practical artifacts would be impossible. Indeed, by providing such quantitative measures it enhances the understanding of the physical phenomena and stimulates further development of theory and physical experiment. Most of the theory underlying physical phenomena is cast in terms of, often involved, differential equations for which closed forms of solution are seldom possible. Numerical approximation or discretization processes are necessary for quantitative solution. Here the first steps were taken at the start of this century by the pioneering work of Richardson introducing finite difference approximations. The invention of relaxation methods by Southwell during the Second World War allowed many practical solutions to be achieved. However, it was the advent of the electronic digital computer that marked the turning point in Computational Mechanics. The dramatic escalation of the power of these machines, which still continues today, allowed the development of the field of Computational Mechanics as we know it. It is through this computer power that such methods of approximations as finite elements, finite differences, boundary solutions and spectral processes became a practical reality, though each was anticipated in the pre computer area. It is not surprising therefore, that the mathematical foundations and the full development of such methods have been accomplished only relatively recently. Today we see the field of activity subdivided between those specializing in the development of the various computational approximation processes and those seeking optimal numerical solutions for their particular field of application. It is the objective of this Congress and indeed of the International Association of Computational Mechanics to provide a forum at which an interdisciplinary exchange of information can take place between the various sections and disciplines of the whole field. Indeed, this is the way progress can best be achieved. Recent history indicates that substantial advances are as frequently made due to a method seeking a new application as through a problem requiring a solution. In recent history we have seen on occasion a liaison of a particular computational approximation method to a field of application occurring through historical accident. Here the intimate association of the finite method and the field of SOLID MECHANICS (CSM or Computational Solid Mechanics) and that of the finite differences with FLUID DYNAMICS (CDF or Computational Fluid Dynamics) can be observed as classical examples. Today the advent of new application fields and a better understanding of the approximation theory are helping to break down the barriers and ensure a more rational matching of objectives and methods. We shall illustrate the lecture with examples of such recent progress and state some possibilities as yet unexplored. Indeed, we are sure that the Congress will achieve in much more detail the same aims. This presentation stresses the essential unity of the subject and discuss some areas where progress and research are currently active. Two of such, adaptive error controlled analysis and treatment of hyperbolic (fluid) problems, are singled out due to their wide applications.
engineering analysis; finite-element analysis; high-speed flows
Mechanics of Flow Through Man-Made Lakes
Man-Made Lakes: Their Problems and Environmental Effects
300-310
2013
10.1029/GM017p0300
This chapter contains sections titled: * Flow Mechanics * Discussion of Results * Conclusions * Notation
Flow mechanics; Froude number; Man-made lakes; Stratified flow; Tennessee Valley Authority (TVA)
The statistical interpretation of quantum mechanics
Science (New York, NY)
1954
... The work, for which I have had the honour to be awarded the Nobel Prize for 1954 ... were, suddenly, two self-contained but quite distinct systems of explanation extant: matrix mechanics and wave mechanics . But Schrödinger himself soon demonstrated their complete equivalence ...
Theory and Mechanics of Accounting (Book)
Accounting Review
12
3
334
1937
Reviews the book "Theory and Mechanics of Accounting," Leo A. Schmidt.
ACCOUNTING; BOOKS -- Reviews; NONFICTION; SCHMIDT, Leo; SCHMIDT, Leo A.; THEORY & Mechanics of Accounting (Book)
A mechanics program for high school pitchers
Texas coach
47
6
36-37
2003
Explains mechanics and suggest drills for high school level baseball pitchers. Explains mechanics and suggest drills for high school level baseball pitchers.
baseball. pitching. drill. biomechanics; Baseball Techniques-and-Skills-Pitching (544273); Baseball Training-and-Conditioning-Drills (544323)
Some questions on the course in mechanics
Journal of Engineering Education
17
10
903-906
1927
Newly appointed committee on Mechanics is undertaking study of several fundamental questions in regard to teaching of subject; several of these questions are stated and discussed.
Education, engineering; Mechanics
Classical and Quantum Mechanics via Lie algebras
arXiv
quant-ph
2008
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
Classical and Quantum Mechanics via Lie algebras
0810.1019
2008
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
Statistical mechanics of random graphs
Physica A
344
56-61
2004
10.1016/j.physa.2004.06.087
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications
Clustering; Complex networks; Monte Carlo method
Stochastic mechanics of reciprocal diffusions
Journal of Mathematical Physics
37
2
769
1996
10.1063/1.531414
The dynamics and kinematics of reciprocal diffusions were examined in a previous paper [J. Math. Phys. 34, 1846 (1993)], where it was shown that reciprocal diffusions admit a chain of conservation laws, which close after the first two laws for two disjoint subclasses of reciprocal diffusions, the Markov and quantum diffusions. For the case of quantum diffusions, the conservation laws are equivalent to Schrödinger’s equation. The Markov diffusions were employed by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math Kl. 144 (1931); Ann. Inst. H. Poincaré 2, 269 (1932)], Nelson [Dynamical Theories of Brownian Motion (Princeton University, Princeton, NJ, 1967); Quantum Fluctuations (Princeton University, Princeton, NJ, 1985)], and other researchers to develop stochastic formulations of quantum mechanics, called stochastic mechanics. We propose here an alternative version of stochastic mechanics based on quantum diffusions. A procedure is presented for constructing the quantum diffusion associated to a given wave function. It is shown that quantum diffusions satisfy the uncertainty principle, and have a locality property, whereby given two dynamically uncoupled but statistically correlated particles, the marginal statistics of each particle depend only on the local fields to which the particle is subjected. However, like Wigner’s joint probability distribution for the position and momentum of a particle, the finite joint probability densities of quantum diffusions may take negative values.
Effects of control mode in a cross-ply Ti-MMC at ambient and high temperature in air and in vacuum
International Journal of Fatigue
20
5
339-349
1998
10.1016/S0142-1123(97)00128-X
Fatigue crack growth rates from unbridged defects in a [0/90°]2s Ti–6Al–4V/SCS-6 cross-ply laminate composite have been measured to assess the effects of the control conditions under a stress ratio of R=0.1 and at a frequency of 10Hz, whilst varying the initial stress intensity factor range (ΔKini.), the test temperature and the environment. Initial fatigue crack growth rates in air were found to increase with increasing test temperature. ΔKini. transition values leading to fatigue crack arrest compared with eventual specimen catastrophic failure are, at ambient temperature, approximately equal to 14MPa√m in load control but are approximately 40% higher in position control. In addition, at a temperature of 450°C in air, the limiting value ofΔKini. promoting crack arrest decreases to 8MPa√m in load control. In contrast, the ΔKini. transition in vacuum at a temperature of 450°C is identical to that at ambient temperature in air under load control. Under position control at the elevated test temperature, a period of constant nominal stress intensity factor range (ΔKnom.) occurs. The crack growth rate at a test temperature of 450°C, in vacuum, is approximately 4×10−7mm/cycle in the constant ΔKnom. region, and this is somewhat less than that observed in air at the same test temperature (5×10−6mm/cycle), while crack arrest at ambient temperature in air is observed. Finally, it is suggested that position control experiments are of some advantage for the studies of the underlying crack growth mechanisms.
control mode; crack arrest; fatigue crack growth; laminates; titanium metal matrix composites
Comparison between crack growth in fracture mechanics specimens and feature component tests carried out in a low-alloy steel
Journal of pressure vessel technology
2000
In both power generation plants and the chemical industries there is a need to assess the significance of defects which may exist in high temperature equipment operating in the creep range. This paper examines the methods of analysis used in laboratory creep crack growth data and their relevance to crack growth data derived from feature component tests which best simulate actual components under controlled testing condition. The material examined was a 21/4Cr1Mo steel in the new condition at 550 o C and 600 o C. The creep crack growth properties was determined on compact tension specimens. The data was compared with representative crack growth data from feature test components. These consisted of cracked rings, thick-walled cylinders and thin walled tubes containing axial or circumferential defects under combinations of axial and internal pressure loading. Little influence of size or temperature on the measured crack propagation rates was observed when the results were plotted against the creep fracture mechanics parameter C*. This is shown to be because the relevant condition had little effect on the appropriate crack tip creep ductilities of the material. Good correspondence was observed between the compact tension and the feature component tests suggesting the feasibility of the C* method for predicting short term laboratory tests using different geometries.
Real Gamification Mechanics Require Simplicity And, Yes, Game Designers Can Do It
Tech Crunch
2012
The mysteries of mechanics are the reason why gamification seems like voodoo. And it shouldn't be. Game mechanics should be simple to explain, with clear actions and outcomes. So why do we get so confused by this, and how do we separate the "real" mechanics from the "fake"..
Fracture mechanics applied to concrete
European Structural Integrity Society
Volume 26
183-210
2000
10.1016/S1566-1369(00)80050-3
The aim of this contribution is to show the value of fracture mechanics tools in dealing with engineering fracture problems of concrete, either plain or reinforced. The first part is a review of modeling concrete fracture in tension: the suitability of linear elastic fracture mechanics ({LEFM)} as an asymptotic approach is considered first, followed by an outline of classical fracture models based on stress-strain relations and their associated problems of non-objectivity. And, finally, cohesive process zone models based on stress-displacement relations are shown to be one of the simplest models capturing the essential features of fracture processes in concrete. The second part gives some practical examples of applications of fracture mechanics to concrete, mostly drawn from the authors' experience: the difference between strength and toughness in concrete is clearly shown in the example of piles. The size effect in flexural strength, unobtainable with classical strength theories, is accurately predicted with the cohesive process zone model. For plain concrete and large concrete structures such as dams, {LEFM} was proven suitable. Fracture in reinforced concrete is a more involved problem; nevertheless some promising results for lightly reinforced concrete beams are discussed. The paper ends with some comments on fracture of fiber reinforced concrete ({FRC)} and an application of this concept to the fracture of {FRC} tunnel lining, presented in a Japanese standard.
Cohesive process zone; Concrete; Crack; Fracture; Size effect
About fractional supersymmetric quantum mechanics
Czechoslovak Journal of Physics
55
9
1063–1066
2005
10.1007/s10582-005-0106-y
Fractional Euler–Lagrange equations are investigated in the presence ofGrassmann variables. The fractional Hamiltonian and the path integral of the fractional supersym- metric classical model are constructed.
fractional calculus; grassmann variables
Students' reasonings in solid mechanics
Physics Education
29
4
242-246
1994
10.1088/0031-9120/29/4/011
Describes an investigation that explores students' understanding of the translation, rotation, and deformation of an object. Findings illustrate that students have difficulty appreciating that these different phenomena can occur simultaneously. Discusses some implications for teaching.
Chaotic evolution in quantum mechanics
Physical Review E
53
5
4524-4527
1996
10.1103/PhysRevE.53.4524
A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function increases exponentially.
Statistical mechanics of complex networks
arXiv:cond-mat/0106096
1
54
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Adaptation and Self-Organizing Systems; Data Analysis; Disordered Systems and Neural Networks; Mathematical Physics; Networking and Internet Architecture; Statistical Mechanics; Statistics and Probability
Soil Mechanics for Unsaturated Soils
Stress The International Journal on the Biology of Stress
517
1993
"A Wiley-Interscience publication.". Includes bibliographical references (p. 490-507) and index.
On Quantum Mechanics
arXiv
hep-th
1994
We reformulate the problem of the "interpretation of quantum mechanics" as the problem of DERIVING the quantum mechanical formalism from a set of simple physical postulates. We suggest that the common unease with taking quantum mechanics as a fundamental description of nature could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer independent time. Following an an analysis of the measurement process as seen by different observers, we propose a reformulation of quantum mechanics in terms of INFORMATION THEORY. We propose three different postulates out of which the formalism of the theory can be reconstructed; these are based on the notion of information about each other that systems contain. All systems are assumed to be equivalent: no observer-observed distinction, and information is interpreted as correlation. We then suggest that the incorrect notion that generates the unease with quantum mechanichs is the notion of OBSERVER INDEPENDENT state of a system.
Metaphysics of Quantum Mechanics
Compendium of Quantum Physics
52
5
384-389
2009
10.1007/978-3-540-70626-7_119
Quantum mechanics, like any physical theory, comes equipped with many metaphysical assumptions and implications. The line between metaphysics and physics is often blurry, but as a rough guide, one can think of a theory's metaphysics as those foundational assumptions made in its interpretation that are not usually directly tested in experiment. In classical mechanics some examples of metaphysical assumptions are the claims that forces are real, that inertial mass is primitive, and that space is substantival. The distinctive feature of these claims is that they are all rather far removed from ordinary tests of the theory. Newton defended all three of the above claims at one time or other, whereas Mach attacked each one; however, both scientists agreed on enough of the formalism and its connection to experiment to predict (e.g.) the same periods for given pendulums. What they disagreed about were the ingredients necessary to use classical mechanics to explain and understand the world.
Boundary discontinuous Fourier solution for plates and doubly curved panels using a higher order theory
Composites Part B: Engineering
42
4
842-850
2011
10.1016/j.compositesb.2011.01.014
A new analytical solution to the problem of a finite-dimensional general cross-ply plates and doubly curved panels of rectangular planform is presented using a higher order shear deformation theory (HSDT). A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach, is used to solve the highly coupled linear partial differential equations, generated by the HSDT-based laminated shell analysis, with the SS1-SS3-mixed type simply supported boundary conditions prescribed at all four edges. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. The accuracy of the present solution is checked by studying the convergence characteristics of deflections and moments of an antisymmetric cross-ply shell and results are also compared with the finite element counterparts using commercially available software for distributed load. The primary aim of this study is to understand the effect of in-plane (or surface-parallel) boundary conditions, quantify this effect and provide benchmark comparisons and verifications of numerical results such as finite element, boundary element, etc. The effects of curvature, lamination, material property, thickness, and different types of loads as well as their interactions are also investigated in detail. ?? 2011 Elsevier Ltd. All rights reserved.
A. Laminate; C. Analytical modeling; C. Laminate mechanics
Laser surface preparation for bonding of aerospace composites
Proceedings of the ICE - Engineering and Computational Mechanics
164
3
133-138
2011
10.1680/eacm.2011.164.3.133
<p> Adhesive bonds are critical to the integrity of built-up structures. Disbonds can often be detected but the strength of adhesion between surfaces in contact cannot be determined without destructive testing. Typically the major problem in a bonded structure is surface contamination, and by extension, surface preparation. Standard surface preparation techniques, including grit blasting, manual abrasion, and peel ply, are not ideal because of variations in their application. Etching of carbon-fibre-reinforced plastic (CFRP) panels using a neodymium-doped yttrium aluminum garnet (Nd:YAG) laser appears to be a highly precise, controlled, and reliable way to both clean a composite surface prior to bonding and provide a bond-promoting patterned surface akin to peel ply without the inherent drawbacks from the same (i.e. debris and curvature). CFRP surfaces prepared using laser patterns conducive to adhesive bonding were compared with typical pre-bonding surface treatments through optical microscopy, contact angle goniometry and post-bonding mechanical testing. This paper is the work of the US Government and is not subject to copyright protection in the USA.</p>
composite structures; materials technology; strength & testing of materials
Mathematical Foundations of Quantum Mechanics
American Mathematical Monthly
72
1
96
1955
10.2307/2313034
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.
Finite-Element Analysis of Laminated Bimodulus Composite-Material Plates.
Computers and Structures
12
2
245-251
1980
10.1016/0045-7949(80)90011-5
Finite element analysis of the equations governing the small-deflection elastic behavior of thin plates laminated of anisotropic bimodulus materials is presented. Single-layer and two-layer cross-ply, simply-supported rectangular plates subjected to sinusoidally distributed normal pressure and uniformly distributed normal pressure are analyzed. For the sinusoidally loaded case, the finite element solutions are close to the exact closed-form solutions.
Edge-jump inversion in the Si L-3,L-2-edge optical XAFS of porous silicon
Journal of Synchrotron Radiation
6
215-216
1999
10.1107/S0909049599001314
We present a study of the progressive inversion of the edge jump of the Si L-3,L-2-edge XANES (X-ray Absorption Near Edge Structures) recorded with photoluminescence yield (PLY) for a series of porous silicon samples with varying thickness. It is found that edge jump inversion occurs as the thickness of the film increases from the thin to the thick regime.
Elementary Molecular Quantum Mechanics
Elementary Molecular Quantum Mechanics
449-465
2013
10.1016/B978-0-444-62647-9.00011-7
In this chapter, the three fundamental Schroedinger’s postulates of quantum mechanics are re-examined and explained in the light of the physical principles based on the measurement of observable quantities. Starting from the wave–particle dualism, the study of the Compton effect reveals the atomicity of matter, Planck’s law the atomicity of energy, the de Broglie’s hypothesis the atomicity of linear momentum, and the Bohr’s hypothesis the atomicity of angular momentum. This implies the peculiar character that any experimental measurement has in atomic physics (namely, on a microscopic scale), particularly its limits, that become apparent through the Heisenberg’s principle as a direct consequence of the interaction between the experimental apparatus and the object of measurement. This affects the physical property that must be measured at the microscopic level, as shown by the ‘Gedanken experiment’ of Heisenberg’s γ-rays microscope.
Atomicity of matter; Compton effect; Heisenberg microscope; Heisenberg principle; Measure of observables; Orbital model; Postulates of quantum mechanics; State function; Wave–particle dualism
Edge impact modeling on stiffened composite structures
Composite Structures
126
314-328
2015
10.1016/j.compstruct.2015.02.020
Finite Element Analysis of low velocity/low energy edge impact has been carried out on carbon fiber reinforced plastic structure. Edge impact experimental results were then compared to the numerical “Discrete Ply Model” in order to simulate the edge impact damage. This edge impact model is inspired to out-of-plan impact model on a laminate plate with addition of new friction and crushing behaviors. From a qualitative and quantitative point of view, this edge impact model reveals a relatively good experiment/model agreement concerning force–time and force–displacement curves, damage morphology or permanent indentation after impact. In particular the correlation is faithful concerning the results of the parameters retained by industry; the maximum crack length on the edge and the permanent indentation. Finally, it can be noticed that the model quickly answers in crushing mode and goes in an inadequate way from the dynamic behavior to the quasi-static behavior. In order to correct this problem it seems necessary to implement a strain rate effect in the behavior law on the fiber failure in compression. The next step is to apply this model to the compression after impact.
Carbon fiber; Damage mechanics; Discrete Ply Model; Finite element modeling; Impact behavior
Comment on "Anomalous temperature dependence of the Casimir force for thin metal films" [arXiv:0712.1395]
Arxiv preprint
2
2008
Recently V. A. Yampol'skii, S. Savel'ev, Z. A. Mayselis, S. S. Apostolov, and F. Nori [Phys. Rev. Lett., v.101, 096803 (2008),arXiv:0712.1395] claimed that the Casimir force between a thin metal film described by the Drude model and an ideal metal semispace can decrease with temperature whereas for bulk samples the Casimir force increases with temperature. On this basis the experimental observation of the decreasing temperature dependence of the Casimir force magnitude between a film and a bulk ideal metal was proposed. We demonstrate that, contrary to what is claimed by the authors, the magnitude of the Casimir force decreases with temperature in a wide temperature region for bulk samples described by the Drude model. This decrease is shown to be much larger than that for a thin film and it has already been experimentally excluded.
Other Condensed Matter; Quantum Physics; Statistical Mechanics
Performance comparison between two axial active support schemes for 1-m thin meniscus primary mirror
Journal of Instrumentation
8
2013
Artn T03010\rDoi 10.1088/1748-0221/8/03/T03010
Active support scheme may decide the deformation of the optical surface figure of the primary mirror. Two main active axial support schemes are often adopted to the thin meniscus primary mirror, one scheme is that the axial supports normal to the mirror bottom surface, and the other is that the active forces parallel to the optical axis. In order to compare the performance of the two support schemes, 1-m thin meniscus primary mirror is conducted. Finite element analysis (FEA) is employed to analyze the optical surface figures of the primary mirror, and optimizations are carried out by using ANSYS for each support scheme to obtain the locations and active forces. The axial support force sensitivities are calculated for the two support schemes in a case that a single axial support has a force error of 0.5 N. The correction ability of the active support system for both of the support schemes are analyzed when an arbitrary axial support is failure. Several low order Zernike modes are modeled with MATLAB procedure, and active optics corrections are applied to these modes for the two active supports. The extra mirror surface error due to thermal deformation is also corrected with the two support schemes.
instrument optimisation; mirror quality factor; optics; overall mechanics design (support structures and m; system; telescope
Tensile Testing of thin-film specimens on polyamide substrates using SPDIC
SEM Annual Conference and Exposition on Experimental and Applied Mechanics 2006
2
1062-1067
2006
Design and performance parameters for a micro-tensile test apparatus have been presented. Thin-film coatings on compliant polyamide substrates have been used as specimens for this paper even though the device is well suited for conducting micro-tensile testing on a variety of test samples with high aspect ratios. Sub-Pixel Digital Image Correlation technique may be employed to obtain local strain fields with resolutions of upto 10nm. The resolution of the linear motion of the actuator is around ±0.3μm and applied forces upto 20 N can be continuously measured using a high precision load cell with a resolution of around 1mN. A laboratory computer running a measurement and automation software using a 16-bit A/D converter was used as the DAQ and data logging device.
Aspect ratio; Digital Image Correlation; High precision load cell; Micro-tensile testing; Optical resolving power; Polyamides; Strain; Tensile testing; Thin films
Thin Film Thickness Measurement of Whole Field Based on Spatial Carrier Frequency Interferometry
Fourth International Conference On Experimental Mechanics
7522
Opt & Photon Soc Singapore; Theoret & Applied Mech
2010
10.1117/12.849647
The kernel of modern interferometry is to the obtain necessary surface\nshape and parameter by processing interferogram with a reasonable\nalgorithm. On the basis of the study the basic principle of interferometry\nby using 2-D FFT arithmetic, a new method to measure the thin film\nthickness is proposed based on the FFT algorithm. A test sample is\nplaced into the light path in Twyman-Green interferometer, the interference\nfringes were generated by the reference beam with the tested beam\nreflected respectively from the film surface and the substrate surface.\nThe interferogram is collected by the image acquisition system. The\nalgorithm processing software is prepared to realize identification\nof the films edge, regional extension, filtering, unwrapping the\nwrapped phase etc, the film thickness distribution in whole field\ncan be obtained to realize the thickness measurement of thin film\nsamples automatically. The results indicate that the new method has\nthe advantages of high precision, whole test and non-contact measurement.
Monte Carlo Eigenvalue Methods in Quantum Mechanics and Statistical Mechanics
Methods
105
1-41
1998
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the underlying mathematics is quite similar in that they are stochastic implementations of the power method. In all cases, optimized trial states can be used to reduce the errors of Monte Carlo estimates.
Condensed Matter
Design Sensitivity of Buckled Thin-Walled Composite Structural Elements
Applied Mechanics Reviews
50
11
S3
1997
10.1115/1.3101848
This paper presents a theory and applications to account for changes in the fundamental, buckling, and post-buckling states when design parameters of a composite material are modified. The influence of micro-mechanical parameters (the volume fraction and the fiber orientation) and of cross-sectional dimensions is investigated. A numerical example for columns made of composite materials is presented. Sensitivity is studied for local buckling loads. Explicit expressions are obtained for the sensitivities in the form of perturbation expansions. A beam under transverse load is also investigated, and geometric design parameters employed to investigate sensitivity. The information from the sensitivity analysis can be used to improve a design by modification of the buckling load.
composite; design sensitivity
Mechanical property characterization of Cu-Sn-In intermetallic thin films using microcantilevers
Proceedings of the International Symposium on the Physical and Failure Analysis of Integrated Circuits, IPFA
2011
Young's modulus, residual stress and fracture strength of Cu-Sn-In intermetallic thin films are characterized using deflection of microcantilevers and beam mechanics. It is shown through finite element modelling and experiments that deflection of the beams at multiple locations allows correction for non-ideality of the beams originating from the undercut, anticlastic curvature and stress gradient. This method has the advantage over common indentation-based approaches, in that with a single sample we can simultaneously extract the Young's modulus, residual stress and fracture strength of the film. Additionally, knowledge of the Poisson's ratio is not required for the calculation of the Young's modulus. © 2011 IEEE.
Anticlastic curvature; Composite micromechanics; Copper; Elasticity; Elastic moduli; Electric network analysis; Extraction; Failure analysis; Finite element modelling; Fracture; Integrated circuits; Micro-cantilevers; Nonideality; Poisson ratio; Poisson's ratio; Residual stresses; Single sample; Stress gradient; Thin films; Tin; Young's Modulus
Surface enhanced SHG from macrocycle, catenane and rotaxane thin films: experiments and theory
Proceedings of SPIE
5724
139-148
2005
Surface enhanced second harmonic generation experiments on supramolecules: macrocycles, catenanes and rotaxanes, monolayers and multilayers deposited by vacuum evaporation on silver layers are reported and described. The measurements show that the molecules are ordered in thin films. The highest order is observed in the case of macrocycles and the lowest in thin films of fumaramide [2] rotaxanes. Also a better ordering is observed in the case of monolayers. The observed second harmonic generation activity is interpreted in terms of electric field induced second harmonic generation. The electric field contributing to SHG signal is created by silver atoms on the surface of silver layers. The measured second order NLO susceptibilities for a fumaramide [2] rotaxane is compared with that obtained by considering only EFISH contribution to SHG intensities. The electric filed on the surface of silver layer is calculated using TINKER molecular mechanics/dynamics software and the Embedded Atom model. An excellent agreement is observed between the calculated and the measured SHG susceptibilities.
Analysis of the heat load of thin metal foil during electron beam scanning
International Journal of Applied Electromagnetics and Mechanics
14
1-4 SPEC.
209-213
2001
The thermal loading of thin metal foils used as extraction windows in high current electron accelerators is one of the most important processes which should be analysed during the design of such devices. Heat loads at metal surface are also of special interest in many other plasma applications. The distribution of heat loads at the surface of thin metal foil is evaluated from the energy absorption in the foil and forced cooling with air flow. Time dependence of temperature distribution at the foil surface is calculated from the two-dimensional heat conduction equation. The simplified heat transient analysis is also given to determine the influence of scanning frequencies, electron beam size and shape, shape of current impulses in scanning coils, energy loss in foil, the beam current and air cooling coefficient on time evolution of temperature for an arbitrary fixed point at the foil in first period of electron beam scanning.
Effect of the electric field on the wave flow regimes of a thin film of a viscous dielectric fluid
Journal of Applied Mechanics and Technical Physics
51
3
359-368
2010
10.1007/s10808-010-0049-3
Waves on the surface of a thin film of a viscous dielectric fluid flowing down the inner surface of one plate of a plane capacitor with alternating voltage applied is considered. It is shown that the volume forces acting from the inhomogeneous electric field are negligibly small in the case of long waves, and the influence of the electric field reduces to the influence of additional pressure onto the film surface. A model equation for determining the deviation of the film thickness from the undisturbed value is derived in the long-wave approximation. Some numerical solutions of this equation are given. © 2010 MAIK/Nauka.
Alternating electric field; Alternating voltages; A-plane; Computer simulation; Dielectric; Dielectric fluid; Down-flowing film; Electric field measurement; Electric fields; Film model; Film surfaces; Inhomogeneous electric fields; Inner surfaces; Long-wave approximation; Long waves; Mathematical models; Model equation; Model equations; Numerical analysis; Numerical solution; Thin films; Volume force; Wave flow; Wave regimes
Fractional Quantum Mechanics
arXiv.org
math-ph
2008
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the L\'evy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the L\'evy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schr\"odinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.\n\nPublished in: Physical Review E62 (Sept 2000) 3135-3145
Local Petrov-Galerkin method for a thin plate
Applied Mathematics and Mechanics
25
2
210-218
2004
Abstract The meshless local Petrov-Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving leastsquares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three-dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply-supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.
Mechanics of Selected Sport Skills.
In Carr, G. |a University of Victoria (ed.), Sport mechanics for coaches. 2nd ed, Champaign, Ill., Human Kinetics, c2004, p.177-201;227.
2004
The mechanics of various sport skills are explained: running, swimming, jumping, throwing, striking, kicking, pulling, pushing, lifting, and carrying, swinging, rotating, balance and stability, and arresting motion.
ABILITY; BALANCE; *BIOMECHANICS; CARRYING; *COACHING (Athletics); *JUMPING; *KICKING (Football); PULLING; PUSHING; ROTATION; *RUNNING; STABILITY; STRIKE; *SWIMMING; SWINGS; *THROWING (Sports); *WEIGHT lifting
Damage Mechanics in Engineering Materials
Studies in Applied Mechanics
46
303-320
1998
In this paper, the derivation of a mechanism-based constitutive law is presented to model the mechanical behavior of fiber-reinforced composites. It allows to account for matrix-cracking, inter facial debonding and sliding in the framework of Continuum Damage Mechanics. Applications are performed on a unidirectional SiC/SiC composite and on concrete specimens.
Hybrid Quantum Mechanics/ Molecular Mechanics Methods and their Application
Handbook of Materials Modeling
241-258
2005
Hybrid quantum mechanics (QM)/molecular mechanics (MM) methods allow simulations for much larger systems than accessible by QM methods alone. The size of many systems of topical interest in chemistry and biochemistry prevents efficient and accurate treatment by quantum mechanical ab initio methods. For reactions in condensed phase and surfaces periodic boundary conditions (PBC) can be applied reducing the size of the problem to a unit cell [1–3]. However, many interesting structure features such as defects or active sites require larger unit cells due to broken space and translation symmetry. A computationally appealing alternative are interatomic potential functions ranging from molecular mechanics force fields to ion-pair potentials. They yield accurate equilibrium structures for the type of systems for which they are parameterized [4], but are usually not suitable to describe the active sites of catalysts with sufficient accuracy. Moreover, unless special modifications are made, they cannot be used to model reactions in which chemical bonding is changed. The cluster model approach is an alternative that makes the calculations on active sites and defects feasible to ab initio methods [5]. Only a fragment of the structure is considered that contains the interesting part, and the surroundings are neglected or approximately included. There exist, however, classes of problems, which require a computational treatment of the whole system. A prominent example is shape selectivity in zeolite catalysis. Although zeolite catalysts with different framework structures have the same active sites in common, they may show very different catalytic performances.
Condensed Matter Physics; Continuum Mechanics and Mechanics of Materials; Nanotechnology; Numerical and Computational Physics; Theoretical and Computational Chemistry
Fractional quantum mechanics
Physical Review E
62
3 Pt A
3135-45
2000
10.1103/PhysRevE.62.3135
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Levy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schrodinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.
Progress in Fracture Mechanics
Progress in Fracture Mechanics
113-115
1983
10.1016/B978-0-08-028691-4.50025-0
This chapter discusses the research activities and industrial applications of fracture mechanics in Portugal. The majority of research activities in fracture mechanics involve welding of structures. The discipline does not only provide a means for selecting steels suited for welding, but also serves a useful purpose in quality control. It can characterize the influence of micro-alloy and carbon-manganese steel weld joints in fracture toughness. In addition, fracture mechanics also finds its application in vehicle structures where weld-joint construction is common. To complement the experimental research activities, finite element methods are developed to calculate the stresses and/or displacements in structural members with cracks. Many of the aforementioned activities in fracture mechanics are being carried out in various universities and industries. Fracture mechanics has yet been widely applied in industry although much of the current research work is directed for future application. Among the areas that deserve attention are high-pressure reservoirs used in chemical and petro-chemical plants, bridges, equipment for hydraulic and thermal power stations, rolling stock, and bus structures and cranes.
Simulation model based on non-newtonian fluid mechanics applied to the evaluation of the embolic effect of emulsions of iodized oil and anticancer drug.
Cardiovascular and interventional radiology
23
4
285-90
2000
10.1007/s002700010070
PURPOSE: To verify the difference in embolic effect between oil-in-water (O-W) and water-in-oil (W-O) emulsions composed of iodized oil and an anticancer drug, epirubicin, using a simulation model based on non-Newtonian fluid mechanics.\n\nMETHODS: Flow curves of pure iodized oil and two types of O-W and W-O emulsions immediately and 1 hr after preparation were examined with a viscometer. Using the yield stress data obtained, we simulated the stagnation of each fluid with steady flow in a rigid tube.\n\nRESULTS: The W-O emulsions were observed to stagnate in the thin tube at a low pressure gradient. However, the embolic effect of the W-O emulsions decreased 1 hr after preparation. The O-W emulsions were stable and did not stagnate under the conditions in which the W-O emulsions stagnated.\n\nCONCLUSION: The simulation model showed that the embolic effect of the W-O emulsions was superior to that of the O-W emulsions.
Antibiotics, Antineoplastic; Antibiotics, Antineoplastic: pharmacology; Carcinoma, Hepatocellular; Carcinoma, Hepatocellular: therapy; Chemoembolization, Therapeutic; Chemoembolization, Therapeutic: methods; Contrast Media; Contrast Media: pharmacology; Drug Combinations; Emulsions; Epirubicin; Epirubicin: pharmacology; Hepatic Artery; Humans; Injections, Intra-Arterial; Iodized Oil; Iodized Oil: pharmacology; Iopamidol; Iopamidol: pharmacology; Liver Neoplasms; Liver Neoplasms: therapy; Models, Biological; Viscosity
Poincaré transformations in nonholonomic mechanics
Applied Mathematics Letters
43
96-100
2015
10.1016/j.aml.2014.12.004
We report on the application of the Poincaré transformation (from the theory of adaptive geometric integrators) to nonholonomic systems-mechanical systems with nonintegrable velocity constraints. We prove that this transformation can be used to express the dynamics of certain nonholonomic systems at a fixed energy value in Hamiltonian form; examples and potential applications are also discussed.
Chaplygin reducing multiplier; Fixed energy; Geometric integrators; Hamiltonians; Hamiltonization; Mathematical transformations; Mechanical systems; Mechanics; Non-holonomic mechanics; Nonholonomic mechanics; Nonholonomic systems; Velocity constraints
Super Chern-Simons Quantum Mechanics
Quantum
24-29
2004
The Super Chern-Simons mechanics, and quantum mechanics of a particle, on the coset super-manifolds SU(2|1)/ U(2) and SU(2|1)/U(1)X U(1), is considered. Within a convenient quantization procedure the well known Chern-Simons mechanics on SU(2)/U(1) is reviewed, and then it is shown how the fuzzy supergeometries arise. A brief discussion of the super-sphere is also included.
High Energy Physics - Theory
The large deviation approach to statistical mechanics
Physics Reports
478
89
2008
10.1016/j.physrep.2009.05.002
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
Statistical Mechanics
Quantitative characterization of the interfacial adhesion of Ni thin film on steel substrate: A compression-induced buckling delamination test
Journal of the Mechanics and Physics of Solids
74
19-37
2015
10.1016/j.jmps.2014.09.012
A compression-induced buckling delamination test is employed to quantitatively char- acterize the interfacial adhesion of Ni thin film on steel substrate. It is shown that buckles initiate from edge flaws and surface morphologies exhibit symmetric, half-penny shapes. Taking the elastoplasticity of film and substrate into account, a three-dimensional finite element model for an edge flaw with the finite size is established to simulate the evolution of energy release rates and phase angles in the process of interfacial buckling- driven delamination. The results show that delamination propagates along both the straight side and curved front. The mode II delamination plays a dominant role in the process with a straight side whilst the curved front experiences almost the pure mode I. Based on the results of finite element analysis, a numerical model is developed to evaluate the interfacial energy release rate, which is in the range of 250–315 J/m2 with the corresponding phase angle from ?41° to ?66°. These results are in agreement with the available values determined by other testing methods, which confirms the effectiveness of the numerical model.
a; adhesion of ni thin; compression-induced buckling delamination test; film on steel substrate; hor; interfacial; quantitative characterization of the; s accepted manuscript
Thin-sheet flow between coalescing bubbles
Journal of Fluid Mechanics
773
R3
2015
10.1017/jfm.2015.253
When two spherical bubbles touch, a hole is formed in the fluid sheet between them, and capillary pressure acting on its tightly curved edge drives an outward radial flow which widens the hole joining the bubbles. Recent images of the early stages of this process (Paulsen et al., Nat. Commun., vol. 5, 2014) show that the radius of the hole rE at time t grows proportional to t1/2, and that the rate is dependent on the fluid viscosity. Here, we explain this behaviour in terms of similarity solutions to a third-order system of radial extensional-flow equations for the thickness and velocity of the sheet of fluid between the bubbles, and determine the growth rate as a function of the Ohnesorge number Oh. The initially quadratic sheet profile allows the ratio of viscous and inertial effects to be independent of time. We show that the sheet is slender for rE≪a if Oh≫1, where a is the bubble radius, but only slender for rE≪Oh2a if Oh≪1 due to a compressional boundary layer of length L∝OhrE, after which there is a change in the structure but not the speed of the retracting sheet. For Oh≪1, the detailed analysis justifies a simple momentum-balance argument, which gives the analytic prediction rE∼(32aγ/3ρ)1/4t1/2, where γ is the surface tension and ρ is the density.
breakup/coalescence; capillary flows; drops and bubbles
Research directions in computational mechanics
Comput. Methods Appl. Mech. Eng.
192
7-8
913-922
2003
Summary: This article is derived from a report prepared by the US National Committee on Theoretical and Applied Mechanics. It is part of that committee's agenda to develop position papers on research directions in various areas of mechanics. This is the most recent work devoted to computational mechanics. The report was authored by a subcommittee consisting of Tinsley Oden (Chair), Ted Belytschko, Ivo Babuska and Thomas Hughes. It also incorporates suggestions made by the USNCTAM at large
Research directions in computational mechanics
Comput. Methods Appl. Mech. Engrg.
192
913-922
2003
This article is derived from a report prepared by the US National Committee on Theoretical and Applied Mechanics. It is part of that committee's agenda to develop position papers on research directions in various areas of mechanics. This is the most recent work devoted to computational mechanics. The report was authored by a subcommittee consisting of Tinsley Oden (Chair), Ted Belytschko, Ivo Babuska and Thomas Hughes. It also incorporates suggestions made by the USNCTAM at large.
Statistical Mechanics of the Glass Transition
arxiv
4
2006
The statistical mechanics of simple glass forming systems in 2 dimensions is worked out. The glass disorder is encoded via a Voronoi tessellation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, $T_g$ and $T_k$, the first associated with jamming and the second associated with the appearance of a quasi-crystal at very low temperatures.
Materials Science; Statistical Mechanics
Erwin Schrodinger and the rise of wave mechanics. II. The creation of wave mechanics
Foundations of Physics
17
12
1141-1188
1987
10.1007/BF01889592
This article (Part II) deals with the creation of the theory of wave mechanics by Erwin Schrödinger in Zurich during the early months of 1926; he laid the foundations of this theory in his first two communications toAnnalen der Physik. The background of Schrödinger's work on, and his actual creation of, wave mechanics are analyzed.
Teaching mechanics via closed-circuit television
Journal of Engineering Education
52
5
311-324
1962
Experiments made at Dept of Aeronautical Eng, Univ of Minnesota, in teaching mechanics and procedures employed are described in connection with discussion of results; experiments were conducted on regular courses during regular class hours; comparison of effectiveness; comparison in statics, and in deformable body mechanics; students and instructor's reaction; studio procedures; summary of experimental mechanics for 7 quarters, statics for 2 quarters, and mechanics of materials 1 quarter.
Engineering education
Design the Structural Mechanics Network Curriculum
{IERI} Procedia
2
362-366
2012
http://dx.doi.org/10.1016/j.ieri.2012.06.102
Abstract In this paper, the Structural Mechanics network curriculum is designed to assist the classroom teaching. Based on Structural Mechanics network curriculum, the design thought, the design measure and the attention matters of network curriculum is introduced. In practice, using this Structural Mechanics network curriculum, the students learning initiative and interest are increased, and better teaching result is obtained.
Design; Network curridulum; Structural mechanics
Respiratory mechanics and bronchodilator responsiveness in patients with the adult respiratory distress syndrome.
Critical care medicine
21
1
78-83
1993
To study the effects of salbutamol (a selective beta 2-adrenergic receptor agonist) on respiratory mechanics in patients with the adult respiratory distress syndrome (ARDS).
Adolescent; Adult; Airway Resistance; Airway Resistance: drug effects; Albuterol; Albuterol: pharmacology; Albuterol: therapeutic use; Female; Humans; Male; Middle Aged; Positive-Pressure Respiration; Prospective Studies; Pulmonary Ventilation; Pulmonary Ventilation: drug effects; Respiration; Respiration, Artificial; Respiration: drug effects; Respiratory Distress Syndrome, Adult; Respiratory Distress Syndrome, Adult: physiopathol; Respiratory Distress Syndrome, Adult: therapy; Respiratory Mechanics; Respiratory Mechanics: drug effects
The spacetime approach to quantum mechanics
Vistas in Astronomy
37
569-583
1993
10.1016/0083-6656(93)90097-4
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schr\"odinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. Sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not "at definite moments of time". An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics is the set of the alternatives defined by whether a particle never crosses a fixed spacetime region or crosses it at least once. The general notion of a set of spacetime alternatives is a partition (coarse-graining) of the histories into an exhaustive set of exclusive classes. With this generalization the sum-over-histories formulation can be said to be in fully spacetime form with dynamics represented by path integrals over spacetime histories and alternatives defined as spacetime partitions of these histories. When restricted to alternatives at definite moments of times this generalization is equivalent to Schr\"odinger-Heisenberg quantum mechanics. However, the quantum mechanics of more general spacetime alternatives does not have an equivalent Schr\"odinger-Heisenberg formulation. We suggest that, in the quantum theory of gravity, the general notion of "observable" is supplied by diffeomorphism invariant partitions of spacetime metrics and matter field configurations. By generalizing the usual alternatives so as to put quantum theory in fully spacetime form we may be led to a covariant generalized quantum mechanics of spacetime free from the problem of time.
The Spacetime Approach to Quantum Mechanics
Quantum
76
6
571-590
1992
10.1016/0083-6656(93)90097-4
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schr"odinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. Sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not ``at definite moments of time''. An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics is the set of the alternatives defined by whether a particle never crosses a fixed spacetime region or crosses it at least once. The general notion of a set of spacetime alternatives is a partition (coarse-graining) of the histories into an exhaustive set of exclusive classes. With this generalization the sum-over-histories formulation can be said to be in fully spacetime form with dynamics represented by path integrals over spacetime histories and alternatives defined as spacetime partitions of these histories. When restricted to alternatives at definite moments of times this generalization is equivalent to Schr"odinger-Heisenberg quantum mechanics. However, the quantum mechanics of more general spacetime alternatives does not have an equivalent Schr"odinger-Heisenberg formulation. We suggest that, in the quantum theory of gravity, the general notion of ``observable'' is supplied by diffeomorphism invariant partitions of spacetime metrics and matter field configurations. By generalizing the usual alternatives so as to put quantum theory in fully spacetime form we may be led to a covariant generalized quantum mechanics of spacetime free from the problem of time.
Buckling, postbuckling, and nonlinear vibrations of imperfect plates
AIAA Journal
25
10
1338-1346
1987
Formulations and computational procedures are presented for studying the geometrically nonlinear behavior, including buckling, postbuckling, and nonlinear vibrations of perfect and imperfect, isotropic and laminated thin plates. The finite-element method is used. The element used is a 48 degree-of-freedom thin flat plate rectangular element capable of modeling arbitrary imperfections. The incremental and total stiffness matrices for large displacement behavior are derived based on the total Lagrangian approach in conjunction with the Hamilton's principle. The geometric imperfections are treated by considering additional terms in the strain-displacement relations. Numerical results are presented for a variety of examples including: (1) postbuckling analysis of an isotropic, imperfect flat plate; (2) postbuckling analysis of a thin, cross-ply laminated imperfect plate; (3) free vibrations of an angle-ply laminated plate; (4) free-vibrations of an imperfect isotropic plate under the action of axial loads; (5) nonlinear free-vibrations of isotropic perfect flat plates; (6) nonlinear vibrations of axially loaded, isotropic perfect flat plates; and (7) nonlinear vibrations of an imperfect laminated plate. The results obtained are compared with existing solutions and good agreement is seen
buckling; vibrating bodies
States in Quantum Mechanics
Compendium of Quantum Physics
742-744
2009
10.1007/978-3-540-70626-7_210
The most general meaning of the term state is a manner of existing, a combination of attributes belonging to a thing (paraphrased from the Oxford English Dictionary). In physics the term state has various, more specific meanings in thermodynamics, in classical mechanics, and in quantum mechanics, but all include the notion that a knowledge of the state is sufficient to make predictions about the future behavior of the system.
Tribology and engine mechanics
MTZ worldwide
63
19-24
2002
Friction and wear-induced material damage within the area of engine mechanics mainly take place on the nanometre scale, and wear progresses at rates of just a few nanome- tres per hour. This article discusses the combination of highly accurate wear measure- ment in real time and physical/chemical analysis of the surface on the micro- and nanoscale as a promising approach to solving customer-defined tribological problems in engine mechanics.
Quantized fracture mechanics and related applications for predicting the strength of defective nanotubes
Convegno IGF XVII Bologna 2004
1-6
2008
A new energy-based theory, Quantized Fracture Mechanics (QFM), is presented. In contrast to Linear Elastic Fracture Mechanics (LEFM) QFM has no restrictions on treating defects of any size and shape. An application for predicting the strength of defective nanotubes concludes the paper.
Dynamic Fracture Mechanics
Journal of Applied Mechanics
59
1
245
1992
10.1115/1.2899458
This volume emphasizes fundamental concepts, both on the development of mathematical models of fracture phenomena and on the analysis of these models. Cases involving stress waves impinging on cracks, tractions suddenly applied to the faces of cracks, and rapid crack growth and arrest are considered in detail. Most of the work is concerned with the behavior of nominally elastic materials, but available results on elastic-plastic and elastic-viscoplastic materials are included. Connections to experimental results and to applications in structural mechanics, seismology, and materials science are noted whenever possible.
Dynamic fracture
Dynamic Fracture Mechanics
Dynamic fracture mechanics
563
1990
10.1017/CBO9780511546761
This volume emphasizes fundamental concepts, both on the development of mathematical models of fracture phenomena and on the analysis of these models. Cases involving stress waves impinging on cracks, tractions suddenly applied to the faces of cracks, and rapid crack growth and arrest are considered in detail. Most of the work is concerned with the behavior of nominally elastic materials, but available results on elastic-plastic and elastic-viscoplastic materials are included. Connections to experimental results and to applications in structural mechanics, seismology, and materials science are noted whenever possible.
Fundamental Notions of Mechanics
Meta
34
4
753-763
1989
Mechanical notions are confined in the mind of most lay persons to items relating to auto mechanics, & their mental representations are often somewhat vague. Some terms & concepts essential to the understanding the description of machines are discussed for French & English. Terms related to the operation of simple machines such as the lever & the inclined plane, terms related to complex machines, & terms involving transmission & transformation of forces & movements are discussed. 2 Tables, 12 References. B. Annesser Murray
English (en2); French (fr2); Lexicology (le5); Translation and Interpretation (tr5); translation, French/English mechanics terminology
Suite of computer-based tools for teaching mechanics of materials
Computer Applications in Engineering Education
4
1
41-49
1996
10.1002/(sici)1099-0542(1996)4:1<41::aid-cae5>3.0.co;2-4
In this article we describe an integrated suite of multimedia and simulation software developed to support the teaching of mechanics of materials. The materials are designed to support both classroom presentation and student-directed learning, provide direct manipulation and visualization, and foster exploration and experimentation.
Wronskian formula for confluent second-order supersymmetric quantum mechanics
Physics Letters A
338
1
7
2005
10.1016/j.physleta.2005.02.020
The confluent second-order supersymmetric quantum mechanics, for which the factorization energies tend to a single value, is studied. We show that the Wronskian formula remains valid if generalized eigenfunctions are taken as seed solutions. The confluent algorithm is used to generate SUSY partners of the Coulomb potential.
coulomb potential; second order supersymmetric quantum mechanics
The evolution of the harmonic oscillator in Quantum Mechanics with Spontaneous Localization
Il Nuovo Cimento B
103
5
511-536
1989
10.1007/BF02753136
The dynamical equation for the harmonic oscillator in Quantum Mechanics with Spontaneous Localization is solved. The evolution of the harmonic oscillator in such a theory is studied. In the case of atomic or nuclear dimensions the results of ordinary quantum mechanics are recovered.
Rheology and local structure of thin films confined between thermally corrugated walls
Physica A: Statistical Mechanics and its Applications
240
328-339
1997
10.1016/S0378-4371(97)00156-8
The rheological behavior of a monolayer film of spherically symmetric molecules confined between two solid surfaces (i.e., walls) is investigated in isostress-isostrain ensemble Monte Carlo simulations. The walls consist of individual atoms interacting with film molecules via the Lennard-Jones potential. By employing the Einstein model, wall atoms are also subject to a harmonic binding potential and may depart from their equilibrium lattice sites so that the walls are thermally corrugated. The film can be exposed to a shear strain by moving the walls relative to each other in transverse directions. Molecular expressions for the shear stress are derived which differ from the ones previously obtained for thermally decoupled walls (i.e., in which wall atoms are rigidly fixed in their equilibrium lattice positions). Unlike the film's local structure the shear stress depends sensitively on the degree of thermal corrugation of the walls. The larger it is the more plastic is the response of the film to an applied shear strain.
A membrane model for the response of thin plates to ballistic impact
Journal of the Mechanics and Physics of Solids
25
4
237-256
1977
10.1016/0022-5096(77)90011-4
The axisymmetric response of an infinite plate to an impacting projectile is determined analytically on the hypothesis that, for large deformations, a ductile plate behaves to a good approximation like a membrane under uniform tension. The lowest projectile velocity that results in perforation (the ballistic limit), and the residual velocity after perforation, then are determined on the basis of a critical-strain failure criterion. A figure of merit that depends only on the material properties of the target and characterizes the resistance of the material to impact appears naturally in the analysis. Variations in the ballistic limit with target thickness and projectile dimensions can be determined when this figure of merit is known. The theoretical ballistic limit and residual velocity for a steel cylinder impacting a titanium plate are found to agree with available measured values. Further support for the membrane model and an estimate of its range of validity are obtained by comparing the maximum displacement of an impulsively-loaded, circular membrane with experimental data for circular plates.
Ultra-thin phospholipid layers physically adsorbed upon glass characterized by nano-indentation at the surface contact level.
Nanotechnology
20
19
195702
2009
10.1088/0957-4484/20/19/195702
Dipalmitoylphosphatic acid was chosen as a model to interpret how molecules physically adsorbed upon glass responded to an infinitesimal oscillation force at the surface contact level. Oscillation of a nano-indentation tip toward the phospholipid layers was driven by a dynamic contact module at a constant harmonic frequency; the phase angle of the oscillation frequency was exponentially relaxed along the nano-scale displacement. The tip-on-molecule contact was thereafter identified and influenced by the characteristic of the physically adsorbed phospholipids. By applying the harmonic displacement of the nano-indentation tip and making a distinction between full contact displacements, the thickness of the phospholipid layers was thereafter estimated. Moreover, the additional force required to penetrate through the physically adsorbed molecules was minor compared to the analogous process for the chemically adsorbed ones. The importance of recognizing the physically adsorbed molecules is relevant to applications of contact mechanics for the distinction of various phospholipids. Furthermore it is very promising to interpret the mechanism by which cells convert mechanical stimuli into biochemical responses on the channels of phospholipids.
Adsorption; Glass; Glass: chemistry; Hardness; Hardness Tests; Lipid Bilayers; Lipid Bilayers: chemistry; Macromolecular Substances; Macromolecular Substances: chemistry; Materials Testing; Membranes, Artificial; Molecular Conformation; Nanostructures; Nanostructures: chemistry; Nanostructures: ultrastructure; Nanotechnology; Nanotechnology: methods; Particle Size; Phospholipids; Phospholipids: chemistry; Surface Properties
Optimal control of cracks in elastic bodies with thin rigid inclusions
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
91
125-137
2011
10.1002/zamm.201000058
In this paper we consider the control of cracks in elastic bodies with rigid inclusion. We first describe the problem statement, provide an equivalent formulation as a variational inequality and prove existence and uniqueness of solutions. Furthermore, we consider this problem as a limiting problem when the elasticity parameters of the inclusion tend to infinity. Then we formulate the optimal control problems and derive an explicit formula for the crack sensitivity and for the energy release rate. We show existence of optimal solutions. The authors consider the control of cracks in elastic bodies with rigid inclusion. They first describe the problem statement, provide an equivalent formulation as a variational inequality and prove existence and uniqueness of solutions. Furthermore, the authors consider this problem as a limiting problem when the elasticity parameters of the inclusion tend to infinity. Then they formulate the optimal control problems and derive an explicit formula for the crack sensitivity and for the energy release rate. It is shown the existence of optimal solutions. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Control problem.; Crack; Non-penetration; Rigid inclusion; Variational inequality
Incomplete statistics and nonextensive generalization of statistical mechanics
Chaos Solitons Fractals
12
8
6
2000
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete statistical mechanics is proved to have the same theoretical characteristics as Tsallis one based on the conventional normalization.
On the derivation of the Schrödinger equation from stochastic mechanics
Foundations of Physics Letters
2
2
113-126
1989
10.1007/BF00696108
It is shown that the existing formulations of stochastic mechanics are not equivalent to the Schrödinger equation, as had previously been believed. It is argued that this is a reflection of fundamental inadequacies in the physical foundations of stochastic mechanics.
Structural model of thorax and abdomen for respiratory mechanics
Mathematical Modelling
7
5-8
1083-1098
1986
This paper describes a structural model of the human rib cage and abdomen that incorporates many geometrical and functional features important to the understanding of respiratory mechanics. The rib cage, diaphragm, abdominal wall and lungs are characterized by nonlinear stress-strain characteristics that depend on muscle activity. The positions, volumes, forces and pressures for each set of initial conditions are found by determining mechanical equilibrium. Many such determinations allow predictions for large displacements. The model predicts passive respiratory system behavior and the action of individual respiratory muscles that are qualitatively consistent with physiological data. Respiratory mechanics includes both pulmonary mechanics and mechanics of the chest wall by which we mean the mechanics of the thorax, the abdomen and the diaphragm. The geometrical complexity of the chest wall and its associated muscles of respiration makes rigorous analysis of the mechanics of the respiratory system difficult. This paper describes a structural model of the respiratory system with two degrees of freedom of motion that has been useful for understanding the actions of respiratory muscles. The model was initially developed to test the hypothesis of Goldman and Mead[1] that the diaphragm, contracting by itself, can expand the abdomen and rib cage in the same way as passive inflation of the respiratory system. The model's predictions suggest that coordinated activity of rib cage musculature and diaphragm are required to expand the respiratory system in this way.
Development of a concept inventory for fluid mechanics
33rd Annual Frontiers in Education, 2003. FIE 2003.
1
T3D_23-T3D_28
2003
10.1109/FIE.2003.1263340
Concept inventories are assessment tools designed to determine the degree to which students understand the concepts of a subject and to identify the misconceptions that students hold. The results of a concept inventory can be used to change the methods of instruction to overcome student misconceptions. A cooperative effort between mechanical engineering faculty at the Universities of Wisconsin-Madison and Illinois, Champaign-Urbana has been directed toward development of a fluid mechanics concept inventory (FMCI). Fluid mechanics typically follows thermodynamics in the sequence of courses in thermal sciences, involves both the mechanics and dynamics of fluids, and builds on basic physics and Newtonian mechanics. This paper describes the process used for development of the FMCI, the details of how we determined the content, and examples of actual content of the instrument itself.
assessment tools; concept-based instruction methods; educational courses; Educational institutions; engineering education; Equations; Fluid dynamics; fluid mechanics; fluid mechanics concept inventory; Gravity; Heat transfer; Mechanical engineering; Mechanical factors; Physics; student misconceptions; thermodynamics; Thermodynamics; Writing
Rock Mechanics for underground mining: Third edition
Rock Mechanics for underground mining: Third edition
1-628
2006
10.1007/978-1-4020-2116-9
Although Rock Mechanics addresses many of the rock mechanics issues which arise in underground mining engineering, it is not a text exclusively for mining applications. It consists of five categories of topics on the science and practice of rock engineering: basic engineering principles relevant to rock mechanics; mechanical properties of rock and rock masses; design of underground excavations in various rock mass conditions; mining methods and their implementation; and guidelines on rock mechanics practice. Throughout the text, and particularly in those sections concerned with excavation design and design of mining layouts, reference is made to computational methods of analysis of stress and displacement in a rock mass. The principles of various computational schemes, such as boundary element, finite element and distinct element methods, are considered. This new edition has been completely revised to reflect the notable innovations in mining engineering and the remarkable developments in the science of rock mechanics and the practice of rock engineering that have taken place over the last two decades. Based on extensive professional, research and teaching experience, this book will provide an authoritative and comprehensive text for final year undergraduates and commencing postgraduate students. For professional practitioners, not only will it be of interest to mining and geological engineers but also to civil engineers, structural and mining geologists and geophysicists as a standard work for professional reference purposes.
Electro-capillary instabilities of thin leaky elastic-viscous bilayers
Physics of Fluids
26
12
1-13
2014
10.1063/1.4904199
Electrohydrodynamic stresses originating from the accumulation of free and induced charges at the confined interface of a thin elastic-viscous bilayer composed of weakly conducting elastic or viscous films can stimulate permanent micropatterns such as creases, wrinkles, holes, and columns. We show that a complete linear stability analysis including all the leading order terms from the Maxwell stresses can accurately predict the key short to long-wave transitions in the length scales, as reported recently by the experimental studies. The generic potential employed for the electric field in the present work overcomes the limitations of the existing theories, which could not precisely predict the length scales especially in the short-wave limit. Importantly, unlike the experimentally reported configuration with a dielectric elastic layer confined by a weakly conducting liquid layer, the bilayers with a weakly conducting elastic layer confined by a dielectric liquid layer can develop interfacial patterns with similar periodicity at smaller field intensity. The transitions from long- to short-wave are compared and contrasted for the bilayers with leaky elastic or viscous films by tuning the field intensity, interfacial tension, and thicknesses of the films. The study unveils that the charged interface of a leaky confined bilayer experiences a larger stress due to the accumulation of free and bound charges, which can significantly reduce the length scales of the instability to the sub-micron regime. The results reported can stimulate further investigation related to the patterning and miniaturization exploiting the field induced instabilities of the elastic films.
Study of the yielding and strain hardening behavior of a copper thin film on a silicon substrate using microbeam bending
Dislocations and Deformation Mechanics in Thin Films and Small Structures
673
Generic
2001
Recently a new microbeam bending technique utilizing triangular beams was introduced. For this geometry, the film on top of the beam deforms uniformly when the beams are deflected, unlike the standard rectangular geometry in which the bending is concentrated at the support. The yielding behavior of the film can be modeled using average stress-strain equations to predict the stress-strain relation for the film while attached to its substrate. This model has also been used to show that the gradient of stress and strain through the thickness of the film, which occurs during beam bending, does not obscure the measurement of the yield stress in our analysis. Utilizing this technique, the yielding and strain hardening behavior of bare Cu thin films has been investigated. The Cu film was thermally cycled from room temperature to 500°C, and from room temperature to-196°C. The film was tested after each cycle. The thermal cycles were performed to examine the effect of thermal processing on the stress-strain behavior of the film.
Bending (deformation); Copper; Materials testing; Metallic films; Microbeam bending; Numerical methods; Silicon; Strain; Strain hardening; Stree-strain equations; Thermal cycling; Thermal effects; Yielding; Yield stress
Effects of Thin Meander Dot Dam Inter-bed on Efficiency and Distribution of CO(2) Injection Flow
2009 Isecs International Colloquium on Computing, Communication, Control, and Management, Vol Iv
482-486
2009
In this paper, we build one new coupled CO(2) injection model DBNSC ( Darcy-Brinkman-Navier-Stokes Carbon Dioxide Injection Model) near well opening based on Navier-Stokes equation, Brinkman equation and Darcy equation to simulate the effects of thin meander dot dam inter-beds on efficiency and distribution Of CO(2) injection. CO(2) injection flow moves through perforation and a thin porous layer towards the far field from the well. The fluid flow follows Darcy's law in the far field and Brinkman equation near the well opening, the Navier-Stokes law in the well. For simplicity, in this paper, we assume the layer between well and far field has homogeneous and isotropic hydraulic properties, and the fluid has constant density. The new model triggers weak variables to implement the coupling between Darcy's law and the Brinkman equations. This paper reviews the results and outlines of the mechanics for building this model.
co2 injection; dbnsc; interbeds; model; simulation
Bohm’s ontological interpretation and its relations to three formulations of quantum mechanics
Synthese
117
1
31-52
1999
The standard mathematical formulation of quantum mechanics is specified. Bohm's ontological interpretation of quantum mechanics is then shown to be incapable of providing a suitable interpretation of that formulation. It is also shown that Bohm's interpretation may well be viable for two alternative mathematical formulations of quantum mechanics, meaning that the negative result is a significant though not a devastating criticism of Bohm's interpretation. A preliminary case is made for preferring one alternative formulation over the other.
Inverse method for detection and sizing of cracks in thin sections using a hybrid genetic algorithm based signal parametrisation
Theoretical and Applied Fracture Mechanics
49
2
185-198
2008
A hybrid-GA method, based on signal parameterization, has been reported here for the improved detection and sizing of surface cracks of small sizes/depths in thin sections. The method relies on parameterizing the composite reference from the defect into its individual components i.e., the crack tip diffracted echo and the corner trap echo and subsequently use the relative arrival time technique (RATT). The phased array ultrasonic technique was employed in the investigation. Both experimental and simulated signals were used in the study. It is shown through both simulations and experiments that the hybrid-GA is successful in parameterizing both non-overlapping and overlapping echoes encountered in thin sections. It is additionally shown that the hybrid-GA improves the signal to noise ratio and correct for under-sampling of data. © 2007 Elsevier Ltd. All rights reserved.
Computer simulation; Crack tips; Cracks; Finite d; Computer simulation; Crack tips; Finite difference; Cracks; Hybrid genetic algorithm; Inverse method; Phased
Analytical method for the construction of solutions to the Foppl-von Karman equations governing deflections of a thin flat plate
International Journal of Non-Linear Mechanics
47
3
1-6
2012
10.1016/j.ijnonlinmec.2012.01.004
We discuss the method of linearization and construction of perturbation solutions for the F??ppl-von K??rm??n equations, a set of non-linear partial differential equations describing the large deflections of thin flat plates. In particular, we present a linearization method for the F??ppl-von K??rm??n equations which preserves much of the structure of the original equations, which in turn enables us to construct qualitatively meaningful perturbation solutions in relatively few terms. Interestingly, the perturbation solutions do not rely on any small parameters, as an auxiliary parameter is introduced and later taken to unity. The obtained solutions are given recursively, and a method of error analysis is provided to ensure convergence of the solutions. Hence, with appropriate general boundary data, we show that one may construct solutions to a desired accuracy over the finite bounded domain. We show that our solutions agree with the exact solutions in the limit as the thickness of the plate is made arbitrarily small. ?? 2012 Elsevier Ltd. All rights reserved.
Deflections of thin flat plates; Discrete residual error analysis; F??ppl-von K??rm??n equations; Homotopy analysis; Non-linear PDEs; Perturbation methods
Molecular Dynamics Simulation on Microstructure and Deformation Properties Related to Porosity in Al Thin Film Sputtered on Si Substrate
JSME International Journal Series A Solid Mechanics and Material Engineering
44
2
214-221
2001
A material system of Al sputtered on crystalline Si was dealt with as one of the simple material models for semiconductor material systems. To investigate qualitative properties of sputtered films on an atomic scale, simulations were conducted by a molecular dynamics (MD) method using two film models; i.e. a deposition model based on MD simulations of sputtering process and a crystal model using a crystalline Al film instead of a deposited one. The surface roughness and porosity, which are defined in this work, were found to decrease with an increase in the incident energy of atoms. Relationships between tensile deformation properties and porosities in simulated thin films were also investigated. Although the porosity was found to affect the tensile strength in the direction parallel to the substrate surface, it was revealed that the tensile strength in the direction perpendicular to the substrate surface was hardly influenced by the difference in the porosity.
Emergence of classical theories from quantum mechanics
Journal of Physics: Conference Series
361
012035
2012
10.1088/1742-6596/361/1/012035
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's "first kind of dynamics", and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.
Quantum Entanglement, Bohmian Mechanics, and Humean Supervenience
Australasian Journal of Philosophy
00
00
1-17
2013
10.1080/00048402.2013.832786
David Lewis is a natural target for those who believe that findings in quantum physics threaten the tenability of traditional metaphysical reductionism. Such philosophers point to allegedly holistic entities they take both to be the subjects of some claims of quantum mechanics and to be incompatible with Lewisian metaphysics. According to one popular argument, the non-separability argument from quantum entanglement, any realist interpretation of quantum theory is straightforwardly inconsistent with the reductive conviction that the complete physical state of the world supervenes on the intrinsic properties of and spatio-temporal relations between its point-sized constituents. Here I defend Lewis’s metaphysical doctrine, and traditional reductionism more generally, against this alleged threat from quantum holism. After presenting the non-separability argument from entanglement, I show that Bohmian mechanics, an interpretation of quantum mechanics explicitly recognized as a realist one by proponents of the non-separability argument, plausibly rejects a key premise of that argument. Another holistic worry for Humeanism persists, however, the trouble being the apparently holistic character of the Bohmian pilot wave. I present a Humean strategy for addressing the holistic threat from the pilot wave by drawing on resources from the Humean best system account of laws.
holism; Humean supervenience; quantumentanglement; reductionism
Quantum mechanics in structure-based drug design.
Current opinion in drug discovery & development
9
3
370-9
2006
In principle, quantum mechanics provides a more accurate representation of molecular systems than other modeling approaches. While this notion is not a matter of dispute, it has not yet been definitively demonstrated within the realm of structure-based drug design that the use of quantum mechanical methods over the use of classical modeling approaches is justified in consideration of the increase in expense associated with quantum mechanical methods. Demonstrating that quantum mechanics-based methods can be superior to simpler models, and resolving problems relating to estimating the effects of conformational entropy, will provide key areas of interest in the coming years for in silico structure-based drug design. Recent applications using quantum mechanical methods in structure-based drug design are reviewed herein, and applications ranging from scoring receptor-ligand interactions using quantum mechanics to the generation of quantitative structure-activity relationships using quantum mechanics-derived descriptors are discussed.
Drug Design; Humans; Molecular Structure; Quantum Theory; Structure-Activity Relationship
The physical principles of quantum mechanics. A critical review
The European Physical Journal Plus
127
1
12
2012
10.1140/epjp/i2012-12012-4
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.
The adiabatic static linear response function in nonextensive statistical mechanics
Physica A: Statistical Mechanics and its Applications
414
414-420
2014
10.1016/j.physa.2014.07.057
We analyze the difference between the three generations of the energy constraint in nonextensive statistical mechanics. Using the third generation of the energy constraint, we revise the isothermal static linear response function and then derive the static linear response function under the adiabatic condition. We present the relationship between the isothermal and adiabatic linear response functions.
Adiabatic condition; Linear response theory; Nonextensive statistical mechanics
Covariant geometric quantization of nonrelativistic time-dependent mechanics
J. Math. Phys.
43
56-68
2002
We provide geometric quantization of the vertical cotangent bundle V*Q –> Q –> R equipped with the canonical Poisson structure and treated as a momentum phase space of nonrelativistic time-dependent mechanics. We show that this quantization is equivalent to fiberwise quantization of symplectic fibers of V*Q –>R and that the quantum algebra of time-dependent mechanics is an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra and describes quantum evolution in time-dependent mechanics as a parallel transport.
Life Prediction of Solder Joints by Damage and Fracture Mechanics
Journal of Electronic Packaging, Transactions of the ASME
118
4
193-200
1996
Much research has been done on Surface Mount Technology (SMT) using the Finite Element Method (FEM). Little of this, however, has employed fracture mechanics and/or continuum damage mechanics. In this study, we propose two finite element approaches incorporating fracture mechanics and continuum damage mechanics to predict time-dependent and temperature-dependent fatigue life of solder joints. For fracture mechanics, the J-integral fatigue formula. da/dN = C(ΔJ) m, is used to quantify fatigue crack growth and the fatigue life of J-leaded solder joints. For continuum damage mechanics, the anisotropic creep-fatigue damage formula with partially reversible damage effects is used to find the initial crack, crack growth path, and fatigue life of solder joints. The concept of partially reversible damage is especially novel and, based on laboratory tests we have conducted, appears to be necessary for solder joints undergoing cyclic loading. Both of these methods are adequate to predict the fatigue life of solder joints. The advantage of the fracture mechanics approach is that little computer time is required. The disadvantage is that assumptions must he made on the initial crack position and the crack growth path. The advantage of continuum damage mechanics is that the initial crack and its growth path are automatically evaluated, with the temporary disadvantage of requiring a lot of computer time.
Fracture mechanics
London, Edward Arnold
23
10
303
1986
10.1007/978-94-007-2595-9
The application of fracture mechanics to the design of ceramic structures will require the precise measurement of crack growth and fracture resistance of these materials over their entire range of anticipated service temperatures and standardized test methods for making such measurements. The development of a standard test for measuring the plane strain fracture toughness is sought. Stress intensity factor coefficients were determined for three varieties of chevron-notch specimens, and fracture toughness measurements were made on silicon nitrides, silicon carbides, and aluminum oxides to assess the performance of each specimen variety. It was determined that silicon nitride and silicon carbides have flat crack growth resistance curves, but aluminum oxide does not. Additionally, batch-to-batch differences were noticed for the aluminum oxide. Experiments are continuing to explain the rising crack growth resistance and batch-to-batch variations for the aluminum oxide.
Contact mechanics
Cambridge University Press
1985
10.1016/0301-679X(86)90085-X
This treatise is concerned with the stresses and deformation of solid bodies in contact with each other, along curved surfaces which touch initially at a point or along a line. Examples are a railway wheel and rail, or a pair of gear wheel teeth. Professor Johnson first reviews the development of the theory of contact stresses since the problem was originally addressed by H. Hertz in 1882. Next he discusses the influence of friction and the topographical roughness of surfaces, and this is incorporated into the theory of contact mechanics. An important feature is the treatment of bodies which deform plastically or viscoelastically. In addition to stationary contact, an appreciable section of the book is concerned with bodies which are in sliding or rolling contact, or which collide.
Picosecond transient reflectance of thin metal films.
Journal of Applied Physics
66
7
2968
1989
10.1063/1.344178
Reports on the picosecond transient reflectance (PTR) of thin metal films. Temperature dependence of PTR of metals; Extraction of the thermal transport parameters of thin films; Thermal diffusivity of thin metal films.
METALS; REFLECTANCE; THERMAL diffusivity; THIN films
The mechanics of a semi-erect posture: locomotor force studies in Alligator.
Am. Zool.
40
6
1260 (Abstract only)
2000
Most studies of locomotor mechanics have focused on species utilizing erect postures. In order to begin to understand the mechanics of non-erect postures, we quantify the single limb locomotor function and whole body mechanics of Alligator mississippiensis using force platform arrays. Whole body mechanics are used to evaluate phase relationships of potential and total kinetic energies used by Alligator during high walks. Single limb data are used to quantify limb function in body support, acceleration/deceleration, and lateral impulse.
anatomy; gait; locomotion; mississippiensis
The space of density states in geometrical quantum mechanics
Differential Geometric Methods in Mechanics and Field Theory
35-56
2007
We present a geometrical description of the space of density states of a quantum system of finite dimension. After presenting a brief summary of the geometrical formulation of Quantum Mechanics, we proceed to describe the space of density states $\D(\Hil)$ from a geometrical perspective identifying the stratification associated to the natural $GL(\Hil)$--action on $\D(\Hil)$ and some of its properties. We apply this construction to the cases of quantum systems of two and three levels.
Quantum Physics
Thermodynamics and statistical mechanics in the special theory of relativity
Physics Reports
1
2
31-54
1971
10.1016/0370-1573(71)90006-8
We consider that a relativistic formulation of thermodynamics or statistical mechanics has as its aim to provide a unique correspondence between the descriptions which different observers in uniform relative motion will give of a thermodynamic system. We show how this favours Ott's formulation of relativistic thermodynamics. We also show in how far one is led to the same conclusion by considering a relativistic formuation of statistical mechanics. In our discussions we restrict ourselves throughout to the special theory of relativity.
Applications of density matrix in the fractional quantum mechanics
Arxiv preprint arXiv10124958
1-11
2010
10.1016/j.physleta.2011.05.055
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theory in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics.
mathematical physics; quantum gases; quantum physics
Trapped interacting Bose gas in nonextensive statistical mechanics
Physical Review E
65
4
046105
2002
10.1103/PhysRevE.65.046105
We study the Bose-Einstein condensation (BEC) phenomenon in an interacting trapped Bose gas using the semiclassical two-fluid model and nonextensive statistical mechanics. The effects of nonextensivity characterized by a parameter are explored by calculating the temperature dependent thermodynamic properties, fraction of condensed particles, and density distributions of condensed and thermal components of the system. It is found that nonextensivity in the underlying statistical mechanics may have large effects on the BEC transition temperature.
Minimum uncertainty wave packet in relativistic quantum mechanics
American Journal of Physics
78
2
176
2010
10.1119/1.3238469
In nonrelativistic quantum mechanics in one dimension a wave packet can be constructed for which the minimum uncertainty relation for position and momentum, Δ x Δ p = ℏ / 2 , holds exactly. The wave function of the wave packet is Gaussian and satisfies the Schrödinger equation for a harmonic oscillator potential. We illustrate a similar situation in relativistic quantum mechanics for the one-dimensional Dirac equation.
The physics behind path integrals in quantum mechanics
American Journal of Physics
51
1983
328
1983
10.1119/1.13472
We present a simple pedagogical discussion of the physics of path integrals in nonrelativistic quantum mechanics. Rather than show that the path integral gives the standard results of quantum mechanics, as is usually done in the literature, we instead discuss why it does so. Specifically, we discuss why the phase factor associated with each path is given by the classical action. We construct the path integral using Huygens’ principle. Finally, we show that the existence of many paths is a consequence of the spreading of the quantum‐mechanical wave function.
Causality and Probability in Quantum Mechanics
AIP Conference Proceedings
1101
1
150-160
2009
10.1063/1.3109935
This paper critically examines the view of quantum mechanics that emerged shortly after the introduction of quantum mechanics and that has been widespread ever since. Although N. Bohr, P. A. M. Dirac, and W. Heisenberg advanced this view earlier, it is best exemplified by J. von Neumann’s argument in Mathematical Foundations of Quantum Mechanics\r\n(1932) that the transformation of “a [quantum] state … under the action of an energy operator … is purely causal,” while, “on the other hand, the state … which may measure a [given] quantity … undergoes in a measurement a non‐casual change.” Accordingly, while the paper discusses all four of these arguments, it will especially focus on that of von Neumann. The paper also offers an alternative, noncausal, view of the quantum‐mechanical situation and considers the differences between the ensemble and the Bayesian approaches to quantum mechanics from this perspective.
Statistical mechanics of phase–space curves
Physica A: Statistical Mechanics and its Applications
393
244-255
2014
10.1016/j.physa.2013.09.023
Abstract\nWe study the classical statistical mechanics of a phase–space curve. This unveils a mechanism that, via the associated entropic force, provides us with a simple realization of effects such as confinement, hard core, and asymptotic freedom. Additionally, we obtain negative specific heats, a distinctive feature of self-gravitating systems, and negative pressures, typical of dark energy.
Fractional Superspace Formulation of Generalized Mechanics
Dimension Contemporary German Arts And Letters
May
15
1993
Supersymmetric (pseudo-classical) mechanics has recently been generalized to it fractional/ supersymmetric mechanics. In such a construction, the action is invariant under fractional supersymmetry transformations, which are the F ,rm th roots of time translations (with F=1,2,...). Associated with these symmetries, there are conserved charges with fractional canonical dimension $1+1/F. Using pg variables satisfying t F=0, we present a fractional-superspace formulation of this construction.
Probability and the Interpretation of Quantum Mechanics
The British Journal for the Philosophy of Science
24
1
1029
1973
10.1093/bjps/24.1.1
I present a simple, Intuitive account of quantum mechanics as an essentially statistical theory of a determinate domain. I defend this account against objections stemming from the no-Hidden-Variable proofs by developing a classical, Propositional language for the theory that admits of ordinary bivalent valuations. The no-Joint-Distribution proofs are then used to show that these valuations allow for precisely the probabilities of quantum mechanics-Nothing less but also nothing more.
Is Quantum Mechanics the Whole Truth ?
Quo Vadis Quantum Mechanics?
Leggett
8
2004
10.1063/1.2947702
I first briefly review the reasons for speculating that the linear formalism of standard quantum mechanics may break down at some stage between the level of the atom and that of human consciousness. Next, I review the existing experimental evidence on this question, with particular emphasis on the spectacular advances of the last two years in quantum optics and condensed matter physics. Finally, I speculate on possible directions for future experiments in this area.
Alternative descriptions in quaternionic quantum mechanics
Journal of Mathematical Physics
46
1-16
2005
10.1063/1.1873040
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum optical physical system, in the realm of quaternionic quantum mechanics, while no alternative can exist in complex quantum mechanics, and we discuss some differences between them.
Remarks on Mohrhoff's interpretation of quantum mechanics
Foundations of Physics
34
1
59-73
2004
10.1023/B:FOOP.0000012009.79192.ff
In a recently proposed interpretation of quantum mechanics, U. Mohrhoff advocates original and thought-provoking views on space and time, the definition of macroscopic objects, and the meaning of probability statements. The interpretation also addresses a number of questions about factual events and the nature of reality. The purpose of this note is to examine several issues raised by Mohrhoff's interpretation, and to assess whether it helps providing solutions to the long-standing problems of quantum mechanics.
Some fundamental issues of damage mechanics
Mechanics of Materials
21
3
217-230
1995
The present paper focuses on the discussion of a set of rational criteria for the selection of the damage parameter. The paper considers scalar, second-, fourth-, and six-order tensor representations of damage and evaluates the accuracy with which they approximate exact, micromechanical solutions. Considerations of geometrical, stiffness and failure criteria favor the selection of effective stiffness as being the most appropriate choice for the damage parameter.
Brittle failure; Characteristic lengths; Damage; Damage parameter; Effective continuum models; Elastic percolation; Microcracks
Nicolai map in supersymmetric quantum mechanics
Theoretical and Mathematical Physics
86
1
50-54
1991
10.1007/BF01018496
The Nicolai map is found in the case of quantum mechanics with a fermionic degree of freedom. It is shown that in quantum mechanics the existence of this map does not require the presence of supersymmetry. For the example of the problem of an electron in a two-dimensional magnetic field the connection between supersymmetry and stochastic Markov processes of the most general form is demonstrated. The Nicolai map and the correspon- ding Fokker-Planck equation for the Coulomb problem in two dimensions are given explicitly.
Mechanics of plates
Change
1983
30
2011
The theory of deformed plates in mechanical equilibrium is formulated and properties of circular plates lifted at the center are discussed.
Quantum Mechanics
Lectures in Mathematical Sciences
23
168
2004
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio $|x|/|v|$ between the space coordinate $x$ and the velocity $v$. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schr\"odinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function $\phi$ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.
Quantum Physics
Quantum Mechanics
arXiv
168
2004
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio $|x|/|v|$ between the space coordinate $x$ and the velocity $v$. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schr\"odinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function $\phi$ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.
Quantum Physics
XDP Mechanics
OCEANS 87
200,201,202,203,204,205,206
1987
10.1109/OCEANS.1987.1160872
Interaction between the oceanic vertical shear field and the natural response of a recently developed expendable dissipation profiler (XDP) causes errors to be introduced in small scale velocity measurements. A numerical model was developed to study this problem and two sources of errors were determined, the primary source being the shear induced torques at the instrument length scale.
Fracture mechanics
International Journal of Solids and Structures
37
171-183
1986
10.1007/978-94-007-2595-9
The application of fracture mechanics to the design of ceramic structures will require the precise measurement of crack growth and fracture resistance of these materials over their entire range of anticipated service temperatures and standardized test methods for making such measurements. The development of a standard test for measuring the plane strain fracture toughness is sought. Stress intensity factor coefficients were determined for three varieties of chevron-notch specimens, and fracture toughness measurements were made on silicon nitrides, silicon carbides, and aluminum oxides to assess the performance of each specimen variety. It was determined that silicon nitride and silicon carbides have flat crack growth resistance curves, but aluminum oxide does not. Additionally, batch-to-batch differences were noticed for the aluminum oxide. Experiments are continuing to explain the rising crack growth resistance and batch-to-batch variations for the aluminum oxide.
The importance of rock mechanics to the petroleum industry
Ninth International Congress on Rock Mechanics, Vol 3, Proceedings
1525-1549
2002
This general report is a summary of the most recent breakthroughs in rock mechanics applied to petroleum engineering. Whenever possible, the major differences from traditional civil and mining engineering concerns are clearly defined. For the noninitiated, a description is given of each topic and its importance to the industry. This is followed by a brief discussion of recent developments and opinionated proposals for future research needs.
anisotropic poroelasticity; berea sandstone; borehole; discrete multifractals; double-porosity; flow; fluid; mandels problem; naturally fractured reservoirs; porous-media
Modified de Broglie-Bohm approach to quantum mechanics
Journal of Genetic Counseling
2002
August
329-343
2002
10.1023/A:1021212410819
A modified de Broglie-Bohm (dBB) approach to quantum mechanics is presented. In this new deterministic theory, which uses complex methods in an intermediate step, the problem of zero velocity for bound states encountered in the dBB formulation does not appear. Also this approach is equivalent to standard quantum mechanics when averages of dynamical variables like position, momentum and energy are taken.
15; 2002; 4; august 2002; modified de broglie-bohm approach; ndations of physics letters; no; to; vol
Classical and quasi-classical aspects of supersymmetric quantum mechanics
Methods
8
1995
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the classical equations of motion are given and their properties are discussed in some detail. The corresponding quantum model is constructed by canonical quantization. The quantum model is analyzed by Feynman's path integral within a stationary-phase approximation. A quasi-classical quantization rule is derived, which is applicable when supersymmetry is exact or spontaneously broken.
Molecular Mechanics (MM3) Parameterization of Hydroxylamine and Methyl Derivatives
Journal of computational …
15
8
866-874
1994
http://dx.doi.org/10.1002/jcc.540150808
Based on results of electron diffraction, gas phase infrared spectroscopy (IR), and MP2/6-31 + G* ab initio calculations, a set of molecular mechanics (MM3) parameters was developed for molecules containing the N(sp(3))-O(sp(3)) moiety. Using this set of parameters, MM3 is able to reproduce structures (bond lengths and bond angles) and vibrational spectra satisfactorily. (C) 1994 by John Wiley and Sons, Inc.
ecular mechanics; mm3; parameterization of hydroxylamine and
Latency Versus Complementarity: Margenau and Bohr on Quantum Mechanics
British Journal for the Philosophy of Science
37
2
1986
Margenau claims that his interpretation of quantum mechanics is superior to bohr's. i show how evaluation of his claim turns on their rival views of the following: the physical paradoxes, the nature of physical theory, realism, the proper objects of quantum theory, the meaning of the indeterminacy relations, and the meaning of latency and complementarity.
Bohr, N; Margenau, H; Physical Theory; Quantum Mechanics; Science
Instanton molecular vacuum in N = 1 supersymmetric quantum mechanics
Nuclear Physics B
274
2
475-508
1986
10.1016/0550-3213(86)90295-6
The vacuum of N = 1 quantum mechanics is shown to be the dilute gas of instanton-anti-instanton molecules with zero topological charge. The quantum fluctuations near these molecules are nontrivial due to the quasizero mode. The special technique of integration along this mode in the functional space beyond the gaussian approximation is worked out. We also discuss nonsupersymmetric quantum mechanics with fermions and calculate the nonperturbative part of the corresponding vacuum energy.
On the representation of the energy equations in fluid mechanics in integral form
Contributions on transport phenomena in fluid mechanics and related topics
401-409
1979
A comparison between the energy equation in fluid mechanics (kinetic energy equation) and that for thermo-fluid mechanics (first law of thermodynamics) in their integral forms is presented.
Continuum Damage Mechanics : Part I — General Concepts
Journal of Applied Mechanics
55/29
2013
Continuum Damage Mechanics (C.D.M.) has developed continuously since the early works of Kachanov and Rabotnov. It constitutes a practical tool to take into account the various damaging processes in materials and structures at a macroscopic continuum level. The main basic features of C.D.M. are considered in the first part together with its present capabilities, including damage definitions and measures, and its incorporation into a thermodynamic general framework. Practical damage growth equations will be reviewed in the second part of the paper.
Fracture Mechanics of Delamination in ARALL Laminates
Engeneering Fracture mechanics
30
6
827-837
1988
fFracture mechanics of delamination in ARALL lanlinates is examined by using a finite element method employing special singular elements. Since these special elements contain the exact stress singularity, the delamination stress intensity factors and energy release rates can be evaluated conveniently. Solution convergence is studied to demonstrate the efficiency of this method. To ensure the validity of the result, the numerical prediction is compared with experimental results. Very good agreement is obtained.
Pathway Model and Nonextensive Statistical Mechanics
Sciences-New York
October 2010
14
2010
The established technique of eliminating upper or lower parameters in a general hypergeometric series is profitably exploited to create pathways among confluent hypergeometric functions, binomial functions, Bessel functions, and exponential series. One such pathway, from the mathematical statistics point of view, results in distributions which naturally emerge within nonextensive statistical mechanics and Beck-Cohen superstatistics, as pursued in generalizations of Boltzmann-Gibbs statistics.
Mathematical Physics; Statistical Mechanics
A molecular mechanics-type approach to turbulence
Mathematical and Computer Modelling
26
12
85-96
1997
10.1016/S0895-7177(97)00242-2
A molecular mechanics-type formulation is applied to the cavity problem to generate primary vortices, secondary vortices, and turbulent flow. The fluid considered is water. Turbulence is defined in terms of the absence of a primary vortex and the rapid appearance and disappearance of many small vortices. The mechanism fbr generating turbulent flow lies in the generation of large repulsive forces between the particles of the model. This results from the increase in particle speeds due to the increase in wall speed.
molecular mechanics; turbulence; vortices
Localization, resonance and non-Hermitian quantum mechanics
Physica A
314
1-4
170-176
2002
10.1016/S0378-4371(02)01070-1
A type of non-Hermitian generalization of quantum mechanics is discussed. We introduce an imaginary vector potential to the Hamiltonian of systems such as Anderson-localization systems and mesoscopic systems. In these systems the imaginary part of the wave number of the eigenfunction asymptote ??(x) ??? eikx is of fundamental interest. We propose the use of the imaginary vector potential for the measurement of the localization length and the resonance lifetime. ?? 2002 Elsevier Science B.V. All rights reserved.
Anderson localization; Ballistic conduction; Mesoscopic system; Non-Hermitian quantum mechanics; Resonance
Structural mechanics for electromagnetic rail guns
2004 12th Symposium on Electromagnetic Launch Technology
127-132
2004
10.1109/ELT.2004.1398060
The objective of this investigation is to explore potential designs and appropriate materials for a lightweight fieldable electromagnetic rail gun. Lessons learned from the previous launcher designs are reviewed and discussed from a mechanics point of view. Analyses are performed with a conceptually workable gun bore to illustrate the requirement of a fieldable gun construction. Both static and dynamic responses of the rail gun are discussed. The study provides a fundamental understanding for developing a fieldable rail gun in terms of mechanics and material requirement.
Recent Developments in Supersymmetric Quantum Mechanics
Turkish Journal of Physics
19
230-248
1995
Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of Pauli's Hamiltonian are also considered. In particular, the paramagnetisation of a non-interacting electron gas is related to a modified version of Witten's index. We also show that the supersymmetry in this system provides a new counter example for the paramagnetic conjecture.
C.4
Mechanics of Textile Composites Conference - Part 2
NASA
October
1995
This document is a compilation of papers presented at the Mechanics of Textile Composites Conference in Hampton, Virginia, December 6-8, 1994. This conference was the culmination of a 3-year program that was initiated by NASA late in 1990 to develop mechanics of textile composites in support of the NASA Advance Composites Technology Program (ACT). The goal of the program was to develop mathematical models of textile preform materials and test methods to facilitate structural analysis and design. Participants in the program were from NASA, academia, and industry.
Thin film encapsulation of thin-cathode organic electroluminescent devices
Imid/Idmc 2006: The 6th International Meeting on Information Display/the 5th International Display Manufacturing Conference, Digest of Technical Papers
1034-1037
2006
We have developed a novel thin film encapsulation method for thin-cathode OLED by introducing organic (not polymer)/inorganic multiple thin films to protect device, which is shown to slow down the permeation rate of moisture and oxygen. From the stability test of devices, the projected lifetime of thin-cathode OLED device with thin film encapsulation was similarly to that with glass lid encapsulation.
encapsulation; LIGHT-EMITTING DEVICES; thin-cathode
Statistical Mechanics
Statistical Mechanics
2011
This classic text, first published in 1972, is designed for graduate physics courses in statistical mechanics. The second edition, published in 1996, incorporated three comprehensive chapters on phase transitions and critical phenomena. This third edition includes new sections on Bose-Einstein condensation and degenerate Fermi behavior of ultracold atomic gases, and two new chapters on computer simulation methods and the thermodynamics of the early universe. We have also added new sections on chemical and phase equilibrium, and expanded our discussions of correlations and scattering, quantized fields, finite-size effects and the fluctuation-dissipation theorem. We hope this new edition will continue to provide new generations of students with a solid training in the methods of statistical physics. -Bose-Einstein condensation in atomic gases -Thermodynamics of the early universe -Computer simulations: Monte Carlo and molecular dynamics -Correlation functions and scattering -Fluctuation-dissipation theorem and the dynamical structure factor -Chemical equilibrium -Exact solution of the two-dimensional Ising model for finite systems -Degenerate atomic Fermi gases -Exact solutions of one-dimensional fluid models -Interactions in ultracold Bose and Fermi gases -Brownian motion of anisotropic particles and harmonic oscillators. © 2011 Elsevier Ltd All rights reserved.
Quantum Mechanics
American Journal of Physics
53
9
168
2004
10.1119/1.14383
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio $|x|/|v|$ between the space coordinate $x$ and the velocity $v$. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schr\"odinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function $\phi$ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.
Econophysics, statistical mechanics approach to
Encyclopedia of Complexity and System Science
24
2009
This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.
Applications; Data Analysis; Physics and Society; Statistical Finance; Statistical Mechanics; Statistics and Probability
Mechanics and the Relativity Postulate
The Genesis of General Relativity
250
1199-1212
2007
It would be highly unsatisfactory if the new conception of the notion of time, which is characterized by the freedom of Lorentz transformations, could be accepted as valid for only a subfield of physics. [98] Now, many authors state that classical mechanics is opposed to the relativity postulate, which has been taken here to be the foundation of electrodynamics.
Fracture-Mechanics of Bone
Journal of Biomechanical Engineering-Transactions of the Asme
115
4
549-554
1993
This paper reviews the progress that has been made in applying the principles of fracture mechanics to the topic of fracture of long bones. Prediction of loading conditions which result in the propagation of fractures in bones has been of interest to the field of trauma biomechanics and orthopedics for over one hundred years. Independent verifications, by various investigators, of bone fracture mechanics parameters are reviewed and investigations of the effects of bone density and specimen thickness on the critical fracture mechanics parameters and of other factors such as critical crack length and plastic zone size in bovine femoral bone, and the effects of crack velocity on fracture mechanics parameters in bovine tibial bone are discussed. It took over ten years for the techniques of bone fracture mechanics to be applied to human compact bone, due primarily to geometric constraints from the smaller size of human bones. That work will be reviewed along with other continuing work to define the orientation dependence of the fracture mechanics parameters in bone and to refine the experimental techniques needed to overcome the geometric constraints of specimen size. A discussion is included of work still needed to determine fracture mechanics parameters for transverse and longitudinal crack propagation in human bone and to establish the effects of age on those parameters. Finally, a discussion will be given of how this knowledge needs to be extended to allow prediction of whole bone fracture from external loading to aid in the design of protective systems.
compact bone; density; specimen thickness
Quantum and subquantum mechanics
Nuovo Cimento B
58B
2
286-300
1980
Proposes an interpretation of microstructures which describes the particle in an objective way and which contains quantum mechanics as a limit case. In the author's picture there is no measurement paradox, probabilities are associated in a simple fashion to single microsystems, the Einstein-Podolsky-Rosen paradox loses its paradoxical aspect and the difficulties inherent in the Heisenberg principle are avoided
indeterminancy; measurement theory
On Quantum Mechanics
Zeitschrift F��r Physik
33
9
42
1998
We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization.
Theoretical and Applied Mechanics
Theoretical and Applied Mechanics
117-133
1985
10.1016/B978-0-444-87707-9.50016-6
An overview over important wave load problems for ships and offshore structures are given. Three main topics are dealt with in details. These area) ship motions at forward speed, b) slowly varying and mean wave loads and c) separated flow problems. A brief introduction to the topics are given. Unsolved theoretical problems of practical interest are discussed.
Quantum mechanics gets physical
Science News
180
4
12
2011
The article focuses on a report in the July 2011 issue of the periodical "Physical Review A," by researches including theoretical physicist Giulio Chiribella of the Perimeter Institute for Theoretical Physics. The study attempts to find a set of axioms to obtain a better physical understanding of quantum mechanics. Topics include the purification principle, entanglement, and teleportation.
Pulmonary mechanics and gas transfer after VAD implantation: Pilot study of pulmonary function test measures before and after LVAD implimplantation
Chest
140
4 MEETING ABSTRACT
2011
PURPOSE: Pulmonary mechanics and gas transfer in congestive heart failure (CHF) patients are abnormal. LVEF is one of the independent factors that affects FEV1 besides age and smoking. Respiratory abnormalities such as airway obstruction, restrictive defects, and inspiratory muscle weakness are more pronounced in patients with severe CHF than in those with mild-to-moderate disease. Left ventricular assist device (LVAD) implation for severe CHF improves cardiac output and likely accounts for most of the improved exercise ability. The contribution of any improvements in lung function is not well understood and there is scant data about pulmonary function testing (PFT) in LVAD patients. METHODS: We evaluated pre- and post-LVAD implantation PFTs to determine if LVADs improve the mixed ventilation and gas transfer disorders observed in CHF patients. We scanned our database of LVAD patients (169) looking for those who have PFTs performed before and after LVAD implantation and found four. Three of them had pre-LVAD PFTs performed at 139, 7 and 43 days before LVAD implantation and post-LVAD PFTs at 210, 285 and 795 days after LVAD, respectively. The fourth patient had PFTs preformed289 days before LVAD and 931 days post LVAD and is not included in the group analysis because of the long time differences. RESULTS: We noted significant improvement (paired T-test) in FEV1 (p=0.007) and FVC (p=0.02) post VAD implantation in the first three patients though the FEV1/FVC ratio remained same. The TLC (p=0.08) and DLCO (p=0.051) also improved but did not reach statistical significance in our small group. CONCLUSIONS: Our small retrospective study suggests that pulmonary mechanics and gas transfer may be improved post LVAD implantation and further studies are needed. CLINICAL IMPLICATIONS: The knowledge gained from these studies may yield predictive information about the tolerability of the LVAD procedure and use, timing cardiac transplantation, and other important outcomes.
air conditioning; airway obstruction; congestive heart failure; data base; diseases; exercise; *gas diffusion; heart output; heart transplantation; human; *implantation; *left ventricular assist device; lung function; *lung function test; *lung mechanics; muscle weakness; patient; *pilot study; procedures; retrospective study; smoking; statistical significance; Student t test; thin layer chromatography
Fracture Mechanics
Fracture Mechanics
227-246
2012
10.1016/B978-0-12-385001-0.00009-2
The cohesive zone fracture model was introduced partially to remove the stress singularity in the classical continuum crack model and partially to incorporate the physically more realistic material separation mechanisms at the atomic scale. The cohesive zone model adds a zone of vanishing thickness ahead of the crack tip with the intention of describing more realistically the fracture process without the use of stress singularity. The cohesive zone is idealized as two cohesive surfaces, which are held together by a cohesive traction. The material failure is characterized by the complete separation of the cohesive surfaces and the separation process is described by a cohesive law that relates the cohesive traction and the relative displacement of the cohesive surfaces. Hence, a physical crack extension occurs when the separation displacement at the tail of the cohesive zone (physical crack tip) reaches a critical value. One of the key advantages offered by the cohesive zone model is that it has an intrinsic fracture energy dissipation mechanism in contrast to the classical continuum based fracture mechanics for which such a mechanism is absent.
Spinning Basics - The Art of Plying
Spin-Off Magazine
Spring 2006
30-34
2006
Why ply? Plying, as many spinning teachers will tell you, covers a multitude of sins—at least of the textile kind! It does this in a number of ways: it makes the finished yarn more consistent, much stronger, and certainly more stable. The consistency comes from averaging out the diameters of the singles as they are plied together. When we ply, thin and thick places will often merge together, and, when they don’t, there are good plying tricks to help this happen. Of course, the more singles used to make a plied yarn, the more opportunities available to make an even yarn.
Spinning, plying, fibre
Econophysics, Statistical Mechanics Approach to
Arxiv preprint
2007
This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.
Applications; Data Analysis; Physics and Society; Statistical Finance; Statistical Mechanics; Statistics and Probability
Molecular mechanics and the CAMSEQ processor
Computers & …
1977
Computers & Chemistry. Vol. 1, pp. 157 154. Pergamoe Press. 1977. Printed in Creel Brunie MOLECULAR MECHANICS AND THE CAMSEQ PROCESSOR R. , JR.*, EUZASETH CAVtCCHI*, HJR WEINTRAUBt and AJ HOPFINGER*t (Received 14 January 1977)
Computational mechanics of composite structures
Computational Mechanics
1994
The present issue is primarily directed at advances in the analysis of composite material construction. Papers by invited specialists cover two main aspects in detail. One relates to micromechanical analysis of single fibres in a
Statistical mechanics of random graphs
SIAM Review
6
2003
10.1016/j.physa.2004.06.087
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
Statistical Mechanics
Relational Holism and Quantuns Mechanics
The British Journal for the Philosophy of Science
1986
and Quantuns Mechanics. P TELLER The British journal for the philosophy of science 37:11, 71-81, Oxford University Press, 1986.
Experimental Investigation of Elastodissipative Characteristics of Carbon-Fiber-Reinforced Plastics
Mechanics of Composite Materials
39
5
393-398
2003
10.1023/B:MOCM.0000003289.12297.84
A procedure is described for the experimental study of elastodissipative properties of carbon-fiber-reinforced plastic (CFRP) structures. Experimental values of dissipation factors are given for angle-ply structures with a reinforcing angle varying from 0 to 90°. Elastodissipative characteristics of two types of CFRP are identified. The values obtained can be used for predicting the properties of complex CFRP structures. It is shown that the energy absorption in sandwich structures with CFRP skins and a honeycomb core is mainly governed by properties of the skins.
carbon-fiber-reinforced plastic; Carbon-fiber-reinforced plastic; elastodissipative characteristics; Elastodissipative characteristics; experiment; Experiment
Effects of chemical treatments on durability properties of Gigantochloa scortechinii strips and ply-bamboo.
Asian Journal of Biological Sciences
6
3
153-160
2013
The aim of this study is to investigate the effect of some preservative treatment on the durability properties of bamboo (Gigantochloa scortechinii) strips and bamboo laminated product. The durability properties are examined by exposed the of bamboo samples to termite (Coptotermes curvignathus) for 4 weeks and white rot fungal (Pycnophorous sanguineus Wulfex Fries) for 12 weeks. The efficacy of treatments on bamboo strips and laminates against white rot and termite attacks were evaluated based on their weight loss after exposure to those biodeteriorating agents. All preservative-treated materials had resulted lower weight loss values compared to untreated and water-boiled bamboo treatment. The Water-Borne Preservatives (WBP) (5.80% weight loss) gave the best protection against termite whereas borax acid-treated (39.3%) materials had the least efficacy on protecting the strips. For the bamboo laminates, TBTO gave the best protection against termite attacks with only 8.9% of weight loss. The durability test against white rot fungal show that all preservative increased the resistance of bamboo strips and laminates. TBTO was found to be the best preservative to protect both bamboos strips (10.7% weight loss) and laminates (9.71% weight loss). Boiling in water for 30 minutes had decreased the resistance of the strips against white rot with the weight loss value for this strip was 21.8 while 22.4% for the laminates.\n
angiosperms; animals; arthropods; bamboo; bamboos; biodeterioration; borax; Coptotermes; Coptotermes curvignathus; Cyperales; durability; eukaryotes; forest pests; fungal diseases; fungi; fungus; Gigantochloa; Gigantochloa scortechinii; Hexapoda; insect pests; insects; invertebrates; Isoptera; minor forest products; monocotyledons; non-timber forest products; non-wood forest products; pest insects; phytopathogenic fungi; phytopathogens; plant diseases; plant pathogenic fungi; plant-pathogenic fungi; plant pathogens; plants; Poaceae; preservation; preservatives; Rhinotermitidae; social insects; Spermatophyta; storage pests; stored-product pests; stored products pests; TBTO; tributyltin oxide; weight losses; white rot
The influence of surface ply fibre angle on the compressive strength of composite laminates containing delamination
Aeronautical Journal
116
1186
1315-1330
2012
A combination of uniaxial compression tests and Strip Model and Finite Element analyses of laminates artificially delaminated to create circular [±θ] sublaminates is used to assess the influence of fibre angle on the compressive strength of composite laminates. Sublaminates with 0° < θ < 40° are found to fail by sublaminate-buckling-driven delamination propagation and provide poor tolerance of delamination. This is a consequence of their relatively high axial stiffnesses, low sublaminate buckling strains, Poisson’s ratio induced compressive transverse strains and extension-twist coupling which produces unexpected sublaminate buckling mode shapes. Sublaminates with 40° < θ < 60° are most tolerant to delamination; axial and transverse stiffnesses are minimal, formation of sublaminate buckles is resisted, high laminate buckling strains reduce interaction between laminate and sublaminate buckling mode shapes and extension-twist coupling is minimal. Sublaminates with 60° < θ < 90° are shown to produce varied tolerance of delamination. Sublaminate buckling is generally prevented owing to transverse tensile strains induced by mismatches between laminate and sublaminate Poisson’s ratios but may occur in laminates with low Poisson’s ratios.
Research progress of meso-damage mechanics for ductile fracture criterion in metal forming
Shanghai Jiaotong Daxue Xuebao/Journal of Shanghai Jiaotong University
40
10
2006
With the profound research in meso-damage of ductile material, meso-damage mechanics will play more and more important role in forecasting ductile fracture of metal material. Differing from macroscopic fracture mechanics, meso-damage mechanics emphasizes particularly on the influence on macroscopic fracture with the evolvement of meso-damage. The background of meso-damage mechanics was introduced, and an overview on the research and development of meso-damage mechanics was given. Then the key problems for the development of meso-damage mechanics were discussed, and the promotion of mechanism-based strain gradient plasticity theory to the development of meso-damage mechanics was proposed as well.
Damage mechanics; Ductile fracture; Failure (mechanical); Mechanism-based strain gradient plasticity theory; Meso-damage mechanics; Metal forming; Plastic deformation
thin films
Superconductor Science and Technology
22
4
043001
2009
10.1088/0953-2048/22/4/043001
Great progress has been made in the deposition ofMgB2 thin films since the discovery of superconductivity at 39 K in this two-band superconductor. In this review, deposition techniques used for MgB2 are described, with an emphasis on their meeting the critical requirements for growing high-quality MgB2 thin films. The availability of these thin films has contributed significantly to the research on the two-gap superconductivity in MgB2.MgB2 thin films have also been investigated for applications in high-field magnets, superconducting electronic devices and circuits, and radio-frequency cavities used in accelerators.
Discrete wave mechanics: An introduction.
Proceedings of the National Academy of Sciences of the United States of America
83
August
5360-5363
1986
10.1073/pnas.83.15.5360
Discrete wave mechanics is formulated for particles in one-dimensional systems by use of a simple finite difference equation. The solutions involve wave vectors (instead of wave functions) as well as a newly defined "wave vector energy." In the limit, as c --> infinity, the treatment reduces to that of Schrödinger's wave mechanics. Specific calculations are made for completely free particles as well as for particles confined to a one-dimensional box. The results exhibit a striking compatibility with relativistic considerations. The wave vectors show properties that can be identified with particles and anti-particles-each possess identical probability distributions with energies that add up to zero.
The interpretation of quantum mechanics
European Journal of Physics
7
1
43-48
1986
10.1088/0143-0807/7/1/008
It is argued that the reduction of the wavepacket following a measurement is no more than a\r computational convenience to which no meaning should be attached. In a strict application of quantum\r mechanics all measuring instruments must be included in a single wavefunction, along the lines of an\r early important paper of Mott. Thus the activity of physics is treated as the analysis of public\r information, as conveyed by instruments, with quantum mechanics the accepted analytical procedure\r rather than a model of objective reality. Finally the classical world of particle trajectories that\r can be agreed on by all observers is shown to be a natural corollary. Only very simple examples are\r employed, and all derivations are segregated in appendices, so that the argument (which contains no\r revolutionary features) may be readily accessible.
Knot-Theory And Statistical-Mechanics
Reviews of Modern Physics
64
4
1099-1131
1992
DOI 10.1103/RevModPhys.64.1099
This is a tutorial review on knot invariants and their construction using the method of statistical mechanics. We begin with brief reviews of the elements of knot theory and relevant results in statistical mechanics. We then show how knot invariants, including those discovered recently, can be obtained by applying techniques used in solving lattice models in lattice statistics. Our approach is based on the consideration of solvable models with strictly local Boltzmann weights. The presentation, which is self-contained and elementary, is intended for a general readership. A table of polynomial invariants for knot and links containing up to six crossings is included in the Appendix.
Geometrical setting of solid mechanics
Annals of Physics
326
8
1983-1997
2011
10.1016/j.aop.2011.02.010
The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation. © 2011 Elsevier Inc.
Lagrangian system; Linearization; Logarithmic strain; Riemannian symmetric space; Solid mechanics; Time-discrete approximation
General relativity and quantum mechanics
Challenges for the 21st century: International …
2001
JB Department of Physics, University of California, Santa Barbara, CA 93106-9530 USA Email: @ cosmic. physics. ucsb. edu Usual quantum mechanics requires a fixed, background, spacetime geometry and its
Quantum Mechanics in Phase Space
arXiv:0706.0237 [quant-ph]
2007
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
Statistical Mechanics of Complex Networks
Analysis of Complex Networks
23-45
2009
10.1002/9783527627981.ch2
This chapter contains sections titled: * Introduction * Macroscopics: Entropies for Networks * Microscopics: Hamiltonians of Networks – Network Thermodynamics * Ensembles of Random Networks – Superstatistics * Conclusion * References
complex networks; Hamiltonians of networks; network entropies; network thermodynamics; random networks; statistical mechanics; superstatistics
Design of fastenings based on the fracture mechanics
ICF XI - 11th International Conference on Fracture
2005
In the present paper the concrete cone failure mode is reviewed. Considered are headed stud anchors loaded by tensile load (pull-out) and by shear load against an edge of a concrete member. The influence of the material and geometrical parameters on the failure load and the size effect are discussed. The numerical and experimental studies confirm that fracture mechanics governs concrete break out failure. Consequently, there is a strong size effect on the nominal concrete cone strength that can be well described by a design formula that is based on linear elastic fracture mechanics.
Medication use in a group of aircraft mechanics
Aviation, Space, and Environmental Medicine
71
11,Sect1
1148-1150
2000
Aeromedical studies of human factors have focused on the pilot and pilot error rather than on aircraft maintenance workers and maintenance error. This is a report of a survey on medication use in a group of 409 US Air Force aircraft mechanics. A questionnaire was used to retrospectively examine aircraft mechanic medication use, side effects experienced, and return to work. Of those surveyed, 67% returned to work while taking medication that could potentially impair job performance. It is concluded that, for flying safety reasons, occupational medicine education for aircraft mechanics and their supervisors should address on-the-job use of prescribed medication and self-medication. (PsycINFO Database Record (c) 2009 APA, all rights reserved)
Aircraft; Air Force Personnel; Job Performance; Prescription Drugs; Psychopharmacology; returning to work following medication use; US Air
Molecular mechanics modeling of carbon nanotube fracture
Carbon
45
9
1769-1776
2007
10.1016/j.carbon.2007.05.009
The fracture of carbon nanotubes (CNTs) is studied in this paper. Molecular mechanics models that incorporate the modified Morse potential and reactive empirical bond-order potential are developed to envisage the fracture behavior of perfect CNTs. The tensile strength, fracture strain, and fracture angle under tension are discussed, and special attention is paid to the effects of tube chirality. Explicit expressions for the fracture solutions for achiral carbon nanotubes are presented, but only numerical results are available for chiral carbon nanotubes. The predicted results of the present model are in good agreement with existing data and those of molecular mechanics simulations via the Materials Studio software package, which indicates the effectiveness of the developed models. (c) 2007 Elsevier Ltd. All rights reserved.
Mechanics and dynamics of reconstituted cytoskeletal systems.
Biochimica et biophysica acta
2015
10.1016/j.bbamcr.2015.06.013
The intracellular cytoskeleton is an active dynamic network of filaments and associated binding proteins that control key cellular properties, such as cell shape and mechanics. Due to the inherent complexity of the cell, reconstituted model systems have been successfully employed to gain an understanding of the fundamental physics governing cytoskeletal processes. Here, we review recent advances and key aspects of these reconstituted systems. We focus on the importance of assembly kinetics and dynamic arrest in determining network mechanics, and highlight novel emergent behavior occurring through interactions between cytoskeletal components in more complex networks incorporating multiple biopolymers and molecular motors.
Actin; Active soft matter; Biopolymer rheology; Composite networks; Cytoskeleton; Dynamic arrest
Modulus Prediction of a Cross-Ply Fiber Reinforced Fabric Composite With Voids
Polymer Composites
13
4
285-294
1992
Voids or bubbles in polymer composites have a detrimental effect on the proper- ties of the material. Such voids are found in PMR15/graphite fiber (fabric type) composites. The matrix, PMR15, is formed in-situ during the molding process and undergoes two major stages of reactions, viz., imidization and crosslinking. Volatiles are formed as by-products of these reactions and may remain trapped in the matrix to form voids or bubbles. Photomicrographs of composite cross sections suggested the classification of voids as two different phases in two different directions, each aligned with the fibers, resulting in a five phase model. The composites were tested in three-point bending tests to obtain the flexural modu- lus. By combining Weng’s inclusion approach (1) and Ishikawa and Chou’s crimp method (2). a n analytical model has been developed to predict the elastic moduli of such a multiphase composite material. Thus, the voids have been treated as inclusions in an enclosing matrix, which in turn is reinforced by woven fibers in two directions. The stiffness behavior obtained analytically was within 10% of the experimental values.
Dynamic response of adaptive cross-ply cantilevers featuring interlaminar bonding imperfections
AIAA journal
38
3
499-506
2000
The implications of slip-type interfacial bonding imperfections on the dynamic behavior of adaptive laminated beams with surface-bonded piezoactuator layers are investigated. Numerical results are supplied, and pertinent conclusions on the free and forced flexural motions under transient distributed loadings, as a function of the measure of bonding imperfections, are outlined. Near the end of this problem approach, a recently developed theory of anisotropic laminated plates that incorporates the effect of imperfect interlaminae bondings and fulfils the shear traction continuity requirements is used. The control is achieved via the action of a piezoelectrically induced bending moment at the tip of the beam, and in this context four different feedback control laws are employed. The obtained results reveal the powerful role played by the proposed control methodology toward suppressing vibrations and attenuating the detrimental effect induced by the interlaminae bonding flaws.
R.D. Mindlin and Applied Mechanics
R.D. Mindlin and Applied Mechanics
1-24
1974
10.1016/B978-0-08-017710-6.50006-8
The Applied Mechanics Reviews summary paper by Mindlin† is taken as the point of departure for a review of the past and present status of photoelasticity and a projection of the future. Some later developments are described and supplemental remarks made on earlier work. Recent advances in optical techniques and in optical analysis are seen as opening the way to many more new and valuable experimental and theoretical studies. Far more sophisticated modeling of materials and the more incisive use of photoelasticity as a tool of materials science and engineering appear as likely consequences.
The maze of quantum mechanics
European Journal of Physics
23
5
513-522
2002
Students can explore quantum mechanics with a concept map that uses only the most elementary solutions to Schrodinger's equation. The content has been slightly modified from the traditional introduction to the subject because the issue of interpretation is postponed until Parseval's theorem is reached and used to postulate two fundamental equations of probability, simultaneously. A set of canonical but approximate equations can describe wavepacket motion for most linear waves. If restricted to certain special cases, these equations of wavepacket motion are easily derived and can serve as a temporary substitute for Ehrenfest's theorem. A number of exercises can be incorporated into this maze of quantum mechanics.
Statistical mechanics of Lamé solitons
Physica Scripta
73
6
545-555
2006
10.1088/0031-8949/73/6/005
We study the exact statistical mechanics of Lam\'e solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schr\"odinger equation with the periodic Lam\'e potential. Since the latter is a quasi-exactly solvable system, an analytical evaluation of the partition function can be done only for a few temperatures. We also study approximately the finite temperature thermodynamics using the ideal kink gas phenomenology. The zero-temperature "thermodynamics" of the soliton lattice solutions is also addressed. Moreover, in appropriate limits our results reduce to that of the sine-Gordon problem.
Exactly Solvable and Integrable Systems; Mathematical Physics; Pattern Formation and Solitons; Statistical Mechanics
Mechanics of jointing in rocks
Geological Magazine
96
2
149-167
1959
"The current theories dealing with the mechanics of joint development are discussed critically. An analysis of the stress conditions which can exist in competent rocks in the crust is presented. The conclusion is reached that 'master' and 'regional' joints can be, generically, either 'tensional' or 'shear' structures. They are, however, post-tectonic phenomena which develop as a result of uplift. Joints form a part of 'movement pictures' because their orientation is determined by residual stresses. Reasons are given which indicate that the mechanism described is generally applicable to joint development in folded sediments, igneous rocks, and also to incompetent material."
fractures; joints; Mechanics of formation
Radial Tire Cord-Rubber Composites
Rubber Chemistry and Technology
49
4
1095-1110
1976
10.5254/1.3534991
Abstract Experimental and theoretical results are presented in terms of the elements of the compliance matrix for the material properties which are needed to characterize a calendered ply of various cord-rubber composites commonly used in the body and belt of radial tires. It is shown that a single ply can be represented as a linear, elastic, homogeneous, orthotropic material to a level of accuracy sufficient for modeling inflated, but otherwise unloaded, radial tires. Cord load distributions in the body, belt, and turnup ply endings are predicted and plotted from the bead to the crown of inflated radial tires using principles of structural mechanics to represent the laminated material properties of the tire and finite element techniques to calculate the stresses in the cords. Predictions are also made for rubber strains and tire growth at the crown due to inflation pressure loading. The effects of changing various tire construction and/or material property parameters on such responses are assessed; these...
\nDistribution Functions in Classical and Quantum Mechanics\n
Progress of Theoretical Physics Supplement
98
98
109-156
1989
10.1143/PTPS.98.109
The correspondence between classical and quantum mechanics is an important subject for the better understandings of "quantum chaos". In particular, it is very important to investigate the correspondence between distribution functions in classical mechanics and in phase space representation of quantum mechanics. This is the review of our recent progresses in the study of distribution functions in classical and quantum mechanics, namely distribution functions in classical mechanics and in coarse-grained classical mechanics as well as the Wigner function and the Husimi function. Topics dealt with include formulations of the Wigner representation, the Husimi representation and coarse-grained classical mechanics, and their applications to the analyses of the eigenstates and time developments of the distribution functions.
Quantum mechanics on fundamental domains of Coxeter groups
opensigle.inist.fr
1984
Title: mechanics on fundamental domains of groups. Authors: Raszillier, H. Bonn Univ. (Germany, FR). Physikalisches Inst. Issue Date: 1984.
Summary of results of a study of methods of teaching mechanics
Journal of Engineering Education
18
7
703-707
1928
Tabulation covering replies received from 69 teachers of mechanics in 29 institutions.
Engineering education
Experimental Mechanics in Nano and Biotechnology, Pts 1 and 2
Micro cell incubator with on-chip integrated carbon dioxide generator as a self pH controller
326-328
879-882
2006
A novel micro cell incubator is described in this paper. pH of animal cell culture media must be tightly controlled, and this is accomplished by supplying defined concentration of carbon dioxide. In order to fabricate a small self-contained carbon dioxide supply unit, we adopted chemical production of carbon dioxide rather than compressed storage of the gas which requires huge tank. Carbon dioxide can be chemically produced by pyrolysis of sodium bicarbonate. The produced gas passes through a thin polymer membrane which is known to admit diffusion of gases. Liquid media separated from gas area by polymer membrane can uptake the gas, then. This micro cell incubator would be a suitable model for the development of portable and arrayed cell chips.
carbon dioxide; cell culture; cell incubator; sodium bicarbonate
Thin and thick plate bending element based on incompatible methods and degenerated solid concept
Gongcheng Lixue/Engineering Mechanics
25
8
64-69
2008
A plate bending element is derived from the familiar 8-node brick element. To overcome the thickness locking of the element, the degenerated solid approach is adopted by modifying the elastic constitutive relation. A user-defined local coordinate system is established to conveniently introduce the incompatible modes, which are effective to rectify the shear locking. To pass the patch test, the constant strain matrix is modified. The element is suitable for laminated structures by calculating the element stiffness matrix over the subdomains. Numerical examples show the applicability and effectivity of the element formulation.
Degenerated solid plate element; Finite element; Incompatible element; Laminated plates; Patch test
Some weakly nonlinear amplitude equations describing the behavior of a thin layer in a two-phase flow of viscous heat-conducting liquids along a cylinder
Journal of Applied Mechanics and Technical Physics
38
1
161-168
1997
The weakly nonlinear stability of a two-phase flow of viscous heat-conducting liquids along a hollow pipe is studied. One of the phases is separated from the surface of the pipe by a thin layer of the second liquid. The character of stability for this class of two-phase flows is important for some natural and technological processes. Using the long-wave approximation of the boundary layer theory and the Stokes approximation, the dynamics of perturbation in the thin layer does not depend on the evolution of fluctuations in the core when the dynamic viscosities of liquids are equal and other conditions are satisfied. A modification of the corresponding amplitude equations are considered taking into account the thermodynamic effects.
Approximation theory; Boundary layer flow; Heat conduction; Integrodifferential equations; Long wave approximation; Perturbation techniques; Pipe flow; Stokes approximation; Thermodynamics; Two phase flow; Viscous flow; Viscous heat conducting liquids; Weakly nonlinear amplitude equations
Thin film scratch testing in two dimensions—Experiments and analysis
Journal of materials research
13
4
1002
1998
We have modified the microscratch test to create a near plane strain loading condition. In the Microwedge Scratch Test (MWST), a wedge-shaped diamond indenter tip is drawn along a fine line (i.e., narrow strip of film), while simultaneously being driven into the line. We compare microwedge scratching of zone 1 (voided grain boundaries) and zone T (metallurgical grain boundaries) thin film specimens of sputtered tungsten on thermally grown SiO2. Symptomatic of its weak grain boundaries, the zone 1 film displays three separate crack systems. Because of its superior grain boundary strength, the zone T film displayed only one of these—an interfacial crack system. By correlating fracture phenomena to signature events in the load-displacement curve, we develop governing equations for propagating interfacial cracks, including expressions for strain energy release rate, bending strain, and mode mixity. Grain boundary fracture causes zone 1 films to spall before a stable crack is formed. Zone T films survive the bending strains, and hence adhesions may be inferred from stable crack growth mechanics. We conclude by contrasting and comparing experimental results for plane strain indentation versus plane strain scratching.
Numerical simulation of rarefied gas flow through a thin orifice
Journal of Fluid Mechanics
518
35-60
2004
10.1017/S0022112004000710
ABSTRACT Rarefied gas flow through a thin orifice is studied on the\nbasis of the direct simulation Monte Carlo method. The mass flow\nrate and the flow field are calculated over the whole range of the\nKnudsen number for various values of the pressure ratio. It is found\nthat at all values of the pressure ratio a significant variation\nof the flow rate occurs in the transition regime between the free-molecular\nand hydrodynamic regimes. In the hydrodynamic regime the flow rate\ntends to a constant value. In the case of finite pressure ratio the\nflow field qualitatively differs from that for outflow into vacuum\nand namely vortices appear in the downflow container on approaching\nthe hydrodynamic regime. Then and in the hydrodynamic regime the\ngas flow forms a strong jet. A comparison of the numerical results\nwith experimental data available in the open literature has been\nperformed.
Computational evaluation of interfacial fracture toughness of thin coatings
Surface Effects and Contact Mechanics Ix
85-94
2009
Doi 10.2495/Secm090081
A computational method to evaluate fracture toughness of single- and multilayered coatings using first-principles density functional theory (DFT) calculations was proposed. This method was first applied to calculate elastic properties and fracture toughness K(IC) of single crystalline TiC and several transition metal nitrides with cubic structure, such as TiN, CrN, ZrN, VN and HfN. After comparison with known experimental data and other DFT results, the reliability of present calculations was favourably confirmed. Next, DFT was applied to calculate the ideal work of adhesion W(ad), Young's modulus E and interfacial fracture toughness K(IC)(Int) for bi-layer combinations of five transition metal nitrides in (100) and (110) surface orientations. For the analyzed coatings, the following trends were observed: E(100) > E(110), W(ad)(100) < W(ad)(110) and K(IC)(Int)(100) < K(IC)(Int)(110), demonstrating that it is the W(ad) that plays a decisive role in determining interfacial fracture toughness of these materials. All interfaces formed with TiN in the (110) orientation showed the best combination of adhesion and Interfacial fracture toughness.
1st-principles; ab-initio; adhesion; carbides; elastic properties; erosion; films; first-principles calculations; fracture toughness; indentation; interfacial fracture toughness; mechanical-properties; nitrides; thin coatings
Methodlogies to detect defects in thin layered material
World Applied Sciences Journal
29
10
1267-1272
2014
10.5829/idosi.wasj.2014.29.10.1437
The Cost Effective and reliable detection of defects in thin layered material can be obtained by NDE methods. Potential defects are identified and classified by its types at which they could occur and their effects are listed. Criticality of defect types are assessed by an experimental fracture mechanics based approach. The range of NDE techniques identified based on pertinent characteristics required for inspection and classified based on applicability. This report addresses four specific aspects of defect identification: (1) Identification of the types of defects in composites and aluminium material. (2) Determination of the potential effect of selected defects on the performance and integrity of the system.(3) Identification of state-of-the-art quality assurance and non-destructive evaluation (NDE) technologies that can be used for detecting defects. (4) Preliminary investigation of selected technologies that have a high likelihood of being successfully used for purposes of quality assurance. © IDOSI Publications, 2014.
Aluminium material; NDE techniques; Specific aspects
Numerical Simulation of Cold Press Forging Forming for Stepped Hole of Thin Sheet Metal
Applied Mechanics and Materials
121-126
249-253
2011
10.4028/www.scientific.net/AMM.121-126.249
An optimum process for a two-step press forging of stepped holes in a metal sheet was proposed. Numerical simulation on the two-step process was carried out by using DEFORM-3D. Distributions of effective strain and effective stress were obtained. The study showed that the process not only can form the stepped, but also can increase the surface quality and strength of stepped holes in sheet metal parts, According to the numerical simulation's process parameter, an experimental die was designed, the simulation results were in good agreement with the experimental data.
Cold press forging forming; Numerical simulation; Stepped hole
Recent progress in the numerical modeling for organic thin film solar cells
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY
54
3
375-387
2011
10.1007/s11433-011-4248-6
Device modeling is constructive in finding the dependency of devices\nefficiency on structure parameters and material properties. For the sake\nof looking into the physics mechanism of organic solar cells (OSCs), as\nwell as predicting their maximum attainable efficiency, numerical\nmodeling is widely utilized to simulate the behavior of OSCs. Although\nsome indispensable parameters are neglected or hypothesized because of\ninexplicitness in simulation models for OSCs, numerical modeling can\ndescribe the kinetic process in OSCs intuitively. This paper summarizes\nthe optical/electrical models in the BHJ solar cell, as well as\naddresses their corresponding development in recent years on the basis\nof device physics and its working principle. Applications of numerical\nmodeling and comments on modeling results are summarized. Meanwhile,\nprecision and open questions about every model are discussed.
Fracture mechanics sub-critical events and structure of polyphase ceramics
ICF 5, Cannes, France
1981
Fracture mechanics sub-critical events and structure of polyphase ceramics R. G. Cooke
Is negative refraction, perfect focusing compatible with quantum mechanics?
arXiv
1120
2000
305447
2003
In light of experiments in atom optics, the compatibilty of negative refraction, perfect focusing with quantum mechanics is brought into question.
Contribution to understanding the mathematical structure of quantum mechanics
Optics and Spectroscopy
103
3
21
2006
10.1134/S0030400X07090135
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, commutation and uncertainty relations, probability density current, momentum operator, rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of the delta-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems and the postulates of quantum mechanics are also discussed.
classical mechanics; probability theory; quantum mechanics
Experimental and theoretical characterization of structure in thin disordered films.
Acta crystallographica. Section A, Foundations of crystallography
55
Pt 2 Pt 1
178-187
1999
10.1107/S0108767398008769
The electron microscope provides an ideal environment for the structural analysis of small volumes of amorphous and polycrystalline materials by enabling the collection of scattering information as a function of energy loss and momentum transfer. The scattered intensity at zero energy loss can be readily processed to a reduced density function, providing information on nearest-neighbour distances and bond angles. A method for collecting and processing the scattered intensity, which allows for the collection of an energy-loss spectrum for a range of momentum transfers, is discussed. A detailed structural determination from a reduced density function alone is difficult and it is shown that a more detailed structural model can be obtained by combining the experimental reduced density function with model structures obtained from molecular dynamics based on first-principles quantum mechanics. This method is applied to tetrahedral amorphous carbon, as an example of a monatomic network, and to aluminium nitride, as a prototype for a binary amorphous alloy.
Optimization of induction brazing for thin-walled aluminum tubes
WSEAS Transactions on Applied and Theoretical Mechanics
5
2
134-145
2010
Major environmental concerns have triggered lately some important developments in applicative research. Innovation programs for manufacturing industry are intended to achieve both lower emissions of carbon dioxide and smaller specific energy consumption. Since use of inductive brazing for aluminum has remained restricted to few applications,a complex research program has been pursued in order to develop an optimized joining technology for tubes with thin walls. The new technology should be suitable for large scale production,to replace torch brazing at better costs and lower carbon dioxide emissions. An experimental study,which includes complete design of technology and equipment for inductive brazing,has proved that use of induction could produce high quality joints and eliminate the considerable scrap level generated by torch brazing. Induction brazing also lowers energy consumption and totally eliminates direct emission of carbon dioxide.
Aluminum;Carbon dioxide;Energy utilization;Global; Aluminum tubes;Carbon dioxide emissions;Direct emi; Brazing
A numerical method for laterally loaded thin plates
Computer Methods in Applied Mechanics and Engineering
49
1
1-15
1985
10.1016/0045-7825(85)90047-7
A numerical method for dealing with laterally loaded thin plates is presented and compared to the similar but more basic numerical technique used in [1, 2]. This method considers the plate to be embedded in the infinite plane and uses point load sources external to the plate boundary to satisfy boundary conditions as in collocation. The exact solution for a constant lateral load acting over an arbitrary polygon in the infinite plane is first derived and then used to couple the effects of lateral loading to the collocation method described above. The results show that less than half the number of collocation points used in [1, 2] is needed for the same accuracy and that the computer execution time is reduced several hundred times. This method is not limited to particular plate shapes, boundary condition types or load distributions. Five examples are used to illustrate the method.
Channel-cracking of thin films with the extended finite element method
Engineering Fracture Mechanics
70
18
2513-2526
2003
The recently developed extended finite element method (XFEM) is applied to compute the steady-state energy release rate of channeling cracks in thin films. The method is demonstrated to be able to model arbitrary singularities by using appropriate enriching functions at selected nodes with a relatively coarse mesh. The dimensionless driving force for channeling cracks is obtained as a function of elastic mismatch, crack spacing, and the thickness ratio between the substrate and the film. The results are compared with those from several previous studies when available. Emphasis is placed on the cases with compliant substrates, for which much less information is available from previous studies. It is found that, while it is quite challenging to model the cases with very compliant substrates using regular finite element method because of the strong singularities, the present approach using XFEM is relatively simple and straightforward. (C) 2003 Elsevier Ltd. All rights reserved.
Identification of dynamic pressure distribution applied to the elastic thin plate
Inverse Problems in Engineering Mechanics {II}
129-138
2000
http://dx.doi.org/10.1016/B978-008043693-7/50086-6
Publisher Summary This chapter deals with a strategy for identification of dynamic pressure distribution applied to the elastic thin plate. Boundary element method is adopted to obtain discretized matrix relation between input loading and output signal, where strain information is used as supplementary information of the inverse analysis in the study. Laplace transform and numerical inverse Laplace inversion are introduced in order to treat the dynamic behavior. The coefficient matrix to be solved is given on the Laplace-transformed domain as the form of transfer function relating input and output signals. As the inverse analysis requires regularization to stabilize the ill-posed solutions, Tikhonov regularization has been employed with singular value decomposition, where the optimal parameter of Tikhonov method was determined by Hansen's L-curve method. Through some numerical simulation on the circular plate subjected to dynamically distributed loading, the chapter reviews the usefulness of the present method based on the Laplace-transformed-BEM.
Diamond like Carbon (DLC) Thin Films: Preparation and Characterization
Applied Mechanics and Materials
575
292-295
2014
10.4028/www.scientific.net/AMM.575.292
Diamond-like carbon (DLC) thin films are prepared using plasma enhanced chemical vapour deposition (PECVD) process at different bias voltage. We have studied their microstructural and electrical properties using Raman spectroscopy and current (I) - voltage (V) relationships. Electrical conductivity is gradually decreases with bias voltage as the films are becoming more and more diamond like carbon as observed from Raman spectroscopy results. Raman spectroscopy result shows that the ID/IG ratio gradually decreases indicating formation of more diamond like carbon films that responsible for the decrease of conductivity of the films. The full width half maximum of G peak increase with increase the bias voltage indicating the ring-like sp2 transforms to sp2 chains and raises the amount of sp3-chains. The structural disorder arises from the bond angle and bond length distortions in amorphous carbon films. Thus the structural disorder and mechanical properties such as hardness and elastic modulus increase with bias voltage. © (2014) Trans Tech Publications, Switzerland.
DLC; Raman; V-I characteristics
Spherical indentation of nickel thin film on steel - 4340 substrate
ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011
3
745-750
2011
In this paper, finite element simulations of spherical indentation of Nickel thin film on Steel-4340 are studied for single and multiple cycle of indentation as well. The objective was to understand the mechanics of coated systems, from load-displacement (P-h) curves, stress distribution in the film and the effect of substrate yield strength on the indentation response. The loading portion of P-h curve showed displacement bursts and the reason for this is investigated. A transition in the deformation behavior of the film from Hertz-type to flexure was observed for a normalized indentation depth of h/tf≈0.2. The influence of coating-substrate properties on P-h curve is also investigated for different h/tf ratios and yield strains. Attempts are also made to explore the possibility of understanding the creep-fatigue behavior of coated specimen subjected to cyclic indentation at room temperature from Indentation depth v/s time, Indentation depth v/s number of cycles and Plastic dissipation energy v/s number of cycles curve. Copyright © 2011 by ASME.
Coated systems; Coating-substrate; Creep-fatigue;; Creep; Exhibitions; Mechanical engineering; Nicke; Loading
General relativistic statistical mechanics
arXiv.org
gr-qc
2012
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = hbar d tau/ds, with k the Boltzmann constant, hbar the Planck constant, ds proper time and d tau the equilibrium thermal time.
Curious
Mechanics or Micropolar Continua
Contributions to Mechanics
1969
The recent theory of micromorphic materials developed by Eringen and his coworkers is presented in a simpler form suitable for mathematical and experimental work. Microfluids and microelastic solids are explained. The concept of micropolar fluids and micropolar solids as special classes of micromorphic materials are presented. The thermodynamical restrictions on elasticity and viscosity coefficients are discussed. The field equations and boundary conditions are derived for both micropolar fluids and solid media. The solution is given for a channel flow of micropolar fluids which bring out some new and interesting physical phenomena not encountered in the classical theory of viscous fluids.
Mechanics of Advanced Materials
Mechanics of Advanced Materials
155-179
2015
10.1007/978-3-319-17118-0
Compared to conventional materials, materials with a negative Poisson’s ratio are endowed with many specific mechanical features; consequently, there are many potential applications for them. For the last two decades, many efforts have been made on this sort of metamaterial both experimentally and theoretically. This paper provides a brief review of those studies with a focus on mechanical properties and deformation mechanisms of the metamaterials. The latter are explained using a structure of a multi-phase metamaterial system for a more comprehensive under- standing and as an inspiration for future works. Additionally, respective manufac- turing methods and applications are also summarised.
Re-thinking NHL mechanics.
Hockey Business News
14
6
18-19
2009
The article offers information on a lecture by Marty Miller and Allan Russell of the National Association of Sports Medicine regarding body and motion mechanics which will be presented at the Professional Hockey Athletic Trainers Society--Society of Professional Hockey Equipment Managers annual meeting in Phoenix, Arizona. They noted the importance of the information for hockey players who are on the advantage side in terms of improved performance and less injury. It will help the National Hockey League to rethink its safety and prevention protocols.
ARIZONA; *BODY movement; *HOCKEY players; LECTURES & lecturing; NATIONAL Hockey League; *SPORTS injuries
THREE DISLOCATION CONCEPTS AND MICROMORPHIC MECHANICS
Developments in Mechanics
6
349-358
1971
This paper contains three separate results. First, the initial stress-couple stress problem is formulated using incompatible micropolar elasticity; continuous distributions of dislocations and disclinations are treated. Second, dislocation rate effects are investigated by including the dislocation rate tensor in the construction of constitutive relations. The relationship between this rate approach and a recent Russian plasticity theory is discussed. Finally, motivated by an interpretation of micromorphic kinematics, a slip motion is defined which is shown to lead to classical plasticity and the plastic strain tensor.
CRYSTALS; MATERIALS-Defects; MATERIALS-Plasticity; MECHANICS; MICROMORPHIC MECHANICS; MICROPOLAR ELASTICITY
Dynamic load balancing in computational mechanics
Computer Methods in Applied Mechanics and Engineering
184
485-500
2000
10.1016/S0045-7825(99)00241-8
In many important computational mechanics applications, the computation adapts dynamically during the simulation. Examples include adaptive mesh refinement, particle simulations and transient dynamics calculations. When running these kinds of simulations on a parallel computer, the work must be assigned to processors in a dynamic fashion to keep the computational load balanced. A number of approaches have been proposed for this dynamic load balancing problem. This paper reviews the major classes of algorithms and discusses their relative merits on problems from computational mechanics. Shortcomings in the state-of-the-art are identified and suggestions are made for future research directions.
Adaptive mesh refinement; Dynamic load balancing; Parallel computer
On the Structure and Mechanics of the Protozoan Flagellum
The Ohio Journal of Science
45
6
247-303
1945
Author Institution: Department of Zoology and Entomology, The Ohio State University
The mechanics of wool fibres and structures
Textile Asia
22
2
39-52
1991
The study of the mechanics of wool fibres and structures provides the necessary insight for successful innovation in wool fabrics testing and metrology, data base management, fabric development, process control and quality assurance. The mechanics of wool fibres and structures provide an amazing variety of fascinating problems involving large strain non-linear deformations in materials of very complex geometry exhibiting both viscoelastic and frictional energy losses. We need to develop solutions to these problems in order to provide a scientific basis for the physical and chemical modification of wool, specification of wool fabric quality and performance, development of new wool products and control of key textile manufacturing operations. It will be necessary to apply available techniques of micromechanics and macromechanics, fabric objective evaluation technology, and unit cell approaches based on continuum mechanics.
Computer utilization in engineering mechanics education
Computers and Education
11
3
215-218
1987
10.1016/0360-1315(87)90057-1
For the last 20 years, the Mechanics Division of the American Society for Engineering Education has surveyed engineering schools to ascertain trends in mechanics education. Every five years an extensive instrument is sent to over 200 engineering schools. This year, for the first time, a series of questions dealing with computer utilization was included. This paper will report results of computer related items only. The timing of the reported results is critical, since the advent of moderately priced computers is fairly recent and no coherent plans for computer use in mechanics have been formulated. © 1987.
Statistical mechanics of choice
Maximum Entropy and Bayesian Methods
79
329-334
1996
We derive an equilibrium distribution for a population of decision makers, such as consumers or voters, in which each member makes choices not known with certainty. It is shown that, when the shares held by available choice alternatives are known, the MaxEnt distribution of the ensemble belongs to the product-form family.
Mechanics and Electrodynamics
Mechanics and Electrodynamics
112-135
1972
10.1016/B978-0-08-016739-8.50013-5
The interaction of material particles is described in ordinary mechanics by means of a potential energy of interaction, which is a function of the coordinates of the interacting particles. This manner of describing interactions contains the assumption of instantaneous propagation of interactions. A mechanics based on the assumption of instantaneous propagation of interactions contains within itself a certain inaccuracy. In reality, if any change takes place in one of the interacting bodies, it will influence the other bodies only after the lapse of a certain interval of time. Dividing the distance between the two bodies by this time interval, the velocity of propagation of the interaction is obtained. This velocity should be called the maximum velocity of propagation of interactions. It determines that interval of time after which a change occurring in one body begins to manifest itself in another by the arrival of a signal. The existence of a maximum velocity of propagation of interactions implies, at the same time, that the motions of bodies with greater velocity than this are impossible in nature. From the principle of relativity, it follows that the velocity of propagation of interactions is the same in all inertial frames of reference. Thus, the velocity of propagation of interactions is a universal constant. This chapter shows how to obtain formulae that enable to find, from the coordinates of an event in one reference frame, the coordinates of the same event in a second reference frame. It also shows how to find formulae relating the velocity of a material particle in one reference frame to its velocity in a second reference frame.
Stochastic isometries in quantum mechanics
Mathematical Physics, Analysis and Geometry
1-23
1999
10.1023/A:1009822315406
The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and symmetry transformations. Here a characterization of the isometric stochastic maps is given and possible physical applications are indicated.
and phrases; earlier version of; etry; helpful comments on an; hilbert space; isom-; quantum mechanics; reversibility; state operator stochastic map; thank pekka lahti for; the author wishes to; trace class
Timeless path integral for relativistic quantum mechanics
Classical and Quantum Gravity
30
12
125004
2013
10.1088/0264-9381/30/12/125004
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of a timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by ℏ. The timeless path integral manifests the timeless feature as it is completely independent of the parametrization for paths. For the special case that the Hamiltonian constraint is a quadratic polynomial in momenta, the transition amplitude admits the timeless Feynman's path integral over the (relativistic) configuration space. Meanwhile, the difference between relativistic quantum mechanics and conventional nonrelativistic (with time) quantum mechanics is elaborated on in light of the timeless path integral.
Quantum Mechanics Based Multiscale Modeling of Materials
American Physical Society
2013
We present two quantum mechanics based multiscale approaches that can simulate extended defects in metals accurately and efficiently. The first approach (QCDFT) can treat multimillion atoms effectively via density functional theory (DFT). The method is an extension of the original quasicontinuum approach with DFT as its sole energetic formulation. The second method (QM/MM) has to do with quantum mechanics/molecular mechanics coupling based on the constrained density functional theory, which provides an exact framework for a self-consistent quantum mechanical embedding. Several important materials problems will be addressed using the multiscale modeling approaches, including hydrogen-assisted cracking in Al, magnetism-controlled dislocation properties in Fe and Si pipe diffusion along Al dislocation core.
Averaging method in non-linear mechanics
International Journal of Non-Linear Mechanics
2
1
69-96
1967
http://dx.doi.org/10.1016/0020-7462(67)90020-0
The current work is a survey of the method of averaging in non-linear mechanics. Results of the fundamental studies of N. N. Bogolyubov as applied to the plane method of averaging are discussed. This work has stimulated wide application of the method of averaging for solving many numerical problems in physics, mechanics and engineering. The paper reduces to fundamentals the many numerical results obtained by various authors by the method of averaging during the past few years. It also discusses solutions of new classes of problems from a standpoint of both breadth and depth.
Noether's Theory in Classical Nonconservative Mechanics
Acts Mechanics
23
17-27
1975
10.1007/BF01177666
Noether's Theory in Classical Nonconservative Mechanics, Noether's theorem and ~Noether's inverse theorem for mechanical systems with nonconservative forces are established. The existence of first integrals depends on the existence of solutions of the generalized Noether- Bessel-ttagen equation or, which is the same, on the existence of solutions of the Killing system of partial differential equations. The theory is based on the idea that the transfor- mations of time and generalized coordinates together with dissipative forces determine the transformations of generalized velocities, as it is the case with variations in a variational principle of Hamilton's type for purely nonconservative mechanics [17], [18]. Using the theory a few new first integrals for nonconservative problems are obtained.
Conformal Field Theory and Statistical Mechanics
… methods in lowdimensional statistical …
July
2008
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
Questions concerning the mechanics of masonry
Stable - unstable?: Structural consolidation of ancient buildings
249-264
1988
The mechanics of masonry is a very young science. The authors regard mechanics here as a rational and rationally developed science from hypotheses sufficiently generalized to allow the applications of these developments to a wide range of problems and questions. The need for a generalized theory is evident, and this becomes even more so when one contemplates what is happening at present to those places where one very often sees strengthening activities which evidently have no clear origin. Sometimes, monuments which have defied centuries of calamity and deformation, are subjected to interventions, for the simple reason that they are locally deteriorated. These interventions are described as "static prevention," are brought about by the knowledge that the edifice is threatened.
masonry; mechanics (physics); strengthening; structural analysis; structural stability
p-Adic and Adelic Quantum Mechanics
Proceedings of the First Int. Conf. on p-Adic Mathematical Physics
1-18
2003
p-Adic mathematical physics emerged as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale. One of its main achievements is a successful formulation and development of p-adic and adelic quantum mechanics, which have complex-valued wave functions of p-adic and adelic arguments, respectively. Various aspects of these quantum mechanics are reviewed here. In particular, the corresponding Feynman's path integrals, some minisuperspace cosmological models, and relevant approache to string theory, are presented. As a result of adelic approach, p-adic effects exhibit a spacetime and some other discreteness, which depend on the adelic quantum state of the physical system under consideration. Besides review, this article contains also some new results.
Toward a microrealistic version of quantum mechanics. Part II
Foundations of Physics
6
6
661-676
1976
10.1007/BF00708945
In this paper, possible objections to the propensity micro realistic version of quantum mechanics proposed in Part I are answered. This version of quantum mechanics is compared with the statistical, particle, micro realistic viewpoint, and a crucial experiment is proposed designed to distinguish between these two micro realistic versions of quantum mechanics.
Mechanics of growing materials
International Journal of Mechanical Sciences
20
8
493-504
1978
10.1016/0020-7403(78)90047-4
Assuming the constitutive equations in the form proposed by Noll for the so-called linear hygrosteric materials, systematization and generalization of the solutions known for a class of three-dimensional problems are made. The behavior of an infinitely long hollow cylinder subject to an internal uniform pressure, in the presence of mass sources acting in the material, is analysed in some detail.
Extended Supersymmetric Quantum Mechanics
arXiv.org
hep-th
1999
10.1016/S0370-2693(99)00773-X
A parametrization of the Hamiltonian of the generalized Witten model of the SUSY QM by a single arbitrary function in d=1 has been obtained for an arbitrary number of the supersymmetries N. Possible applications of this formalism have been discussed. It has been shown that the N=1 and 2 conformal SUSY QM is generalized for any N. Published in: Phys.Lett. B460 (1999) 365-370
Statistical mechanics of point vortices
Physical Review E
51
5
4432-4452
1995
10.1103/PhysRevE.51.4432
Thermodynamical functions and probability distributions are found in an explicit form for a mul- ticomponent vortex gas. A key point in the derivation is the interpretation of integration in phase space as an average, with respect to some "complex measure. " The exact formulas for the probability distribu- tion of a vortex gas are used to obtain the averaged equations for two-dimensional fluid motion. The ex- act formulas for thermodynamical entropy and temperature, which, in contrast to the classical models of statistical mechanics, are not equivalent for a vortex gas.
Computational Mechanics in Structural Engineering
Computational Mechanics in Structural Engineering
259-265
1999
10.1016/B978-008043008-9/50058-2
This chapter discusses structural analysis and failure process in civil engineering. There are three prerequisites to perform structural analysis: constitutive law of specific material, which can be obtained by small-scale test; effective numerical methods, such as finite element method (FEM), direct integration, etc; graph display software, and visual system. Furthermore, this chapter illustrates the philosophy of computer simulation in structural engineering using flow chart representation, along with mathematical model for engineering problem. This chapter closes with some simulation examples visualizing numerical results.
Matrix Methods in Quantum Mechanics
American Journal of Physics
36
9
814
1968
10.1119/1.1975154
Some standard results of matrix theory are derived in a manner designed to appeal to physicists and are illustrated by examples from quantum mechanics. Sylvester's formulas, expressing a function of any n-dimensional square matrix as a linear combination of the first n−1 powers of A , are applied to the evaluation of the rotation matrices D (i) (R) for low values of j . The neutral K meson is used as an example of the usefulness of matrix techniques for systems with two basis states.
Billow Mechanics
Radio Science
4
12
1299-1308
1969
10.1029/RS004i012p01299
Billows are the most common form of dynamic instability in the free air where the air is stably stratified. They occur mainly in layers where the static stability is much larger than average and therefore where there are already large gradients of temperature and humidity. They are produced predominantly by the tilting of these very stable layers in the wavy airflow produced by hills. The billows form a cat's-eye pattern of motion that becomes statically unstable in the closed circulations. Consequently, the gradients inside are destroyed by the buoyancy-induced mixing, and large gradients are produced at the boundary of the circulations. The original stable layer is thus replaced by two stable layers at a distance apart of the order of 5 times the depth of the original layer. During the overturning, large gradients of temperature are produced at the wavy boundary, which is itself corrugated by the internal mixing motions.
ON THE FRACTURE-MECHANICS OF PIEZOELECTRIC SOLIDS
International Journal of Solids and Structures
29
21
2613-2622
1992
A fracture mechanics analysis is developed within the realm of two-dimensional linear piezoelectricity. The asymptotic expressions for the electromechanical fields in the vicinity of the crack are deduced, and their behavior is illustrated through several examples. The modelling of the electric field's effects on crack arrest and crack skewing constitutes one of the important features of this article.
Testing quantum mechanics in the neutral kaon system
Physics Letters B
July 1992
10
1992
10.1016/0370-2693(92)91493-S
The neutral kaon system is a sensitive probe of quantum mechanics. We revive a parametrization of non-quantum-mechanical effects that is motivated by considerations of the nature of space-time foam, and show how it can be constrained by new measurements of $K_L \rightarrow 2\pi$ and $K_{L,S}$ semileptonic decays at LEAR or a $\phi$ factory.
Quantum mechanics in terms of non-negative distribution functions
Physica A: Statistical Mechanics and its Applications
184
1-2
231-243
1992
10.1016/0375-9601(92)90542-T
We construct a formalism which enables us to express quantum mechanics in terms of any non-negative smoothed Wigner function. Quantum mechanics in terms of the well known Husimi function turns out to be just a special case of this general formalism. 1992.
A simplified model for ballistic initiation of thin energetic targets by micro-flier impact
International Journal of Mechanical Sciences
84
1-17
2014
http://dx.doi.org/10.1016/j.ijmecsci.2014.04.006
Abstract Novel techniques involving high-speed impact (~500–1500 m/s) of laser generated micro-fliers with thin metallic targets having a layer of reactive solid deposited on their back side ( ~ 10 – 100 μ m ) are being developed to interrogate its shock-induced chemistry. Because mass spectrometry is performed in vacuo on the reactive side of the target to identify the chemical species produced, it is important to initiate chemistry without perforation of the target plate by the flier. An analytically tractable model is formulated in this paper to guide experimental development by predicting the ballistic response of large numbers of micro-flier–target configurations in a computationally inexpensive manner. The model is posed in terms of multi-component conservation principles and interaction terms that account for important features of both the early-time wave mechanics and the longer-time target deformation mechanics including flier–target adhesion. The model, validated using published data for larger scale inert flier–target configurations, is used to predict the response of micro-scale configurations consisting of aluminum fliers and steel targets. Scanning Electron Microscopy (SEM) of post-impact, inert flier–target micro-scale configurations is used to both highlight target deformation and damage and to motivate modeling simplifications. To illustrate the model, configurations that result in initiation (detonation) of the high-explosive PETN (C5H8N4O12) without perforation of the steel substrate are parametrically characterized in the form of ballistic initiation maps based on its empirical critical shock energy.
Energetic materials; Micro-flier Impact; Perforation; Reduced-order model; Shock initiation; Shock-to-detonation transition
Chapter 2 - Statistical Mechanics
Theory of Simple Liquids (Third Edition)
11-45
2006
http://dx.doi.org/10.1016/B978-012370535-8/50004-5
Publisher Summary This chapter provides a summary of the principles of classical statistical mechanics, a discussion of the link between statistical mechanics and thermodynamics. It also discusses the definition of certain equilibrium and time-dependent distribution functions of fundamental importance in the theory of liquids. The focus of the chapter is on atomic systems. Time evolution and kinetic equations are first described. Time averages and ensemble averages are discussed next. Certain thermodynamic properties of a physical system may be written as averages of functions of the coordinates and momenta of the constituent particles. These are the so-called “mechanical” properties, which include internal energy and pressure. Canonical and isothermal—isobaric ensembles are detailed. A canonical ensemble is a collection of systems characterized by the same values of N, V and T. The chapter moves on to the grand canonical ensemble. The argument is extended to the situation where the number of particles may vary by interchanging with the surroundings, but retain the assumption that the system is homogeneous. The thermodynamic state of an “open” system is defined. Particle densities and distribution functions are discussed next. Particle densities in the grand canonical ensemble are described. The importance of computer simulation, molecular dynamics, and Monte Carlo method is detailed.
The geometric semantics of algebraic quantum mechanics
Arxiv 1410.7277
2014
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Molecular mechanics (MM3) study of organogermanes
Journal of Physical Organic Chemistry
12
7
528-540
1999
10.1002/(SICI)1099-1395(199907)12:7<528::AID-POC114>3.0.CO;2-#
The MM3 force field has been extended to permit the treatment of organogermanes. The vibrational spectra, molecular structures, moments of inertia, dipole moments and conformational energies of 21 compounds were studied. The available experimental data are mostly well reproduced.
MM3 force field; molecular mechanics; organogermanes
A quantum mechanics/molecular mechanics study of the reaction mechanism of the hepatitis C virus NS3 protease with the NS5A/5B substrate
… Structure
2007
Combined quantum mechanics and molecular mechanics (QM/MM) calculations were carried out to characterize the reaction mechanism of the NS3 protease with its preferred substrate ( NS5A / 5B ). The main purpose of this study was to locate the barrier states and ...
Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory
Quantum
67
6
6
2006
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.
Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory
Physics
6
6
2006
10.1088/1742-6596/67/1/012035
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.
High Energy Physics - Theory; Quantum Physics
MECHANICS OF DISORDERED SOLIDS .3. FRACTURE PROPERTIES
PHYSICAL REVIEW B
47
2
713-722
1993
10.1103/PhysRevB.47.713
Brittle fracture of disordered media are studied using Monte Carlo\nsimulations in both two and three dimensions (3D). Elastic and\nsuperelastic percolation networks with central and bond-bending forces\nare used as models of disordered media. We find that the distribution of\nfracture strength in a solid with broadly distributed microscopic\nheterogeneities, and in randomly reinforced materials, is adequately\ndescribed by the classical Weibull distribution, rather than the\nrecently proposed Gumbel distribution. System-size dependence of the\nexternal stress F for fracture is also studied. We find that, contrary\nto recent claims, for a d-dimensional system of size L, F is given by F\nis similar to L(d-1)/(lnL)psi, where 0 less-than-or-equal-to psi\nless-than-or-equal-to 0.5. The fractal dimension of the cracks is found\nto be about 1.7 in 2D, close to that of fracture surfaces of natural\nrocks at small scales. The scaling of the fracture stress sigma(f) near\nthe percolation threshold p(c) is found to obey, sigma(f) is similar to\n(p-p(c))T(f), where p is the fraction of intact springs (or the damage\nlevel) and, T(f) congruent-to 2.42 in 2D and T(f) congruent-to 2.64 in\n3D. The 2D result is in agreement with the experimental estimate of T(f)\nfor fracture of thin perforated metal foils. These values are also close\nto the lower bound, T(f) greater-than-or-equal-to f-nud(min), where f is\nthe critical exponent of the elastic moduli of the system, nu the\ncorrelation-length exponent of percolation, and d(min) the fractal\ndimension of the shortest paths on a percolation cluster. Finally, we\nstudy the similarities and differences between fractured and percolation\nnetworks.
Bending of cord composite cylindrical shells
Journal of Applied Mechanics-Transactions of the Asme
67
1
117-127
2000
An analytical method for determining the load-deformation behavior of cord composite cylindrical shells is developed by considering the mechanics of the matrix, the cords, and the shell. To illustrate the method, a circular cylindrical shell with a single ply of uniformly spaced cords parallel to the shell axis is considered. The differential equations for the displacements are derived. These equations are solved analytically in closed form for a shell with the cords on the middle surface and subjected to axisymmetric loading. The deformations are strongly dependent upon the properties of the constituents, including the extension-twist coupling of the cords, and the geometry, boundary conditions, and loading. [S0021-8936(00)02701-X].
wire rope mechanics
Teaching elementary concepts in quantum mechanics with computer graphics
Computers and Graphics
2
3
125-128
1977
Students in a beginning quantum mechanics course worked with interactive computer graphics before being introduced to the formal structure of the subject. The computer programs and their use in teaching different concepts are described. © 1977.
Gamasutra's Best Of 2008: Top 5 Gameplay Mechanics
Gamasutra.com
21380
1-10
2009
Next, we'll cover this year's top five gameplay mechanics (with ten other honorable mentions), calling \nattention to a number of innovative, novel, or particularly well-executed individual elements of game \ndesign from throughout the year.
{Some remarks on classical representations of quantum mechanics}
Foundations of Physics
24
7
1089-1094
1994
10.1007/BF02054650
{Abstract It is shown that, to a certain extent, the statistical framework of Hilbert-space quantum mechanics can be reformulated in classical terms.}
Quantum Mechanics and 3\emph{N}-Dimensional Space
Philosophy of Science
73
5
778-789
2006
I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wave function evolving in 3N-dimensional space.
Quantum Mechanics; Spacetime; Physics
Exact solutions of the non-linear wave equations arising in mechanics
Journal of Applied Mathematics and Mechanics
54
3
372-375
1990
10.1016/0021-8928(90)90140-6
Solitary and cnoidal waves solving three equations commonly used to describe wave processes in mechanics - the Burgers-Korteweg-de Vries, Kuramoto-Sivashinsky and Kawahara equations - are obtained by analytical means.
On the interpretation of Quantum Mechanics and Relativity Theory
Symposium on the Foundations of Modern Physics
1993
Realist and emirist interpretations of quantum mechanics and relativity theory are compared. Methodological and physical arguments are discussed favoring an emirist interpretation of quantum mechanics. Analogous arguments are found for an enpirist interpretation of relativity theory.
Arch bridge and mechanics in ancient China
Wen wu bao hu yu kao gu ke xue = Sciences of Conservation and Archaeology
10
2
31-36
1998
The theories of mechanics and physics are rarely seen in the vast collection of ancient books and records of China. However, surviving ancient technical achievements are numerous, and the ancient arch bridge is one of them. The bridge construction abundantly embodies the theory of mechanics and other subjects of science. Exploring the level of sophistication reflected by the arch bridge structure, the author found that many of its aspects exemplify modern principles of mechanics involving analysis and calculation. Considering the source of the arch bridge and referring to related books and records, the author analyzed the development of the arch bridge form and related mechanics. It appears that this technique was conceived in the Spring and Warring States period, came into being in the Qin and Han dynasties, matured in the Sui and Tang dynasties, was developed and perfected in the Song and Yuan dynasties, and was carried on and popularized in the Ming and Qing periods. The process shows a general trend of slow development in a disconnected, nonlinear way. The article considers the reasons for these facts and their meaning for the progress of today's science.
bridges (built works); China; industrial history; mechanics (physics)
Exact solutions of the non-linear wave equations arising in mechanics
Journal of Applied Mathematics and Mechanics
54
3
372-375
1990
10.1016/0021-8928(90)90140-6
Solitary and cnoidal waves solving three equations commonly used to describe wave processes in mechanics - the Burgers-Korteweg-de Vries, Kuramoto-Sivashinsky and Kawahara equations - are obtained by analytical means.
Coordination of teaching in physics and engineering mechanics
Journal of Engineering Education
37
8
618-621
1947
Author recounts some personal experiences in cooperation between departments of physics and mechanics; enumeration of some of shortcomings or faults of instruction in physics as seen by department of mechanics.
Education; Physics
Fracture mechanics application to reinforced concrete members in flexure
Applications of fracture mechanics to reinforced concrete
2002
413-436
1992
This volume is based on the papers presented at the International Workshop on the Applications of Fracture Mechanics to Reinforced Concrete held in Turin, Italy, 6 October 1990.
Broken Z2 symmetries and fluctuations in statistical mechanics
Arxiv
1
1-6
2012
An analogy is developed between the breaking of space-inversion symmetry in equilibrium statistical mechanics and the breaking of time-reversal symmetry in nonequilibrium statistical mechanics. In this way, similar relationships characterizing fluctuations are obtained in both contexts.
A Modern Approach to Quantum Mechanics (2nd ed.).
American Journal of Physics
81
12
959
2013
10.1119/1.4821806
This article reviews A Modern Approach to Quantum Mechanics (2nd ed.). by John S. Townsend 586 pp. , 2012. Price: $81.81 (hardcover) ISBN 978-1-891389-78-8.
Holomorphic Supersymmetric Quantum Mechanics, Generalized Supersymmetry, and Parasupersymmetry
Annals of Physics
236
2
219-240
1994
10.1006/aphy.1994.1111
We construct the generalized supersymmetry structure for the holomorphic supersymmetric quantum mechanics and calculate the corresponding GSQM indexes. We also show that the two-dimensional representation of the parasupersymmetric quantum mechanics can be constructed by means of the supersymmetric involutions.
Experimental tests of quantum mechanics versus local hidden variable theories
J. Phys. A: Math. Gen
11
L167
1978
We propose new inequalities involving polarisation correlation parameters as tests of local hidden variable theories versus quantum mechanics. These are derived using Bell’s formulation of Einstein’s locality condition.
N-fold supersymmetry in quantum mechanics: general formalism
Nuclear Physics
2001
10.1016/S0550-3213(01)00516-8
We report general properties of -fold supersymmetry in one-dimensional quantum mechanics. -fold supersymmetry is characterized by supercharges which are th polynomials of momentum. Relations between the anti-commutator of the
Mathematical programming applications to structural mechanics: some introductory thoughts
Engineering Structures
6
1
2-6
1984
10.1016/0141-0296(84)90055-5
The paper outlines the author's view of the historical development and future prospects of mathematical programming applied to the analysis of structural problems.
Thin and thinner: Wireless poised to shake up thin client landscape
ENT
5
16
30-32
2000
The most prevalent application delivered through thin-client systems is email, cited by 89 percent of sites with thin-client systems. Another 83 percent offer thin-client access to databases, and 81 percent offer thin-client connectivity to file and print servers. Another 73 percent offer access to personal productivity applications.
Thin-Film Silicon Solar Cells
Advanced Silicon Materials for Photovoltaic Applications
311-353
2012
10.1002/9781118312193.ch9
This chapter contains sections titled: * Introduction * Second-Generation Solar Cells: Advantages Compared to the First Generation * Drift-Type Thin-Film Silicon Solar Cells: Substrates and Configuration * Material Considerations for Thin-Film Silicon Solar Cells * Present Status of Drift-Type Thin-Film Silicon Solar Cells * Technological Issues * Third-Generation Thin-Film Silicon Cell * Solar Cells on Plastics * Hybrid Cells * Industrial Scenario of Thin-Film Silicon-based Solar Cells * Challenges for Thin-Film Silicon Solar-Module Fabrication * Acknowledgements * References
c-Si solar cells, dominating the PV scene; multijunction thin-film, optical effects for light; QD doping thermodynamics ‘self-purification effect; Si thin-film PV, role of nc-Si, and low production; solar progress in CdTe-based thin-film PV; thin-film PV potentialities, boost for future succ; thin-film Si bottleneck, and deposition increase,; thin-film silicon solar, and module efficiency dat; thin-film silicon solar cells; thin-film silicon, superstrate, p-i-n and substrat
Enhancing the Learning of Fluid Mechanics
Journal of Engineering Education
October
381-388
2007
This paper reports the results of a study into the impact of com- puter simulations on the understanding of fluid mechanics by engineering students. A “lesson study” approach was taken, using constructivist educational theory combined with the variation theory of learning from phenomenography to inform the design of learning activities and to assess their impact. Student difficul- ties with fluid mechanics concepts were assessed using questions from the Fluid Mechanics Concept Inventory (FMCI). Students had the greatest difficulties with pressure measurement, fluid flow through pipes with changing diameter, and velocity profiles for fluid between flat plates. We developed a set of three simulations to address these difficulties. The impact of the simulations was gauged by a second administration of the FMCI. Most of the stu- dents in the sophomore fluid mechanics class participated in the whole of this exercise. Students showed significant improvement in two of the three areas of difficulty. Student feedback on this as an additional learning exercise was very positive.
computer simulations; fluid mechanics
Nanoindentation-induced defect-interface interactions: Phenomena, methods and limitations BT - Proceedings of the 1998 ACTA Materiala Workshop on 'Materials Science and Mechanics of Interfaces', Oct 25-Oct 30 1998
Acta Materialia
47
15-16
4115-4123
1999
Nanoindentation for measuring thin film mechanical properties is probably the most popular yet ill-understood method due to its inherent complexities. As opposed to burst pressure or microtensile tests of lithographed structures, where relatively uniform stress fields may be generated, the indentation-induced stress gradients can produce unique challenges. Because of the test's simplicity and ability to mechanically probe the smallest of scales, it is becoming increasingly applied. Five possible stages of deformation are suggested from Hertzian elastic to film delamination and double buckling. In particular metal films on harder substrates are emphasized where it is shown that dislocation nucleation and arrest are only partially understood. Later stages of film delamination are illustrated with Cu/SiO2/Si where it is shown that the true work of adhesion is 0.6 J/m2. Current limitations of indentation-induced delamination measures of toughness involve large scatter associated with sensitivity of the fracture radius to the contact radius ratio.
Adhesion; Copper; Delamination; Dislocations (crystals); Fracture toughness; Interfaces (materials); Mechanical testing; Metallic films; Silica; Silicon; Stress analysis; Stress concentration; Thin films
Phase Space Quantum Mechanics
arXiv
1009.0150
2010
The paper review and develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative $\star$-product and the deformation of the Poisson bracket to an appropriate Lie bracket is the key element in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of Hamiltonian systems without any constrains and for a very wide class of deformations. The considered class of deformations and the corresponding $\star$-products contains all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of $\star$-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the $\star$-multiplication. The most important result of the paper shows that developed formalism is more fundamental then the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. In addition, examples of a free particle and a simple harmonic oscillator illustrating the formalism of the deformation quantization and its classical limit are given.
Phase Space Quantum Mechanics
Arxiv preprint arXiv:1009.0150
94
2010
The paper review and develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative $\star$-product and the deformation of the Poisson bracket to an appropriate Lie bracket is the key element in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of Hamiltonian systems without any constrains and for a very wide class of deformations. The considered class of deformations and the corresponding $\star$-products contains all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of $\star$-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the $\star$-multiplication. The most important result of the paper shows that developed formalism is more fundamental then the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. In addition, examples of a free particle and a simple harmonic oscillator illustrating the formalism of the deformation quantization and its classical limit are given.
Mathematical Physics; Quantum Physics
6 – Fracture Mechanics and Fatigue Crack Propagation
Fatigue Testing and Analysis - Theory and Practice
237-284
2004
10.1016/B978-075067719-6/50007-5
Use of crack propagation laws based on stress intensity factor ranges is the most successful engineering application of fracture mechanics. This chapter gives a review of the basic concepts of fracture mechanics. In contrast to the traditional stress-life and strain-life approaches to fatigue, cracks are assumed to exist in materials and structures within the context of fracture mechanics. Fracture parameters such as K and J can be used to characterize the stresses and strains near the crack tips. A fundamental understanding of fracture mechanics and the limit of using the fracture parameters is needed for appropriate applications of fracture mechanics to model fatigue crack propagation.
Macro-Residual Strains Due to Cyclic Loading of Composites
Mechanics of Advanced Materials and Structures
6
3
257-266
1999
10.1080/107594199305557
Macro-residual strains produced by load cycles on elastic-brittle composites are analytically expressed in terms of the effective thermal expansion coefficients of the composite as affected by the damage states developing during the cycling. Limiting values of residual strain are evaluated for unidirectional fiber composites and cross-ply laminates. Frictional losses due to internal sliding are not considered.
cte
Mechanical properties and adhesion of PZT thin films for MEMS
Materials Research Society Symposium - Proceedings
594
Warrendale, PA, United States
225-230
2000
Piezoelectric films are attractive materials for use in microelectromechanical systems (MEMS) due to their ability to act as both sensors and actuators. One of the primary modes of deformation is the deflection of lead zirconate titantate (PZT) beams and membranes, where the adhesion of the film is critical for the reliability of the device. Thin films of PZT between 250 and 750 nm have been grown via solution deposition routes onto platinized silicon substrates. The films have been tested using nanoindentation techniques. Two failure mechanism in these films have been observed. Indentation induced delamination at the PZT-Pt interface occurs after the indenter tip is removed from the film when loads between 1 and 10 mN are applied to the sample, and at large loads (>75 mN) failure can be generated between the underlying oxide film and the silicon substrate while the tip is still engaged with the sample. Since each of these failure modes has a different mechanics solution, the results are compared to determine adhesion energy of the films. Fracture around the delaminated regions has been examined using scanning probe and electron microscopy. Freestanding PZT membranes above micromachined cavities have been mechanically deformed to examine the mechanical response and failure modes in these structures. The adhesion of the PZT improves with increased percent crystallization due to the introduction of residual tensile stresses. Processing, mechanical properties, and failure modes in these devices will be discussed.
Adhesion; Crystallization; Delamination; Dielectric films; Fracture; Interfaces (materials); Lead compounds; Lead zirconate titanate; Microactuators; Microelectromechanical devices; Microsensors; Nanoidentation test; Piezoelectric materials; Tensile stress; Thin films
Erwin Schrodinger and the rise of wave mechanics. I. Schrodinger's scientific work before the creation of wave mechanics
Foundations of Physics
17
11
1051-1112
1987
10.1007/BF01889803
This article is in three parts. Part l gives an account of Erwin Schr6dinger's grow- ing up and studies in Vienna, his scientific work--first in Vienna from 1911 to 1920, then in Zurich from 1920 to 1925--on the dielectric" properties of matter, atmospheric electricity and radioactivity, general relativity, color theory and physiological optics, and on kinetic theory and statistical mechanics. Part H deals with the creation of the theory of wave mechanics by Schr6dinger in Zurich during the earl), months of 1926; he laid the foundations of this theory in his first two communications to Annalen der Physik. Part Ill deals' with the ear(v applications of wave mechanics to atomic problems--including the demonstration of equivalence of wave mechanics with the quantum mechanics of Born, Heisenberg, and Jordan, and that of Dirac--by SchrOdinger himself and others. The new theory was immediately accepted by the scientific community.
Quantum Mechanics and the Nature of Continuous Physical Quantities
Journal of Philosophy
1979
Quantum mechanics never attributes precise, point valued positions or precise point valued momenta. consequently, either objects never have precise values for either quantity, or quantum mechanics is descriptively (as opposed to predictively) incomplete. the article embraces the first alternative, appealing to the imprecision of language and the process of conceptual refinement, arguing that non-point valued positions and velocities are a viable refinement of prescientific concepts alternative to the idealizations of classical physics. the article includes discussion of the distinction between idealizations and approximations and a summary of technical literature on rigged hilbert spaces and fuzzy phase space reconstructions of quantum mechanics.
Continuum; Physics; Quantum Mechanics; Science
Model for predicting thermal stresses in thin polycrystalline films
Journal of the Mechanics and Physics of Solids
45
4
511-534
1997
This paper reports the development of a numerical model to analyze thermal stresses induced in thin polycrystalline films deposited on thick substrates. The model accounts for viscoplastic deformations due to crystallographic slip in each grain of the polycrystal. The microstructural processes, which constrain dislocation slip due to the substrate, surface layer, and grain boundaries as well as due to hardening on the slip systems themselves, are considered and incorporated into the model. Using this model, the predicted stress-temperature curves for aluminium films with a natural oxide layer are in good agreement with the measured curves, especially for thicker films. It was found that the predictions of stress-temperature curves for <111> fiber textured films are not substantially affected by reasonable deviations from a perfect fiber texture. Therefore, one can globally model the deformation of a <111> textured polycrystalline film by assuming it to be a single crystal provided the film is in a state of equal biaxial strain. However, it is also shown that for an equal biaxial thermal strain, the local stress state at the grain level is more complicated due to the effect of the orientation of the individual grains, although the global stress state will be equal biaxial for a <111> textured film. In fact, very high local stress gradients might have to be accommodated.
A. strengthening mechanisms; A. stress relaxation; A. thin films; B. polycrystalline material; B. thermal stress
Multimedia Application for Fluid Mechanics Teaching
Computational Intelligence and Software Engineering, 2009. CiSE 2009. International Conference on
1-4
2009
The necessity of multimedia in modern fluid mechanics teaching was discussed. The objectives, characteristics and innovations of constructing multimedia source material database for fluid mechanics teaching were analyzed, and the technical means, the soft and hardware conditions were presented. The basic application strategies of multimedia for fluid mechanics teaching was to well combine multimedia materials and teaching links including electronic teaching plan, teaching design, classroom explanation, problem discussion, practice and experiment teaching, etc., and to create teaching situations to improve teaching effect.
classroom explanation; computer aided instruction; electronic teaching plan; fluid mechanics; fluid mechanics teaching; multimedia resource materials; physics computing; physics education; teaching design
Gold nanoparticle thin films
Colloids and Surfaces A: Physicochemical and …
2002
reserved. thin films. gold. Author Keywords: ; ; Thin films; Maxwell–Garnett; Optical properties.
Study of the effect of different plasma-enhanced chemical vapour deposition reactor configurations on the properties of hydrogenated amorphous silicon thin films
Philosophical Magazine B-Physics of Condensed Matter Statistical Mechanics Electronic Optical and Magnetic Properties
80
4
475-486
2000
Doi 10.1080/13642810008209755
In this work we present a study performed in a plasma-enhanced chemical vapour deposition reactor, where different rf electrode configurations were used with the aim of achieving conditions that lead to growth of highly uniform amorphous silicon films, with the required electronic quality, at high growth rates. This study consists in determining the plasma characteristics under different electrode configurations, in an argon plasma, using as diagnostic tools a Langmuir probe and impedance probe. These results were correlated with the hydrogenated amorphous silicon films produced, thereby allowing us to establish the best electrode configuration to grow electronic-grade-quality amorphous silicon films.
discharges; h alloys
Metal organic chemical vapor deposition of thin Al(2)O(3) films on HP40 alloy as oxidation barriers
Transferability and Applicability of Current Mechanics Approaches
385-389
2009
Amorphous alumina films were deposited by metal-organic chemical vapor deposition (MOCVD) on HP40 alloy. The deposition process was carried out in nitrogen with aluminum-tri-sec-butoxide (ATSB) as the precursor at atmospheric pressures. The effects of deposition temperature, growth rate and film thickness on the resistant corrosion properties have been investigated using optical microscopy (OM), scanning electron microscopy (S EM), X-ray diffraction (XRD) and atomic force microscopy (AFM). The results showed that alumina films deposited at 330 degrees C were smooth, uniform, and dense.
al(2)o(3); amorphous alumina films; anti-corrosion; coatings; growth rate; high-temperature corrosion; hp40; mocvd; oxidation barriers
Critique of Southwell plots with proposals for alternative methods [in elastic analysis of thin-walled structural elements]
Experimental Mechanics
15
8
303-310
1975
10.1007/bf02318661
The theory of the Southwell plot is outlined and its history traced. Examples are given in which the technique fails to give a straight line; these are classified into low-load and higher-load nonlinearities. A new approach involving `pivot points' is introduced and used to formulate plots which may help to linearize the data; an application to one of Karman's classical column tests is given. A new graphical technique is proposed for finding Pc for plates with small imperfections, and applied to example data from published test results. A more general numerical technique is also proposed and applied to results from a test during which the experimental boundary conditions were changing
elastic constant measurement
Theories of failure in soil mechanics
Rheological aspects of soil mechanics; John Wiley & Sons
62
1969
Small section of a chaper which shows the relationship between the Coulomb yield criterion and the Hvorslev surface. The Hvorslev equation is basically Coulomb's law with the recognition that the cohesion intercept is a function of the consolidation pressure.
Coulomb yield envelop; Hvorslev surface; Mohr yield locus; soil mechanics
Molecular Mechanics of Peroxides. II. Cyclic Compounds
Journal of Computational Chemistry
10
7
911-920
1989
The conformat ions of various cyclic peroxides have been determined using a molecular mechanics force field developed by the authors and previously applied to linear peroxides. Comparison of the results with those of experimental and ab initio studies shows that this force field may be employed without correction for cyclic compounds.
alkyl peroxides; molecular mechanics
Annual review of fluid mechanics. Volume 27
Annual review of fluid mechanics. Volume 27
586
1995
This volume contains 15 papers on various topics in fluid mechanics. The book begins with a review article on the progress in turbulence research in China. Other subjects discussed
annual review; GEOGRAPHICAL ABSTRACTS: PHYSICAL GEOGRAPHY -- 71; Note(s): Special Features: indexes
HOW AMPLITUDE TIES INTO STROKE MECHANICS
Swimming World
47
8
37
2006
The article focuses on swimming stroke mechanics. A kinesiology expert and biomechanics teacher writes that in order to swim faster, swimmers need to reduce amplitude of movement and increase frequency. The author writes that swimmers should seek to combine high frequency, in a dolphin kick for example, with optimal amplitude.
*ATHLETES; *BIOMECHANICS; *HUMAN mechanics; *KINESIOLOGY; *SWIMMERS; *SWIMMING
The Anti-Vaxjo Interpretation of Quantum Mechanics
Arxiv
18
2002
In this note, I try to accomplish two things. First, I fulfill Andrei Khrennikov's request that I comment on his "Vaxjo Interpretation of Quantum Mechanics," contrasting it with my own present view of the subject matter. Second, I try to paint an image of the hopeful vistas an information-based conception of quantum mechanics indicates.
Quantum Physics
A QUICKSTEP-based quantum mechanics molecular mechanics approach for silica
Journal of Chemical Physics
124
15
2006
Artn 154707\rDoi 10.1063/1.2187485
Quantum mechanics/molecular mechanics (QM/MM) approaches are currently used to describe several properties of silica-based systems, which are local in nature and require a quantum description of only a small number of atoms around the site of interest, e.g., local chemical reactivity or spectroscopic properties of point defects. We present a QM/MM scheme for silica suitable to be implemented in the general QM/MM framework recently developed for large scale molecular dynamics simulations, within the QUICKSTEP approach to the description of the quantum region. Our scheme has been validated by computing the structural and dynamical properties of an oxygen vacancy in alpha-quartz, a prototypical defect in silica. We have found that good convergence in the Si-Si bond length and formation energy is achieved by using a quantum cluster of only eight atoms in size. We check the suitability of the method for molecular dynamics and evaluate the Si-Si bond frequency from the velocity-velocity correlation function. (c) 2006 American Institute of Physics.
ab-initio; alpha-quartz; dynamics simulations; force-field; functional method; local-density approximation; neutral oxygen vacancy; pressure; pseudopotentials; sio2
STRESS-STRAIN STATE OF THIN-WALLED CYLINDERS WITH A STIFFENED CUTOUT TAKING INTO ACCOUNT PHYSICAL AND GEOMETRIC NONLINEARITIES
International Applied Mechanics
374
8
598-603
1993
The basic equations and numerical results of investigations of the stress-strain state of a cylinder near a stiffened circular cutout are presented. The influence of nonlinear factors on the stress distribution near the cutout is studied as a function of the stiffness of the stiffeners on the basis of a numerical solutien of different variants of nonlinear and linear problems. The most suitable parameters of a stiffen- ing element are determined for a cylinder under prescribed internal pressure.
Mechanics of materials, 2 An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials
Endeavour
2
4
192
1978
This text is a revised and extended third edition of the highly successful text initially published in 1977 intended to cover the material normally contained in degree and honours degree courses in mechanics of materials and in courses leading to exemption from the academic requirements of the Engineering Council. It should also serve as a valuable reference medium for industry and for post-graduate courses. Published in two volumes, the text should also prove valuable for students studying mechanical science, stress analysis, solid mechanics or similar modules on Higher Certificate, Higher Diploma or equivalent courses in the UK or overseas and for appropriate NVQ* programmes. The study of mechanics of materials is the study of the behaviour of solid bodies under load. The way in which they react to applied forces, the deflections resulting and the stresses and strains set up within the bodies, are all considered in an attempt to provide sufficient knowledge to enable any component to be designed such that it will not fail within its service life. Typical components considered in detail in the first volume, Mechanics of Materials I , include beams, shafts, cylinders, struts, diaphragms and springs and, in most simple loading cases, theoretical expressions are derived to cover the mechanical behaviour of these components. Because of the reliance of such expressions or certain basic assumptions, the text also includes a chapter devoted to the important experimental stress and strain measurement techniques in use today with recommendations for further reading. Building upon the fundamentals established in Mechanics of Materials 1, this book extends the scope of material covered into more complex areas such as unsymmetrical bending, loading and deflection of struts, rings, discs, cylinders plates, diaphragms and thin walled sections. There is a new treatment of the Finite Element Method of analysis, and more advanced topics such as contact and residual stresses, stress concentrations, fatigue, creep and fracture are also covered. Each chapter of both books contains a summary of essential formulae which are developed within the chapter and a large number of worked examples. The examples have been selected to provide progression in terms of complexity of problem and to illustrate the logical way in which the solution to a difficult problem can be developed. Graphical solutions have been introduced where appropriate. In order to provide clarity of working in the worked examples there is inevitably more detailed explanation of individual steps than would be expected in the model answer to an examination problem. All chapters conclude with an extensive list of problems for solution by students together with answers. These have been collected from various sources and include questions from past examination papers in imperial units which have been converted to the equivalent SI values. Each problem is graded according to its degree of difficulty as follows: A A/B B C Gratitude is expressed to the following examination boards, universities and colleges who Relatively easy problem of an introductory nature. Generally suitable for first-year studies. Generally suitable for second or third-year studies. More difficult problems generally suitable for third-year studies. have kindly given permission for questions to be reproduced: City University East Midland Educational Union Engineering Institutions Examination Institution of Mechanical Engineers Institution of Structural Engineers Union of Educational Institutions Union of Lancashire and Cheshire Institutes University of Birmingham University of London C.U. E.M.E.U. E.I.E. and C.E.I. I .Mech .E. 1.Struct .E. U.E.I. U.L.C.I. U.Birm. U.L. Both volumes of the text together contain 150 worked examples and more than 500 problems for solution, arid whilst it is hoped that no errors are present it is perhaps inevitable that some errors will be detected. In this event any comment, criticism or correction will be gratefully acknowledged. The symbols and abbreviations throughout the text are in accordance with the latest recommendations of BS 1991 and PD 5686t As mentioned above, graphical methods of solution have been introduced where appropriate since it is the author’s experience that these are more readily accepted and understood by students than some of the more involved analytical procedures; substantial time saving can also result. Extensive use has also been made of diagrams throughout the text since in the words of the old adage “a single diagram is worth 1000 words”. Finally, the author is indebted to all those who have assisted in the production of this text; to Professor H. G. Hopkins, Mr R. Brettell, Mr R. J. Phelps for their work associated with the first edition, to Dr A. S. Tooth’, Dr N. Walker2, Mr R. Winters2 for their contributions to the second edition and to Dr M. Daniels3 for the extended treatment of the Finite Element Method which is the major change in this third edition. Thanks also go to the publishers for their advice and assistance, especially in the preparation of the diagrams and editing and to Dr. C. C. Perry (USA) for his most valuable critique of the first edition.
Alternative Hamiltonian Desciptions and Statistical Mechanics
Int. J. Modern Physics A
17
6
3779-3788
2002
10.1142/S0217751X02009898
We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of Statistical Mechanics, i.e. that alternative Hamiltonian descriptions do lead to the same thermodynamical description of any physical system.
Quantum Physics
Random Matrix Theory in Lattice Statistical Mechanics
mathuzhch
10
2002
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and secondly it appears to be an effective tool to find new integrable models. Various examples from quantum and classical statistical mechanics are presented.
Integrating Mechanics with Literature and Writing.
English Journal
76
6
51-52
1987
Proposes an integrated approach to teaching mechanics that focuses on literature and writing to maintain student interest, but incorporates enough mechanics to eliminate isolated skill lessons. Illustrates the method with an imaginary class discussion of wording in a seventh grader's short story that prompts revision of spelling and diction. (JG)
Classroom Techniques; English Instruction; Grammar
Quantum Mechanics.
Origins
371
1989
20120523
2013
10.1098/rsta.2012.0523
-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics.
STABILITY ASSESSMENT OF A UNIFIED VARIATIONAL BOUNDARY INTEGRAL METHOD APPLICABLE TO THIN SCATTERERS AND SCATTERERS WITH CORNERS
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
111
3-4
305-321
1994
10.1016/0045-7825(94)90136-8
The objective of this study is to assess the stability, especially at\nand near critical frequencies, of a new unified, stable, symmetric,\ndomain finite element and boundary integral methodology for solving\ntime-harmonic interface problems for scatterers of arbitrary shape. The\nvalidity of this energy-based variational procedure for rigid and\npenetrable smooth scatterers, including the existence, uniqueness and\noptimal convergence of the corresponding numerical approximations, has\nbeen proved rigorously in the context of fluid-structure interaction\nproblems. The emphasis here is on investigating the applicability of\nthis procedure to the case of scatterers with corners, using square and\nthin rectangular two-dimensional rigid obstacles as prototypes. We also\nestablish that the apparently distinct direct boundary integral\nformulation due to Burton and Miller and the combined single- and\ndouble-layer indirect formulation due to Leis, Brakhage and Werner, and\nPanich, introduced to insure that boundary integral equations for\nscattering problems are uniquely solvable for all wavenumbers, are\nentirely equivalent within our variational setting. By examining the\ncondition number of the matrix of coefficients of the discretized\nequations, as well as the resulting solutions, both directly on the\nsurface of the scatterers and in the far field, it is demonstrated that\nthe new methodology is robust, and completely insensitive to critical\nfrequencies, even for thin objects. Most significantly, the precise\nsingular behaviour of the pressure field at corners is also predicted\nquite accurately by using standard finite elements along the boundary of\nthe scatterer, without having to introduce special singularity\nfunctions, which for general interface problems, may not be known in\nadvance.
Evaluation of interface strength between thin films fabricated on a silicon substrate for mixed mode of fracture
The Ninth Intersociety Conference on Thermal and Thermomechanical Phenomena In Electronic Systems (IEEE Cat. No.04CH37543)
2
192-198
2004
10.1109/ITHERM.2004.1318282
Since electronic devices are made of multi-layered sub-micron films, delamination along the interface is one of the major failure mechanisms. This paper aims to develop a method for evaluating the mechanical criterion of interface cracking between thin films on a substrate. The focus is put on crack initiation from the edge of the interface where the stress concentrates due to the mismatch of deformation. For evaluating the interface fracture, specimens and loading systems were proposed. They are applied to sub-micron films (Si<sub>3</sub>N<sub>4</sub>/Cu/TaN) on Si-substrate. A crack initiates at the edge of interface and the stress singularity field due to the mismatch of deformation between materials of films is dominant. On the basis of the fracture mechanics concept, the evaluated interface fracture toughness is 20 MPa·m<sup>λ</sup> (λ=0.07). It is independent of shapes of specimens and loading systems and characterizes the interface strength. The fracture mechanism can be classified into two types: opening mode and sliding mode. Corresponding with fracture modes, the fracture toughness varies. The interface fracture toughness of sliding mode is smaller than that of opening mode. The three-dimensional finite element analysis reveals that the structures of the corner on the interface causes the increasing of the shear stresses and affects the singularity field.
Fluid mechanics of heart valves
Annual Review of Biomedical Engineering
6
331
2004
Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review
Biomedical Engineering; complications; fluid mechanics; Heart; Mechanics; TISSUE
Rock Mechanics for underground mining
Rock Mechanics for underground mining: Third edition
628
2006
10.1007/978-1-4020-2116-9
Although Rock Mechanics addresses many of the rock mechanics issues which arise in underground mining engineering, it is not a text exclusively for mining applications. It consists of five categories of topics on the science and practice of rock engineering: basic engineering principles relevant to rock mechanics; mechanical properties of rock and rock masses; design of underground excavations in various rock mass conditions; mining methods and their implementation; and guidelines on rock mechanics practice. Throughout the text, and particularly in those sections concerned with excavation design and design of mining layouts, reference is made to computational methods of analysis of stress and displacement in a rock mass. The principles of various computational schemes, such as boundary element, finite element and distinct element methods, are considered. This new edition has been completely revised to reflect the notable innovations in mining engineering and the remarkable developments in the science of rock mechanics and the practice of rock engineering that have taken place over the last two decades. Based on extensive professional, research and teaching experience, this book will provide an authoritative and comprehensive text for final year undergraduates and commencing postgraduate students. For professional practitioners, not only will it be of interest to mining and geological engineers but also to civil engineers, structural and mining geologists and geophysicists as a standard work for professional reference purposes.
Mechanics of hairspring in mechanical watch movement
Applied Mechanics and Materials
117-119
252-255
2012
10.4028/www.scientific.net/AMM.117-119.252
Hairspring is a fine spiral spring, which is the key component in mechanical watch movement for timekeeping. According to literatures, there are only few studies on hairsprings or spiral springs. Using the Castiliago’s method, the mechanics of hairspring is studied in details. And Computer simulation with Matlab® and experimental validation are also conducted to show the spring frequency. Experiment shows that the theoretical analysis and computer simulation can be used to guide and facilitate the design of hairspring or spiral spring.
Hairspring; Mechanical Watch Movement; Mechanics Analysis
Bohmian Mechanics Stanford Encyclopedia of Philosophy
Stanford Encyclopedia of Philosophy
Spring
2013
Bohmian Mechanics First published Fri Oct 26, 2001; substantive revision Mon Mar 4, 2013 Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's equation. However, the wave function provides only a partial description of the system. This description is completed by the specification of the actual positions of the particles. The latter evolve according to the “guiding equation,” which expresses the velocities of the particles in terms of the wave function. Thus, in Bohmian mechanics the configuration of a system of particles evolves via a deterministic motion choreographed by the wave function. In particular, when a particle is sent into a two-slit apparatus, the slit through which it passes and its location upon arrival on the photographic plate are completely determined by its initial position and wave function
Bohmian mechanics; pilot waves; quantum mechanics
The Physical Principles of Quantum Mechanics
Arxiv
1930
1-27
2011
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.
Quantum Physics
Ground state structure in supersymmetric quantum mechanics
Annals of Physics
178
2
313-329
1987
10.1016/0003-4916(87)90018-2
We present a rigorous analysis of the vacuum structure of two models of supersymmetric quantum mechanics. They are the quantum mechanics versions of the two-dimensional N = 1 and N = 2 Wess-Zumino quantum field models. We find that the N = 2 quantum mechanics has degenerate vacua. The space of vacuum states is bosonic, and its dimension is determined by the topological properties of the superpotential.
Statistical Mechanics of Compressed Sensing
Physical Review Letters
2010
DOI: / . PACS numbers: 89.20.Āa, 05.70.Fh, 89.75.Āk Press, Cambridge, 2001). [10] See supplementary material at http://link.aps.org/ supplemental/ / . for deri- vations of results. [11] T. Cover, IEEE Trans. Electron.
Statistical mechanics of complex networks
Reviews of modern physics
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems
ON STATISTICAL-MECHANICS OF SOLVATION
JOURNAL OF CHEMICAL PHYSICS
97
6737-6743
1992
10.1063/1.463651
An exact solution is obtained for the solvation free energy of a\ntwo-level system immerse into dielectric continuum. The solution is\ninvariant with respect to the representation of the quantum electronic\nstates.
Arrival time in quantum mechanics
Physics Reports
338
4
353-438
2000
doi:10.1016/S0370-1573(00)00047-8
The arrival time is a simple classical concept, very common in laboratory practice. This review describes theoretical problems encountered in trying to obtain a quantum mechanical counterpart and the solutions proposed. A summary of current experimental techniques is also included.
Oxide thin film transistor
Teion Porishirikon Hakumaku Toranjisuta no Kaihatsu
243-264
2007
A review including amorphous oxides and device fabrication. [on SciFinder (R)]
Oxides Role: PEP (Physical, engineering or chemica; review oxide TFT; Semiconductor device fabrication; Thin film transistors (oxide thin film transistor)
A variational principle for fluid mechanics
Archive of Applied Mechanics
67
1-2
96-104
1996
A variational principle for fluid mechanics is derived without calling for any additional postulates in any ad hoc way. In the principle derived here, the Lagrangian is essentially the sum of kinetic and heat energy transferred to the fluid, less the sum of its internal and potential energy, less the work done on its exterior (similar to the enthalpy concept), rather than the difference between only kinetic energy and internal energy, as obtained previously by Seliger and Whitham [1] for a more restricted mode of variation.
fluid mechanics; lagrangian; thermodynamics; variational principle
Probability and the Interpretation of Quantum Mechanics
British Journal for the Philosophy of Science
1973
I present a simple, intuitive account of quantum mechanics as an essentially statistical theory of a determinate domain. i defend this account against objections stemming from the no-hidden-variable proofs by developing a classical, propositional language for the theory that admits of ordinary bivalent valuations. the no-joint-distribution proofs are then used to show that these valuations allow for precisely the probabilities of quantum mechanics--nothing less but also nothing more.
Probability; Quantum Mechanics; Science
Teaching Classical Statistical Mechanics: A Simulation Approach
American Journal of Physics
49
1
13-19
1981
Describes a one-dimensional model for an ideal gas to study development of disordered motion in Newtonian mechanics. A Monte Carlo procedure for simulation of the statistical ensemble of an ideal gas with fixed total energy is developed. Compares both approaches for a pseudoexperimental foundation of statistical mechanics. (Author/JN)
College Science; Computer Oriented Programs; Energy; Flow Charts; Higher Education; Mathematical Models; Mechanics (Physics); Motion; Physics; Science Education; Science Instruction; Simulation; Statistics
Information Theory and Statistical Mechanics
Physical Review
106
620-630
1957
10.1103/PhysRev.106.620
Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available.
Quantum Mechanics of Black Holes
arXiv.org
hep-th
1994
These lectures give a pedagogical review of dilaton gravity, Hawking radiation, the black hole information problem, and black hole pair creation. (Lectures presented at the 1994 Trieste Summer School in High Energy Physics and Cosmology)
Quantum mechanics of the rigid rotator
Il Nuovo Cimento B
22
2
337-345
1974
10.1007/BF02726596
A representation of the position and angular-momentum variables of a quantum-mechanical rigid rotator is obtained from general symmetry principles. The method used is similar to the treatment of spin in the case of the quantum particle.
Penetration problems in rock mechanics
Annual ASME Applied Mechanics Division of Rock Mechanics Winter Symposium
3
3
41-71
1973
Although rock can exhibit a wide range of constitutive behavior, 2 particular classes of behavior stand out most predominantly, namely, elastic-brittle (under standard atmospheric conditions) and ductile (at high confining pressures). This provides a convenient division of problems. Thus, Pt. 1 deals with the penetration of elastic-brittle rock while Pt. 2 is concerned with the penetration of plastic rock. Rocks, which are brittle under normal atmospheric conditions, become ductile under sufficiently high confining pressures. The working of tools in ductile rock appears to have the most significance in deep oil wells. Roller-bit teeth penetrate the rock through a low-permeability filter cake caused by the differential pressure between the drilling fluid and the formation fluid. A brief summary of conditions under which rocks become ductile is given. (42 refs.)
reservoir rock; rock drilling; rock mechanics; duc
Realistic FEA modeling of 3D woven composites on meso-scale
19th International Conference on Composite Materials (ICCM19)
1813-1820
2013
Mesoscale modeling of three-dimensional woven composites presents significant challenges related to accurate representation of as-woven geometry of the reinforcement [1]. There are two approaches most commonly used to define the geometry of reinforcement. One is based on the nominal description of composite, and the other one involves fabric mechanics simulations. In our previous publications, we attempted to evaluate the efficiency and accuracy of these two approaches for prediction of the overall elastic properties and residual stresses due to curing for the so-called ply-to-ply reinforcement architecture, see [2]. In this paper, we present a straightforward procedure to develop realistic finite element models of unit cells for 3D woven composites based on the as-woven reinforcement geometry obtained by the textile modeling software DFMA [3]. We consider two configurations of an orthogonally reinforced composite and describe all steps of the model development. Numerical simulations to predict the overall elastic moduli and evaluate the materials’ potential to develop high residual stresses due to curing are described.
3d woven composite; curing; matrix microcracking; mesoscale
Middle ear mechanics of type IV and type V tympanoplasty: II. Clinical analysis and surgical implications
American Journal of Otology
16
5
565-575
1995
Type IV and type V tympanoplasty operations are simple, robust, and well-established techniques to reconstruct middle ears that have been severely altered by chronic otitis media. In a previous paper, the authors developed a simple four-block physiologic model to describe hearing results after these procedures. This paper presents a comparison of model predictions to hearing results obtained from a detailed retrospective clinical review of 30 type IV and type V procedures. Audiograms predicted by the model and those observed clinically show good agreement over a wide frequency range (500-4000 Hz) and for many different clinical conditions. Thus, this model reliably predicts postsurgical hearing results. The application of quantitative analyses provided by this model permits the formation of a few simple surgical rules that may improve postoperative hearing results. (1) The footplate should be left as mobile as possible (e.g., by covering it with a very thin split-thickness skin graft, as opposed to a fascia graft, which will tend to stiffen it). If the footplate is ankylosed, it should be removed and replaced with a compliant tissue graft, such as fat. (2) The round window acoustic graft shield should be made as stiff as possible. If the shield material used is temporalis fascia, then one should consider using more than one layer, or reinforcing it with cartilage. (3) An attempt should be made to create an aerated cavum minor containing at least 0.03 cc of air.
Adolescent; Adult; Audiometry; Child; Chronic Disease; Female; Humans; Male; Middle Aged; Models, Theoretical; Otitis Media/pp [Physiopathology]; *Otitis Media/su [Surgery]; Postoperative Complications; Retrospective Studies; Treatment Outcome; *Tympanoplasty/mt [Methods]; Tympanoplasty/st [Standards]
Fracture mechanics
Journal of Bone and Joint Surgery [Br]
43-B
1
162-166
1961
1. Linear fractures of the shaft of the long bones are divided into four basic types: 1) transverse; 2) oblique transverse; 3) spiral; and 4) oblique. 2. The mode of production of these fractures is deduced on the grounds of simple mechanical theory: 1) transverse fractures are a result of angulation; 2) oblique transyerse are the result of angulation with axial loading; 3) spiral fractures are the result of axial twists with or without axial loading; 4) oblique fractures are the result of angulation and axial twisting in the presence of axial loading.
THE MECHANICS OF BOOK SELECTION
Allerton Park Institute (9th : 1962)
10
10-25
1963
There is not a large mass of literature dealing with the mechanics of book selection. Most references to this or related topics are concerned either with the broader aspects of policy, with the "why" of selection, or with order procedures. It is possible sometimes to ferret pertinent information from these materials; on the other hand, it is obvious that many book selection policies are predominantly concerned with the mechanics of selection rather than with policy.
Vaxjo Interpretation of Quantum Mechanics
Arxiv Preprints
1-13
2003
We present critical arguments against individual interpretation of Bohr’s complementarity and Heisenberg’s uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the possibility to use Statistical Contextual Realist Interpretation of quantum formalism. In spite of all no-go theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...), recently we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces are rough images of the fundamental prespace. Quantum mechanics cannot be reduced to classical one. Both classical and quantum representations induce reductions of prespace information.
Soil mechanics in engineering practice
Engineering Geology
48
1-2
149-150
1997
10.1016/S0013-7952(97)81919-9
One of the best-known and most respected books on geotechnical engineering, this updated version features expanded coverage of vibration problems, mechanics of drainage, passive earth pressure and consolidation. In the years since publication of the past editions there has been a proliferation of soil mechanics research, much of it irrelevant to engineering practice. It is the aim of the authors to bring order out of this confusion.
Foundation; geotechnical
Mathematical-Modeling of Ventilation Mechanics
International journal of clinical monitoring and computing
12
2
105-112
1995
10.1007/BF01142492
Routine application of 'rule of thumb' parameter sets in clinical practice pushes model visions to the background, including the complete framework of assumptions, simplifications, suppositions and conditions. But: models can be a very strong tool, when applied selectively - that means, with a clear idea of destination, definition, parameter selection and verification. This article discusses universal issues of modelling - based on ventilation mechanics models in intensive care medicine.
Anesthesiology; DATA ACQUISITION; Medical Informatics; MODELING; PARAMETER ESTIMATION; SIMULATION; VENTILATION MECHANICS
A MECHANICS FOR THE RICCI FLOW
International Journal of Geometric Methods in Modern Physics
06
05
759-767
2009
10.1142/S0219887809003825
We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent Hamilton-Jacobi equation of the mechanics so defined.
abraham 1; echanics for the ricci; fern; flow; p; s
Quantum Mechanics, Volume 2
Advanced Quantum Mechanics
1978
Beginning students of quantum mechanics frequently have difficulty separatingessential underlying principles from the specific examples to which theseprinciples have historically been applied. This book is especially designed toeliminate that difficulty. Fourteen chapters, augmented by 14 "complementarysections," provide a clarity of organization, careful attention to pedagogicaldetails, and a wealth of topics and examples that allow physics professors totailor courses to meet students' specific needs. Each chapter starts with aclear exposition of the problem to be treated and then logically develops thephysical and mathematical concept. These chapters emphasize the underlyingprinciples of the material, undiluted by extensive references to applicationsand practical examples. (Such applications and practical examples arecontained in the complementary sections.) The book begins with a qualitativeintroduction to quantum mechanical ideas using simple optical analogies andcontinues with a systematic presentation of the mathematical tools andpostulates of quantum mechanics as well as a discussion of their physicalcontent. Applications follow, starting with the simplest ones (two-levelsystems, the harmonic oscillator, etc.), and becoming gradually morecomplicated (the hydrogen atom, approximation methods, etc.). Thecomplementary sections each expand this basic knowledge, supplying a widerange of applications and related topics which make use of the essentialskills. Here the authors include carefully written, detailed expositions of alarge number of special problems and more advanced topics-integrated as anessential portion of the text. These topics, however, are not interdependent;this allows professors to direct their quantum mechanics courses toward bothphysics and chemistry students.
Computational dynamic fracture mechanics
International Journal of Fracture 86
86
127-159
1997
10.1023/A:1007376924191
This paper provides a review on the state of the art in computational\ndynamic fracture mechanics.\n\nThe following important essential ingredients in computational dynamic\nfracture mechanics are included: (i)\n\nfundamental aspects of dynamic fracture mechanics, (ii) types of fracture\nsimulation, (iii) computational models\n\nof dynamic crack propagation, and (iv) use of dynamic J-integral in\ncomputational models.\n\nIn item (i), special attention is focused on the asymptotic eigen\nfields for various states of dynamic crack tips,\n\nwhich provide the foundation of dynamic fracture mechanics asWilliams’\nasymptotic eigen solutions provided the\n\nfoundation of static linear fracturemechanics. In item(ii), a new\nconcept ofmixed-phase simulation is presented for\n\ngeneral nonself-similar crack propagation, in addition to the generation-phase\nand application-phase simulations.\n\nA comprehensive summary of computational models for dynamic crack\npropagation is given in item (iii). Finally,\n\nin item (iv), several attractive features of the dynamic J-integral\nare presented.
asymptotic eigen field; computational modeling; dynamic crack propagation; Dynamic fracture; dynamic J-integral.; finite element method; numerical simulation
Holism in Quantum Mechanics
Compendium of Quantum Physics
295-298
2009
10.1007/978-3-540-70626-7_91
In slogan form, holism is the thesis that the whole is more than the sum of its parts. Explanatory holism is the view that a satisfactory explanation of the behavior of a system cannot be given by explaining the behavior of its parts. Property holism is the view that the properties of a whole are not wholly determined by those of its parts. Ontological holism denies that some supposedly composite object has (proper) parts. Quantum phenomena exhibit holism of at least the first two kinds. Quantum mechanics is often applied to a system as a whole, even though it is known to be composed of many subsystems. Such applications supply many instances of explanatory holism. Interference has been experimentally demonstrated between beams of sodium atoms and of fullerenes (C60 molecules ► mesoscopic quantum phenomena) [11]. The result of these experiments is readily explained by direct application of quantum mechanics to such composite objects. It would be futile to try to explain their behavior by applying quantum mechanics to their quark and lepton components. Many phenomena in condensed matter physics are explained by applying quantum mechanics directly to systems composed of very large numbers of atomic or subatomic particles: only in special cases can the theory be applied at the level of these components [9].
Thin Is In.
Medical Product Outsourcing
9
8
50-64
2011
The article focuses on the demand of original equipment manufacturers (OEMs) for smaller and thinner tubing with better torque-performance and better physical strength for bioprocess and medical applications. It is stated that for reduced costs and manufacturing more options, state-of-the-art equipment plays a major role. Limitations along with challenges associated with the manufacturing of tubular products are also discussed.
Models of the dynamics of otolithic membrane and hair cell bundle mechanics.
Journal of vestibular research : equilibrium & orientation
11
1
33-42
2001
Dynamic behavior of an otolithic membrane (OM) was studied analytically using simplified homogeneous viscoelastic (Kelvin-Voight body) model of the OM. The OM was represented by a thin plate attached to a macular plane. Viscoelastic properties of the OM determine the specific times (T(1) and T(2)) and frequency-dependent behavior of the local displacements of the membrane caused by the inertial time-dependent forces. Two kinds of an otolith stimulation were analyzed: step-function and harmonic accelerations of the membrane. Results of the modeling were compared with the known experimental data to estimate the Young's modulus E and viscosity mu of a gel layer: E is of order of 10 N/m(2), mu is of order of 1 poise in the range of frequency 0.2-2 Hz. It has allowed us to estimate the values of T(1) (10(-5)-10(-6) sec) and T(2) ( approximately 3 x 10(-2) sec). A relationship of the motion equation of the OM with well-known overdamped pendulum model of the otolith was discussed. The model of stereocilia tip-links deformation in the case, when the HCBs passively follow gel deformation, was proposed and analyzed. It was shown that for slender and long HCBs with the lengths comparable to a thickness of effective gel layer, a relative deformation of the tip-links of stereocilia caused by OM acceleration depends on time and the distance from the macular plane. The results of the modeling suggest that this type of the HCB may be responsible for analysis of fine temporal (frequency) structure of the OM acceleration.
Animals; Elasticity; Hair Cells, Auditory; Hair Cells, Auditory: physiology; Humans; Models, Biological; Otolithic Membrane; Otolithic Membrane: physiology; Viscosity
Practice Good Body Mechanics for a Safe Working Environment.
ONS Connect
23
2
24
2008
The article provides information on practicing good body mechanics for a safe working environment and a healthy nursing career. Oncology nurses are advised to maintain the four main principles of good body mechanics such as proper body alignment, a stable center of gravity, a wide base of support and a line of gravity. Tips on how to perform other physical tasks including lifting objects properly to avoid injuries are offered. The benefits of using proper body mechanics are also mentioned.
HUMAN mechanics; HUMAN physiology; KINESIOLOGY; NURSES; WORK environment
Variational formulation of transactional and related interpretations of quantum mechanics
Foundations of Physics Letters
1
3
293-299
1988
The recently proposed transactional and related differential interpretations of quantum mechanics are given a variational formulation. It seems that recurring controversies surrounding the interpretational question in early quantum mechanics, of whether or not a particle knows its environment, arose from the disharmony between the teleological flavor of the integral formulation of quantum transitions and the causal descriptive order in the differential formulation of wave mechanics.
extremal; extremality; extremal-physics; legal-models; legal-theories; particle-exchanges; qm; quantum-strategies; transactional; transactionality; variational; wave-mechanics
Geometry and loading effects on the compressive strength of fibrous composites
Journal of Reinforced Plastics and Composites
12
9
1016-1023
1993
10.1177/073168449301200906
This work addresses the important engineering problem of the compressive strength of fibrous laminated composites, bridging the micromechanics relevant to compressive failure due to fiber kinking with the global characteristics of a composite structure. Simple modeling incorporates the influence of boundary conditions, laminate thickness and layup configuration, as well as the importance of the microgeometry. The mechanism of failure under compression is assumed to be microbuckling of fibers that localizes at points with the maximum initial imperfection and leads to the formation and, under critical conditions, propagation of kink bands. To analyze the mechanics of kinking and to calculate the critical compressive stress, a steady state kink propagation model is utilized for the layers under compression in the fiber direction. The analysis results are used to gain a better understanding of the influence of the macrogeometry (laminate thickness and gauge length) in addition to the microgeometry (fiber diameter and fiber volume fraction), and the fiber and matrix material properties. The predictions of the model are compared with experimental results for carbon/thermoplastic unidirectional laminates under direct compression and cross-ply laminates under four-point bending.
Natural Vibrations of Laminated and Sandwich Plates
Journal of Engineering Mechanics
130
11
1268-1278
2004
10.1061/(ASCE)0733-9399(2004)130:11(1268)
An exact analytical solution based on the propagator matrix method and a semianalytical solution based on a higher-order mixed approach (displacement and stress interpolation) have been presented in this paper to evaluate the natural frequencies as well as the stress and displacement mode shapes of simply supported, cross-ply laminated and sandwich plates. Continuity of the transverse stresses and displacements has been maintained at the laminae interfaces. Results have been presented for orthotropic plates, symmetric as well as nonsymmetric cross-ply composite and sandwich laminates. Results from the propagator matrix agree well with the published results for frequencies as well as displacement and stress mode shapes. Furthermore, the frequencies and displacement and stress eigenvectors obtained from the proposed layerwise mixed method are in excellent agreement with those obtained by three-dimensional elasticity theory. Results obtained from the present equivalent single layer theory are in good agreeme...
composite materials; Composite materials; laminates; Laminates; matrix algebra; Matrix methods; Plates; plates (structures); Sandwich panels; Vibration; vibrations
Regge theory and statistical mechanics
arXiv
May
10
2006
10.1016/j.physletb.2006.05.019
An interesting connection between the Regge theory of scattering, the Veneziano amplitude, the Lee-Yang theorems in statistical mechanics and nonextensive Renyi entropy is addressed. In this scheme the standard entropy and the Renyi entropy appear to be different limits of a unique mathematical object. This framework sheds light on the physical origin of nonextensivity. A non trivial application to spin glass theory is shortly outlined.
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Quantum Physics; Statistical Mechanics
Soil mechanics in engineering practice
Engineering Geology
48
1948
10.1016/S0013-7952(97)81919-9
One of the best-known and most respected books on geotechnical engineering, this updated version features expanded coverage of vibration problems, mechanics of drainage, passive earth pressure and consolidation. In the years since publication of the past editions there has been a proliferation of soil mechanics research, much of it irrelevant to engineering practice. It is the aim of the authors to bring order out of this confusion.
Regge theory and statistical mechanics
Statistics
May
10
2006
10.1016/j.physletb.2006.05.019
An interesting connection between the Regge theory of scattering, the Veneziano amplitude, the Lee-Yang theorems in statistical mechanics and nonextensive Renyi entropy is addressed. In this scheme the standard entropy and the Renyi entropy appear to be different limits of a unique mathematical object. This framework sheds light on the physical origin of nonextensivity. A non trivial application to spin glass theory is shortly outlined.
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Quantum Physics; Statistical Mechanics
Molecular mechanics of single molecules
Structure
14
3
390-391
2006
The mechanics of single molecules of bacteriorhodopsin interacting with purple membrane have been investigated from both sides of the membrane by Kessler and Gaub (2006) in this issue of Structure. Remarkably, barriers can be associated with specific amino acid sequences to an accuracy of (plus or minus)3 amino acids. (copyright)2006 Elsevier Ltd. All rights reserved.
Alzheimer disease; amino acid sequence; atomic force microscopy; bacteriorhodopsin; cell membrane; cytoplasm; diffraction; elasticity; membrane protein; molecular interaction; molecular mechanics; priority journal; protein interaction; purple membrane; scanning tunneling microscopy; short survey; wound healing
Quantum Mechanics of Black Holes
Science (New York, N.Y.)
337
538-540
2012
10.1126/science.1221693
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Geometrical Mechanics on algebroids
arXiv
math-ph
2005
A natural geometric framework is proposed, based on ideas of W. M. Tulczyjew, for constructions of dynamics on general algebroids. One obtains formalisms similar to the Lagrangian and the Hamiltonian ones. In contrast with recently studied concepts of Analytical Mechanics on Lie algebroids, this approach requires much less than the presence of a Lie algebroid structure on a vector bundle, but it still reproduces the main features of the Analytical Mechanics, like the Euler-Lagrange-type equations, the correspondence between the Lagrangian and Hamiltonian functions (Legendre transform) in the hyperregular cases, and a version of the Noether Theorem. Besides, the constructions seem to be more natural and simpler.
70G45; 70H03; 53C99; 53D17; math.DG; math.MP; math-ph
Mechanics of Materials: Preface
Mechanics of Materials
38
5-6
389
2006
10.1016/j.mechmat.2005.09.001
This issue of the Mechanics of Materials on shape memory alloys (SMA) covers contributions on the latest developments related to the modeling and characterization of SMAs and magnetic SMAs. The first two papers cover an overview of SMAs, both single crystals and polycrystals. Some insights on the characterization of SMAs, especially under dynamic loading conditions are also presented. The other main topics discussed include R-phase transformation , effect of overheating on the cyclic transformation of SMAs, deformation behavior of Fe-based SMA, and modeling of the magnetic field controlled deformation response of magnetic SMA.
Orthopaedic Mechanics
Orthopaedic Mechanics
199-302
1981
10.1016/B978-0-12-281602-4.50010-5
Implants are used in orthopaedic surgery for a number of reasons. They are used to hold together segments of traumatically fractured bones while healing takes place. They are used in corrective osteotomies and for the correction of spinal deformities. Occasionally they are used for massive bone replacement and for joint replacement, either as hemiarthroplasty or total arthroplasty. The design criteria in all these cases is governed by a compromise between engineering considerations in relation to the imposed forces and the required function of the implant, and the surgical convenience and anatomical constraints. The criteria for materials selection are numerous, but might be classified into considerations of biocompatibility and mechanical/physical functionality, sometimes referred to as biofunctionality. To achieve optimal results, it is impossible to treat design and materials selection as separate entities. This chapter discusses the interrelation between the concepts, design and use of implants with materials selection, and to review the approaches made to implant surgery that are based on materials selection.
Fluid Mechanics
Fluid Mechanics
227-291
2016
10.1016/B978-0-12-405935-1.00006-X
Computational fluid dynamics (CFD) makes it possible to use the equations governing fluid motion for a large range of complex situations, providing both insight and quantitative predictions. The fluid equations are replaced by discrete approximations at grid points that must be close enough so that the solution is independent of the grid point spacing. The discrete equations are derived using finite differences or finite volumes, linking the different grid points together. Solution strategies using a regular structured grid result in simple, accurate and robust numerical schemes that are suitable for rectangular geometries. These schemes can, however, be extended to more complex domains using body fitted grids and mapped equations. While solution strategies for incompressible and compressible flows have much in common, there are important differences. For incompressible flows the pressure equation connects all grid points in the domain, resulting in a system of algebraic equations that must be solved at each time step, whereas compressible flows often include shocks that need to be treated in a special way. The chapter presents the elementary aspects of CFD and the conclusion contains a brief discussion of more advanced topics.
Complex domains; Computational fluid dynamics; Discretization; Driven cavity; Finite differences; Finite volume; Shock capturing
General equations for buckling of thin, shallow arches of any shape
Journal of Engineering Mechanics
117
2
225-240
1991
10.1061/(ASCE)0733-9399(1991)117:2(225)
General differential equilibrium and stability equations are derived for thin, prismatic quasi-shallow arches with an arbitrary centroidal-axis shape under dead loading. Sanders-type strain-displacement relationships are used in the derivation, subject to Donnell-type quasi-shallow approximations and Kirchhoff assumptions. No simplifications about arch shallowness are made other than those connected with the Donnell approximations. A general criterion is obtained that determines whether the arch equilibrium becomes critical with respect to snap-through or bifurcation buckling. Bifurcation occurs when a particular coefficient vanishes, which takes place when the arch membrane-stress resultant reaches the value necessary to buckle an equivalent straight bar. The equations derived here reduce to those for circular arches as a special case. Discretized versions of the differential equations for pin-ended arches are obtained by using series expansions for the various variables. The veracity of the resulting nonlinear algebraic equilibrium equations is confirmed by the fact that when the appropriate initial-curvature approximations are introduced, they agree with corresponding equations obtained by previous authors using different, but less general, methods.
Convective structures in a thin layer of an evaporating liquid under an airflow
Journal of Applied Mechanics and Technical Physics
48
4
469-478
2007
10.1007/s10808-007-0059-y
Evolution of convective structures in a thin layer of an evaporating liquid (ethanol) located under a turbulent boundary layer of an airflow is studied experimentally and theoretically. Evolution of the structures is examined under conditions of an increased flow velocity. A transition is found from convective cells formed in the absence of the flow to convective rolls elongated in the streamwise direction. The theoretical analysis is performed within a two-dimensional model of the flow in the liquid layer. The boundary conditions on the liquid surface are obtained with the use of self-similar solutions for mean fields in the airflow. The onset and evolution of a periodic system of rolls are simulated numerically. Theoretical conclusions are compared with experimental data. © Springer Science+Business Media, Inc. 2007.
Airflow; Boundary layer flow; "Cold film"; Computer simulation; Convective structure; Convective structures; Ethanol; Evaporation; Flow of gases; Flow velocity; Rayleigh-Benard convection; Shear flow; Temperature boundary layer; Turbulent flow
Impact of Monomer Evaporation on the Statistics of Island Arrays Formed in Thin Film Deposition Simulations
Philosophical Magazine B-Physics Of Condensed Matter Statistical Mechanics Electronic Optical And Magnetic Properties
80
1299-1309
2000
The statistics of island arrays formed in thin film deposition simulations with monomer evaporation are investigated. Island size distributions are found that depend on evaporation rate that also display scaling with substrate coverage. Scaling behaviour in the extreme cases of no evaporation or very strong evaporation are explained in terms of capture zones and the Avrami model, respectively. The scaling in the intermediate cases can be understood from a linear mixture of these two types of extreme. The monomer evaporation also impacts on the spatial ordering of the island arrays. A measure of disorder is introduced that changes monotonically with evaporation rate and coverage to distinguish the systems. In the case of strong evaporation the islands are almost entirely at random positions on the substrate, whereas at lower evaporation rates the islands become more correlated due to inhomogeneity in the time-averaged monomer density on the substrate. This behaviour is reflected in the structure factors for the various island arrays.
Simulation of the Flow Behavior of Thin Polymer Film During Nanoimprint Lithography Based on a Viscoelastic Model
Advanced Design and Manufacture Ii
419-420
509-512
2010
Based on viscoelastic fluid mechanics, this paper presents a simulation model of the flow behaviour of thin polymer film during nanoimprint lithography (NIL). The polymer is imprinted at a constant temperature of 180 degrees C and at a constant imprint speed of 100nm/s by using a tool with a single convex feature of 100 nm in width and 500 nm in height. At the imprint beginning, only a very limited area adjacent to the tool top is affected by the imprint, but subjects to a sudden change of pressure. With the imprint process forward, the wave-like polymer front and the trumpet-shaped profile are predicted to travel out from the imprint patterns. When the tool base intimately contacts the polymer film, another sudden change of the pressure occurs in the area under the interface between the polymer surface and the tool base. These results are of significance to understand the flow behaviour of NIL.
finite element method; nanoimprint lithography; viscoelasticity
Crack problem for a functionally graded thin superconducting film with field dependent critical currents
Mechanics Research Communications
61
36-40
2014
10.1016/j.mechrescom.2014.07.005
In this study, double exponential model is established to investigate the central crack problem for a functionally graded superconducting film with filed dependent critical current. The stress intensity factors (SIFs) are analytically obtained and numerically calculated. Numerical results show the effects of applied magnetic field, model parameters, and crack length on the SIFs. Among others, in the process of field descent, the crack in the superconducting film easily propagates in the mode-I form. Increasing the graded parameter of shear modulus can inhibit crack propagation. For a fixed reduced field (especially for a larger magnetic field), both the mode-I and mode-II SIFs firstly increase, then decrease with the increasing of introduced non-dimensional exponent parameter. This study should be useful for the application of superconducting devices.
Double exponential model; Functionally graded thin superconducting film; Stress intensity factor
Mechanics of the Pleural Space - Fundamental-Concepts (Reprinted from Lung, Vol 165, Pg 249-267, 1987)
Lung
169
S185-S203
1991
The transmission of forces from the respiratory muscles to the lung across the extremely thin pleural space has been poorly understood because of the difficulty of accurately measuring pleural liquid and pleural surface pressure (lung static recoil or transpulmonary pressure). Recent results using relatively noninvasive techniques have indicated that the vertical gradient in pleural liquid pressure is not hydrostatic, that pleural liquid pressure is closely related to lung recoil, and that there exists a very thin but continuous pleural liquid layer. These findings contradict concepts based on hydrostatic equilibrium and on the distinction between pleural liquid and pleural surface pressure due to pleural contact. Pleural liquid pressure is not in hydrostatic equilibrium because the difference between the vertical gradient in pleural liquid pressure and the effect of gravity is always balanced by a pressure loss due to a viscous flow within the pleural space. Fluid lubrication of the pleural surfaces is the primary function of the pleural space. The mechanical interaction between the lung and the chest wall is coupled to the dynamics of liquid within the pleural space, which is viewed as a flow-through system. Homeostasis is achieved in such a system by the adjustment of the viscous flow within the pleural space and the outflow absorption rate by lymphatics to the microvascular filtration rate across pleural capillaries.
heart; intact dogs; liquid pressure; microvascular fluid exchange; permeability; pleural liquid exchange; pleural liquid pressure; pleural surface pressure; rabbits; sheep; surface expansile forces; thickness; vertical gradient; weight
Free vibration analysis of thin cylindrical shells by the differential quadrature method
Journal of Pressure Vessel Technology-Transactions of the Asme
118
1
1-12
1996
By introducing the application of the differential quadrature method (DQM) to the dynamic analysis of thin circular cylindrical shells, the work of this paper makes a step forward in furthering the potential of the DQM in the area of structural mechanics. The problem is identified by art eighth-order system of coupled partial differential equations in terms of the three displacement components. The proposed differential quadrature solution is semi-analytical in that Flugge's representation of the displacement components by trigonometric sine and cosine functions of the circumferential coordinate is employed. The results of the differential quadrature solutions of the natural frequencies of various shell cases are compared and shown to be in excellent agreement with the published, and also some recalculated, results of exact solutions for freely supported, clamped-clamped, clamped-free, and free-free shells. Comparisons are also made with the published experimental data of clamped-clamped and clamped-free shells.
beams; distributed system equations; insights; plates; structural components
Asymptotic Analysis of Plastic Flow along the Generatrix in a Thin Cylindrical Layer
Journal of Applied Mechanics and Technical Physics
51
5
713-720
2010
10.1007/s10808-010-0091-1
An analytical solution is found for the problem modeling quasistatic compression and flow of an ideal rigid plastic (under the Mises-Hencky criterion) material along the generatrix in a thin cylindrical layer. This problem is a generalization of the classical Prandtl problem. The small asymptotic parameter is the ratio of the layer thickness to its length. The radii of the cylinders can have any intermediate order of smallness. It is shown that when the radii and thickness of the layer are of the same order of smallness, the solution is asymptotically exact in the sense that the number of terms of the series describing the kinematic and dynamic parameters of the flow is finite. Limiting transitions to the classical Prandtl solution are investigated. © 2010 MAIK/Nauka.
Asymptotic analysis; Asymptotic expansion; asymptotic expansions; cylindrical layer; flow; ideal rigid plastic flow; Plastic flow; Plastics; Prandtl problem; pressure; Rigid-plastic flow
Numerical simulation of 3-D crack growth in thin rim-gears
International Conference on CRACK PATHS (CP 2006)
2006
Thin-rim gears with an initial crack in the tooth root, caused by various\nreasons, are dealt with in this paper. By standard procedures, it is impossible to gain a\nvery good insight into the conditions appearing at the formation of initial damage.\nBearing this in mind, a numerical model has been elaborated. The boundary element\nmethod and the theory of linear-elastic fracture mechanics have been used for crack\ngrowth simulation. By means of three dimensional (3-D) numerical analysis of gear\nwith initial crack in tooth root, the influence of a different position of a web (in the\nmiddle and at the edge of a rim) upon the direction of crack propagation and the\nremaining service life is researched. The results of the research work offer a more\noptimal concept of gear design and dimensions.\n
Simulation of the Flow Behavior of Thin Polymer Film during Nanoimprint Lithography Based on a Viscoelastic Model
Key Engineering Materials
419-420
509-512
2009
10.4028/www.scientific.net/KEM.419-420.509
Based on viscoelastic fluid mechanics, this paper presents a simulation model of the flow behaviour of thin polymer film during nanoimprint lithography (NIL). The polymer is imprinted at a constant temperature of 180oC and at a constant imprint speed of 100nm/s by using a tool with a single convex feature of 100 nm in width and 500 nm in height. At the imprint beginning, only a very limited area adjacent to the tool top is affected by the imprint, but subjects to a sudden change of pressure. With the imprint process forward, the wave-like polymer front and the trumpet-shaped profile are predicted to travel out from the imprint patterns. When the tool base intimately contacts the polymer film, another sudden change of the pressure occurs in the area under the interface between the polymer surface and the tool base. These results are of significance to understand the flow behaviour of NIL.
Finite Element Model (FEM); Nanoimprint Lithography; Viscoelasticity
Determination of elastic moduli of thin layers of soft material using the atomic force microscope
Biophysical journal
82
5
2798-2810
2002
We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels
Size effects in single crystal thin films: nonlocal crystal plasticity simulations
Eur J Mech A
24
2
183-193
2005
10.1016/j.euromechsol.2005.01.002
Stress relaxation in single crystalline thin films on substrates subjected\nto thermal loading is studied using a recently proposed nonlocal\ncontinuum crystal plasticity theory. The theory is founded on a statistical-mechanics\ndescription of the collective behaviour of dislocations in multiple\nslip, which is coupled to a small-strain continuum crystal plasticity\ndescription. The theory is inherently nonlocal with the length scale\nbeing determined by the evolving dislocation density. Symmetric double\nslip is considered with the film being in plane strain. The predicted\nstress versus temperature response and the evolution of the dislocation\nstructure are analyzed for different orientations and film thicknesses.\nThe effect of film size is associated with the formation of a boundary\nlayer of dislocations at the film-substrate interface which does\nnot scale with the film thickness. The width of the boundary layer\nitself is shown to be dependent on the slip system orientation. The\nresults are consistent with those of recent discrete dislocation\nsimulations.
Effect of variable permeability on the propagation of thin gravity currents in porous media
International Journal of Non-Linear Mechanics
57
168-175
2013
10.1016/j.ijnonlinmec.2013.07.003
A new formulation is proposed to study the influence of deterministic heterogeneity on the propagation of thin two-dimensional gravity currents in a porous medium above a horizontal impervious boundary. Heterogeneity is conceptualized as a monotonic power-law variation of medium permeability transverse or parallel to the direction of propagation. Considering the injection of a constant or time-variable volume of fluid, the nonlinear differential problem admits a similarity solution which describes the shape and rate of propagation of the current. The bounds on parameters necessary to respect model assumptions are derived asymptotically and for finite time, to clarify the range of applicability of the proposed models. An application to the migration of a contaminant gravity current in the subsurface is then discussed, showing the impact of permeability variations on extension and shape of the intrusion. © 2013 Elsevier Ltd. All rights reserved.
Gravity current; Porous; Similarity solution; Variable permeability
First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories
Physical Review D
68
4
14
2003
10.1103/PhysRevD.68.044016
The first law of black hole mechanics is derived from the Einstein-Maxwell (EM) Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills (EYM) theory is also derived.
General Relativity and Quantum Cosmology
Drawing Mechanics
Picturing Machines, 1400-1700
281-308
2004
Introduction\nWolfgang Lef{è}vre\n1\nPART I: WHY PICTURES OF MACHINES?\t\nIntroduction to Part I\t13\n1\tWhy Draw Pictures of Machines? The Social Contexts of Early Modern Machine Drawings\nMarcus Popplow\n17\nPART II: PICTORIAL LANGUAGES AND SOCIAL CHARACTERS\t\nIntroduction to Part II\t51\n2\tThe Origins of Early Modern Machine Design\nDavid McGee\t53\n3\tSocial Character, Pictorial Style, and the Grammar of Technical Illustrations in Craftsmen's Manuscripts in the Late Middle Ages\nRainer Leng\t85\nPART III: SEEING AND KNOWING\t\nIntroduction to Part III\t115\n4\tPicturing the Machine: Francesco di Giorgio and Leonardo da Vinci in the 1490s\nPamela O. Long\t117\n5\tMeasures of Success: Military Engineering and the Architectonic Understanding of Design\nMary Henninger-Voss\t143\nPART IV: PRODUCING SHAPES\t\nIntroduction to Part IV\t173\n6\tRenaissance Descriptive Geometry: The Codification of Drawing Methods\nFilippo Camerota\t175\n7\tThe Emergence of Combined Orthographic Projections\nWolfgang Lef{è}vre\t209\n8\tProjections Embodied in Technical Drawings: D{ü}rer and His Followers\nJeanne Peiffer\t245\nPART V: PRACTICE MEETS THEORY\t\nIntroduction to Part V\t279\n9\tDrawing Mechanics\nMichael S. Mahoney\t281\nAPPENDIX\t\nContributors\t309\nReferences\t311\nName Index\t335\nSubject Index\t339
Visual Representation; History of Science
Cell Mechanics
Cell Mechanics
83
1,3-27
2007
DOI: 10.1016/S0091-679X(07)83001-9
\nMany cellular processes lead to changes in elastic and viscous properties of cells. Rheology is the science that deals with deformation and flow of materials. Fundamental rheologic concepts are explained, and some of the main techniques are discussed. Nonperturbing oscillatory techniques are especially useful for monitoring structure formation including gelation, whereas other techniques such as steady shear flow and creep are useful for determining flow properties. Sample preparation is often a major obstacle, and advantages of different deformation geometries are discussed. Simple biological samples such as purified biopolymers can be investigated with a range of rheologic techniques, and factors affecting gelation of, for example, blood or cytoskeletal proteins can be studied in detail. More complex biological systems such as intact tissues can often only be studied with more qualitative techniques and results. With proper choice of experimental setup, rheologic techniques can give valuable information about cellular systems and dynamics on a timescale that is closely related to biological functions.
Fluid Mechanics
Refrigeration And Air Conditioning
6
3
e18068
2010
http://dx.doi.org/10.1016/j.rser.2004.09.010
Dental thermal pain is a significant health problem in daily life and dentistry. There is a long-standing question regarding the phenomenon that cold stimulation evokes sharper and more shooting pain sensations than hot stimulation. This phenomenon, however, outlives the well-known hydrodynamic theory used to explain dental thermal pain mechanism. Here, we present a mathematical model based on the hypothesis that hot or cold stimulation-induced different directions of dentinal fluid flow and the corresponding odontoblast movements in dentinal microtubules contribute to different dental pain responses. We coupled a computational fluid dynamics model, describing the fluid mechanics in dentinal microtubules, with a modified Hodgkin-Huxley model, describing the discharge behavior of intradental neuron. The simulated results agreed well with existing experimental measurements. We thence demonstrated theoretically that intradental mechano-sensitive nociceptors are not "equally sensitive" to inward (into the pulp) and outward (away from the pulp) fluid flows, providing mechanistic insights into the difference between hot and cold dental pain. The model developed here could enable better diagnosis in endodontics which requires an understanding of pulpal histology, neurology and physiology, as well as their dynamic response to the thermal stimulation used in dental practices.
Thin end of solar.
Chemistry & Industry
12
21-23
2010
The article focuses on the potential of thin film solar technology to become a major factor in the growth of photovoltaic (PV) solar energy. Data reveal that 14% share of the total solar market is attributed to thin film PV in 2008. First Solar is considered as the largest thin film producer in the world. Moreover, it is expected that global cumulative installed PV capacity will increase by at least 40% in 2010.
PHOTOVOLTAIC power generation; PHOTOVOLTAIC power systems; RENEWABLE energy sources; SOLAR energy; SOLAR technology; THIN films industry
Discrete Dislocation Dynamics Simulation of Thin Film Plasticity
Continuum Scale Simulation of Engineering Materials
397-412
2005
10.1002/3527603786.ch18
This chapter contains sections titled: * Thin Film Plasticity * Simulation of Dislocations in Thin Films Boundary Conditions * Thin Film Deformation, Models and Simulation Mobility Controlled DeformationSource Controlled Deformation * References
application to engineering microstructures; continuum scale simulation; discrete dislocation dynamics simulation; engineering materials; models and simulation; thin film deformation; thin film plasticity
Summation formulae in the theory of thin films
Czechoslovak Journal of Physics
12
1
26-34
1962
10.1007/BF01688394
On the basis of general summation formulae for light reflected and transmitted by a thin film the author derives formulae for a thin dielectric film, for a thin metallic film and for a system of thin dielectric films. This solution is based on Stokes's principle of reversibility, which is the idea unifying the cases into one theory. In conclusion he gives the solution of a general case, dealing with light reflected and transmitted by a system of thin dielectric and metallic films.
Applications of scaling ideas to dynamics. III. The mechanics of the renormalization group
Regular and Chaotic Motions in Dynamic Systems.Proceedings of the Fifth
60-63
1985
For pt.II see ibid., p.45-60. Renormalization group methods have recently been found useful in several different contexts in mechanics and related fields. The author gives a feeling for the mechanics involved in these renormalization-group calculations
Vibration of Thick and Thin Plates Using a New Triangular Element
ASCE Journal of Engineering Mechanics
129
11
1235-1244
2004
10.1061/(ASCE)0733-9399(2003)129:11(1235)
Atriangular element based on Reissner–Mindlin plate theory is developed and it is applied to free vibration analysis of plates in different situations. The element has three corner nodes, three mid-side nodes and an internal node at the element centroid where each node contains three usual degrees of freedom ?transverse displacement and bending rotations?. To make the element free from the shear locking problem, the formulation is done in an efficient manner taking transverse displacement and transverse shear rotations as the field variables. The degrees of freedom of the internal node are condensed out to improve the computational elegance. As the condensation cannot be done with a consistent mass matrix, a lumped mass matrix having no mass contribution at the internal node is used. In this context two mass lumping schemes are proposed where the effect of rotary inertia is considered in one of these schemes. All these features have made the element quite elegant, which is tested with numerical examples to show its performance.
Natural frequency; Plates; Vibration
Cooperative mechanisms of thin filament activation and their contribution to the myocardial contractile function: Assessment in a mathematical model
Biophysics
54
1
39-46
2009
10.1134/S0006350909010072
A mathematical model was used for comparative analysis of the contribution to the myocardial mechanical activity of two potentially possible variants of the cooperative influence of myosin cross-bridges on calcium activation of sarcomere actin filaments. One of these variants implies that the cooperative action of the cross-bridge on the affinity of troponin C for calcium is localized within the functional group A7TmTn (seven adjacent globular actin monomers, tropomyosin, and one troponin complex TnC + TnI + TnT) where this bridge is attached. The second variant is based on the assumption that cross-bridges may influence the troponin C affinity for calcium also in neighboring A7TmTn groups (and the closer the group is positioned relative to the bridge, the stronger is the influence on the CaTnC complex affinity in this group). The contribution of each of these two variants to the active mechanical behavior of the cardiac muscle in the contraction-relaxation cycle was assessed. It turned out that adequate simulation of the muscle mechanical activity is provided only by the second variant. Thus, the results of modeling argue in favor of the existence of just this variant of cooperativity. © 2009 Pleiades Publishing, Ltd.
Calcium regulation of muscle contraction; Load-dependent relaxation; Mechanics of active myocardium
Theory of the Effect of a Thin Air Film on the Vibrations of a Stretched Circular Membrane
The Journal of the Acoustical Society of America
26
5
740
1954
10.1121/1.1907409
In the design of condensermicrophones it is standard practice to insert holes or furrows into the electrode face. This modification helps to prevent radial air flow through the electrode‐membrane interstice which can result in large dissipative and reactive effects, provided the separation is small. The theory governing air reactions from an unmodified electrode is presented. An attempt was made to start with general fundamental equations. Only those simplifications which appeared to have a negligible effect on the accuracy of the results were made; for example, body forces and nonlinear terms have been neglected. Air inertia, rotational and irrotational velocity components, and viscous terms have been retained in the theory. Curves showing the effects of air reactions on the amplitude, phase, and impedance of a stretched titanium membrane are shown. The air stiffness, which continuously increased for increasing frequencies in the range 5 to 20 0000 cps, caused the amplitude of the membrane to diminish by more than 20 db. In general, air which is trapped behind the membrane will cause the response of the microphone to rise as the frequency is lowered.
Mechanical Testing of Thin Sheet Magnesium Alloys in Biaxial Tension and Uniaxial Compression
Experimental Mechanics
54
7
1247-1258
2014
10.1007/s11340-014-9892-0
Tension and compression experiments on magnesium rolled sheets and extruded products of AZ31 (Mg + 3%Al + 1%Zn) and ZE10 (Mg + 1%Zn + 0.3%Ce based misc metal) were performed at room temperature. The tests were conducted along the longitudinal and the transverse direction to quantify the in-plane anisotropy. Samples built from adhesively-bonded layers of sheets were used for in-plane as well as through-thickness compression testing. It was verified that this simple testing method leads to identical results as using comb-like dies and equi-biaxial bulge testing, respectively. In the case of uniaxial loading, the longitudinal and transverse strain components were measured using independent extensometers. R-values were calculated from these signals. The mechanical responses were correlated to the microstructure and the texture. The recorded differences between tensile and compressive response reveal the strength differential effect of the materials. The distortional character of the plastic behaviour is evidenced through their responses to equi-biaxial tensile loading. Significant differences in the compressive responses of the two alloys were identified by comparing the respective hardening rates.
Experimental Investigation on Dynamic Characteristics of NOPD Thin-Wall Frame Structure
Applied Mechanics and Materials
71-78
138-143
2011
10.4028/www.scientific.net/AMM.71-78.138
The free vibration experiments for the NOPD frame structure were performed to investigate the dynamic characteristics of the frame. The influences of factors such as particle filling ratio, particle filling scheme and vibration direction of the frame on the damping effect are discussed by means of test data. Test results indicate that the particle filling ratio is a principal influencing factor for the damping effect of the frame. Under the same particle filling scheme and filling ratio, the damping increments for out plane vibration of the frame with smaller structural rigidity are normally larger than those for in plane vibration with larger structural rigidity. Within the three schemes of particle filling, the most prominent damping improvement exists in the particle-in-beam scheme under the same filling ratio and the corresponding maximum damping increment reaches 218% for out plane vibration. To obtain the most significant particle damping effect, the most effective scheme of particle filling is to put particles into the cavities of components with large vibration displacement. © (2011) Trans Tech Publications.
Filling ratio; Frame; Non-obstructive particle damping; Particle filling scheme
SUPERSYMMETRY AND QUANTUM MECHANICS Supersymmetry and quantum mechanics
Phys Rep
251
267-385
1995
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding analytically of why certain potentials solvable and an array of powerful new approximation are not exactly solvable. In this report, we review the theoretical formulation mechanics and discuss many applications. basic ideas which include supersymmetric Familiar solvable potentials quantum are methods for handling potentials which of supersymmetric Exactly solvable potentials can be understood in terms of a few partner potentials, shape invariance and operator transformations. all have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi- soliton solutions of the KdV equation are constructed. Approximation framework of supersymmetric WKB approximation quantum mechanics and in particular it is shown that a supersymmetry is exact for a class of shape invariant potentials. Supersymmetry nice results for the tunneling discuss the problem of a charged Dirac particle in an external magnetic field and other potentials supersymmetric mechanics such as parasupersymmetric a para-fermion of order p. quantum mechanics, Finally, we discuss structures more general than supersymmetric ideas give particularly rate in a double well potential and for improving large N expansions. We also in terms of quantum quantum mechanics in which there is a symmetry between a boson and methods are also discussed within the inspired
CHAPTER 6 Thin Film Materials Technology
Thin Film Materials Technology
405-463
2004
10.1016/B978-081551483-1.50007-1
This chapter illustrates structural control of compound thin films, using sputtered ferroelectric thin films of perovskite, including those with nanometer structures used as examples of compound thin films. The influences of sputtering parameters on the structure and dielectric properties of thin films are also discussed in the chapter. The perovskite materials show a variety of functional properties including ferroelectricity, pyroelectricity, piezoelectricity, nonlinear optical properties, and superconductivity. The ferroelectric thin films of nanometer structure are promising materials for future applications. Perovskite thin films comprise of complex chemical compositions. The ferroelectric property is changed by the chemical composition and/or the microstructure of the thin films. Structural control of ferroelectric thin films is important not only for the fabrication of layered perovskite electronic and photonic devices, but also for understanding their physical, and chemical properties.
Supersymmetry And Quantum-Mechanics
Physics Reports-Review Section Of Physics Letters
251
5-6
268-385
1995
In the past ten years, the ideas of supersymmetry have been profitably\napplied to many nonrelativistic quantum mechanical problems. In particular,\nthere is now a much deeper understanding of why certain potentials\nare analytically solvable and an array of powerful new approximation\nmethods for handling potentials which are not exactly solvable. In\nthis report, we review the theoretical formulation of supersymmetric\nquantum mechanics and discuss many applications. Exactly solvable\npotentials can be understood in terms of a few basic ideas which\ninclude supersymmetric partner potentials, shape invariance and operator\ntransformations. Familiar solvable potentials all have the property\nof shape invariance. We describe new exactly solvable shape invariant\npotentials which include the recently discovered self-similar potentials\nas a special case. The connection between inverse scattering, isospectral\npotentials and supersymmetric quantum mechanics is discussed and\nmultisoliton solutions of the KdV equation are constructed. Approximation\nmethods are also discussed within the framework of supersymmetric\nquantum mechanics and in particular it is shown that a supersymmetry\ninspired WKB approximation is exact for a class of shape invariant\npotentials. Supersymmetry ideas give particularly nice results for\nthe tunneling rate in a double well potential and for improving large\nN expansions. We also discuss the problem of a charged Dirac particle\nin an external magnetic field and other potentials in terms of supersymmetric\nquantum mechanics. Finally, we discuss structures more general than\nsupersymmetric quantum mechanics such as parasupersymmetric quantum\nmechanics in which there is a symmetry between a boson and a para-fermion\nof order p.
Statistical mechanics of neural networks
Physics Today
1987
Title: . Authors: Sompolinsky, Haim. Publication: Physics Today, Volume 41, Issue 12, December 1988, pp.70-80.
Pattern Discovery and Computational Mechanics
Proceedings of the 17\textsuperscript{th} International Conference on Machine Learning
2000
Computational mechanics is a method for discovering, describing and\nquantifying patterns, using tools from statistical physics. It constructs\noptimal, minimal models of stochastic processes and their underlying\ncausal structures. These models tell us about the intrinsic computation\nembedded within a process---how it stores and transforms information.\nHere we summarize the mathematics of computational mechanics, especially\nrecent optimality and uniqueness results. We also expound the principles\nand motivations underlying computational mechanics, emphasizing its\nconnections to the minimum description length principle, PAC theory,\nand other aspects of machine learning.
Lung mechanics in pulmonary edema
Clinics in Chest Medicine
6
3
393-412
1985
Pulmonary edema can cause alterations in lung mechanics that directly contribute to clinical morbidity and mortality rates. Both the location of the edema fluid (interstitital versus alveolar pulmonary edema) and the etiology of the pulmonary edema contribute to the severity and type of abnormalities of lung mechanics observed. The alterations in lung mechanics associated with the adult respiratory distress syndrome may involve the direct effects of released mediators, alterations in pulmonary surfactant, and altered airway reactivity, as well as the direct effects of the edema fluid. [References: 105]
0 (Endotoxins); Animals; Blood Pressure; Body Water/an [Analysis]; Endotoxins/to [Toxicity]; Humans; Lung/an [Analysis]; *Lung/pp [Physiopathology]; Pulmonary Edema/et [Etiology]; *Pulmonary Edema/pp [Physiopathology]; Pulmonary Edema/th [Therapy]; Respiratory Distress Syndrome, Adult/pp [Physiopat
Quantum Mechanics on Phase Space
Studies in History and Philosophy of Modern Physics
1999
This is an essay review of the book "Quantum Mechanics on Phase Space" by F.E. Schroeck, Jr (Kluwer, Dordrecht, 1996, US$ 295). This book is concerned with the positive-operator-valued measure (POVM) approach to quantum mechanics, in which physical properties are studied through their localization properties in phase space. It particularly investigates covariance properties of the POVM when the phase space is a homogeneous symplectic manifold. There is also a very detailed discussion of quantum-mechanical measurement theory from the POVM point of view. The discussion is mainly technical and mathematical, and many examples are provided. The conclusion of the review is that despite some omissions and idiosyncracies this book is an impressive achievement, that philosophers of physics should take notice of.
Phase; Physics; Quantum Mechanics; Schroeck, F; Science; Space
Pattern Discovery and Computational Mechanics
cs/0001027
2000
Computational mechanics is a method for discovering, describing and quantifying patterns, using tools from statistical physics. It constructs optimal, minimal models of stochastic processes and their underlying causal structures. These models tell us about the intrinsic computation embedded within a process---how it stores and transforms information. Here we summarize the mathematics of computational mechanics, especially recent optimality and uniqueness results. We also expound the principles and motivations underlying computational mechanics, emphasizing its connections to the minimum description length principle, PAC theory, and other aspects of machine learning.
Electrical transport and impedance analysis of Au/porous silicon thin films
Proceedings - Electronics, Robotics and Automotive Mechanics Conference, CERMA 2008
3-7
2008
10.1109/CERMA.2008.62
In order to obtain electronic devices based on PS/p-Si structure, we present a study the AC conductivity and Thermo-electrical behavior of Porous Silicon (PS) layers prepared by electrochemical etching in p-type silicon (p-Si) <100>substrates. The beginning is obtaining good electrical contacts on porous layer; for this reason, several Au/PS/Au junctions were electrically characterized to understand the transport mechanisms in porous surface and the temperature dependence in the porous properties studied, also the resistance-temperature characteristic of PS/p-Si thermistor device. Finally, we obtained the AC conductivity in modulo and phase; an electrical equivalent circuit was proposed to fit the experimental frequency response of the different samples.
electrical conductivity; Electrical equivalent circuit; electrochemical etching; Metal-semiconductor-metal structure; Porous silicon
Einstein's statistical mechanics
Revista Mexicana de F\'{i}sica
31
695-722
1985
The foundations of equilibrium classical statistical mechanics laid\ndown in 1902 independently by Gibbs and Einstein. The latter's contribution,\ndeveloped in three papers published between 1902 and 1904, is usually\nforgotten and when not, rapidly dismisses as equivalent to Gibb's.\nWe review in detail Einstein's ideas on the foundations of statitsical\nmechanics and show that they constitute the beginning of research\nprogram that led Einstein to quantum theory. We also show how these\nideas may be used as a starting point for an introductory course\non the subject.
Quantum Mechanics: OntologyWithout Individuals
Found Phys
44
1246-1257
2014
The purpose of the present paper is to consider the traditional interpretive\r\nproblems of quantum mechanics from the viewpoint of a modal ontology of properties.\r\nIn particular, we will try to delineate a quantum ontology that (i) is modal,\r\nbecause describes the structure of the realm of possibility, and (ii) lacks the ontological\r\ncategory of individual. The final goal is to supply an adequate account of quantum\r\nnon-individuality on the basis of this ontology.
Study of molecular interactions and dynamics in thin silica surface layers by proton solid-state NMR spectroscopy
Chemistry of Materials
16
21
4071-4079
2004
10.1021/cm049618o
We present results from proton double-quantum magic-angle spinning NMR spectroscopy in support of tight molecular contacts of the modifier bis(triethoxysilylpropyl) tetrasulfane with the surface of precipitated, amorphous silica. While chemical bonding cannot be proven directly, its presence is indicated by through-space dipolar contacts between surface-OH groups and all aliphatic protons of the modifier, as well as strongly anisotropic motions of the surface-bound molecules. Silica-modifier contacts are further only found when the samples were heated during preparation. Only small amounts of ethanol were seen to leave the silica surface upon modification. A good part of the ethanol set free upon condensation becomes bound to the silica surface, which is supported by the presence of tight contacts in silica treated with pure ethanol. The anisotropy of molecular motions of the surface-bound molecules is characterized by the estimation of proton dipole-dipole coupling constants from double-quantum sideband patterns and build-up curves. Self-condensed samples of the modifier either exhibit very different dynamic properties or show no indication of contacts between hydroxyl and aliphatic protons.
alcohol; anisotropy; Anisotropy; article; bis(triethoxysilylpropyl)tetrasulfane; chemical bond; chemical modification; Condensation; dipole; Ethanol; heating; hydroxyl group; molecular dynamics; Molecular dynamics; molecular interaction; Molecular motions; Nuclear magnetic resonance; polymerization; proton; proton nuclear magnetic resonance; quantum mechanics; silane derivative; Silica; silicon dioxide; Surface bound molecules; surface property; Thin surfaces; unclassified drug
Local perturbation of thin film flow
ARCHIVE OF APPLIED MECHANICS
73
9-10
734-751
2004
10.1007/s00419-004-0326-9
The flow of a thin viscous film over a profiled substrate under the action of an external pressure profile along its free surface, in addition to gravity and capillarity, is considered. Specifically, the linear response of the film flow to localized small pressure perturbations is analyzed. The linear evolution equation of the response analysis is derived from the nonlinear flow equation of the film, which is formulated for the present purpose by reinterpreting the individual terms in the equation of film flow over flat substrates in terms of film thickness or surface curvature. This equation displays an equivalence, within the range of its validity, the lubrication approximation, between a particular, stationary persistent pressure action and the action of a (fixed) substrate topography on the film flow; the equivalence relation is formulated in the paper. The core of the paper is the derivation and analysis of the response of the film to an instantaneous pressure perturbation. For a point source of perturbation this response is the fundamental solution of the linear evolution equation. It is evaluated analytically, exactly or asymptotically, for the two extreme situations of either gravitational or capillary dominance of the flow (i.e. for large and small Bond numbers, respectively), and numerically in the intermediate situations. From the response signal to the instantaneous perturbation the film response to a (harmonically) persistent perturbation is then constructed by superposition. For a steadily acting point source this superposition is a 'Green's' function. Its analytic evaluation for gravitational dominance provides, in addition to those of the fundamental solution, useful support of validation and interpretation for numerical signal evaluations. Such evaluations are given for steady persistent excitation. Finally, the signal analysis is discussed in a process-engineering perspective.
Uncertainty Relations (UR) Have Nothing to do with Quantum Mechanics (QM)
Physics
x
5
2004
Uncertainty relations are shown to have nothing specific for quantum mechanics, being the general property valid for arbitrary function. A wave function of a particle having precisely defined position and momentum in QM simultaneously is demonstrated. Interference on two slits in a screen is shown to exist in classical mechanics. A nonlinear classical system of equations replacing QM Schr\"odinger equation is suggested. This approach is shown to have nothing in common with Bohmian mechanics.
Quantum Physics
Some developments of computational solid mechanics in China
Computers & Structures
30
4
783-788
1988
10.1016/0045-7949(88)90105-8
Solid mechanics is an old discipline of applied science and its development is very much influenced by the advances of technology as is the case of many other disciplines of science. The advent of electronic computers led to an advance for mechanics, activated many branches of mechanics, and enabled theoretical studies and applications to have a rapid development in both depth and scope. Traditionally, solid mechanics is divided into several branches, for example structural mechanics, theory of elasticity, plasticity, plates and shells, geomechanics, etc., which are now well incorporated in the curricula of engineering colleges and institutes. In fact, the basic concepts were derived from the same source. Once the computational barrier is removed, some naturally developed unified approaches can be applied to all those branches, such as the finite element method (FEM) and other numerical methods. With the help of computers, computational structural mechanics has developed a far wider scope than in the past. It no longer limits itself to the study of elastic framed structures or trusses, now covering plates and shells, three dimensional continuum, and other complicated composed structural systems such as coupled structure-soil or structure-fluid systems. The loading conditions are no longer limited within the elastic range but can be extended to plastic, fracture or failure ranges. More importantly, computational structural mechanics not only analyses a given structure in a passive way, but also provides the possibility of finding its optimum design in an active way. The advances of CAD technique further extend the area of computational solid mechanics and the engineers may be provided with final drawings.
Soil Mechanics for Unsaturated Soils
Water Science Technologies
30
1
205-210
1993
10.1016/0267-7261(93)90011-F
"A Wiley-Interscience publication.". Includes bibliographical references (p. 490-507) and index.
Statistical mechanics of complex networks
Rev. Mod. Phys.
74
January
47
2002
. Réka Albert * and Albert-László Barabási Department of Physics, University of Notre
Relativistic Quantum Mechanics. Wave Equations
Springer
424
2000
10.1007/978-3-662-04275-5
Relativistic Quantum Mechanics. Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course. This third edition has been slightly revised to bring the text up-to-date.
Particle and Nuclear Physics; Quantum Physics; Relativistic Quantum Mechanics. Wave Equations
Amherst Interpretation of Quantum Mechanics
Quantum
2002
This paper was withdrawn by the author. It turns out that similar ideas have been presented before. The author apologizes.
Quantum Physics
Nonequilibrium Statistical Mechanics
FewBody Systems
31
2-4
205-210
1985
10.1007/s006010200022
At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity η and on five additional "second-order" hydrodynamical coefficients τ(Π), κ, λ, λ, and λ. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient λ can be evaluated directly by Euclidean means and does not in general vanish.
Review on capsule mechanics
web : http://iam.ntu.edu.tw/stamroc/82/report2.html
1997
This paper gives a review about the current developments in the measurement of the mechanical and interfacial forces of a single cell. The previous methods which include the nano-/micro-indentation methods, the micropipette aspiration technique and the compression method are reported. In addition, a novel technique, the micro-upsetting method, which is recently developed by the author (Liu et al. 1996) is presented here. The fundamental principles of these different techniques are briefly described, and the relative merits and demerits of each method are also discussed in detail.
Symplectic quantum mechanics
Arxiv 1506.02985
i
1-37
2015
10.1016/j.aop.2004.03.009
Using the notion of symplectic structure and Weyl (or star) product of non-commutative geometry, we construct unitary representations for the Galilei group and show how to rewrite the Schrödinger equation in phase space. This approach gives rise to a new procedure to derive Wigner functions without the use of the Liouville-von Neumann equation. Applications are presented by deriving the states of linear and nonlinear oscillators in terms of amplitudes of probability in phase space. The notion of coherent states is also discussed in this context. © 2004 Elsevier Inc. All rights reserved.
Galilei group; Phase space; Weyl Product
Quantum mechanics and metrology
Elektronika
47
5
9-12
2006
The relationship between the quantum mechanics and the metrology created\nthe new division of the metrology - the quantum metrology. The quantum\nmetrology embraces such theoretical problems, as the uncertainty\nof the measurement according to the Heisenberg's uncertainty principle,\nand technical devices: quantum standards and measuring instruments\nabout the extreme sensitivity. In the article one described quantum\nstandards: the standard of voltage, the standard of the electrical\nresistance and the atomic clock
Relativistic forces in Lagangian mechanics
arXiv preprint arXiv:1206.1372
8
2012
We give a general definition of \emph{relativistic force} in the context of Lagrangian mechanics. Once this is done we prove that the only relativistic forces which are linear on the velocities are those coming from differential 2-forms defined on the configuration space. In this sense, electromagnetic fields provide a mechanical system with the simplest type of relativistic forces.
A Hilbert Space Realization of Nonlinear Quantum Mechanics as Classical Extension of Its Linear Counterpart
International Journal of Theoretical Physics
39
3
621-640
2000
10.1023/A:1003685620562
This paper studies the state-effect-probability structure associated with thequantum mechanics of nonlinear (homogeneous, in general nonadditive) operatorson a Hilbert space. Its aim is twofold: to provide a concrete representation ofthe features of nonlinear quantum mechanics on a Hilbert space, and to showthat the properties of the nonlinear version of quantum mechanics here describedhave the structure of a classical logic.
Reduced Haematological Indices in Auto-Mechanics and Fuel Attendants in Elele Nigeria
American Journal of Medical and Biological Research
2
1
1-4
2014
10.12691/ajmbr-2-1-1
Gasoline is largely a mixture of hydrocarbon and hydrocarbon consists of mixture of n-paraffins, naphthalene, olefins and aromatics. Aromatics is mostly a mixture of benzene, toluene and xylene. Fuel attendants and auto mechanics are exposed to gasoline either by direct contact or inhalation. The effect of this exposure in fuel attendants and auto mechanics is determined using haematological parameters. 35 fuel attendants and 35 auto mechanics were used as test group and compared with 30 apparently healthy individuals of same age range. Some haematological parameters were determined using standard manual methods. RBC, Hb, MCH and MCHC were reduced (p < 0.05) in fuel attendants and auto mechanics when compared with control. Fuel attendants exposed to gasoline fumes beyond 2 years have lower (p < 0.05) PCV, Hb, MCH and MCHC than those exposed for 2 years or less while auto mechanics of over two years had their RBC, Hb, MCH and MCHC significantly lower (p < 0.05) than auto mechanics of two years and below. Auto mechanics and fuel attendants are exposed to gasoline vapour leading to decreased haematological indices. Fuel attendants are more at risk than auto mechanics and could be at risk of developing anaemia over time.
Partitioning of respiratory mechanics in mechanically ventilated patients.
Journal of applied physiology (Bethesda, Md. : 1985)
71
6
2425-33
1991
In ten mechanically ventilated patients, six with chronic obstructive pulmonary disease (COPD) and four with pulmonary edema, we have partitioned the total respiratory system mechanics into the lung (l) and chest wall (w) mechanics using the esophageal balloon technique together with the airway occlusion technique during constant-flow inflation (J. Appl. Physiol. 58: 1840-1848, 1985). Intrinsic positive end-expiratory pressure (PEEPi) was present in eight patients (range 1.1-9.8 cmH2O) and was due mainly to PEEPi,L (80%), with a minor contribution from PEEPi,w (20%), on the average. The increase in respiratory elastance and resistance was determined mainly by abnormalities in lung elastance and resistance. Chest wall elastance was slightly abnormal (7.3 +/- 2.2 cmH2O/l), and chest wall resistance contributed only 10%, on the average, to the total. The work performed by the ventilator to inflate the lung (WL) averaged 2.04 +/- 0.59 and 1.25 +/- 0.21 J/l in COPD and pulmonary edema patients, respectively, whereas Ww was approximately 0.4 J/l in both groups, i.e., close to normal values. We conclude that, in mechanically ventilated patients, abnormalities in total respiratory system mechanics essentially reflect alterations in lung mechanics. However, abnormalities in chest wall mechanics can be relevant in some COPD patients with a high degree of pulmonary hyperinflation.
Aged; Airway Resistance; Airway Resistance: physiology; Humans; Lung Compliance; Lung Compliance: physiology; Lung Diseases, Obstructive; Lung Diseases, Obstructive: physiopathology; Lung Volume Measurements; Male; Middle Aged; Positive-Pressure Respiration; Pulmonary Edema; Pulmonary Edema: physiopathology; Respiration, Artificial; Respiratory Mechanics; Respiratory Mechanics: physiology
Kochen's Interpretation of Quantum Mechanics
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
1990
241-249
1990
Kochen has suggested an interpretation of quantum mechanics in which he denies that wavepackets ever collapse, while affirming that measurements have definite results. In this paper I attempt to show that his interpretation is untenable. I then suggest ways in which to construct similar, but more satisfactory, hidden variable interpretations.
Rock Mechanics for Underground Mining
Rock Mechanics Felsmechanik Mecanique des Roches
3
3
2004
10.1007/BF01238443
Although Rock Mechanics addresses many of the rock mechanics issues which arise in underground mining engineering, it is not a text exclusively for mining applications. It consists of five categories of topics on the science and practice of rock engineering: basic engineering principles relevant to rock mechanics; mechanical properties of rock and rock masses; design of underground excavations in various rock mass conditions; mining methods and their implementation; and guidelines on rock mechanics practice. Throughout the text, and particularly in those sections concerned with excavation design and design of mining layouts, reference is made to computational methods of analysis of stress and displacement in a rock mass. The principles of various computational schemes, such as boundary element, finite element and distinct element methods, are considered. This new edition has been completely revised to reflect the notable innovations in mining engineering and the remarkable developments in the science of rock mechanics and the practice of rock engineering that have taken place over the last two decades. Based on extensive professional, research and teaching experience, this book will provide an authoritative and comprehensive text for final year undergraduates and commencing postgraduate students. For professional practitioners, not only will it be of interest to mining and geological engineers but also to civil engineers, structural and mining geologists and geophysicists as a standard work for professional reference purposes. B.H.G. Brady is Emeritus Professor and former Dean of the Faculty of Engineering, Computing and Mathematics at The University of Western Australia, and a consulting rock mechanics engineer. E.T. Brown is Senior Consultant, Golder Associates Pty Ltd, Brisbane, Australia and formerly Senior Deputy Vice-Chancellor of The University of Queensland, Australia.
engineering geology - geotechnical engineering - m
Quantum Mechanics of Neutrino Oscillations
Physical Review D
13
2000
We present a simple but general treatment of neutrino oscillations in the framework of quantum mechanics using plane waves and intuitive wave packet principles when necessary. We attempt to clarify some confusing statements that have recently appeared in the literature.
Astrophysics; High Energy Physics - Experiment; High Energy Physics - Phenomenology
Thin client growth spurred by Windows
ENT
3
20
1998
A recent study by Zona Research Inc. reports that the worldwide thin client market increased 34.7 percent last year to 347,917 units sold. The Thin-Client Market - 1998 and Beyond states that such growth stemmed from the movement of thin client vendors toward providing access to Windows applications, as well as the availability of Java-capable and browser-enabled thin clients.
Experimental determination of the effect of hole interaction on stress concentrations in angle ply graphite/epoxy composite panels.
ASTM Special Technical Publication
Composite Materials: Testing and Design, Eleventh Volume
238-248
1993
Exptl. measured strains and calcd. stress concn. factors are reported for "three hole" combinations representative of geometries found in composite aerostructures. Reasonable correlation is obsd. between measured strains and strain detd. from finite element analyses. Three different stacking sequences are considered, each representative of a bound on equiv. elastic consts. for in-plane loading found in common design practice. The stacking sequences include (0/+45/-45/0)2s, (0/+45/-45/90)2s, and (90/+45/-45/90)2s. After fabrication, a central hole and two sym. "influencing" holes were cut in the panels. Strain gages were then applied to the inside of the central hole and in a region away from the holes to provide free field strains. During tensile loading, strains at both locations were recorded and scaled using a modified secant method to obtain the strain concn. factors. Material orientation was then considered in the computation of stress concn. factors. The exptl. obtained results presented in this paper represent design criteria for several geometries. Addnl. results from extensive finite element analyses are being compiled for publication as a family of design curves. [on SciFinder(R)]
graphite epoxy composite panel stress; hole interaction composite panel stress
{On the representation of quantum mechanics on phase space}
International Journal of Theoretical Physics
31
9
1785-1795
1992
10.1007/BF00671786
{It is shown that Hilbert-space quantum mechanics can be represented on phase space in the sense that the density operators can be identified with phase-space densities and the observables can be described by functions on phase space. In particular, we consider phase-space representations of quantum mechanics which are related to certain joint position-momentum observables.}
Nosé and Hoover nonequilibrium dynamics and statistical mechanics
Molecular Simulation
33
1
13-19
2007
At equilibrium Nosé's 1984 revolutionary thermostat idea linked Newton's mechanics with Gibbs' statistical mechanics. His work expanded the scope of isothermal and isobaric simulations. Nosé–Hoover dynamics has subsequently facilitated the simulation and detailed understanding of nonequilibrium problems. The fractal phase-space distributions, and their close link to the Lyapunov spectrum, provide a novel explanation of irreversibility and a rich field for exploration.
The role of Mechanics in Tumor growth : Modelling and Simulation
ESAIM: Proceedings
33
October
1-9
2011
10.1051/proc/201133001
A number of biological phenomena are interlaced with classical mechanics. In this review are illustrated two examples from tumor growth, namely the formation of primordial networks of vessels (vasculogenesis) and the avascular phase of solid tumors. In both cases the formalism of continuum mechanics, accompanied by accurate numerical simulations, are able to shed light on biological controversies. The converse is also true: non-standard mechanical problems suggest new challenging mathematical questions.
The elliptic interpretation of black holes and quantum mechanics
Nuclear Physics B
271
3
497-508
1986
The old “elliptic interpretation” of the Kruskal manifold is reviewed in the light of quantum mechanics. It is argued that its adoption would require giving up the complex structure of quantum mechanics and working with real Hilbert spaces. This may also be needed in cosmological theories in which the universe is CPT invariant. The cases of de Sitter and anti-de Sitter space are also discussed.
Indeterminacy and entanglement: the challenge of quantum mechanics
The British Journal for the Philosophy of Science
51
4
597 -615
2000
10.1093/bjps/51.4.597
I explore the nature of the problem generated by the transition from classical to quantum mechanics, and I survey some of the different responses to this problem. I show briefly how recent work on quantum information over the past ten years has led to a shift of focus, in which the puzzling features of quantum mechanics are seen as a resource to be developed rather than a problem to be solved.
Many worlds and the emergence of probability in quantum mechanics
Annals of Physics
321
10
23
2005
10.1016/j.aop.2006.02.001
The interpretation of the squared norm as probability and the apparent stochastic nature of observation in quantum mechanics are derived from the strong law of large numbers and the algebraic properties of infinite sequences of simultaneous quantum observables. It is argued that this result validates the many-worlds view of quantum reality.
boolean; foundations; law large numbers; many worlds; probability; quantum mechanics
Conformal Field Theory and Statistical Mechanics
0807.3472
2008
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
Aspects of classical and quantum Nambu mechanics
Letters in Mathematical Physics
1996
475 Aspects of Classical and Quantum Mechanics Mathematics Subject Classifications (1991): 70H99, 58F07. Key words: -Poisson manifolds, Lie algebras
A realistic interpretation for quantum mechanics
quant-ph/9809001
1998
We propose a realistic and nonlocal interpretation for quantum mechanics, which requires new mathematical, physical and philosophical foundations for space-time. Our theory violates Bell's inequality. We also discuss the cat paradox.
Lattice Boltzmann Equation for Quantum Mechanics
hilosophical Transactions of the Royal Society - Series A: Mathematical, Physical and Engineering Sciences
360
1792
429-436
2002
It is shown that the Lattice Boltzmann equation for hydrodynamics can be extended in such a way as to describe non-relativistic quantum mechanics.
Stochastic quantum mechanics for particles with spin
Physics Letters A
31
7
403-404
1970
10.1016/0375-9601(70)91010-8
We show a stochastic theory of quantum mechanics previously developed may be extended to cover the case of particles with integral or half-integral spin; a possible relativistic extension is discussed.
An historical perspective on cell mechanics
Pflugers Archiv-European Journal of Physiology
456
1
3-12
2008
10.1007/s00424-007-0405-1
The physical properties of the protoplasm have long been of interest, and today, several intricate methods, including atomic force microscopy, have been employed in studies of cellular mechanics. However, many current concepts and experimental approaches actually have their beginnings over 300 years ago. Unfortunately, these pioneering studies have been all but forgotten. In this paper, we have reviewed some of the early literature on cellular mechanics to place modern work within an historical framework. It is clear that with current nanoscience approaches, modern experiments employing cell indentation, manipulation, particle rheology and micro- or nano-needle poking are now quantifying mechanical properties which were only qualitatively described 100 years ago. Aside from the variety of approaches our predecessors have employed to understand cellular mechanics, we feel an understanding of the past will help to propel nanoscience into the future. As nanophysiology and nanomedicine are developing, we as a community should take time to consider the early roots of these fields.
atomic force microscopy; ATOMIC-FORCE MICROSCOPY; cell mechanics; CELLS; COLLAGEN FIBRILS; CONFORMATIONAL-CHANGES; elasticity; LIVING; NANOMECHANICAL; NUCLEAR-PORE COMPLEX; PHYSICAL-PROPERTIES; PROPERTIES; protoplasm; SACCHAROMYCES-CEREVISIAE; SEA-URCHIN EGGS; STRUCTURAL FRAMEWORK; viscoelasticity; viscosity
Quantum mechanics in structure-based drug design
Curr Opin Drug Discov Devel
9
3
370-379
2006
In principle, quantum mechanics provides a more accurate representation of molecular systems than other modeling approaches. While this notion is not a matter of dispute, it has not yet been definitively demonstrated within the realm of structure-based drug design that the use of quantum mechanical methods over the use of classical modeling approaches is justified in consideration of the increase in expense associated with quantum mechanical methods. Demonstrating that quantum mechanics-based methods can be superior to simpler models, and resolving problems relating to estimating the effects of conformational entropy, will provide key areas of interest in the coming years for in silico structure-based drug design. Recent applications using quantum mechanical methods in structure-based drug design are reviewed herein, and applications ranging from scoring receptor-ligand interactions using quantum mechanics to the generation of quantitative structure-activity relationships using quantum mechanics-derived descriptors are discussed.
Drug Design; Humans; Molecular Structure; Quantum Theory; Structure-Activity Relationship
Differential Geometry of Time-Dependent Mechanics
dg-ga/9702020
1997
The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical transformations. Our goal is to formulate time-dependent mechanics in gauge-invariant form, i.e., independently of any reference frame. The main ingredient in this formulation is a connection on the bundle $Y\to R$ which describes an arbitrary reference frame. We emphasize the following peculiarities of this approach to time-dependent mechanics. A phase space does not admit any canonical contact or presymplectic structure which would be preserved under reference frame transformations, whereas the canonical Poisson structure is degenerate. A Hamiltonian fails to be a function on a phase space. In particular, it can not participate in a Poisson bracket so that the evolution equation is not reduced to the Poisson bracket. This fact becomes relevant to the quantization procedure. Hamiltonian and Lagrangian formulations of time-dependent mechanics are not equivalent. A degenerate Lagrangian admits a set of associated Hamiltonians, none of which describes the whole mechanical system given by this Lagrangian.
Quantum mechanics for space applications
Appl. Phys. B, Lasers Opt. (Germany)
B84
4
545 - 50
2006
This paper is an introduction to the following articles in the scope of quantum mechanics for space study initiated by ESA and lead by ONERA. The context of quantum mechanics for space is summarised, and the fields under development are briefly introduced. Technological applications of quantum mechanics in space are explored and some tests of quantum mechanics are outlined. We also give a brief presentation of the opto-electronic section of the European Space Agency, and the technology development activities it carries out, with particular emphasis on those activities related to the topics of interest of the quantum mechanics in space workshop. As an example, a summary of two ESA studies on gravity gradiometry and their relevance to the field of atomic interferometry is given. In view of the scientific requirements, derived for both Earth observation and planetology for future space missions, atom interferometry shows promise and may provide an advantage over currently available accelerometer and inertial sensor systems
accelerometers;atom optics;Earth;particle interfer
Mechanics of moderately stressed cracks
'Fatigue Crack Growth Thresholds, Enudrance Limits, and Design' Symposium
252-265
2000
The intrinsic behaviour of fatigue cracks is discussed by a discrete dislocation model and by a BCS-type continuum mechanics approximation. The investigation of a homogeneous material shows that the near threshold regime and the existance of an intrinsic threshold itself can be ascribed to the dislocation nature of plasticity. By incorporating microstructural features in the analysis it is then shown that the intrinsic threshold value is determined only by the mechanism for the dislocation generation and does not depend on microstructural details like the grain size. However, in the near threshold regime and in the lower Paris regime the plastic deformation and the crack growth rates are severely influenced by microstructure. Therefore, a micromechanics approach should be used for the predictions of the plastic response of materials. Only in the upper Paris regime, where the cyclic plastic zone size exceeds several times the microstructural length scale usual continuum plasticity mechanics is appropriate to describe the events at the crack tip. Macroscopic quantities like the yield stress of materials cannot be used to describe moderately stressed fatigue cracks.
Computer simulation; Continuum mechanics; Cracks; Dislocation mechanics; Fatigue of materials; Fatigue threshold; Fracture mechanics; Plastic deformation; Stress analysis
Elastic compliance of the compact tension specimen comprising two linear-elastic materials bonded with a thin layer
Journal of Testing and Evaluation
25
1
28-35
1997
Although the compact-tension C(T) specimen is widely used in conventional fracture mechanics testing, its application to the fracture behavior of layered structures, in the assessment of the toughness and fatigue crack growth behavior of bimaterial interfaces, for example, has been limited due to problems in identifying the crack length. Accordingly, to provide a basis for crack-length monitoring in the sandwich C(T) specimen, comprising two materials bonded with a thin layer under linear-elastic conditions, the linear-elastic compliance based on back-face strain, crack-opening displacement and load-line displacement has been determined for a wide range of substrate/layer material combinations using finite-element analyses. Calculations for sandwich systems, with elastic moduli ratios varying from 0.2 to 5 and with joining layer thicknesses between 0.4 and 2% of the specimen width, show that for crack sizes between 0.25 to 0.75 of the specimen width, the compliance is significantly different from that of the bulk substrates, except when the layer is very thin and the modulus ratio approaches unity. It is concluded that crack-opening displacements are preferable for the monitoring and detection of interfacial and near-interfacial cracks in this specimen geometry, as the compliance based on these displacements is the least sensitive to errors from either measurement site or crack location.
back-face strain (bfs); bimaterial ''sandwich'' specimen; compact-tension geometry; compliance methods; crack-length monitoring; crack-opening displacement (god); fracture; load-line displacement (lld); strength
Maxspeed Revs Thin-Client Notebook ; Maxspeed is making the thin-client environment mobile.
eWeek
20
30
2003
Maxspeed is making the thin-client environment mobile. Maxspeed is relaunching its MaxBook 810, a notebook-style, thin-client device that connects with back-end servers via a built-in wireless PCMCIA 802.11b or 802.11g card.
Quantum Mechanics versus Special Relativity: A forgotten conflict
PhilSci Archive
68
2008
Despite the widespread assumptions on the compatibility between non- relativistic quantum mechanics and special relativity, there still remains a considerable amount of unresolved problems to which few authors explicitly pay attention. Most of them involve the aim of coherently achieving a relativistic description of quantum collapses and quantum entanglements. These processes seem to challenge our present picture of the physical world in terms of space- time structures.
asymptotic independence; causation; locality; nonlocality; quantum collapse; quantum entanglement; quantum mechanics; separability; space-time; special relativity
Econophysics: from game theory and information theory to quantum mechanics
Physica a-Statistical Mechanics and Its Applications
348
505-543
2005
10.1016/j.physa.2004.09.029
Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the Quantum Mechanics principles. using Information and Game Theory. (C) 2004 Elsevier B.V. All rights reserved.
energy; information; optimal laws; quantum mechanic laws; rationality
Student understanding in mechanics: a large population survey
American Journal of Physics
55
8
691-696
1987
There has recently been a considerable growth in research probing student understanding in mechanics. Questions based on four such research probes were included in the end-of-high-school physics examination undertaken by some 5500 students. The results obtained give an indication of the extent to which various interpretations of some physical situations are held in a whole population. The possibilities of using research probes as a basis for assessment questions are also illustrated.
conceptual understanding; empirical studies; end-of-high-school-physics-examination; mechanics
Application of Lie-series to regularized problems in celestial mechanics
Celestial Mechanics
34
1-4
135-143
1984
10.1007/BF01235796
The practical application of the Lie series to the regularized plane-restricted three-body problem is attempted. It is shown that the Lie series provide a fast and very clear method for solving the regularized differential equations. Five Lie terms are sufficient to work with when the computing time needed to evaluate the terms is not too great.
ALGORITHMS; CELESTIAL MECHANICS; DIFFERENTIAL EQUATIONS; HAMILTONIAN FUNCTIONS; LIE GROUPS; SERIES (MATHEMATICS); THREE BODY PROBLEM; TWO BODY PROBLEM
A Universal Variational Formulation for Two Dimensional Fluid Mechanics
Applied Mathematics and Mechanics
22
9
989-996
2001
10.1023/A:1016310906598
A universal variational formulation for two dimensional fluid mechanics is obtained, which is subject to the so-called parameter-constrained equations (the relationship between parameters in two governing equations). By eliminating the constraints, the generalized variational principle (GVPs) can be readily derived from the formulation. The formulation can be applied to any conditions in case the governing equations can be converted into conservative forms. Some illustrative examples are given to testify the effectiveness and simplicity of the method.
On the Representation of Quantum Mechanics on a Classical Sample Space
International Journal of Theoretical Physics
37
1
349-356
1998
10.1023/A:1026683205305
Under the common viewpoint of statistical maps,the concept of observables in quantum mechanics and inclassical probability theory are discussed and compared.It is shown that, by means of injective statistical maps, quantum mechanics can to a certain extentbe reformulated in classical terms. Some characteristicexamples are considered.
QUANTUM MECHANICS: Enhanced: Schrodinger's Cat Is Out of the Hat.
Science (New York, N.Y.)
290
5492
720-1
2000
10.1126/science.290.5492.720
In 1935, Erwin Schrödinger suggested his famous gedanken experiment of the cat that is simultaneously "dead" and "alive" inside its box until the box is opened. But as Tesche explains in her Perspective, such a macroscopic manifestation of quantum mechanics has remained elusive until recently. The experiments by van der Wal et al. are an important step toward demonstrating that quantum mechanics can describe macroscopic phenomena. The approach may be exploited in quantum computing and quantum cryptography.
Quantum mechanics with spontaneous localization and the quantum theory of measurement
Il Nuovo Cimento B
100
1
27-41
1987
10.1007/BF02829774
Quantum mechanics with spontaneous localization (QMSL) is a recently proposed stochastic modification of theN-body Schrödinger equation consistent both with microphysics and macrophysics. QMSL is applied here to the measurement problem. It is shown that the replacement of standard quantum mechanics by QMSL has the only effect of producing an actual reduction of the wave function.
Path integral in energy representation in quantum mechanics
Theoretical and Mathematical Physics
156
1
1041
2008
We consider an alternative path integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is the Laplace transform of the evolution operator) in a form that has the meaning of “the sum over paths” but is much better defined than the usual functional integral. We investigate this representation from different standpoints and compare such an approach to quantum mechanics with the standard approaches.
High Energy Physics - Theory
Issues in the statistical mechanics of sedimentation
Adv. Phys.
50
297-341
2001
A critical review is presented of recent experimental and theoretical work on the steady sedimentation of particulate suspensions in viscous fluids. The point of view is that of a practitioner of non-equilibrium statistical physics rather than classical fluid mechanics.
hydrodynamics; sedimentation
Quantum mechanics and integration in Hilbert space
Physics Letters A
73
4
287-288
1979
We demonstrate that the expectation value of quantum mechanics, EW(A) = tr(WA), can be expressed by means of a functional integral on the underlying Hilbert space asE~(A)= f d~.zw(q)f~(q), where MWj~a Borel measure characterized by Wand fA(0) = Quantum
Levy's stochastic area in stochastic mechanics
Letters in Mathematical Physics
14
1
41-45
1987
10.1007/BF00403468
Using the methods of Hida's white noise calculus, we study Lévy's stochastic area spanned by a two-dimensional stochastic process of relevance in Nelson's stochastic mechanics. An intriguing partial relationship is found with quantum mechanical angular momentum for the associated Schrödinger wave-function.
On statistical mechanics in noncommutative spaces
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY
3, 2
301-304
2007
We study the formulation of quantum statistical mechanics in\nnoncommutative spaces. We construct microcanonical and canonical\nensemble theory in noncommutative spaces and study some basic and\nimportant examples in the framework of noncommutative statistical\nmechanics.
How Game Mechanics can Change Education
TEDxChandler
2011
Snehal is the founder and CEO of Sokikom. He is passionate about improving the way students learn math both in and out of the classroom. In this presentation, he discusses how game mechanics can change education.
Lattice Boltzmann-Equation for Quantum-Mechanics
Physica D
69
3-4
327-332
1993
It is shown that the lattice Boltzmann equation for hydrodynamics can be extended in such a way as to describe non-relativistic quantum mechanics.
Fluid Mechanics in Sommerfeld's School
Annual Review of Fluid Mechanics
47
1
2015
10.1146/annurev-fluid-010814-014534
Sommerfeld’s affiliation with fluid mechanics started when he began his career as an assistant of the mathematician Felix Klein at Göttingen. He always regarded fluid mechanics as a particular challenge. In 1904, he published a theory of hydrodynamic lubrication. Four years later, he conceived an approach for the analysis of flow instability (the Orr-Sommerfeld approach) as an attempt to account for the transition from laminar to turbulent flow. The onset of turbulence also became a major challenge for some of his pupils, in particular Ludwig Hopf and Fritz Noether. Both contributed considerably to elaborate the Orr-Sommerfeld theory. Heisenberg’s doctoral work was another attempt in this quest. When Sommerfeld published his lectures on theoretical physics during World War II, he dedicated one of the six volumes to the mechanics of continuous media. With chapters on boundary layer theory and turbulence, it exceeded the scope of contemporary theoretical physics—revealing Sommerfeld’s persistent appreciation of fluid mechanics. He resorted to Prandtl’s Göttingen school of fluid mechanics in order to stay abreast of the rapid development of these specialties. Expected final online publication date for the Annual Review of Fluid Mechanics Volume 47 is January 03, 2015. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
A realistic interpretation for quantum mechanics
arXiv:quant-ph/9809001
1998
We propose a realistic and nonlocal interpretation for quantum mechanics, which requires new mathematical, physical and philosophical foundations for space-time. Our theory violates Bell's inequality. We also discuss the cat paradox.
Spectral density method in classical statistical mechanics
Physics Letters A
85
4
197-200
1981
10.1016/0375-9601(81)90013-X
The spectral density method in classical statistical mechanics is formulated and application to a linear classical spin system is made in the simplest approximation.
IMPROVED ELECTRONICS RELIABILITY USING THIN FILM SMART MATERIALS FOR MITIGATING HARSH VIBRATIONAL ENVIRONMENT
Proceedings of The American Ceramic Society 107th Annual Meeting
1-10
2005
Microelectromechanical (MEMS) guidance systems currently suffer from severe inaccuracies caused by a critical failure of a MEMS inertial measurement unit (IMU) i.e., the angular rate sensor. This IMU failure is caused by its susceptibility to a harsh extrinsic vibrational environment. This environment, generated from launch, high-G, and/or in-flight vibration forces, causes an out-of-plane motion and/or a false angular rate signal to be generated. This effort will demonstrate a novel enabling technology-materials solution, which will allow guided projectiles to achieve required performance specifications in harsh mechanical vibration environments. We will demonstrate the feasibility of employing active/smart materials for passively damping spurious vibrations of device/die level structures that reduce the accuracy of MEMS inertial guidance systems. This effort will include the design of these efficient energy absorbing materials in thin film form for the first time at the micro-scale level for this purpose with a goal of obtaining > 50% vibration reduction at adverse vibrational frequencies using such composite films. In this work we present a novel approach commensurate with MEMS scale devices to mitigate the effect of spurious vibrations, and which relies on the development of a heterostructure composite bilayer design configuration composed of piezoelectric and shape memory alloy thin films, and the inherent non-linear deformations produced when these materials are mechanically loaded. Validation and verification of this design concept is achieved via continuum mechanics modeling.
Fluid mechanics of heart valves
Annu.Rev.Biomed.Eng
6
1523-9829
331-362
2004
10.1146/annurev.bioeng.6.040803.140111
Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review
Animals; ARTIFICIAL-HEART; Biomechanics; Biomedical Engineering; bioprosthesis; complications; Computer Simulation; Constriction; DESIGN; DISEASE; DURABILITY; fluid mechanics; heart valve; HEART-VALVE; heart valve prosthesis; Heart valves; HEART-VALVES; Heart Valves: physiology; Humans; Mitral Valve; Mitral Valve: pathology; Pathologic; PATHOLOGY; PERFORMANCE; physiology; PORCINE; Prostheses and Implants; Prosthesis Design; PROSTHETIC HEART VALVES; REPLACEMENT; Software; Thrombosis; Thrombosis: pathology; TISSUE; VALVE DESIGN; VALVES; valvular heart disease
Mechanics of hot electron generation during catalytic combustion over late transition metal surfaces
ACS National Meeting Book of Abstracts
1
2008
A flux of hot electrons during catalytic carbon monoxide oxidation over the Pt and Pd thin films and nanoparticles has recently been reported by G. A. Somorjai et al. [Phys. Today 60, 48 (2007)]; its cause has not been completely understood. This paper discusses likely microscopic pathways in charge of the hot electron generation in this, and related catalytic combustion reactions. The energy released upon chemisorption of the molecular oxygen on the metal surface not only suffices to atomize the surface oxygen but also to create the electron-hole pairs within the conduction band of the metal. Some of the holes decay into the hot Auger electrons. As the oxygen molecules dissociate, the adsorbate layer becomes anionic. For a surface anion to give rise to the neutral CO2, the ultimate product of the reaction, the anion must become unstable with respect to the surface. This unstable anion is the (CO2)- born late in the reaction in an excited state to decay into a desorbing CO2 and a hot run-away electron within the autoionization continuum. This example sets up the stage for the development of the qualitative and quantitative theoretical surface science instruments that are also discussed.
Quantum Mechanics: Concepts and Applications, 2nd edn.
Contemporary Physics
52
363-363
2009
10.1080/00107514.2010.547600
Quantum Mechanics: Concepts and Applications provides aclear, balanced and modern introduction to the subject. Writtenwith the student’s background and ability in mind the booktakes an innovative approach to quantum mechanics by combining theessential elements of the theory with the practical applications:it is therefore both a textbook and a problem solving book in oneself-contained volume. Carefully structured, the book starts withthe experimental basis of quantum mechanics and then discusses itsmathematical tools. Subsequent chapters cover the formalfoundations of the subject, the exact solutions of theSchrödinger equation for one and three dimensional potentials,time-independent and time-dependent approximation methods, andfinally, the theory of scattering. The text is richly illustrated throughout with many workedexamples and numerous problems with step-by-step solutions designedto help the reader master the machinery of quantum mechanics. Thenew edition has been completely updated and a solutionsmanual is available on request.
Development of a concept inventory for fluid mechanics
Frontiers in Education, Annual
1
T3D23-28
2003
10.1109/FIE.2003.1263340
Concept inventories are assessment tools designed to determine the degree to which students understand the concepts of a subject and to identify the misconceptions that students hold. The results of a concept inventory can be used to change the methods of instruction to overcome student misconceptions. A cooperative effort between mechanical engineering faculty at the Universities of Wisconsin-Madison and Illinois, Champaign-Urbana has been directed toward development of a fluid mechanics concept inventory (FMCI). Fluid mechanics typically follows thermodynamics in the sequence of courses in thermal sciences, involves both the mechanics and dynamics of fluids, and builds on basic physics and Newtonian mechanics. This paper describes the process used for development of the FMCI, the details of how we determined the content, and examples of actual content of the instrument itself.
Development of a concept inventory for fluid mechanics
Proceedings - Frontiers in Education Conference
1
2003
Concept inventories are assessment tools designed to determine the degree to which students understand the concepts of a subject and to identify the misconceptions that students hold. The results of a concept inventory can be used to change the methods of instruction to overcome student misconceptions. A cooperative effort between Mechanical Engineering faculty at the Universities of Wisconsin-Madison and Illinois, Champaign-Urbana has been directed toward development of a Fluid Mechanics Concept Inventory (FMCI). Fluid mechanics typically follows thermodynamics in the sequence of courses in thermal sciences, involves both the mechanics and dynamics of fluids, and builds on basic physics and Newtonian mechanics. This paper describes the process used for development of the FMCI, the details of how we determined the content, and examples of actual content of the instrument itself.
Building materials effects of Al content and physical properties on the electromagnetic interference shielding of Sn based coating thin layers.
Applied Mechanics and Materials
142
Intelligent Materials, Applied Mechanics and Design Science
142-151
2012
10.4028/www.scientific.net/AMM.142.142
This study coats complex colloid mixed with Sn-xAl powders and polyethylene on glass to examine the shield effect on electromagnetic interference (EMI). In addn., the sputtering specimens and powder coating specimens were compared. The results show that adding Al to the Sn-xAl powders can increase the electromagnetic interference (EMI) shield at lower frequencies. Notably, the no. of cavities in the coating layer increased with the coating thickness, with the result that the EMI shield could not improve with an increase in the coating thickness at higher frequencies. However, the EMI shield of sputtering films had a tendency to increase as the thin thickness increased. The Sn-40Al undergoes a dispersing effect which forms a fine overlapping structure, thereby improving the low frequency EMI shielding. In addn., the Sn-20Al powders possessed the properties of a small particle size, closed structure and higher elec. cond. which improved the high frequency EMI shielding. For the sputtering films, the annealed treatment not only had higher elec. cond. but also increased the high frequency EMI shielding. [on SciFinder(R)]
tin coating layer electromagnetic interference shi
The Flow Induced by the Transverse Motion of a Thin Disk in Its Own Plane Through a Contained Rapidly Rotating Viscous Liquid
Journal of Fluid Mechanics
39
04
831-847
1969
A thin circular disk translates slowly in its own plane transverse to the axis of rotation of parallel plane boundaries filled with viscous incompressible liquid. It is shown that the indeterminateness of the geostrophic flow is removed by constraints imposed by the dynamics of free shear layers (Stewartson layers), which surround a Taylor column whose boundary is not a stream surface. Fluid particles cross the Taylor column at the expense of deflexion through a finite angle. A comparison is made with the flow past a fat body (Jacobs 1964), where the geostrophie flow is determined without appeal to the dynamics of the shear layers. The problem is also considered for a disk in an unbounded fluid, and it is shown that to leading order there is no disturbance.
Not printed
Simulation of flow field and temperature tield in the process of filling and solidification for K424 alloy thin-walled casting
Applied Mechanics and Materials
66-68
1568-1573
2011
In order to improve the utilization of K424 alloy, Z-Cast analysis software is used to get three-dimensional flow field and temperature coupling simulation in the process of K424 alloy castings filling, by considering the effection of pouring temperature, casting speed, shell thermal conductivity and temperature on the morphology of filling. A three-dimensional simulation of temperature changes in solidification process of molten metal was performed based on the filling simulation. The simulation results on flow field and temperature field shows the order of filling and solidification in different parts of the casting, and determines the position where cold shut and misrun appears, which provides theoretical support to the improvement of technology plan. © (2011) Trans Tech Publications, Switzerland.
Flow field simulation; K424 alloy; Temperature field simulation; Thin-section casting
EFFECTS OF RF POWER ON OPTICAL AND ELECTRICAL-PROPERTIES OF PLASMA-DEPOSITED HYDROGENATED AMORPHOUS-SILICON THIN-FILMS
SENSORS AND ACTUATORS A-PHYSICAL
37-8
733-736
1993
10.1016/0924-4247(93)80124-Y
The optical and electrical properties of hydrogenated amorphous silicon (a-Si:H) thin films, prepared by plasma deposition, were studied as a function of r.f. power in the range from 12.5 to 200 mW/cm2. Film analysis performed included spectroellipsometry, FT-IR absorption spectroscopy, photothermal deflection spectroscopy, and dark and photo-electrical conductivity measurements. The initial effect of increasing r.f. power is characterized by a decrease in material density and an increase in film microstructure and structural disorder, resulting in a deterioration of a-Si:H optoelectronic properties. In contrast, at higher r.f. power, film density is hardly affected and microstructure is reduced, as well as the structural disorder. As a consequence, a-Si:H films were obtained at high deposition rate (1 nm/s) with optoelectronic properties comparable with that obtained at low r.f. power (< 0.4 nm/s). These results are discussed in terms of plasma polymerization and ion bombardment mechanics induced by r.f. power.
Development of single cantilever beam method to measure the adhesion of thin film adhesive on silicon chip
Engineering Fracture Mechanics
133
179-190
2015
10.1016/j.engfracmech.2014.10.004
A method to measure the tensile adhesion of thin films on a silicon chip was developed. A new test machine was designed to obtain tensile adhesion by applying a single cantilever beam method. Self-alignment of the specimen was accomplished by a specially designed jig and mount. The specimen was designed to allow fabrication by using a commercial manufacturing process. The developed method was applied to measure the adhesion of die attach films having various thicknesses ranging from 5μm to 20μm. Adhesion between the film adhesive and the top surface of a silicon chip was successfully measured. It was shown that the measured adhesion was independent of crack length and robust against variation of the initial alignment of specimen.
Die attach film; Electronic package; Shear strength; Single cantilever beam; Tensile adhesion
Investigation of Relation between Severities of Impact Damage to Fiber Reinforced Plastic and Hidden Flaws Detection by Thermocamera
Proceedings of 30th Danubia - Adria Symposium on Advances in Experimental Mechanics
43-44
2013
In this paper, application of laser profilometry is demonstrated for surface geometry measurement and compared to results obtained by active thermography as a reference method for damage detection and assessment. Specimens made of eight-ply carbon fiber reinforced PPS matrix laminate in the form of strips 25mm wide, 250mm long and 2mm thick were subjected to simulated impact damage. Both mothods are capable to detect impacts, which is first sign of incurred damage of material. Therefore this methods are suitable for monitoring of damage accumulation during fatigue process.
carbon fibre composite; impact damage; laser profilometry; thermography
Studies on the failure analysis of composite materials with manufacturing defects
Mechanics of Composite Materials
49
1
35-44
2013
10.1007/s11029-013-9318-6
A strategy is discussed for the cost reduction of composite structures by allowing manufacturing defects while satisfying the performance requirements. To implement the strategy, cost/performance trade-offs must be made. These trade-offs require a proper assessment of the effect of defects on the performance-limiting conditions, such as the loss of required stiffness and/or strength. For illustration, two failure modes in composite laminates are considered: the delamination fracture and the progressive ply cracking under quasi-static loading. In the first case, the manufacturing-induced defects are treated directly by examining their effects on the energy release rate, while in the second case, the defects are taken into account indirectly via their influence on the statistics of local failure. 2013 Springer Science+Business Media New York.
Commerce; Composite materials; Computer system recovery; Defects; Laminated composites; Loading; Manufacture
Numerical solutions for stresses near crack tips in time-dependent inelastic fracture mechanics
International journal of fracture
18
293-310
1982
The boundary element method is used to calculate the stresses in a finite planar body with a traction free crack present in it. The body is assumed to undergo time-dependent inelastic deformation and is described by an elastic-power law creep constitutive model. A stationary crack is modelled as a very thin ellipse and numerical solutions to the complete transient problem are obtained by step-wise integration in time. The numerical results for stresses near the crack tip are compared with the asymptotic analytical results obtained by other researchers. These asymptotic results are those for a plate with a line crack where the elastic strain rates are neglected relative to the nonelastic strain rates near the crack tips. Both Mode III and Mode I deformation, under time-independent and time-dependent remote loading, are considered in the calculations
crack-edge stress field analysis
Condensed Matter> Statistical Mechanics Title: The spread of epidemic disease on networks
Journal reference: Phys. Rev. E
2002
Condensed Matter > Statistical Mechanics. Title: . Authors: MEJ Newman. (Submitted on 30 Apr 2002).
X-ray diffraction studies of multiple orientation in poly(9,9- bis(2-ethylhexyl)fluorene-2,7-diyl) thin films
Journal of Physical Chemistry B
107
45
12425-12430
2003
The structural investigation of poly(9,9-bis(2- ethylhexyl)fluorene-2,7-diyl) (PF2/6) in aligned thin films is presented. Formation of a thickness dependent triaxial texturing is identified in thermotropically aligned films. X- ray reflectivity measurements reveal good macroscopic quality, and polarized photoluminescence and dichroic ratios in absorption indicate clear axial alignment. Grazing-incidence X- ray diffraction shows axially aligned mesomorphic structure with a distinct arrangement of helices and large correlation lengths, indicating a high local lateral order. Theoretical models produced using molecular mechanics methods suggest 5/2- helicity. The polymer chains are parallel to the substrate in the c direction. In particular, the hexagonal-like cells are flattened in the direction of the surface normal and reveal two kinds of coexistent crystallites, a multiple orientation where the greater proportion of the crystallites have one crystal axis a perpendicular to the substrate surface, whereas a smaller proportion is aligned with the crystal axis a parallel to the surface. In thinner films the former class of orientation is usually dominant, while the proportion of the parallel orientation type increases with prolonged annealing.
Neural Network Based Hybrid Adaptive Controller for an Autonomously driving Car using Thin Plate Spline Radial Basis Ac tivation Function
Applied Mechanics and Materials
592-594
2184-2188
2014
This paper presents a hybrid lateral and longitudinal controller for a self-driving passenger car. The controller comprises a Proportional Derivative (PD) controller as a closed loop controller and Neural Network (NN) based adaptive compensator as a feed forward controller. The activation function of the NN adaptive stage is based on a poly-harmonic Thin Plate Spline (TPS)\r\nRadial Basis Function (RBF), which promises better accuracy, smoother interpolation and closed form solutions. The controller development and testing has been performed using a non-linear\r\nvehicle dynamics model, which has been developed using the Matlab / Simulink tool. The Controller performance in terms of vehicle lane following (lateral deviation control) and safe cruising control (longitudinal spacing error control) have been verified through simulations. Reductions of lateral deviation error by 15% and longitudinal spacing error by 7% have been achieved.
Quantum mechanics, correlations, and relational probability
Crítica, Revista Hispanoamericana de Filosofía.
41
121
3-22
2009
This article sets forth and discusses the Ithaca Interpretation of Quantum Mechanics (IIQM). Section 1 presents the standard formalism of quantum mechanics and the measurement problem. Section 2 sketches Everett’s interpretation as a preamble to IIQM. Section 3 sets out IIQM’s central claim: it is possible to make sense of quantum mechanics by taking as the proper (and only) subject of physics the correlations among subsystems. Section 4 introduces a theorem of quantum mechanics, the SSC theorem, which supports this claim. Section 5 contends that at least two problems exist with IIQM, and one serious objection against it. Section 6 discusses a strategy based on relational probabilities to go around the objection.
dualism; measurement problem; physical reality; system/subsystem
The analogy study method in engineering mechanics
International Journal of Mechanical Engineering Education
41
2
136-145
2013
0.7227/IJMEE.41.2.6
The course ‘Engineering Mechanics’ plays an essential role as a bridge and bond between fundamental and specialized knowledge, and it has become a basic class for most engineering students. However, there are many complex concepts and formulas to be covered, and this makes it difficult for students to grasp the spirit of engineering mechanics. One way to solve this problem is to use the analogy study method in learning. Following this new route, students can find the linear quantities and angular quantities in theoretical mechanics, and some analogous relations between stress and deformation for fundamental deformations in mechanics of materials. Through these analogy relations, students can appreciate the essence of different physical phenomena. Indeed, it seems that twice as much is accomplished with half the effort.
Interlaminar cracking of composite shells
Theoretical and Applied Fracture Mechanics
27
1
13-20
1997
10.1016/S0167-8442(97)00003-7
Experiments and two-dimensional finite-element analysis are carried out for unidirectional and angle-ply curved laminates. These laminates are used for deep sea applications and offer considerable advantage over their metal counterparts. Much work has recently been devoted to the failure mechanisms of thick composites. Delamination growth of thick composite laminates and shells is also pertinent to the structural performance and certification of underwater composite shells. In this study, specimens are produced and tested for failure. A linear and geometric non-linear two-dimensional finite element analysis of the end-notched flexure specimen is performed to evaluate the compliance and Mode-II strain energy release rate GII.
Crack opening geometry in cracked composite laminates
International Journal of Damage Mechanics
6
1
96-118
1997
10.1177/105678959700600107
Talreja and coworkers have reported brittle and tough polymer matrix composites to show different cross-ply laminate stiffness reductions due to transverse cracks, despite very similar elastic properties. Studies of crack opening displacement (COD) in [0m,90n]s laminates may help in solution of this problem. Approximate analytical models based on the variational approach pioneered by Hashin were therefore applied in addition to FEM-calculations. Approximate models were concluded not to be reliable for future analyses of this problem. Experimental COD for brittle GF/EP laminates at low crack densities was fairly well predicted by FEM-calculations. None of the models were able to predict experimental data at high crack densities. Residual plastic strains are suggested as an explanation and may also be responsible for reported matrix-related differences in stiffness reduction.
Three-Dimensional Analysis laminates With Cross Cracks
Journal of Applied Mechanics
55
389-397
1988
An approximate 3-dimensional analysis to study the effects of a system of transverse and longitudinal matrix cracks in cross-ply laminates is given. The method considers a repeating unit cell containing three subcells in every one of which the displacement vector is expanded to second order. The equilibrium equations, in conjunction with continuity conditions of displacements and tractions, together with the appropriate loading and boundary conditions, provide a system of equations/or the elastic field variables. The dependence of the effective axial stiffness and Poisson's ratio of the laminate on the cross-cracks density is given. The Poisson's ratio appears to be a good indicator for the state of damage of the laminate. The distribution of the axial displacement and stress in the cracked laminate is shown.
Using Physlets To Teach Quantum Mechanics
Proceedings of the 7th Workshop on Multimedia in Physics Teaching and Learning of the European Physical Society
2002
We have produced interactive Physlet®-based curricular materials to support introductory, intermediate, and advanced courses in quantum mechanics. These exercises, emonstrations, and tools address both quantitative and conceptual difficulties encountered by many students. In addition, these quantum mechanics exercises are appropriate for use with the Just-in-Time Teaching technique to actively engage students outside of the classroom. Examples of the curricular materials, the results of our preliminary assessment of their effectiveness, and future directions of this project will be discussed.
Mechanics, materials, and functionalities of biointegrated electronics
The Bridge
43
4
31-38
2013
Robust bioelectronic interfaces present unlimited potentials in wear- able health monitors, implantable devices, and human-machine interfaces. But conventional high-performance electronics, which are based on planar and rigid silicon wafers, are intrinsically incompatible with curvilinear and deformable natural organisms. This challenge is being approached with a mechanics-based strategy involving the use of neutral planes and filamentary serpentine networks. The resulting structural-electrical design has enabled flexible and stretchable electronics to conform to—and deform with—bio-logical tissues for physiological sensing, programmable stimulation, and on-demand therapeutics. This article summarizes the mechanics, materials, and functionalities of such biointegrated electronics and concludes with a discus-sion of future directions.
The mechanics of constitutive modeling[ Recurso electrónico]
Elsevier Engineering Information
2005
Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. Topics covered include: Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The thermodynamic framework for constitutive modelling Thermoplasticity - Uniqueness and discontinuous bifurcations More comprehensive in scope than competitive titles, with detailed discussion of thermodynamics and numerical methods. Offers appropriate strategies for numerical solution, illustrated by discussion of specific models. Demonstrates each topic in a complete and self-contained framework, with extensive referencing
Libros electrónicos; Mechanics, Applied- Mathematical models
Delamination Characterization of Woven Glass/Polyester Composites
Journal of Composites Technology and Research
19
1
20-28
1997
The test methods to determine interlaminar fracture toughness of composite materials require values to be determined at delamination initiation from the thin insert. In woven composites, the location of the insert relative to the yarns will vary which may effect the toughness values at initiation. This work determined the effect of the location of the insert relative to the yarns on interlaminar fracture toughness using the double cantilever beam (DCB) and end-notched flexure (ENF) specimens under quasi-static and fatigue loads. The specimens were configured so that the insert end was placed at the edge of and in the center of a yam and in a mixed position where the insert was at the edge in one ply above and in the center of the ply below. Quasi-static and fatigue tests were conducted for each configuration. The static tests on the DCB resulted in "stick-slip" type fracture, where the delamination grew rapidly across a transverse yarn to the beginning of the next transverse yam and stopped until the load increased sufficiently to cause further stick-slip fracture. As the delamination propagated down the beam, the crack branched either side of the transverse yams eventually resulting in the complete ply bridging the delamination. This resulted in an increase in Glc values. Delamination growth in the ENF static tests also produced crack branching and ply bridging that resulted in stable delamination growth. For both specimen types, the lowest values of Gc were obtained in the specimens with the insert in the center of the yarn and the highest Gc with the insert at the edge of a yarn. The scatter in the fatigue data prevented a clear indication of which insert position resulted in the lowest number of cycles to delamination onset with applied Gmax.
Characterization; Composite materials; Crack initiation; Crack propagation; Delamination; Double cantilever beam; End notched flexure; Fatigue testing; Fracture toughness; Glass fiber reinforced plastics; Loads (forces); Mode I; Mode II; Polyesters; Transverse yarns; Woven composites; Yarn
Flexural rigidity of thin auxetic plates
International Journal of Applied Mechanics
6
2
1450012
2014
10.1142/S1758825114500124
The influence of auxeticity on the mechanical behavior of isotropic plates is considered herein by evaluating the plate flexural rigidity as the Poisson's ratio changes from 0.5 to -1. Since the change in plate's Poisson's ratio is followed by a change in at least one of the three moduli, any resulting change to the plate flexural rigidity is only meaningful when at least one of the moduli is held constant. This was performed by normalizing the plate flexural rigidity by a single modulus, a square root of two moduli product, or a cube root of three moduli product to give a dimensionless plate flexural rigidity. It was found that the plate flexural rigidity decreases to a minimum as the plate Poisson's ratio decreases from 0.5 to 0 when only the Young's modulus is held constant. Thereafter the plate flexural rigidity increases with the plate auxeticity. Results also reveal that when only the shear modulus or when the bulk modulus is held constant, the plate flexural rigidity decreases or increases, respect...
Auxetic solids; flexural rigidity; plates
Combining Quantum Mechanics Methods With Molecular Mechanics Methods In {ONIOM}
Journal of Chemical Theory And Computation
2
3
815-826
2006
Doi 10.1021/Ct050289g
The Purpose of This Paper Is 2-Fold. First, We\nPresent Several Extensions To The Oniom(Qm: Mm)\nScheme. In Its Original Formulation, The\nElectrostatic Interaction Between The Regions Is\nIncluded At The Classical Level. Here We Present The\nExtension To Electronic Embedding. We Show How The\nBehavior of Oniom With Electronic Embedding Can Be\nMore Stable Than Qm/ Mm With Electronic\nEmbedding. We Also Investigate The Link Atom\nCorrection, Which Is Implicit In Oniom But Not In\nQm/ Mm. Second, We Demonstrate Some of The Practical\nAspects of Oniom( Qm: Mm)\nCalculations. Specifically, We Show That The\nPotential Surface Can Be Discontinuous When There Is\nBond Breaking And Forming Closer Than Three Bonds\nFrom The Mm Region.
Econophysics, Statistical Mechanics Approach to
ArXiv
24
2007
This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.
European Journal of Mechanics. A
万方数据资源系统
2000
Dynamic strain localisation in saturated and partially saturated porous media is investigated with a one-dimensional model in this paper. The porous medium is treated as a multiphase continuum, with the pores filled by water and air,
Fracture-mechanics principles
Dental Materials
11
2
111–112
1995
The principles of linear elastic fracture mechanics (LEFM) were developed in the 1950s by George Irwin (1957). This work was based on previous investigations of Griffith (1920) and Orowan (1944). Irwin (1957) demonstrated that a crack shape in a particular location with respect to the loading geometry had a stress intensity associated with it. He also demonstrated the equivalence between the stress intensity concept and the familiar Griffith criterion of failure. More importantly, he described the systematic and controlled evaluation of the toughness of a material. Toughness is defined as the resistance of a material to rapid crack propagation and can be characterized by one parameter, K-IC. In contrast, the strength of a material is dependent on the size of the initiating crack present in that particular sample or component. The fracture toughness of a material is generally independent of the size of the initiating crack. The strength of any product is limited by the size of the cracks or defects during processing, production and handling. Thus, the application of fracture mechanics principles to dental biomaterials is invaluable in new material development, production control and failure analysis. This paper describes the most useful equations of fracture mechanics to be used in the failure analysis of dental biomaterials.
Statistical Mechanics
Statistical Mechanics
452-494
1996
10.1016/B978-075062469-5/50016-5
Evaluation of the statistical averages of the various physical quantities represents, with a high degree of accuracy, the results expected from relevant measurements on the given system in equilibrium. Nevertheless, these results do deviate from—or fluctuate about—these mean values. This chapter presents a discussion of these fluctuations and demonstrates the importance of this study. Understanding of these deviations helps develop a mathematical scheme that is used to estimate the magnitude of the relevant fluctuations under a variety of physical situations. In a single-phase system, the fluctuations are thermodynamically negligible, but they can assume considerable importance in multi-phase systems—especially in the neighborhood of a critical point. Estimating these fluctuations provides a natural framework for understanding Brownian motion, which in turn helps to relate properties such as the mobility of a fluid system and its coefficient of diffusion with temperature through the Einstein relations. Also, the study of fluctuations—as a function of time—leads to the concept of correlation functions, which play a vital role in relating the dissipative properties of a system, such as the viscous resistance of a fluid or the electrical resistance of a conductor, with the microscopic properties of the system in a state of equilibrium. At the same time, a study of the frequency spectrum of fluctuations, which is related to the time-dependent correlation function, is of considerable value in assessing the noise met with in electrical circuits as well as in the transmission of electromagnetic signals.
Quantum Mechanics with Trajectories
A Trajectory Description of Quantum Processes. I. Fundamentals
187-230
2012
10.1007/978-3-642-18092-7
Bohmian mechanics allows to understand the quantum world in a classical-like fashion, by means of trajectories evolving throughout configuration space. This appealing feature has stimulated its application nowadays to many different problems from atomic and molecular physics, condensed matter physics, chemical physics or quantum chemistry, for example. This is a remarkable growth if one takes into account that this causal theory of quantum motion started as a simple hidden-variable model to disproof von Neumann’s theorem on the impossibility of hidden variables in quantum mechanics, and its applications initially covered fundamental problems. In this Chapter, the main elements of this theory are briefly revisited and they will be further developed in Volume 2. Furthermore, a contextualization of Bohmian trajectories with respect to alternative trajectory-based approaches to quantum mechanics, such as Feynman’s path integral, the semiclassical approximation, mixed/hybrid (quantum-classical) formulations or quantum (causal) stochastic trajectories, is also presented.
Mathematical and Computational Physics; quantum physics; Theoretical
Similarity Mechanics
Statistics
2006
The present work provides a new conceptual framework for GUT (Grand Unified Theory) based on a picture of fractal universe. Under a hypothesis of multi-scaled matter structure, we find new clues for the conciliation of quantum and relativity and for the unification of fundamental interactions. A new interpretation for matter wave is proposed as the trajectory of position center of a moving particle with a nucleated structure. The origin of magnetism and gravitation are discussed as the relativistic effects of electrostatic force.
1960; accelerators; a large quantity; been boosted; beginning; building technologies big; development; exploring frontier micro; field particle physics; fundamental interactions; gut; human beings; matter wave; quantum; relativity; s; s 20th century; since 30; thanks; world has
The Craft of Diplomacy: Mechanics and Development of National Representation Overseas.
Public Administration
46
1
105-106
1968
Reviews the book "The Craft of Diplomacy: Mechanics and Development of National Representation Overseas," by Douglas Busk.
BOOKS -- Reviews; BUSK, Douglas; CRAFT of Diplomacy: Mechanics & Development of Nat; INTERNATIONAL relations
Medical building materials of structural properties and electromagnetic interference shielding in the quartz crystal plane coated Ni based thin film.
Applied Mechanics and Materials
599-601
Frontiers of Manufacturing Science and Measuring Technology IV
67-76
2014
10.4028/www.scientific.net/AMM.599-601.67
Medical use quartz components for electromagnetic shielding materials research topics very rarely, therefore, intend to systematic development of coated quartz glass materials. The considerations for against electromagnetic waves (Electromagnetic Interference Shielding, EMI), one conductive coating film is required. The anti-high-frequency electromagnetic waves also need magnetic coating film. The thin film is translucent with a poor crystallinity, must be heat-treated to have good crystn. and cond., and therefore finds the feasible of Ni-based coating and interface effects also have the academic importance. This program is to deposit Ni-based thin film on different quartz planes (Ni/SiO2), and explores the effect of heat treatment on the structure. That contains cryst. characteristics (doping concn.: the Ni-base matrix doping Fe, 10at%∼ 50at.%), optical properties and elec. cond. Finally, the electromagnetic shielding effect (EMI) of the coating structure is assessed. So, the application data for the characteristics of interface layer and anti-electromagnetic (EMI) properties are obtained. building materials extended to the health care system materials systems. The results show that Sn-40Al-xNi film increased the electromagnetic interference (EMI) shielding after annealed. For the Sn-40Al-10Ni films with higher Ni at. concn., the low frequency EMI shielding could be improved. For the sputtering films the annealed treatment not only had higher elec. cond. but also increased the high frequency EMI shielding. [on SciFinder(R)]
medical building material electromagnetic interfer
Relativistic viscoelastic fluid mechanics
ArXiv
2011
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski spacetime become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Fluid Dynamics; High Energy Physics - Theory; Nuclear Theory; Statistical Mechanics
On the variational formulation of problems in continuum damage mechanics
Modelling Measurement & Control B: Solid & Fluid Mechanics & Thermics, Robotics Mechanical Systems, Civil Engineering
71
5
23-40
2002
Presents a comprehensive treatment of constitutive equations and variational formulation of problems in continuum damage mechanics. A careful study of the constitutive equations of materials undergoing a process of damage has been made having described the constitutive equations within the framework of convex analysis. Our paper, which can be regarded as a generalization of the work of Han and Reddy (1995) (centred on (i) analytical and (ii) numerical aspects of the 'initial value' problems arising from the quasi-static hardening of plasticity), presents additional fundamental concepts in continuum damage mechanics (CDM)
continuum mechanics; elastoplasticity; fracture mechanics; variational techniques
Applications of computational fluid mechanics at Sandia National Laboratories
3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
10-12
2005
In the spirit of representing the industrial perspective (at least the high-end-application user) on computational fluid mechanics at this 3rd MIT Conference, we present the results of recent calculations in three areas of fluid mechanics of interest at Sandia National Laboratories. The ability to simulate these phenomena at extremely-high fidelity on massively- parallel, distributed, computer platforms has only recently been achieved using Sandia's SIERRA and NEVADA software architecture. These simulations represent the broad range of compressible fluid mechanics now being applied to problems of national security at Sandia National Laboratories. © 2005 Elsevier Ltd.
Computational fluid dynamics;Fires;Fluid mechanics
Role for Frac Mechanics in Conventional Reinforced Concrete Design
NATO ASI Series, Series E: Applied Sciences
94
639-666
1985
Fracture mechanics role within the framework of the ACI Building Code will be significant if fracture mechanics provides answers to public safety issues, and relatively insignificant if fracture mechanics only provides a different theoretical viewpoint for provisions which already provide an adequate margin of public safety. Public safety issues for which fracture mechanics can provide answers include size effects, appropriate finite element analyses procedures, new materials, minimum reinforcement ratios, maximum reinforcement spacings, and time dependent effects. Issues for which fracture mechanics can provide a consistent theoretical basis include the diagonal tension cracking capacity for shear, torsion, and combined shear and torsion loadings.
Contribution to understanding the mathematical structure of quantum mechanics
Optics and Spectroscopy
103
3
434-450
2007
10.1134/S0030400X07090135
Abstract Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed.\nIt is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, the Born rule, commutation\nand uncertainty relations, probability density current, momentum operator, and rules for including the scalar and vector potentials\nand antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and\ntime. Equations of motion of quantum mechanics, the Klein-Gordon equation, the Schrödinger equation, and the Dirac equation\nare obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of th\ne δ-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Manyparticle systems and the\npostulates of quantum mechanics are also discussed.
FUNDAMENTALS OF THE PHENOMENOLOGICAL THEORY OF NONLINEAR FRACTURE MECHANICS.
Journal of Applied Mechanics, Transactions ASME
50
4 b
1042-1051
1983
Following an outline of the full range of objectives of nonlinear fracture mechanics, the paper focuses on the phenomenological, or semiempirical, approach to the initiation of crack growth and the subsequent quasi-static crack growth and loss of stability under monotonic load histories. Nonlinear fracture mechanics encompasses a semiempirical approach, which for the most part is an extension of linear elastic fracture mechanics to account for large-scale inelastic effects, and a more basic approach whose aim is to predict (as opposed to correlate) fracture conditions by accounting for mechanisms of separation at the microscopic level.
FRACTURE MECHANICS; MATHEMATICAL TECHNIQUES - Nonlinear Equations
Design of cold-formed thin-walled steel fixed-ended channels with complex edge stiffeners under axial compressive load by direct strength method
Applied Mechanics and Materials
226-228
1232-1235
2012
The stability bearing capacity of axially compressive loaded fixed-ended channels with complex edge stiffeners were analyzed by direct strength method in this paper. A total of 292 examples with different parameters were selected to be studied by nonlinear finite element analysis. As the members with fix-ends, the failure modes include local and flexural-torsional interactive buckling, distortional and flexural-torsional interactive buckling. The revised direct strength method was put forward. After revise, the formula is in good agreement with experimental results. It is shown that direct strength method is valid for predicting the stability capacity of axially loaded fixed-ended channel columns with complex edge stiffeners. We suggest using the DSM3 to calculate the cold-formed thin-walled steel fixed-ended channels with complex edge stiffeners under axial compressive load. © (2012) Trans Tech Publications, Switzerland.
Channels with complex edge stiffeners; Direct strength method; Elastic buckling stress; Stability bearing capacity
Normalized stress intensity factor range solutions of an inner-surface circumferential crack in thin- to thick-walled cylinder under thermal striping by semi-analytical numerical method
Journal of Thermal Stresses
27
3
253-267
2004
Doi 10.1080/01495730390271027
The normalized stress intensity factor (SIF) range of an inner-surface circumferential crack in a thin to thick-walled finite-length cylinder under thermal striping was considered in this paper. The edges of the cylinder were rotation-restrained and the outer surface was adiabatically insulated. The inner surface of the cylinder was heated by a fluid with sinusoidal temperature fluctuation. An analytical temperature solution for the problem and our semianalytical numerical SIF evaluation method for the crack were combined and, as a result, it was shown that the transient SIF solution can be expressed in a generalized form by dimensionless parameters such as mean-radius-to-wall-thickness ratio, Biot number, normalized striping frequency, and Fourier number. Finally, normalized SIF ranges for the first cycle and steady state were given for these dimensionless parameters in tables for mean-radius-to-wall-thickness ratio of 10, 5, and 1.
circumferential crack; fracture mechanics; shock; stress intensity factor; thermal stress; thermal striping
Analytical solution in frequency domain of dynamic response of thin-wall pipe piles with variable wave impedance under low strain transient concentrated load
Yantu Lixue/Rock and Soil Mechanics
30
Compendex
1793-1798
2009
Dynamic response of pipe piles under low strain transient concentrated load is a three dimensional wave problem. Based on the three dimensional wave theory, the computational model and wave equation of dynamic response of thin-wall pipe piles with variable wave impedance are established. Combined the initial and boundary conditions, the analytical solution of wave equation in frequency domain is obtained by Laplace transformation method. The time domain response is obtained by Fourier inverse transformation. By comparing the results of analytical solution with that of 3D finite element method, the following conclusions are achieved: the wave crest of the results of analytical solution can well meet that of the 3D-FEM results; and the displacement responses of them have little difference. The dynamic responses at different points on top of the pile and the high-frequency interference problem are also researched. The characteristics of dynamic responses of variable modulus piles and variable section piles are studied.
Computation theory; Differential equations; Dynamic response; Frequency response; Laplace equation; Laplace transforms; Piles; Pipe; Sailing vessels; Three dimensional; Wave equations
Superintegrable systems in quantum mechanics and classical Lie theory
Journal of Mathematical Physics
42
2
659-673
2001
The relation is established between some concepts of quantum mechanics\nand those of soliton theory. In particular, superintegrable systems\nin two-dimensional quantum mechanics are shown to be invariant under\ngeneralized Lie symmetries and to allow recursion operators. (C)\n2001 American Institute of Physics.
integrable hamiltonian-systems winternitz system e
Five-dimensional Hamilton-Jacobi approach to relativistic quantum mechanics
Advances in Imaging and Electron Physics
132
247-285
2004
10.1016/S1076-5670(04)32005-7
A five-dimensional Hamilton-Jacobi approach was introduced to study relativistic quantum mechanics. The motion of particles in Minkowski space was calculated using this approach. The dynamics of particle was described by considering its coordinates as functions of the independent Lorentz-invariant variable. The results show that the time-like position coordinate need not increase monotonically as in classical mechanics.
Application of fiber optic sensors to fracture mechanics problems
Engineering Fracture Mechanics
38
6
491-498
1991
10.1016/0013-7944(91)90098-L
An experimental study is conducted to show the application of fiber optic sensors to fracture mechanics problems. Mode I stress intensity factors are obtained using single mode optical fibers in single edge notched specimens fabricated from aluminium. A Mach–Zehnder interferometric set up is used during the experiments. The experimental results compare well with theoretical predictions.
Multiscale Modeling and Simulation for Fluid Mechanics at the Nanoscale
Carbon Nanotube Devices
229-290
2008
10.1002/9783527622597.ch6
This chapter contains sections titled: * Introduction * Computational Modeling: from Quantum to Atomistic and Continuum Descriptions * Fluid--Solid Interfaces at the Nanoscale * Fluids in Confined Geometries * Fluid Mechanics at the Nano---Bio Interface * Outlook -- τα παυτα ρυι -- Even at the Nanoscale * Acknowledgments * List of Symbols
nanosystems; multiscale modeling; fluid mechanics
{Derivation of Feynman's path integral theory based on stochastic mechanics}
Physics Letters A
137
9
437-439
1989
10.1016/0375-9601(89)90220-X
{We show that Feynman's path integral theory can be derived in the framework of stochastic mechanics. The probability of a particle moving from a space-time point ( x 0 , t 0 ) to another space-time point ( x , t ) is the stochastic mechanics transition probability instead of the absolute square of the kernel as proposed by Feynman.}
The Significance of Some Experimental Tests of Quantum Mechanics
Danish Yearbook of Philosophy
27
93-108
1992
The roles of the argumentation of Einstein, Podolsky and Rosen, Bell's inequalities and the experiment of Aspect in the debate about foundations of quantum mechanics are assessed. It is argued that thesignificance of Aspect's achievements is mainly pedagogical.
Experiment; Logic; Mathematics; Quantum Mechanics; Science
Computational mechanics of materials and structures
Engineering Structures
31
6
1288-1297
2009
Mechanics of Materials and Structures has become a popular new name of former Institutes for Strength of Materials and/or Structural Analysis at European Universities of Technology. This designation stands for a scientific program aimed at a symbiosis of material and structural mechanics. The adjective "computational" refers to the algorithmic component of Mechanics of Materials and Structures, which is frequently underrated. It was the advent of the digital computer that opened the door to computational mechanics, which has become a scientific discipline with a tremendous influence on our lives. This survey paper contains a report about a selection of recent research projects carried out at the Institute for Mechanics of Materials and Structures of Vienna University of Technology. Its aim is to demonstrate that the trinity of Computational Mechanics - Materials - Structures has a strong impact on modern life. (C) 2009 Elsevier Ltd. All rights reserved.
bound limit analysis; cement-based materials; cohesive-frictional materials; continuum micromechanics; ellipsoidal inclusion; fire load; hydration model; insensitive elastic structures; materials; nanoindentation; structures; viscoelastic properties
Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory
Foundations of Physics Letters
18
7
637-650
2005
... 0894-9875/05/1200-0637/0 © 2005 Springer Science+Business Media, Inc. Page 2. [3]; see also, eg, De Muynck [4], Plotnitsky [5], Marchildon [6] and Khrennikov [7] for recent discussions. The crucial point of our approach is that a prequantum classical mechanics is not the ... \n
appl-adic; consciousness; harmonic; khrennikov; measure; physics; probability; quantum mechanics; statistics
Rheological properties of thin liquid films by molecular dynamics simulations
Journal of Non-Newtonian Fluid Mechanics
69
2-3
169-193
1997
DOI: 10.1016/S0377-0257(96)01520-0
In this paper we present the molecular dynamics simulations of thin\nfluids films sheared in Couette flow geometry between two structured\nplane walls. An NVT ensemble of atoms was chosen and simulation conducted\nin isothermal conditions. To keep the temperature at the required\nlevel a Gaussian thermostat was employed. This method was shown to\nbe superior to the simple velocity rescaling method, especially at\nhigh shear rates. The Gaussian thermostat method gave results for\nviscosity in good agreement with the results of other researchers\nwho used the reservoir method. The results for density and velocity\nprofiles were obtained for a wide range of simulation parameters.\nThe effects of shear rate and wall-fluid interaction strength were\ninvestigated in detail over a wide range of parameters. The material\nfunctions and normal stress differences were also obtained and the\neffects of shear rate and wall strength parameter on these properties\nwere studied. The effect of film thickness on the viscosity was investigated\nand was compared with what we found for bulk fluid using the SLLOD\nalgorithm. the existence of a non-Newtonian region with shear-thinning\neffect is found and examined for various films. The results suggest\nan increase in viscosity for thinner films in the Newtonian regime,\nthough this is valid only for a limited range of wall-fluid interaction\nstrength. A decrease in viscosity was also observed when the attraction\nforce of the wall was increased.
Molecular dynamics
Shaum's outline of theory and problems of continuum mechanics
Tradução portuguesa Probabilidade e
221
1970
For comprehensiveand comprehensiblecoverage of both theory and real-world applications, you cant find a better study guide than Schaums Outline of Continuum Mechanics. It gives you everything you need to get ready for tests and earn better grades! You get plenty of worked problemssolved for you step by stepalong with hundreds of practice problems. From the mathematical foundations to fluid mechanics and viscoelasticity, this guide covers all the fundamentalsplus it shows you how theory is applied. This is the study guide to choose if you want to ace continuum mechanics!
Applications of fracture mechanics in fretting fatigue life assessment
ASTM Special Technical Publication
1367
80-99
2000
Models based on fracture mechanics are developed in order to describe crack growth in fretting fatigue. Particular attention is given to a recently developed model, the `Crack Analogue' in which certain aspects of equivalence are recognized between contact mechanics and fracture mechanics. Here, an analogy is invoked between the sharp edged contact region between two contacting surfaces and the geometry of the near-tip regions of a double edge-cracked plate. Based on this approach, a new life prediction methodology is developed for fretting fatigue.
Improving Student's Understanding of Quantum Mechanics
Unpublished
284
2011
Learning physics is challenging at all levels. Students’ difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in students’ preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to students’ common difficulties in learning upper-level undergraduate quantum mechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students’ difficulties in learning quantum mechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantum mechanics through a guided approach. Preliminary assessments indicate that students’ understanding of quantum mechanics is improved after using the researchbased learning tools in the junior-senior level quantum mechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students’ understanding of quantum mechanics concepts in one spatial dimension. The validity and reliability of this quantum mechanics survey is discussed
measurement; peer instruction tools; quantum mechanics; tutorials
Does Quantum Mechanics Need Interpretation?
arXiv
quant-ph
2009
Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, perhaps one day, practical quantum computers. Many believe that, in turn, quantum information theory has bearing on foundational research. This is largely related to the so-called epistemic view of quantum states, which maintains that the state vector represents information on a system and has led to the suggestion that quantum theory needs no interpretation. I will argue that this and related approaches fail to take into consideration two different explanatory functions of quantum mechanics, namely that of accounting for classically unexplainable correlations between classical phenomena and that of explaining the microscopic structure of classical objects. If interpreting quantum mechanics means answering the question, "How can the world be for quantum mechanics to be true?", there seems to be no way around it.\n\nPublished in: Proc. of ICQNM09 Meeting (IEEE, Los Alamitos, California, 2009),\npp. 11-16
Advanced Soil Mechanics 4th edition
CRC press, Taylor & Francis Group
2014
10.1029/EO066i042p00714-02
Advanced Soil Mechanics provides a general review of grain-size distribution, nature of water in clay, consistency of cohesive soils, weight - volume relationships and soil classification systems. It also covers the fundamental concepts of elasticity, equations of equilibrium and compatibility as they relate to the determination of stress and displacement in a soil medium. Relationships based on the theory of elasticity are presented to show how to estimate the stress and displacement in a soil mass due to various types of loading. The book sets out, in a logical and sequential manner, novel or refined procedures as they relate to hydraulic conductivity of granular and cohesive soils and flow through porous media, consolidation, shear strength and settlement of foundations. Advanced Soil Mechanics is an upper undergraduate and beginning graduate level textbook for students of civil engineering, engineering mechanics and soil mechanics, as well as professionals working in these fields. Each chapter concludes with a list of references for further in-depth review or research and further study problems are included at the end of the book.
Integrating quantum and molecular mechanics
Journal of Computational Chemistry
20
15
1618-1633
1999
A computer algorithm is developed for integrating density functional quantum mechanics into a molecular mechanics program. The computationally infeasible aspects of the standard LCAO-MO approach (the iterative calculation of eigenvectors and the requirement of orthogonal expansions for the orbitals) are replaced with an efficient use of optimization via the trace theorem of linear algebra. The construction of a basis is also described for expanding the electron density that transforms with the molecular geometry. The combination of the trace method and the basis allow the solution for one configuration of atoms and electrons to be tracked over a wide range of internal conformations. The approach is readily adaptable to being used in the context of an imposed classical field that allows it to be used on part of a macromolecular complex. The initial implementation in the program AMMP is described. (C) 1999 John Wiley & Sons, Inc.
quantum mechanics molecular mechanics trace theore
Special section : Thin beds Recent progress in analysis of seismically thin beds
Interpretation
3
3
15-22
2015
Various approaches exist for quantitative or qualitative predictions of seismically thin beds and their physical properties. The evolving definition of thin beds, the use of seismic attributes indicative of thin beds, thin-bed imaging on geologic-time surfaces, and thin-bed thickness estimation represent some of the most active aspects of the research and application. We reviewed some theoretical and technological developments in thin-bed analysis over recent decades. We also reviewed the data processing steps that affect seismic resolution and thin-bed evaluation.
Part 2: introduction to continuum mechanics
Continuum
51
3
171-186
1984
10.1115/1.3167763
This book presents an introduction to the classical theories of continuum mechanics; in particular, to the theories of ideal, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. These theories are important, not only because they are applicable to a majority of the problems in continuum mechanics arising in practice, but because they form a solid base upon which one can readily construct more complex theories of material behavior. Further, although attention is limited to the classical theories, the treatment is modern with a major emphasis on foundations and structure
What is a state in quantum mechanics?
American Journal of Physics
72
348-350
2004
In quantum mechanics, states are supposed to be\nspecified by vectors in Hilbert space. However,\nstudents become confused about the representation of\nstates and the meaning of "state" itself. We discuss\nconsequences of the fact that quantum mechanics is\nintrinsically a probabilistic theory, and the\nubiquitous confusion over whether quantum states, when\nspecified as well as nature permits, are described by\nstate vectors or rays.
Lagrangian fractional mechanics—a noncommutative approach
Czechoslovak Journal of Physics
55
11
1447–1453
2005
The extension of coordinate–velocity space with noncommutative algebra structure is proposed.For action of fractional mechanics considered on such a space the respec- tive Euler–Lagrange equations are derived via minimum action principle.It appears that equations of motion in the noncommutative framework do not mix left and right deriva- tives thus being simple to solve at least in the linear case.As an example, two models of oscillator with fractional derivatives are studied
euler; fractional derivative; fractional mechanics; lagrange equations
On dissipative nonlinear evolutionary problems in mechanics
Proceedings of the 4th International Conference on Nonlinear Mechanics
54-57
2002
In this talk, we shall discuss the nonlinear interaction between dissipative mechanisms and instabilities in evolutionary systems arising from mechanics. Through theoretical and numerical investigations, various exciting phenomena have been revealed in the past two decades, including stationary patterns, phase transition layers, time-periodic and time-quasiperiodic patterns, even chaos. We review some of these results and related works.
chaos; equations; fluid; phase boundaries; stability; system; transition
Finite fracture mechanics for fractal cracks
Solid Mechanics and its Applications
10
223-231
2009
10.1007/978-1-4020-9033-2-21
We extend the recently developed Quantized Fracture Mechanics (QFM) by Pugno and Ruoff (2004) for fractal cracks. Using an equivalent smooth blunt crack for a given fractal crack, we show that assuming that radius of curvature of the corresponding blunt crack is a material property, the crack roughens while propagating, i.e., fractal dimension at the crack tip is a monotonically increasing function of the nominal crack length. In other words, the presence of the Mirror-Mist-Hackle phenomenon for fractal cracks is analytically demonstrated. © 2009 Springer Science+Business Media B.V.
Quantum mechanics is about quantum information
quant-ph/0408020
2004
I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive -- just as, following Einstein's special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right.
Statistical Mechanics Model for Protein Folding
arXiv.org
physics.bi
2010
We present a novel statistical mechanics formalism for the theoretical description of the process of protein folding$\leftrightarrow$unfolding transition in water environment. The formalism is based on the construction of the partition function of a protein obeying two-stage-like folding kinetics. Using the statistical mechanics model of solvation of hydrophobic hydrocarbons we obtain the partition function of infinitely diluted solution of proteins in water environment. The calculated dependencies of the protein heat capacities upon temperature are compared with the corresponding results of experimental measurements for staphylococcal nuclease and metmyoglobin.
Computational Fluid Mechanics and Heat Transfer
Series in computational and physical processes in mechanics and thermal sciences
791
1997
This comprehensive text provides basic fundamentals of computational theory and computational methods. The book is divided into two parts. The first part covers material fundamental to the understanding and application of finite-difference methods. The second part illustrates the use of such methods in solving different types of complex problems encountered in fluid mechanics and heat transfer. The book is replete with worked examples and problems provided at the end of each chapter.
The molecular mechanics of eukaryotic translation
Annual Review of Biochemistry
73
657-704
2004
10.1146/annurev.biochem.73.030403.080419
Great advances have been made in the past three decades in understanding the molecular mechanics underlying protein synthesis in bacteria, but our understanding of the corresponding events in eukaryotic organisms is only beginning to catch up. In this review we describe the current state of our knowledge and ignorance of the molecular mechanics underlying eukaryotic translation. We discuss the mechanisms conserved across the three kingdoms of life as well as the important divergences that have taken place in the pathway.
Fluid mechanics of heart valves
Annu. Rev. Biomed. Eng …
6
331-62
2004
10.1146/annurev.bioeng.6.040803.140111
Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review.
Animals; Biomechanical Phenomena; Bioprosthesis; Computer Simulation; Constriction; Heart Valve Prosthesis; Heart Valves; Heart Valves: physiology; Humans; Mitral Valve; Mitral Valve: pathology; Pathologic; Prostheses and Implants; Prosthesis Design; Software; Thrombosis; Thrombosis: pathology
Fluid Mechanics of Heart Valves
Annual Review of Biomedical Engineering
6
331-362
2004
10.1146/annurev.bioeng.6.040803.140111
Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review.
bioprosthetic valves; computational fluid dynamics; laser doppler velocimetry; mechanical heart valves; native heart valves
Fluid mechanics of heart valves
Annual Review of Biomedical Engineering
6
331-362
2004
Valvular heart disease is a life-threatening disease that afflicts millions of people worldwide and leads to approximately 250,000 valve repairs and/or replacements each year. Malfunction of a native valve impairs its efficient fluid mechanic/hemodynamic performance. Artificial heart valves have been used since 1960 to replace diseased native valves and have saved millions of lives. Unfortunately, despite four decades of use, these devices are less than ideal and lead to many complications. Many of these complications/problems are directly related to the fluid mechanics associated with the various mechanical and bioprosthetic valve designs. This review focuses on the state-of-the-art experimental and computational fluid mechanics of native and prosthetic heart valves in current clinical use. The fluid dynamic performance characteristics of caged-ball, tilting-disc, bileaflet mechanical valves and porcine and pericardial stented and nonstented bioprostheic valves are reviewed. Other issues related to heart valve performance, such as biomaterials, solid mechanics, tissue mechanics, and durability, are not addressed in this review.
Animals; Biomechanics; Bioprosthesis; Computer Simulation; Constriction; Heart Valve Prosthesis; Heart Valves/physiology; Humans; Mitral Valve/pathology; Pathologic; Prostheses and Implants; Prosthesis Design; Software; Thrombosis/pathology
On deformational and configurational poro-mechanics: dissipative versus non-dissipative modelling of two-phase solid/fluid mixtures
Archive of Applied Mechanics
80
9
969-984
2010
DOI 10.1007/s00419-009-0353-7
This manuscript aims at a particular (simple) geometrically nonlinear formulation of poro-mechanics which is inspired by the format of thermo-mechanics. Thereby the motivation is two-fold: the formulation allows, on the one hand, to design a non-dissipative version of poro-elasticity as opposed to the classical dissipative Darcy-type version and, on the other hand, to derive and analyse the configurational setting of poro-mechanics in an easy and transparent fashion. Thus, this contribution intends to alleviate studies of defects and fracture in two-phase solid/fluid mixtures based on the concepts of configurational mechanics.
configurational mechanics; dissipationless poro-elasticity; elastic waves; formulation; frequency range; hyperelastodynamics; material settings; media models; poroelasticity; poro-mechanics; propagation; thermodynamics; thermoelasticity
Experiments in PT-symmetric quantum mechanics
CZECHOSLOVAK JOURNAL OF PHYSICS
54
1
151-156
2004
Extended quantum mechanics using non-Hermitian (pseudo-Hermitian)\nHamiltonians H = H-double dagger is briefly reviewed. A few related\nmathematical experiments concerning supersymmetric regularizations,\nsolvable simulations and large-N expansion techniques are summarized.\nWe suggest that they could initiate a deeper study of nonlocalized\nstructures (quasi-particles) and/or of their unstable and many-particle\ngeneralizations. Using the Klein-Gordon example for illustration, we\nshow how the PT symmetry of its Feshbach-Villars Hamiltonian H-(FV)\nmight clarify experimental aspects of relativistic quantum mechanics.
On a realistic interpretation of quantum mechanics
Arxiv preprint quant-ph/9908071
1999
\nAbstract. The best mathematical arguments against a realistic interpretation\nof quantum mechanics – that gives definite but partially unknown values\nto all observables – are analysed and shown to be based on reasoning that is\nnot compelling.\nThis opens the door for an interpretation that, while respecting the indeterministic\nnature of quantum mechanics, allows to speak of definite values for\nall observables at any time that are, however, only partially measurable.\nThe analysis also suggests new ways to test the foundations of quantum\ntheory.
Nanoscience and engineering in mechanics and materials
Inhomogeneous and strongly correlated materials and the study of matter at extreme conditions
65
8-9
1501-1506
2004
The transcendent technologies include nanotechnology, microelectronics, information technology and biotechnology as well as the enabling and supporting civil infrastructure systems and materials. These technologies are the primary drivers of the 21st century and the new economy. Mechanics and materials are essential elements in all of the transcendent technologies. Research opportunities, education and challenges in mechanics and materials, including nanomechanics, carbon nanotubes, bioinspired materials, coatings, fire-resistant materials as well as improved engineering and design of materials are presented and discussed in this paper.
A variational principle for fluid mechanics
Archive of Applied Mechanics
67
1
96-104
1996
10.1007/BF00787143
A variational principle for fluid mechanics is derived without calling for any additional postulates in any ad hoc way. In the principle derived here, the Lagrangian is essentially the sum of kinetic and heat energy transferred to the fluid, less the sum of its internal and potential energy, less the work done on its exterior (similar to the enthalpy concept), rather than the difference between only kinetic energy and internal energy, as obtained previously by Seliger and Whitham [1] for a more restricted mode of variation.
Variational Constrained Mechanics on Lie Affgebroids
0809.4609
2008
In this paper we discuss variational constrained mechanics (vakonomic mechanics) on Lie affgebroids. We obtain the dynamical equations and the aff-Poisson bracket associated with a vakonomic system on a Lie affgebroid ${\mathcal A}$. We devote special attention to the particular case when the nonholonomic constraints are given by an affine subbundle of ${\mathcal A}$ and we discuss the variational character of the theory. Finally, we apply the results obtained to several examples.
Critical State Soil Mechanics
Soil Use and Management
25
3
128-105
1968
10.1111/j.1475-2743.1987.tb00718.x
This book is about the mechanical properties of saturated remoulded soil. It is written at the level of understanding of a final-year undergraduate student of civil engineering; it should also be of direct interest to post-graduate students and to practising civil engineers who are concerned with testing soil specimens or designing works that involve soil. Our purpose is to focus attention on the critical state concept and demonstrate what we believe to be its importance in a proper understanding of the mechanical behaviour of soils. We have tried to achieve this by means of various simple mechanical models that represent (with varying degrees of accuracy) the laboratory behaviour of remoulded soils. We have not written a standard text on soil mechanics, and, as a consequence, we have purposely not considered partly saturated, structured, anisotropic, sensitive, or stabilized soil. We have not discussed dynamic, seismic, or damping properties of soils; we have deliberately omitted such topics as the prediction of settlement based on Boussinesq's functions for elastic stress distributions as they are not directly relevant to our purpose. The material presented in this book is largely drawn from the courses of lectures and associated laboratory classes that we offered to our final year civil engineering undergraduates and advanced students in 1965/6 and 1966/7. Their courses also included material covered by standard textbooks such as Soil Mechanics in Engineering Practice by K. Terzaghi and R. B. Peck (Wiley 1948), Fundamentals of Soil Mechanics by D. W. Taylor (Wiley 1948) or Principles of Soil Mechanics by R. F. Scott (Addison-Wesley 1963). In order to create a proper background for the critical state concept we have felt it necessary to emphasize certain aspects of continuum mechanics related to stress and strain in chapter 2 and to develop the well-established theories of seepage and one-dimensional consolidation in chapters 3 and 4. We have discussed the theoretical treatment of these two topics only in relation to the routine experiments conducted in the laboratory by our students, where they obtained close experimental confirmation of the relevance of these theories to saturated remoulded soil samples. Modifications of these theories, application to field problems, three-dimensional consolidation, and consideration of secondary effects, etc., are beyond the scope of this book. In chapters 5 and 6, we develop two models for the yielding of soil as …
The Mechanics of Composite Materials with Curved Structures (a Survey). Continual Theory, Fibrous Composites
Soviet Applied Mechanics
27
5
429-443
1991
Summary (translated from the Russian): ``We present a survey of papers on problems in the mechanics of composite materials with curved structures within the framework of continual theory and also within the framework of a model of a piecewise-homogeneous body for fibrous composite materials. We explain the development of continual theories in connection with composites with curved structures, and indicate a number of directions for further investigations in the areas of the mechanics of composites that are touched upon in this paper.'' The general thrust seems to be directed at an infinite elastic media reinforced by curved fibers. Difficult.
Composite structures and materials (73B27) Mechan; Continuum mechanics of solids (constitutive descr; homogenization; Mechanics of solids; Mechanics of structures; Nonhomogeneous materials
Growth mechanisms of polycrystalline thin films
Science and Technology of Thin Films
1-28
1995
10.1142/2685
k, , in: Science and Technology of Thin Films, n.d. pp. 1–28.
Thin-Ideal Implicit Association Test
PsycTESTS
2006
10.1037/t04810-000
Purpose: The purpose of the Thin-Ideal Implicit Association Test is to identify individuals who endorse the thin ideal and associate it with positive attributes.
Attitude Measures; Body Image; Internalization; Test Development; Test Validity; Thin-Ideal Implicit Association Test
Recent work in rock mechanics
Géotechnique
13
2
99-120
1962
Third Rankine Lecture. Rock mechanics as used by the civil engineer 10 years ago was already split into two phases: first, the measurement of the mechanical characteristics of rocks and, second, the application of the knowledge gained to different practical problems. The measures sought were: (i) the elastic modulus of the rock, and (ii) the stresses in the rock in situ. The elastic modulus was generally measured in the field by the jacking method. This, to my knowledge, was used for the first time, around 1935, by the Irrigation Department in Algeria. A jack was placed across a gallery, its foot against one wall and its head thrusting against the opposite wall, where the rock surface had been carefully dressed flat and true. The thrust of the jack was increased and the rock deformation measured and expressed as a function of the applied stress.
Rankine Lecture; Rock mechanics
Constraint formalism of classical mechanics
Physical Review D
18
6
1881-1886
1978
10.1103/PhysRevD.18.1881
The constraint formalism for classical mechanics is developed with an eye toward facilitating a manifestly covariant relativistic quantization of classical mechanics. The very close relationship of this formalism to the more familiar Hamiltonian formalism has long obscured its independent status. In this paper, after defining the concept of a classical trajectory in a particularly natural and intrinsic way (that is, without reference to a special parameter such as the time), we prove that the trajectories satisfy the Hamilton equations of motion. In the following paper, the power of this formalism is demonstrated, when as an illustrative example it is employed to solve the nontrivial relativistic two-body problem, both classically and quantum mechanically.
FLUID MECHANICS AND HOMELAND SECURITY
Annual Review of Fluid Mechanics
38
1
87-110
2005
10.1146/annurev.fluid.38.050304.092111
Abstract Homeland security involves many applications of fluid mechanics and offers many opportunities for research and development. This review explores a wide selection of fluids topics in counterterrorism and suggests future directions. Broad topics range from preparedness and deterrence of impending terrorist attacks to detection, response, and recovery. Specific topics include aircraft hardening, blast mitigation, sensors and sampling, explosive detection, microfluidics and labs-on-a-chip, chemical plume dispersal in urban settings, and building ventilation. Also discussed are vapor plumes and standoff detection, nonlethal weapons, airborne disease spread, personal protective equipment, and decontamination. Involvement in these applications requires fluid dynamicists to think across the traditional boundaries of the field and to work with related disciplines, especially chemistry, biology, aerosol science, and atmospheric science.
Damage Mechanics in Engineering Materials
Studies in Applied Mechanics
46
351-367
1998
10.1016/S0922-5382(98)80052-4
A mechanical material model is derived for 4D Carbon/Carbon composites. By using an anisotropic damage mechanics approach, a very simple mathematical model of the material mechanical behavior, based on some remarkable experimentally-observed properties, is built at the macroscopic scale. The identification of the material parameters is presented. The predictions of the model are then compared to different tests. Fiber yarn debonding near edges is also studied through a material mesomodel, with the mesoconstituents being: the fiber yarns, the matrix and the interfaces. Initial results are shown for a tension specimen.
USING SI UNITS IN MECHANICS.
Journal of Engineering Education
67
7
683-685
1977
There are two educational areas that must be treated differently during the transition period SI units. The first area concerns the basic engineering science courses in which SI units can and should now be pursued. The second area involves design courses, where a full treatment in SI units depends on the availability of such standard design information as structural shapes, fasteners, and gearing. Among the engineering science courses nowhere does the adoption of the SI system have a greater impact than in mechanics, upon which so much of the analytical structure of engineering depends. It is essential for all schools of engineering to undertake a vigorous program of converting instruction to the SI system without further delay. The United States is already about five years late in its changeover, and engineering education should not be responsible for causing further retardation.
ENGINEERING EDUCATION; MECHANICS; METRIC SYSTEM
Mathematical Methods in Quantum Mechanics
Physics Today
25
6
56
1972
10.1063/1.3070894
This manuscript provides a self-contained introduction to mathematical methods in quantum mechanics (spectral theory) with applications to Schrodinger operators. The first part covers mathematical foundations of quantum mechanics from self-adjointness, the spectral theorem, quantum dynamics (including Stones and the RAGE theorem) to perturbation theory for self-adjoint operators. The second part starts with a detailed study of the free Schrodinger operator respectively position, momentum and angular momentum operators. Then we developWeyl-Titchmarsh theory for Sturm-Liouville operators and apply it to spherically symmetric problems, in particular to the hydrogen atom. Next we investigate self-adjointness of atomic Schrodinger operators and their essential spectrum, in particular the HVZ theorem. Finally we have a look at scattering theory and prove asymptotic completeness in the short range case.
Numerical and experimental analyses of a fracture mechanics test for adhesively bonded joints
Journal of Adhesion Science and Technology
13
8
931-957
1999
10.1163/156856199X00758
The use of a fracture mechanics test to evaluate the joint strength through the determination of the strain energy release rate G is nowadays well established. The joint strength for fluorinated polymer (PVDF) sheets bonded with an epoxy adhesive was studied using a double cantilever beam (DCB). In order to obtain small-scale yielding, the adhesive joint of the polymer specimens was strengthened by steel sheets. Pre-cracks were initiated at the center of the bond thickness separating the two PVDF surfaces, with nominal lengths ranging from 5 to 27.5 mm. We did not measure the evolution of the crack length, which is generally very difficult to obtain with good precision. The measurement of the load-point displacement was used instead. The opening load versus this load-point displacement was recorded. The slope of the first part of this curve gives the value of the initial stiffness of the joint specimen. The stiffness of the various specimens enables us to access the real experimental initial crack length, which was smaller than the nominal value, by comparison of the experimental values with the numerical ones. From the second part of the curve, the strain energy release rate values for the crack propagation in the initial step (G(1)) and in the steady step (G,) are deduced. They were calculated from a least-squares linear fit obtained from the load-point displacement versus the inverse square of the load curve. The experimental results are discussed in light of an analytical analysis using the thin beams approach, improved with an elastic foundation model developed by Maugis describing the deformation of materials behind the crack tip, and of a numerical approach based on a finite element analysis. In this numerical model, an elastic-plastic behavior of the materials has been assumed. Analytical and numerical approaches are compared and their validity and limitations are discussed.
DCB; Fracture; Gc; Modelling; PVDF
Amputee socks: Thickness of multiple socks.
Prosthetics and orthotics international
2013
10.1177/0309364613506915
Background and aim:It is unclear how total sock ply and thickness are related when more than one sock is worn. The objectives were to determine whether the thickness of one multi-ply amputee sock of ply P was the same as the thickness of a stack of reduced-ply socks of total ply P, and whether the thickness of N single socks stacked one on top of the other was equal to the sum (1 to N) of the single sock thicknesses.Technique:Using a custom instrument, compressive stresses were applied while sock thickness was measured.Discussion:The thickness of one multi-ply sock of ply P was typically less than the thickness of a stack of reduced-ply socks of total ply P. The thickness of N single socks stacked one on top of the other was approximately equal to the sum (1 to N) of the single sock thicknesses.Clinical relevanceOur findings suggest three 1-ply socks to be 20% greater in thickness than one 3-ply sock, and one 3-ply + two 1-ply socks to be 30% greater in thickness than one 5-ply sock.
26 july 2013; 6 september 2013; accepted; date received; limb management; prosthetic fit; prosthetic socks; residual limb; volume accommodation
Statistical mechanics of complex networks
Reviews of Modern Physics
74
47–97
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Recent work in rock mechanics
Geotechnique
13
2
99-120
1962
Third Rankine Lecture. Rock mechanics as used by the civil engineer 10 years ago was already split into two phases: first, the measurement of the mechanical characteristics of rocks and, second, the application of the knowledge gained to different practical problems. The measures sought were: (i) the elastic modulus of the rock, and (ii) the stresses in the rock in situ. The elastic modulus was generally measured in the field by the jacking method. This, to my knowledge, was used for the first time, around 1935, by the Irrigation Department in Algeria. A jack was placed across a gallery, its foot against one wall and its head thrusting against the opposite wall, where the rock surface had been carefully dressed flat and true. The thrust of the jack was increased and the rock deformation measured and expressed as a function of the applied stress.
Rankine Lecture; Rock mechanics
Uncertainty relations of Statistical Mechanics
0910.2867
2009
Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum Mechanics. Such a complementarity is expressed as the impossibility of perform an exact simultaneous determination of the system energy and temperature by using an experimental procedure based on the thermal equilibrium with other system regarded as a measure apparatus (thermometer). In this work, we provide a simple generalization of this latter approach with the consideration of a thermodynamic situation with several control parameters.
FRACTURE MECHANICS OF SOLID PROPELLANTS.
Fract Mech, Symp on Nav Struct Mech, 10th
Washington
387-398
1978
This chapter discusses the application of quasi-static viscoelastic fracture mechanics to composite solid propellant and composite modified double-base (CMDB) propellant. Both types are used in modern case-bonded solid rockets. Generally speaking, these propellants consist of a soft matrix which is highly filled with hard particles of varying size. The average particle size in composite propellants is typically 0. 002-0. 005 inches, while in CMDB propellants it is approximately ten times greater. Another difference is the matrix in the former propellants is commonly a polyurethane or polybutadiene cross-linked rubber, while in the latter case it is nitrocellulose. In spite of these differences, their fracture behavior is quite similar.
FRACTURE MECHANICS - Applications; ROCKETS AND MISSILES
Statistical mechanics of complex networks
Review of Modern Physics
74
1-54
2002
Complex networks describe a wide range of systems in nature and society.\nFrequently cited examples include the cell, a network of chemicals\nlinked by chemical reactions, and the Internet, a network of routers\nand computers connected by physical links. While traditionally these\nsystems have been modeled as random graphs, it is increasingly recognized\nthat the topology and evolution of real networks are governed by\nrobust organizing principles. This article reviews the recent advances\nin the field of complex networks, focusing on the statistical mechanics\nof network topology and dynamics. After reviewing the empirical\ndata that motivated the recent interest in networks, the authors\ndiscuss the main models and analytical tools, covering random graphs,\nsmall-world and scale-free networks, the emerging theory of evolving\nnetworks, and the interplay between topology and the network's robustness\nagainst failures and attacks.
Statistical mechanics
Thin Capitalization Rules : An Anglo-American Comparison
International Tax Journal
24
2
36
1998
Focuses on the use of the thin capitalization rules in the Anglo-American countries of Australia, Canada, New Zealand, the United Kingdom and the United States, in relation to the specific recommendations concerning thin capitalization practices internationally. Definition of thin capitalization; Information on taxation policy choices for avoiding thin capitalization; Identification on the Anglo-American thin capitalization rules
Optical Properties of Thin Films
Optical Properties of Condensed Matter and Applications
297-323
2006
10.1002/0470021942.ch13
This chapter contains sections titled:\n\n* Introduction\n* Optics of thin films\n* Reflection–Transmission Photoellipsometry for Optical-Constants Determination\n* Applications of Thin Films to Energy Management and Renewable Energy Technologies\n* Conclusions\n* References
anisotropic films; electrochromic thin films; optical-constants determination; optical functional TiO2 thin film; reflection-transmission photoellipsometry; thin film application in energy management; thin film optics
Mechanics parameters deterioration laws of unloading rock mass by meso-damage mechanics
Zhongnan Daxue Xuebao (Ziran Kexue Ban)/Journal of Central South University (Science and Technology)
44
1
275-281
2013
Based on the meso-damage mechanics and unloading mechanics theories, the mechanics parameters of test stops on continuous mining pit No. 92 was taken as initial values, and the equivalent model of rock mass unloading was established by RFPA software. By calculating the step and continuous unloading of the equivalent model, the failure process and acoustic admission effect were studied, and the change curves and deterioration laws of unloading rock mass mechanics parameters were obtained. The result shows that by the unloading step 19, the unloading stress is 3.8 MPa, and the rock mass shows damage. The rock mechanical parameters, i.e. the internal friction angle, cohesion and the modulus of elasticity, show a gradual weakening trend, and the values are gradually decreased to 54%, 50% and 52% of the initial value. Poisson's ratio is gradually increased to the 1.16 times of the initial value. The rock mass mechanical parameters are deteriorated by unloading effect. The theoretical basis of dynamic analysis for mining mechanics response is provided by the fitted curves and of unloading rock mass mechanical parameters function of deterioration laws.
Of Quantum Mechanics
Analysis
3
1927
1-18
1986
The Dirac theory has a hidden geometric structure. This talk traces the concep- tual steps taken to uncover that structure and points out significant implications for the interpre- tation of quantum mechanics. The unit imaginary in the Dirac equation is shown to represent the generator of rotations in a spacelike plane related to the spin. This implies a geometric interpreta- tion for the generator of electromagnetic gauge transformations as well as for the entire electroweak gauge group of theWeinberg-Salam model. The geometric structure also helps to reveal closer con- nections to classical theory than hitherto suspected, including exact classical solutions of the Dirac equation.
General relativistic statistical mechanics
Phys. Rev. D
87
8
084055
2013
10.1103/PhysRevD.87.084055
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = hbar d tau/ds, with k the Boltzmann constant, hbar the Planck constant, ds proper time and d tau the equilibrium thermal time.
Determinism behind Quantum Mechanics
arXiv
12
2002
Contrary to common belief, it is not difficult to construct deterministic models where stochastic behavior is correctly described by quantum mechanical amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What is difficult however is to obtain a Hamiltonian that is bounded from below, and whose ground state is a vacuum that exhibits complicated vacuum fluctuations, as in the real world. Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. This may lead to a sufficiently complex vacuum state, and to an apparent non-locality in the relation between the deterministic ("ontological") states and the quantum states, of the kind needed to explain away the Bell inequalities. Theories of this kind would not only be appealing from a philosophical point of view, but may also be essential for understanding causality at Planckian distance scales.
Realism violates quantum mechanics
Science
5-8
2007
Recently, [{arXiv:0810.3134}] is accepted and published. We show that local realistic theories violate separability of $N$-qubit quantum states by a factor of $3^N$. Thus we have a violation factor of 3 when N=1. Realistic theories violate a proposition of a single qubit (a state with two-dimensional space) system, the Bloch sphere machinery of quantum mechanics. Our method uses the ratio of each of the scalar products. The maximal possible value of the scalar product in local realistic theories grows exponentially larger than one in $N$-qubit separable states when the number of qubits increases. We find the violation factor $3^N$ when the measurement setup is entire range of settings for each of the local observers.
Quantum Physics
THE MECHANICS OF WHOLESALING
Journal of Marketing
14
2
225-231
1949
The article presents information about the mechanics of the wholesaling process in the tobacco industry. The author describes the process of transforming raw materials into finished products such as cigarettes, cigars, and chewing tobacco and presents details related to the marketing and distribution of these commodities. Procedural information related to phases of the distribution process such as order processing, shipping, and replacement of inventory is presented. The importance of responsible sales personnel and a diverse line of merchandise is mentioned.
CONSUMER goods; DISTRIBUTORS (Commerce); INDUSTRIAL management; MARKETING; ORGANIZATIONAL structure; PHYSICAL distribution of goods -- Management; PRODUCTION engineering; SALES personnel; TOBACCO industry; WHOLESALE trade
General relativistic statistical mechanics
Physical Review D
87
8
084055--
4
Understanding thermodynamics and statistical mechanics in the fully general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the nonrelativistic limit but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer and is given by kT=ℏdτ/ds, with k the Boltzmann constant, ℏ the Planck constant, ds proper time and dτ the equilibrium thermal time.
Everything Old Is Thin Again.
Library Journal
126
17
20
2001
Article
Discusses how thin client technology could be used in libraries. Definition of a thin client as a computer terminal capable of running a color graphical interface, without a central processing unit; Stability of thin client units; Statement that thin clients are similar to an older technology known as dumb terminals; Advantages of thin client networks in libraries; Varieties and prices of thin clients, including Neoware Eon and Citrix Metaframe.
A study of the development of impact damage in cross-ply carbon fibre/PEEK laminates using acoustic emission
Composites Science and Technology
31
1
1-14
1988
http://dx.doi.org/10.1016/0266-3538(88)90073-5
Instrumented falling weight impact tests were performed on [0/90]10S laminates of carbon fibre/PEEK in order to investigate damage development. The specimens were afterwards subjected to four-point bending with acoustic emission monitoring (AE). In the impact tests a range of input energies were investigated (3·2 to 8·8 Joules) and it was observed that at 4·9 Joules the onset of delamination occurred. Ultrasonic C-scans of the impacted specimens confirmed this in a semi-quantitative manner. Replicate tests on other specimens also confirmed a delamination mechanism when they were sectioned for macroscopic examination with a dye-penetrant technique. In the bend tests this critical level of impact energy was associated with a sharp change in the evolution of AE under increasing load. At absorbed energies in impact, below that for the onset of delamination (4·9 Joules), the cumulative AE events count increased with load in the classical exponential manner. Above 4·9 Joules, where extensive damage was sustained, the exponential development at lower loads gave way, at a critical load, to a faster constant-rate evolution. This critical load, or displacement, which is defined as the ‘OCR’ point (Onset of Constant Rate AE), was dependent on the area of delamination damage in an inverse-type relationship. Bend tests on model specimens were performed in order to examine whether the transition in AE behaviour was associated with the relative movement between adjacent surfaces or the onset of crack growth at delaminations. Shorth-beam shear tests were also conducted in order to investigate the spread of crack in carbon fibre/PEEK, where little AE activity was observed up to an OCR point, which in turn coincided with the onset of shear delamination.
Experimental and theoretical characterization of structure in thin disordered films.
Acta Crystallographica A
55
Pt 2 Pt 1
178-187
1999
The electron microscope provides an ideal environment for the structural analysis of small volumes of amorphous and polycrystalline materials by enabling the collection of scattering information as a function of energy loss and momentum transfer. The scattered intensity at zero energy loss can be readily processed to a reduced density function, providing information on nearest-neighbour distances and bond angles. A method for collecting and processing the scattered intensity, which allows for the collection of an energy-loss spectrum for a range of momentum transfers, is discussed. A detailed structural determination from a reduced density function alone is difficult and it is shown that a more detailed structural model can be obtained by combining the experimental reduced density function with model structures obtained from molecular dynamics based on first-principles quantum mechanics. This method is applied to tetrahedral amorphous carbon, as an example of a monatomic network, and to aluminium nitride, as a prototype for a binary amorphous alloy.
Off lattice anomalous diffusion in a thin sticks system
Physica a-Statistical Mechanics and Its Applications
312
1-2
35-49
2002
An off lattice Monte Carlo simulation of a diffusion process through a random sticks network in two dimensions is presented in this paper. The statistical properties of the hindered motion are analysed according to the geometric characteristics and concentration of obstacles, here represented by randomly disperse segments parallel to one another. In particular, short and long time behaviour of the mean square displacements are considered with respect to the type of interactions between the tracer and the sticks. The diffusion coefficient is estimated and a power law dependence on the obstacle length is determined. Finally, an application of the present results to experimental data of diffusion processes in inhomogeneous media is discussed. (C) 2002 Elsevier Science B.V. All rights reserved.
dependence; diffusion; equation; fractional diffusion; gas-diffusion; Monte Carlo simulations; partially crystalline polymers; porous-media; random processes; relaxation; single-particle tracking; temperature; transport
Stress-Analysis of Thin Polyimide Films Using Holographic-Interferometry
Experimental Mechanics
31
2
178-184
1991
It is proposed that the residual stresses due to curing in a spin-coated polyimide film can be determined using the solution to the problem of a vibrating membrane. The membrane is biaxially constrained and supported on a metal washer or copper substrate. A piezoelectric transducer is used to excite the sample. The membrane vibrates uniformly in response to its resonant frequencies. The vibration pattern is recorded using time-average holographic interferometry. The pattern produced is indicative of the mode of vibration. The biaxial stress in the film can be calculated from measuring the characteristic frequency, the density of the material, and the mode of vibration. The effect of mass loading of air on the apparent stress in these membranes is also investigated. Measurements made in vacuum appear to resolve this problem. The stresses calculated are on the order of 10 MPa.
Nonlinear Flow of Wave Crests Past a Thin Pile
Journal of the Waterways Harbors and Coastal Engineering Division
102
4
365-377
1973
The measured pattern of peak water line around a vertical circular pile in periodic wave action can disagree with wave-scattering theory, showing a nonlinear dependence on incident wave height when the pile radius is very small compared to the wavelength. The peak water line was measured around piles of several diameters in relatively shallow water with various incident laboratory waves. Features of the patterns indicate that a disturbance like a ship’s bow wave forms during peak crest flow when a certain Froude number, incident crest velocity head divided by pile radius, becomes large, on the order of 0.1 - 1.0. The laboratory tests shoudl reproduce basic flow effects in situations of coastal and ocean engineering interest, because field and lab situations have the same Froude number, implying geometric flow similarity.
Coastal engineering; Head (fluid mechanics); Hydraulics; Ocean engineering; Piles; Surface properties; Wave power; Wave propagation; Wave runup; Waves
Drying mechanics of gels
Third International Conference on Ultrastructure Processing of Ceramics, Glass, and Composites. Abstracts
21
1987
A model has been developed to describe the stresses and strains that develop during drying of a gel. It is assumed that contraction is driven by interfacial energy, and the strain rate is controlled by the viscosity of the solid phase and by the rate of flow of liquid in the pores. In the early stages of drying, the stress is found to be directly proportional to the drying rate and inversely proportional to the permeability. The magnitude of the stress is dependent on the shape of the gel, decreasing in the order: plate greater than cylinder, greater than sphere. The model predicts that when a plate is dried by evaporation from only one side, it will become first concave up, then concave down. This is consistent with our experimental observations.
ceramics (objects); drying; gel; glass (material); mechanics (physics)
Exactly Solvable Quantum Mechanics
The Universe
2
2
2-32
2014
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.
Valleys in quantum mechanics
Physics Letters B
424
1-2
93–100
1998
Conventionally, perturbative and non-perturbative calculations are performed independently. In this paper, valleys in the configuration space in quantum mechanics are investigated as a way to treat them in a unified manner. All the known results of the interplay of them are reproduced naturally. The prescription for separating the non-perturbative contribution from the perturbative is given in terms of the analytic continuation of the valley parameter. Our method is illustrated on a new series of examples with the asymmetric double-well potential. We obtain the non-perturbative part explicitly, which leads to the prediction of the large order behavior of the perturbative series. We calculate the first 200 perturbative coefficients for a wide range of parameters and confirm the agreement with the prediction of the valley method.
Dentists versus auto mechanics: are there ethical differences?
The Journal of the American College of Dentists
80
2
25-31
2013
The different ethical perspectives of dentists and auto mechanics include primary concern, billing procedures, advertising, emergency care, the level of autonomy granted to their patients/ clients, the amount of disclosure given to their patients/clients, the ability to judge the work of others, and the freedom to pursue romantic relationships with their patients/clients. In analyzing these differences, one finds dentists to have much greater ethical obligations than auto mechanics. There are subtle differences between the ethical expectations of Canadian and United States dentists.
Advertising as Topic; Advertising as Topic: ethics; Canada; Deception; Dentists; Dentists: ethics; Fees, Dental; Fees, Dental: legislation & jurisprudence; Humans; Mechanics; Occupations; Occupations: ethics; Practice Management, Dental; Practice Management, Dental: ethics; Professional Role; Students, Dental; United States
Spreadsheet analysis of fluid mechanics problems
Frontiers in Education 1997 - 27th Annual Conference, Proceedings, Bols I - Iii
1334-1337
1997
This paper presents a study to obtain solutions to some fluid mechanics problems by spreadsheet analysis. By utilizing some of the many features available in spreadsheets, which are increasingly gaining popularity in the industry and academia, different aspects of fluid flow problems can be easily and graphically examined. It has been successfully used to study a majority of topics covered in a typical undergraduate fluid mechanics textbook. Some of the topics covered were determination of hydrostatic pressure and forces, buoyancy and stability, Bernoulli's equation and open channel flow. The spreadsheet solutions provided a simple means to solve fluid mechanics problems and proved to be effective tool in teaching undergraduate technology students.
Teaching reform on the soil mechanics and foundation
Measurement Technology and its Application III
568-570
1947-1950
2014
10.4028/www.scientific.net/AMM.568-570.1947
The soil mechanics and foundation is a course with strong theoretical and practical features. Based on the possible problems in the teaching process, the author provided some considerations and suggestions such as transforming teaching concept, strengthening the systematicness of the teaching content, electing textbook and improving teaching method, increasing the interest of student, valuing the practical teaching link. A series of inside and outside tests at school were introduced to help the student master knowledge in all aspects. (2014) Trans Tech Publications, Switzerland.
Materials; Mechanics; Soil mechanics
Fundamental disagreement of wave mechanics with relativity
Physics Essays
15
1
87-100
2002
10.4006/1.3025514
A number of well-known difficulties in physics resulted from merging the theory of relativity with the Compton-de Broglie wave mechanics. Two such problems were the failure of Dirac's relativistic wave equation to predict the correct velocity of the electron, and the fact that the measured yield from nuclear fission was found to be substantially less than the theoretical yield. It is shown that the origin of these and other problems stem from the inconsistency of the relativistic mass-energy equivalence principle with the fundamental assumptions of wave mechanics. An alternative view of the concept of mass-energy equivalence that results in a very good agreement between theory and experiment is demonstrated. The conclusions of this paper will be quite important for ongoing research, such as the current problem of the neutrino's mass.
Beta decay; Nuclear fission; Relativistic wave equation; Special relativity; Wave mechanics
Analysis of soil erosion based on mechanics
Soil Erosion and Dryland Farming
635-642
2000
Taking fluid and soil mechanics as the theoretical basis, this paper analyzes the mechanism of soil erosion based on mechanics. Fluid flow applies a shearing force to the soil surface, while the soil has a resisting structural force. Most erosion research studies only consider the forces in erosion-striking force by raindrops, shearing force by runoff, soil structure force, driving force by runoff and frictional force by loose soil grains. When the striking force and shearing force exceed the limiting value of the soil structure force, soil structure will be destroyed, and soil erosion will occur. The soil erosion mechanics analysis is an effective and direct method to study soil erosion mechanisms and has important theoretical and practical significance for studying and controlling soil erosion.
Multiscale analysis of cancer cell mechanics
2014 40th Annual Northeast Bioengineering Conference (NEBEC)
1-2
2014
10.1109/NEBEC.2014.6972864
Physiological phenomena occur in complex 3D environments. However, the mechanics of cells in 3D under relevant conditions such as flow and chemical signals are not well understood. These mechanics can have important implications in pathological events such as cancer metastasis, where cancer cells undergo transformations that enable invasive behavior across constrictive physiological barriers. In our work, we have taken an integrated computational and experimental approach to establish a multiscale understanding of the fundamental mechanical properties of cancer cells in native-like conditions.
biomechanics; cancer; Cancer; cancer cell mechanics; cancer cell transformations; cancer metastasis; cellular biophysics; chemical signals; complex 3D environments; Computational modeling; Computer architecture; constrictive physiological barriers; flow signals; integrated computational approach; invasive behavior; mechanobiology; microfluidics; Microfluidics; Microprocessors; multiscale analysis; native-like conditions; pathological events; physiological phenomena; Physiology; Three-dimensional displays
Principles and Dynamics of Quantum Mechanics
arXiv
2009
Title: . Authors: Efthimiades, Spyros. Publication: eprint arXiv:0904.0960. Publication Date: 04/2009. Origin: ARXIV
dynamics; quantum
Note on plane wave quantum mechanics
Physics Letters B
565
253-265
2003
10.1016/S0370-2693(03)00758-5
We study the quantum mechanics of BMN operators with two scalar impurities and arbitrarily many traces, at one loop and all genus. We prove an operator identity which partially elucidates the structure of this quantum mechanics, provides some support for a conjectured formula for the free all genus two-point functions, and demonstrates that a single O(g_2^2) contact term arises in the Hamiltonian as a result of transforming from the natural gauge theory basis to the string basis. We propose to identify the S-matrix of this quantum mechanics with the S-matrix of string theory in the plane-wave background.
High Energy Physics - Theory
On the phenomenological aspects of damage mechanics
Modelling Measurement & Control B: Solid & Fluid Mechanics & Thermics, Robotics Mechanical Systems, Civil Engineering
72
5
25-39
2003
It is a well know and documented fact that it is very difficult to give clear definition of a mechanical damage variable. It is also a known fact that there is almost no distinction or differences (macroscopically) between a highly damaged volume element and a virgin volume element. In this paper, we present a note on the phenomenological aspects of damage mechanics. We survey the theory surrounding the variables which are of course representatives of the deteriorate state of the matter
continuum mechanics
Stochastic computational fluid mechanics
Computing in Science & Engineering
9
2
21-29
2007
Stochastic simulations in computational fluid dynamics let researchers model uncertainties beyond numerical discretization errors. The authors present examples of stochastic simulations of compressible and incompressible flows and provide analytical solutions for verifying these newly emerging methods for stochastic modeling.
differential-equations; generalized polynomial chaos; integration
Fluid Mechanics
Academic Press
80
1
766
2002
For many researchers, next generation sequencing data holds the key to answering a category of questions previously unassailable. One of the important and challenging steps in achieving these goals is accurately assembling the massive quantity of short sequencing reads into full nucleic acid sequences. For research groups working with non-model or wild systems, short read assembly can pose a significant challenge due to the lack of pre-existing EST or genome reference libraries. While many publications describe the overall process of sequencing and assembly, few address the topic of how many and what types of reads are best for assembly. The goal of this project was use real world data to explore the effects of read quantity and short read quality scores on the resulting de novo assemblies. Using several samples of short reads of various sizes and qualities we produced many assemblies in an automated manner. We observe how the properties of read length, read quality, and read quantity affect the resulting assemblies and provide some general recommendations based on our real-world data set.
Cell Mechanics
Methods In Cell Biology
83
07
3-27
2007
10.1016/S0091-679X(07)83001-9
Many cellular processes lead to changes in elastic and viscous properties of cells. Rheology is the science that deals with deformation and flow of materials. Fundamental rheologic concepts are explained, and some of the main techniques are discussed. Nonperturbing oscillatory techniques are especially useful for monitoring structure formation including gelation, whereas other techniques such as steady shear flow and creep are useful for determining flow properties. Sample preparation is often a major obstacle, and advantages of different deformation geometries are discussed. Simple biological samples such as purified biopolymers can be investigated with a range of rheologic techniques, and factors affecting gelation of, for example, blood or cytoskeletal proteins can be studied in detail. More complex biological systems such as intact tissues can often only be studied with more qualitative techniques and results. With proper choice of experimental setup, rheologic techniques can give valuable information about cellular systems and dynamics on a timescale that is closely related to biological functions.
Cell Mechanics
Methods in cell biology
83
89-111
2007
10.1016/S0091-679X(07)83005-6
Engineering of the cellular microenvironment has become a valuable means to guide cellular activities such as spreading, motility, differentiation, proliferation, or apoptosis. This chapter summarizes recent approaches to surface patterning such as topography and chemical patterning from the micrometer to the nanometer scale, and illustrates their application to cellular studies. Particular attention is devoted to nanolithography with self-assembled diblock copolymer micelles that are biofunctionalized with peptide ligands-a method that offers unsurpassed spatial resolution for the positioning of signaling molecules over extended surface areas. Such interfaces are defined here as "nano-digital surfaces," since they enable the counting of individual signaling complexes separated by a biologically inert background. The approach enables the testing of cellular responses to individual signaling molecules as well as their spatial ordering. Detailed consideration is also given to the fact that protein clusters such as those found at focal adhesion sites represent, to a large extent, hierarchically organized cooperativity among various proteins.
Animals; Cell Adhesion; Fibroblasts; Fibroblasts: cytology; Fibroblasts: ultrastructure; Gold; Hela Cells; Humans; Mice; Micelles; Nanostructures; Nanotechnology; Nanotechnology: methods; Osteoblasts; Osteoblasts: cytology; Polymers; Receptors, Cell Surface; Receptors, Cell Surface: metabolism; Tissue Engineering
MOLECULAR MECHANICS CALCULATIONS OF CONFORMATIONAL
Journal of Molecular Structure: THEOCHEM
106
3-4
333-353
1984
10.1016/0166-1280(84)85038-1
Results of molecular mechanics (MM) calculations of conformational structures, energies, barrier heights and torsional force constants in halogen substituted propenes, 1,3-butadienes and biphenyls are given. These reproduce reasonably well experimental gas-phase data on these compounds. Potential parameters for the non-bonded interaction terms halogen ⋯ C(sp2) and C(sp2) ⋯ C(sp2) have been included for the first time within the Morse formulation.
Quantum Mechanics in a Rotating Frame
arXiv
8
2003
The rotating frame is considered in quantum mechanics on the basis of the position dependent boost relating this frame to the non rotating inertial frame. We derive the Sagnac phase shift and the spin coupling with the rotation in the non relativistic limit by a simple treatment. By taking the low energy limit of the Dirac equation with a spin connection, we obtain the Hamiltonian for the rotating frame, which gives rise to all the phase shifts discussed before. Furthermore, we obtain a new phase shift due to the spin-orbit coupling.
Quantum Mechanics in Phase Space
Arxiv.org
1-15
2011
10.1142/S2251158X12000069
Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.
Quantum Mechanics in Phase Space
Reports on Mathematical Physics
19
3
1-15
2011
Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known much less generally accepted until the late 20th century.
2A3D Mechanics of Materials ( II )
Studies in health technology and informatics
152
Ii
13-26
2010
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
Biocompatible Materials; Biocompatible Materials: chemistry; Biological; Biomechanics; Biomedical Engineering; Chemical; Models; Physics
Life Prediction of Composite Pressure Vessels Using Multi-Scale Approach
Proceedings of the Asme Pressure Vessels and Piping Conference 2010, Vol 6, Pts a and B
1179-1185
2010
A multi-scale fatigue life prediction methodology of composite pressure vessels subjected to multi-axial loading has been proposed in this paper. The multi-scale approach starts from the constituents, fiber, matrix and interface, leading to predict behavior of ply, laminates and eventually the composite structures. The life prediction methodology is composed of two steps: macro stress analysis and micro mechanics of failure based on fatigue analysis. In the macro stress analysis, multiaxial fatigue loading acting at laminate is determined from finite element analysis (FEM) of composite pressure vessel, and ply stresses are computed using a classical laminate theory (CLT). The micro-scale stresses are calculated in each constituent (i.e. matrix, interface, and fiber) from ply stresses using a micromechanical model. Micromechanics of failure (MMF) was originally developed to predict the strength of composites and now extended to prediction of fatigue life. Two methods are employed in predicting fatigue life of each constituent, i.e. an equivalent stress method for multi-axially loaded matrix, and a critical plane method for the interface. A modified Goodman diagram is used to take into account the generic mean stresses. Damages from each loading cycle are accumulated using Miner's rule. Each fiber is assumed to follow a probabilistic failure depending on the length. Using the overall micro and macro models established in this study, Monte Carlo simulation has been performed to predict the overall fatigue life of a composite pressure vessel considering statistical distribution of material properties of each constituent and manufacturing winding helical angle.
unidirectional composite
Shear-lag analysis of notched laminates with interlaminar debonding
Engineering Fracture Mechanics
22
6
1013-1029
1985
This study considers a method of analysis for predicting the fracture behavior of a notched, unidirectional lamina in the presence of surface constraint layers with debonding between the unidirectional ply and the constraint layers. Two particular cases are presented, the first being a debonded zone of finite width with no longitudinal damage in the unidirectional ply. This solution is then extended to include longitudinal matrix yielding and splitting in the unidirectional ply at the crack tip. The analysis is based on a materials modeling approach using the classical shear-lag assumption to describe the shear transfer between fibers. The fracture behavior of the laminate is studied as a function of initial crack length, the relative physical and geometric properties of the constraint plies and the unidirectional lamina, and width of the debonded zone. The results indicate that debonding can reduce the maximum fiber stress at the crack tip on the order of ten percent. This effect is maximum for a debond width of two or three fiber spacings and is independent of the initial crack length. As the debond width grows beyond this point, the maximum stress increases. For widths of about ten fiber spacings or more, the maximum fiber stress is larger than for the fully bonded case. In the presence of longitudinal matrix damage the same general behavior is found; however, the location of the maximum fiber stress is quite complex. In some cases with large matrix damage and a high constraint ratio, the maximum fiber stress can occur at the end of the debonded zone away from the crack tip. © 1985.
COMPOSITE MATERIALS; DEBONDED ZONE; LAMINATED PRODUCTS - Fracture; LONGITUDINAL MATRIX DAMAGE; MAXIMUM FIBER STRESS; NOTCHED COMPOSITE LAMINATES; STRESSES - Shear
Orthodox Quantum Mechanics Free from Paradoxes
Arxiv Preprints
21
2005
A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.
Chapter One Classical and Relativistic Mechanics
Interface Science and Technology
Volume 15
1-78
2008
http://dx.doi.org/10.1016/S1573-4285(07)00001-4
Publisher Summary This chapter discusses the classical and relativistic mechanics. Mechanics is part of field theory and generally concerned with the statics and dynamics of any material body or medium. The theory of relativity, as the name purports, deems the concept of absolute motion as physically un-meaningful. Its special version appeared immediately as the best candidate for conciliating electromagnetism to gravitation and, in particular, for the unification of electromagnetic phenomena. Classical mechanics was developed into two complementary views, vectorial and analytical. The first isolates the particles, modeled as they were individual, and makes direct use of Newton's second law of motion. Accordingly, one should be able to separate each resultant particle force, and proceed with solving the associated differential equations.
Quantum Mechanics in Probabilistic in Nature
Journal of Mind and Behavior
1993
Elitzur (1991) maintained that my version of Schrodinger's cat gedankenexperiment does not provide the basis for demonstrating the effect of consciousness on the course of the physical world. The nature of the difference between Elitzur's and my views concerning the gedankenexperiment is discussed, and the key to this difference concerns the fundamentally probabilistic nature of quantum mechanics. Elitzur has failed to see that in quantum mechanics consciousness fundamentally is that through which the physical world is known. Elitzur's characterization of my thesis concerning consciousness and human observation a reflecting radical idealism is discussed. A second gedankenexperiment is noted in which the observer's circumstance, other than the time of measurement, is also a variable and which tests whether or not mind, or consciousness, has an impact on the course of the physical world.
Idealism; Metaphysics; Nature; Quantum Mechanics; Science
The statistical origin of quantum mechanics
0810.2394
2008
It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability. The third is energy conservation in the mean. The fact that Schroedinger's equation may be derived from these premises, which are all purely statistical in character, is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics.
Optimal cuts in graphs and statistical mechanics
Mathematical and Computer Modelling
26
1-11
1997
10.1016/S0895-7177(97)00195-7
We survey well known problems from statistical mechanics involving optimal cuts of graphs. These problems include finding the ground states for the spin glass problem or for the random field Ising model, as well as finding the lowest energy barrier between the two ground states of a ferromagnet. The relations between the results in graph theory and in physics are outlined. In particular, the solvability of a special max cut problem which arises in statistical mechanics is an easy consequence of a gauge invariance. Throughout the paper, we review some useful algorithms and results. We also give a simple solution of the cutwidth problem in the case of a regular tree.
Discrete optimisation; Ground state properties; Optimal cuts; Statistical mechanics
Fracture-Mechanics of Microcrystalline Cellulose Powders
International Journal of Pharmaceutics
66
1-3
143-148
1990
A fracture mechanics approach has been successfully applied to determine K(IC), the critical stress intensity factor and a measure of brittleness of materials, using notched beam specimens in four point flexure testing. Seven chemically equivalent microcrystalline cellulose samples have been examined and, based on determined values of K(IC), all samples have been classified as semi-brittle with respect to crack propogation and fracture mechanics. The generally minor differences found in K(IC) values between different suppliers and grades are attributed to alternative processing conditions and variations in solid-state properties.
4-point beam; bending; critical; fracture mechanics; microcrystalline cellulose powder; notched beam specimen; stress intensity factor
Conformal Field Theory and Statistical Mechanics
arXiv
cond-mat.s
2008
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
cond-mat.stat-mech; hep-th
Using concept questions in teaching mechanics
International Journal of Mathematical Education in Science and Technology
22
5
749-157
1991
10.1080/0020739910220506
It has for some time been recognized that many sixth form students have great difficulty assimilating the fundamental concepts in mechanics, instead developing their own alternative conceptions. This paper first summarizes the current state of sixth form students understanding of mechanics, as revealed by recent research, describing a framework into which students approaches to problems fit. It then moves on to describe how simple concept problems can be used to challenge students alternative conceptions and improve understanding of mechanics. These problems require a qualitative approach that promotes student discussion and highlights the deficiencies of students alternative conceptions, leading to a need for the students to revise their original ideas.
DMD/sup TM/ pixel mechanics simulation
Texas Instruments Technical Journal
15
3
64-74
1998
Great strides in Digital Imaging's (DI) theoretical simulation of digital micromirror device/sup TM/ (DMD(TM)) pixel mechanics have occurred over the past two years, culminating in a customized TI-proprietary DMD pixel simulation tool (DMDPST) that is on the leading edge of microelectromechnnical-systems (MEMS) modeling. This publication covers the following topics as they pertain to the DMDPST: development history, requirements for effective simulation, experimental-theoretical calibration methods, critical roles in DI and detailed illustrative examples of some of its capabilities.
Calibration; Calibration methods; Customized TI-proprietary DMD pixel simulation too; Digital Imaging; Digital micromirror device; DMD/sup TM/ pixel mechanics simulation; Electromechanical effects; mems; Microelectromechnnical systems modeling; Micromechanical devices; Mirrors; Pixel mechanics; Smart pixels; Theoretical simulation
Relativistic viscoelastic fluid mechanics
Physical Review E
84
2
2011
Artn 026316\rDoi 10.1103/Physreve.84.026316
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
irreversible-processes; reciprocal relations; thermodynamics
Red blood cell mechanics.
Journal of the Indian Medical Association
109
9
668-70, 682
2011
During the 120-day life span, the erythrocyte undergoes excessive passive deformation. Cell shape, cytoplasmic viscosity and membrane deformability and stability are key features in red cell deformability. These three cellular components are described in a nutshell in this review article.
Blood Viscosity; Blood Viscosity: physiology; Cytoplasm; Cytoplasm: physiology; Erythrocyte Deformability; Erythrocyte Deformability: physiology; Erythrocyte Membrane; Erythrocyte Membrane: physiology; Humans
Statistical Mechanics of Dictionary Learning
Arxiv preprint
4
2012
Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.
Statistical Mechanics of Dictionary Learning
Europhysics Letters
28008
2-5
2012
10.1209/0295-5075/103/28008
Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.
Statistical-Mechanics in Ecological Hierarchies
Mathematical and Computer Modelling
14
699-704
1990
A statistical mechanical approach to the properties of ecological hierarchies is discussed, with particular reference to the non-equilibrium ("intermediate disturbance") view of the nature of certain ecological communities. A notion of statistical equilibrium for such systems is described, and the effect of transient perturbations from this equilibrium (i.e. "intermediate disturbances") considered, both in their short and long term effects.
community structure; hierarchy; statistical mechanics; transient perturbation
Quantum Mechanics in Phase Space
Asia Pacific Physics Newsletter
1
1
37
2012
Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and José Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known — much less generally accepted — until the late 20th century.
Quantum Mechanics in Phase Space
Asia Pacific Physics Newsletter
01
01
37
2012
10.1142/S2251158X12000069
Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.
Tensor coordinates in noncommutative mechanics
Journal of Mathematical Physics
50
1-7
2009
10.1063/1.3119005
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly used, and the object of noncommutativity ${\mathbf \theta}^{ij}$ plays a fundamental rule as an independent quantity. The presented classical theory, as its quantum counterpart, is naturally invariant under the rotation group $SO(D)$.
Mechanics of Materials and Structures
JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES
7
1
45-84
2012
Damage growth in composites involves complex and progressive failure modes. Current computational tools are incapable of predicting failure in composite materials mainly due to their mathematical struc- ture. However, peridynamic theory removes these obstacles by taking into account nonlocal interactions between material points. This study presents an application of peridynamic theory to predict how damage propagates in fiber-reinforced composite materials subjected to mechanical and thermal loading condi- tions.
Materials classification for fine mechanics
Precision {E}ngineering
11
4
203 209
1989
Materials selection processes consider not only the basic properties\nof materials but also products and ratios of groups of properties.\n{T}his paper explores which groups might be used generally as the\nbasis for classifying materials according to their performance in\ndifferent application areas of precision mechanics and discusses\nhow the data can be efficiently presented. {T}he approach is illustrated\nby considering a selection of materials often used in precision designs.
Damage Mechanics in Engineering Materials
Studies in Applied Mechanics
46
275-286
1998
10.1016/S0922-5382(98)80047-0
An axisymmetric thermomechanical constitutive model is proposed for airfield concrete pavement under very rapid heating and cooling processes due to high-temperature exhaust gas from axisymmetric vectored thrust engines. Newman's crack growth model is applied to estimate the delamination (thermal spalling) time of the airfield concrete pavement at various locations due to the internal pore pressure. Furthermore, coupled heat and mass transfer in concrete pavement is considered.
Statistical Mechanics of Dictionary Learning
Arxiv
4
2012
Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.
I. 2. Mechanics of Materials
Basic Engineering for Medics and Biologists: An …
152
13-26
2010
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
Biocompatible Materials; Biocompatible Materials: chemistry; Biological; Biomechanics; Biomedical Engineering; Chemical; Models; Physics
Existence of trajectories for Bohmian mechanics
International Journal of Theoretical Physics
32
12
2245-2251
1993
10.1007/BF00672996
We discuss the problem of global existence and uniqueness of Bohmian mechanics, focusing on the role played by the quantum probability flux. The relation to the self-adjointness of the Hamiltonian is alluded to.
Curve fitting technique in soil vehicle mechanics
Journal of Terramechanics
1
2
44-55
1964
10.1016/0022-4898(64)90064-3
It is pointed out that the fitting of experimental curves with those described by a chosen form of equation is an important part of soil vehicle mechanics. Various contemporary methods of doing this are reviewed and shown to be inadequate. A new simple method is proposed for certain types of equation.
Phase-Space Dynamics and Quantum-Mechanics
Theoretica Chimica Acta
81
4-5
329-337
1992
In a recent paper Deal has postulated a new dynamical equation for quantum mechanical phase-space distribution functions. We analyze the new equation and show that it may be related to the traditional standard and antistandard phase-space representations of quantum mechanics. A brief review of these and other representations is also given.
1675; Correspondence Rules; Phase-Space Dynamics; Quantum Theory; Schrodinger Equation
Measures and mismeasures of the applied mechanics literature
Technological Forecasting and Social Change
31
4
323-333
1987
A 1975 study of the archival literature of applied mechanics showed it to be following a classic growth pattern for a scientific field. The present study, with ten years' additional data, tests some extrapolations of the 1975 data and finds them wanting. How such well-behaved data can prove unreliable for forecasting is explored.
Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory
Journal of Physics: Conference Series
6
6
2007
10.1088/1742-6596/67/1/012035
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.
Characterization of mechanical properties of thin films using nanoindentation test
Mechanics of Materials
38
12
1182-1198
2006
Using finite element modeling (FEM), this work investigates using finite element modeling (FEM) the mechanical behavior of film on substrate composites during the penetration of a rigid tip. In order to understand the magnitude of the substrate effect, the difference of strain gradient through the thickness of a given layer, deposited first on a softer substrate and then on an harder substrate can be observed. In this specific case, up to a critical ratio (h/t) = 0.35 (with h the indentation depth and t the film thickness), the mechanical behavior of the layer is quite similar. But, for h/t > 0.35, two different behaviors may be observed: (i) in the first case Hf/HS [less-than or equal to] 1 (with Hf and HS, respectively, the film and substrate hardness values), the total strain remains contained within the film thickness up to a ratio h/t close to 1 and (ii) in the second case Hf/HS greater than or equal 1, the total strain extends deeply into the substrate. These results show that the empirical 10% rule is not valid, even for a hard film on a softer substrate. The main error is caused by a wrong estimation of the contact depth between the indenter tip and the film surface. Indeed, the simulation runs exhibit the formation of pile-up depending on the ratios (h/t) and Yf/YS (with Yf and YS, respectively, the film and substrate yield stress values). As a function of the used model for calculating the contact depth, at least three variation of hardness may be found from load-displacement curves obtained by FEM. In these conditions, it seems ambiguous to try to determine a weighting function to extract meaningful mechanical properties of the thin film. Another way to determine film properties consists in using the loading phase. A relationship between the applied load (P) and the indentation depth (h) is studied during the loading phase. For the case of a soft film on harder substrate (Hf/HS [less-than or equal to] 1), it is possible to determine the yield stress of the film, from the previous relationship. This approach is applied to experimental amorphous Al2O3 films formed by electron beam evaporation on silicon substrate. © 2006 Elsevier Ltd. All rights reserved.
Deposition; Electron beams; Evaporation; Finite element method; Hardness; Indentation; Nanotechnology; Thin films
Contact stress and deformation of a thin elastic layer
The Quarterly Journal of Mechanics and Applied Mathematics
4
1
94-105
1951
10.1093/qjmam/4.1.94
The rollers used in drafting textile fibres are disk-shaped, the lower one made of steel, the upper with a metal centre and a fairly thin elastic cover. The length over which the rollers are in contact, and the pressure distribution over this length, are factors which affect their performance as drafting agents. The purpose of this paper is to show how these quantities vary with the material and thickness of the cover, the pressure between the rollers, anil the roller size. The effect of allowing slippage at the inner boundary is also considered.The system can be considered mathematically as one of generalized plane stress in an elastic layer, with given displacement conditions on its inner boundary (the interface between metal and cover will be termed the ‘inner boundary’ of the cover) and subject to pressure by a body of given shape on its free face. The layer is sufficiently thin for the inner boundary conditions to affect the stresses in the contact zone.The analysis of contact stresses was first carried out by Hertz (1), and quoted in Love (2). The application to the two-dimensional case is given by Thomas and Hoersch (3)—their results, which are for plane strain, may be converted by the usual modification of the Poisson's ratio to those of generalized plane stress. These analyses, however, only hold if the contact stresses are the only effective forces over the contact zone.The effect of the boundary conditions on the bolution for a single isolated force may be found straightforwardly by a method given in Coker and Filon (4). The displacement due to any pressure distribution over the contact zone can then be determined, and the actual pressure distribution may be found by imposing the condition of known displacement over this zone. It has been found most convenient, in practice, to determine the difference between the pressure distributions for an infinite and finite thickness; this difference can be expressed as a Fourier series, and a sufficient number of the coefficients can be found to give any desired accuracy.
Mechanics of the Left-Ventricle
Biophysical Journal
39
3
279-288
1982
A theory is presented for the mechanics of the left ventricle. A linear continuum description of the myocardium is developed, which incorporates anisotropic elastic effects due to the fiber direction field. The relation between fiber tension and fiber strain contains a time-dependent activation function that drives the ventricle around its cycle. The theory is applied to a simplified geometry consisting of a thick-walled finite cylinder in which fibers spiral on helical paths and terminate on planar end surfaces. The helix pitch angle varies continuously through the wall. The ventricular cycle is analyzed by specifying the pressures at which the aortic and mitral valves open and close. Key quantities are tabulated which permit a simple determination of the properties of the model under changes of wall thickness, fiber angles, muscle parameters, preload, afterload, etc. It is shown how the active muscle parameters can be inferred from a measurement of the end systolic pressure-volume line.
left ventricle; LEFT-VENTRICLE; MECHANICS
Irreversibility in Classical Mechanics
Physics
15
2006
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to describe of the non-potential interaction of a systems. The procedure of splitting of a system into equilibrium subsystems, presentation of subsystem's energy as the sum of energy of their relative motion and their internal energy was the basis of the approach which was used for the analysis of nonequilibrium systems. As a results the generalized Liouville equation and equation of subsystems interaction was obtained. Based on these equations, the irreversible transformation of energy of the relative motion of subsystems into their internal energy was proved. The formula which expresses the entropy via the work of subsystems' interaction forces was submitted. The link between classical mechanics and thermodynamics was discussed.
Classical Physics; General Physics
Nonequilibrium Statistical Mechanics
StatMechBook
1998
10.1007/978-94-017-2438-8
The statistical mechanics of J. C. Maxwell and L. Boltzmann is for dy- namical processes in dilute monatomic gases and is based on the evolution equation-kinetic equation-for the singlet distribution function. Starting from the basic ideas of Maxwell and Boltzmann on the statistical treat- ment of systems of many particles, J. W. Gibbs synthesized a general for- mal theory of statistical mechanics, at least, for equilibrium phenomena which covers all states of aggregation of matter. This equilibrium ensem- ble theory of Gibbs-statistical thermodynamics-is a deductive approach based on a set of postulates which aims to give the thermodynamics of reversible processes-equilibrium thermodynamics-a molecular represen- tation. It does succeed in the attempt because the mathematical structure of the phenomenological theory of reversible thermodynamic processes is well founded on the thermodynamic laws through the concept of entropy enunciated by R. Clausius. The generalization achieved by the Gibbs the- ory, however, came with a cost since the theory, with no kinetic equation, is limited to equilibrium phenomena and the underlying thermodynamics is necessarily that of reversible processes.
Temperature-curvature relationships in asymmetric angle ply laminates by considering the effects of resin layers and temperature dependency of material properties
Journal of Composite Materials
48
9
1071-1089
2013
10.1177/0021998313482155
It is well-known that asymmetric composite laminates can have bi-stable response to different kind of loadings. In this research, the non-linear temperature-curvature relationship for the asymmetric composite laminates is studied using Rayleigh-Ritz technique. Attention is focused on studying the effect of material temperature dependency and resin layers; especially in the bifurcation point by use of analytical method. To this end, the well-known analytical theories are extended and used to consider the temperature dependency of material. The results obtained from the theory are then compared with the finite element simulations results and a good correlation is obtained. Finally, an experimental investigation is carried out and several specimens with [90/0]T, [60/-30]T and [30/-30]T compositions were manufactured. In order to study the effect of resin layers, optical microscopy is utilized and the exact thickness of different layers in the manufactured specimens is determined. The thermal responses of the manufactured plates were measured and used to validate the results obtained from the analytical theory and finite element simulations.
Potential of functional image processing technique for the measurements of contact area and contact pressure of a radial ply tire in a soil bin testing facility
Measurement
46
10
4038-4044
2013
10.1016/j.measurement.2013.07.019
Abstract\nThe exploration principally deals with a promising applicability of image processing method for contact area determination. A digital camera mounted on a single-wheel tester was utilized to take images of contact area at four levels of tire inflation pressure (i.e. 70, 100, 140, and 175 kPa) and six levels of wheel load (i.e. 0.75, 1.75, 2.75, 3.75, 4.75, and 5.75 kN). Contact pressure measurements, subsequently, were performed utilizing seven embedded load cells incorporated in an instrumented housing in longitudinal and perpendicular direction of traversing. It was observed that contact area is a polynomial (with order of two) function of wheel load while there was a reverse linear relation between contact area and inflation pressure. Furthermore, contact pressure has linear relation with vertical load and inflation pressure. Models for contact area and contact pressure were developed by multiple regression analysis while a classical predicting model was assessed using contact area results of image processing technique. The models indicated acceptable coefficient of determinations amounts of 0.974 and 0.953 for contact area and contact pressure models, respectively. However, applied image processing method denoted R2-value of 0.988 for contact pressure equation.
Supersymmetric quantum mechanics, anomalies and factorization
J. Phys. A
25
7
L347-L352
1992
The explicit symmetry breaking phenomenon in supersymmetric quantum mechanics (SUSY QM) is analysed in terms of anomalies. The anomalous behaviour can be assigned to the supersymmetric charges which define the two Hamiltonians of the model. The relation between the presence of anomalies and the factorization of the Schrodinger equations is also discussed.
SUSY QM
Octonionic Quantum Mechanics and Complex Geometry
Progress of Theoretical Physics
96
4
823-831
1996
10.1143/PTP.96.823
The use of complex geometry allows us to obtain a consistent formulation of octonionic quantum mechanics (OQM). In our octonionic formulation we solve the hermiticity problem and define an appropriate momentum operator within OQM. The nonextendability of the completeness relation and the norm conservation is also discussed in details.
Remarks on Our Understanding of Quantum Mechanics
arXiv
quant-ph
2007
Interpretations of key concepts, such as uncertainty relations, kinetic energy, value of an observable, probability distributions, the projection or collapse of a wave function postulate, and discrete versus continuous values, that appear in several excellent textbooks on quantum mechanics are reviewed and found not to be consistent with our current understanding of quantum theory. Possible alternatives are suggested.
Objectivism and Irreversibility in Quantum Mechanics
Artificial Intelligence
149
1
8
2003
A hypothetical formulation of quantum mechanics is presented so as to reconcile it with macro-realism. On the analogy drawn from thermodynamics, an objective description of wave packet reduction is postulated, in which a characteristic energy scale and a time scale are introduced to separate the quantum and classical conceptions.
On a Free-Boundary Problem in Fluid-Mechanics
European Journal of Mechanics B-Fluids
10
1
75-95
1991
In this paper, the two-dimensional, steady flow of an incompressible, irrotational, inviscid fluid moving towards a porous wall is considered. We establish existence and uniquess theorems for this problem. Using a finite element method, we compute the solution of the problem for two examples.
jet flows
Generalized Conformal Quantum Mechanics of D0-brane
arXiv.org
hep-th
1999
We study the generalized conformal quantum mechanics of the probe D0-brane in the near horizon background of the bound state of source D0-branes. We elaborate on the relationship of such model to the M theory in the light cone frame.\n\nPublished in: Phys.Rev. D60 (1999) 064016
Nonextensive Statistical Mechanics - An Approach to Complexity
Chaos In Astronomy, Conference 2007 Book Series: astrophysics And Space Science Proceedings
309-318
2009
Central concepts within extensive statistical mechanics axe briefly reviewed, namely the extensivity of the nonadditive entropy S(q), the finite entropy production per unit time for weakly chaotic systems, and its connections with q-generalized central limit theorems. Bibliography for current applications in astrophysical systems is provided as well.
Quantum-Mechanics with a Non-Hermitian Hamiltonian
Physics Letters A
172
5
350-354
1993
Doi 10.1016/0375-9601(93)90116-H
It is shown that a satisfactory version of nonlinear quantum mechanics with a non-Hermitian Hamiltonian can be constructed. Tests to check for the existence of nonlinear terms in the Hamiltonian are discussed. It is proposed to use the theory to describe dissipative phenomena in open quantum systems.
Quantum Mechanics and Other Fields of Science
Foundations of Science
7
1-2
1-9
2002
In recent times, a particular attention has been devoted to the significance of quantum theory for other disciplines. The articles collected in this issue discuss some interesting cases, characterized by an interaction between quantum theory and other fields. Some basic notions of the mathematical formalism of the theory are here summarized.
Axiomatization; Interpretation; Quantum Mechanics; Science
Quantum Mechanics and the Cookie Cutter Paradigm
Arxiv Preprints
18
2000
What has so far prevented us from decrypting quantum mechanics is the Cookie Cutter Paradigm, according to which the world's synchronic multiplicity derives from surfaces that carve up space in the manner of three-dimensional cookie cutters. This insidious notion is shown to be rooted in our neurophysiological make-up. An effort is made to liberate the physical world from this innate fallacy.
Comment on "Quantum mechanics of smeared particles"
Journal of Physics A: Mathematical and General
36
5
2
2003
10.1088/0305-4470/36/5/324
In a recent article, Sastry has proposed a quantum mechanics of smeared particles. We show that the effects induced by the modification of the Heisenberg algebra, proposed to take into account the delocalization of a particle defined via its Compton wavelength, are important enough to be excluded experimentally.
Cosmology and the causal interpretation of quantum mechanics
Physics Letters A
114
7
365-370
1986
10.1016/0375-9601(86)90716-4
We answer the objections raised recently by Tipler to the trajectory interpretation of quantum mechanics by analyzing in detail the scattering of a particle from a semi-transparent surface. We conclude that the notion of the “wavefunction of the universe” poses no particular problems for this interpretation.
No time asymmetry from quantum mechanics
Physical Review Letters
70
26
4034-4037
1993
10.1103/PhysRevLett.70.4034
With CPT-invariant initial conditions that commute with CPT-invariant final conditions, the respective probabilities (when defined) of a set of histories and its CPT reverse are equal, giving a CPT-symmetric universe. This leads me to question whether the asymmetry of the Gell-Mann--Hartle decoherence functional for ordinary quantum mechanics should be interpreted as an asymmetry of {\it time} .
Evaluation of Teaching Mechanics [and] Author's Response
Journal of Research in Science Teaching
26
6
557-560
1989
Discusses the correctness of the directions of acceleration at various points in a pendulum problem shown in Reif (1987). Provides the author's responses to the comments on the problem. (YP)
Acceleration Physics; Illustrations; Mechanics Physics; Misconceptions; Physics; Science Instruction; Scientific Concepts; Secondary Education; Secondary School Science; Vectors Mathematics
Mechanics of the utility M&A process
Securities Regulation Law Journal
27
4
383-399
2000
Since the passage of the Energy Policy Act of 1992 federal and state regulatory developments have lead to major changes in the nature of the electric utility industry. In this article the author examines the mechanics of the merger and acquisition process during the energy industry's transition from natural monopoly to competitive marketplace and provides advice for participating companies.
Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature
Journal of Mathematical Sciences
125
4
419-532
2005
10.1007/s10958-005-0001-x
The technique of topological analysis of integrable problems developed by A. T. Fomenko is applied for studying certain problems of celestial mechanics.
The Britannica guide to relativity and quantum mechanics
Physics explained
xvi, 249 p.
2011
Explores relativity and quantum mechanics as well as the lives of those individuals who helped advance these fundamental areas of physics.
Physics Popular works.; Quantum theory Popular works.; Relativity (Physics) Popular works.
A new approach of mechanics simulation based on game engine
Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012
619-622
2012
Mechanics is a subject based on experiments which usually are inconvenient and expensive in reality. Computer simulation is a reasonable substitute for real mechanics experiments, but traditional mechanics simulation approaches also have many disadvantages, such as low interactivity, low flexibility, low reusability, high development difficulty and etc. Considering that the traditional technique has many disadvantages, this paper proposes a new method - mechanics simulation based on game engine. In game engine, the physicsengine provides a bottom technical support to make the mechanics apparatus run under the control of the physics laws. That increases the development efficiency greatly, and improves the interactivity, the flexibility and the reusability. This paper mainly discusses the advantages of mechanics simulation based on game engine, introduces the physics engine technology in detail and emphasizes on showing how to use game engine to simulate mechanical devices. © 2012 Crown Copyright.
Game engine; Mechanical devices; Mechanics simulation; Physics engine
Application of methods of nonlinear mechanics in the theory of …
Časopis pro pěstování matematiky a fysiky
1935
Volume 64; Issue 5. Article. First Page Preview. , Nicolas ; Bogoliuboff, Nicolas. Application of methods of nonlinear mechanics in the theory of stationary oscilations. (French). Časopis pro pěstování matematiky a fysiky, vol. 64 (1935), issue 5, pp.
Convergence of Logarithmic Quantum Mechanics to the Linear One
Letters in Mathematical Physics
81
3
253-264
2007
10.1007/s11005-007-0183-x
We study the nonlinear logarithmic Schr�dinger equation in three dimensions. We establish the existence of the solutions of general quasi-linear Schr�dinger equations. Finally, we show the convergence of the logarithmic quantum mechanics to the linear regime.
Physics and Astronomy
Classical Limit of the Generating Functional for the Non-Equilibrium Statistical Mechanics
Journal of the Physical Society of Japan
59
3553-3562
1990
By using the path integral representation of the double path generating functioal W[j1,j2] for the non-equilibtium statistical mechanics, the classical limit of W is discussed. ...
Intuitive mechanics, psychological reality and the idea of a material object
Spatial Representation: Problems in Philosophy and Psychology
162-176 ST - Intuitive mechanics, psychological r
1993
There is a constitutive link between the capacity to perceive objects as material objects and possession of an intuitive mechanics.
mind--intuitive physics--spatial aspects mind--spa
Critical Realism and Quantum Mechanics: Some Introductory Bearings
After Postmodernism: An Introduction to Critical Realism
116-131
2001
Quantum mechanics brings to the fore some serious problems for critical realism. The notion of continuous uncertainty is a paradox that critical realism must reconcile.
CP(n) supersymmetric mechanics in U(n) background gauge fields
Arxiv Preprint
7
2011
We construct a new N=4 supersymmetric mechanics describing the motion of a particle over a $CP^n$ manifold in U(n) background gauge fields.
High Energy Physics - Theory
Mech Tech offers Puerto Rico's only associate degrees in mechanics.
Caribbean Business
32
15
S26-S26
2004
Provides information on Caguas Institute of Mechanical Technology, the only school in Puerto Rico to confer associate degrees in mechanics. Curriculum; Faculties; Campus.
CURRICULA (Courses of study); EDUCATION; EDUCATIONAL innovations; EDUCATIONAL technology; MECHANICAL engineering; SCHOOL facilities
The theory of coupled differential equations in supersymmetric quantum mechanics
Journal of Physics A: Mathematical and General
23
23
L1217-L1222
1990
10.1088/0305-4470/23/23/006
There is a close relationship between the theory of coupled differential equations and supersymmetric quantum mechanics. The authors set up the bridge connecting these fields with two theorems concerning both the coupling and noncoupling cases.
Quantum Mechanics and a Preliminary Investigation of the Hydrogen Atom
Proceedings of the Royal Society of London. Series A
1926
561 Quantum Mechanics and a Preliminary Investigation of the Hydrogen Atom. By PAM DIRAC, 1851 Exhibition Senior Research Student, St. John's College, Cambridge. (Communicated by RH Fowler, FRS-Received January 22, 1926.) 1.
Mechanics of heavy metal accumulation and toxicity in fish.
Metal Metabolism in aquatic Environments.
321-350
1998
Olsson P.E., Kling P., Hogstrand C. 1998. Mechanics of heavy metal accumulation and toxicity in fish. In Langston, W.J., Bebianno, M.J. (eds.) Metal Metabolism in aquatic Environments. Chapman and Hall, London: 321-350.
Supersymmetric Quantum Mechanics and The Atiyah Singer Index Theorem
Acta Physica Polonica B
B15
5
435-452
1984
A new proof of the Atiyah-Singer index theorem is given using simple techniques developed in the context of supersymmetric field theories.
A Modified Derivation of BET Isotherm in Statistical Mechanics
Bulletin of the Chemical Society of Japan
21
7-12
36-39
1948
10.1246/bcsj.21.36
(1) The BET adsorption isotherm was derived by statistical mechanics, using the saddle point method. (2) The constants in BET isotherm can be represented by the internal partiton functions of the adsorbed phase.
Analysis of respiratory mechanics during artificial ventilation.
Biomedizinische Technik. Biomedical engineering
43
4
107-15
1998
Mechanical or artificial ventilation is the most important life-saving therapeutic instrument in modern intensive care medicine. The ventilator takes on the convective transport of the respiratory gas, i.e. delivery of oxygen and removal of carbon dioxide. The technical gas delivery system (ventilator, respiratory tubing system, gas humidifier) and the respiratory system (lungs and thorax) of the patients form a connected pneumatic system of high complexity. The respiratory system produces a mechanical impedance to ventilator output. Impedance is composed of an elastic, a non-elastic, i.e. resistive, and an inertive part. The corresponding indices describing respiratory mechanics are compliance, flow resistance and inertance. Based on the equation of motion of the respiratory system, several methods of analysing respiratory mechanics during mechanical ventilation are described. Quantitative analysis of respiratory system mechanics (a) is a prerequisite for the understanding of the complex patient-ventilator interaction, (b) provides important clinical information on pulmonary function and the course of disease, and (c) allows the physician at the bedside to adjust the ventilatory settings to the needs of the individual patient.
Biomechanics; Humans; Lung Volume Measurements; Mathematical Computing; Respiration, Artificial; Respiratory Mechanics; Respiratory Mechanics: physiology; Ventilators, Mechanical
Review of R. Omnes, THE INTERPRETATION OF QUANTUM MECHANICS
quant-ph/9505008
1995
Omnes' interpretation of quantum mechanics is summarized, and compared with other consistent-history approaches by Gell-Mann and Hartle, and by Griffiths.
Spin glasses and the statistical mechanics of protein folding
Proceedings of the National …
1987
Proc. Nati. Acad.Sci. USA Vol. 84, pp. 7524-7528, November Biophysics Spin glasses and the statistical mechanics of protein folding (disordered systems/irreversible denaturation/molten-globule state/biomolecular self-assembly)
Born series and unitarity in noncommutative quantum mechanics
Physical Review D
77
2
027704
2008
10.1103/PhysRevD.77.027704
This paper is dedicated to present model independent results for noncommutative quantum mechanics. We determine sufficient conditions for the convergence of the Born series and, in the sequel, unitarity is proved in full generality.
Soil mechanics - a new chapter in engineering science
A century of soil mechanics.
152-187
1969
Theoretical studies on angle of repose, experimental work, reprint of original paper published in 1883
Two No-Go Theorems for Modal Interpretations of Quantum Mechanics
Studies in History and Philosophy of Modern Physics
1999
In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one system. (edited)
Interpretation; Modality; Physics; Quantum Mechanics; Science
Some modeling and optimization problems in space flight mechanics
International Applied Mechanics
40
1
30-50
2004
The paper addresses some problems arising in modeling of spacecrafts, optimization of their parameters and trajectories, and optimal control of motion in model gravity fields and atmosphere.
The mechanics of human smooth pursuit eye movement
The Journal of Physiology
1965
Page 1. ;180;569-591 . . DA movement. The mechanics of human smooth pursuit eye This information is current as of March 10, 2008
Continuum Damage Mechanics - Present State and Future-Trends
Nuclear Engineering and Design
105
1
19-33
1987
Mechanics (CDM) has developed since the initial works of Kachanov and Rabotnov. The paper gives a review of its main features, of the present possibilities and of further developments. {&}{#}x02022; - use of CDM for local approaches of fracture.
A new formulation of stochastic theory and quantum mechanics
Physics Letters A
27
9
594-595
1968
10.1016/0375-9601(68)90068-6
A new formulation of stochastic theory is given by a generalization of Newtonian mechanics and from which Schrödinger's equation emerges in a natural way. Non-markovian terms may be important for possible extensions.
Contextuality without contextuality: Fine's interpretation of quantum mechanics
Reports on Philosophy
2000
The aim of this papre is to provide an introduction to Arthur Fine's local hidden variable interpretation of quantum mechanics and to show how it can resolve the non-locality problem articulated in the EPR-Bell theorem.
Cooperation between departments of physics and mechanics in engineering colleges
Journal of Engineering Education
37
9
720-726
1947
Discussion of what teacher of engineering mechanics can expect his students to know about physics; writer believes that most of deficiencies and erroneous ideas that students have stem from too little time having been allocated to various courses.
Education; Mechanical engineering
On the statistical mechanics of planar and spherical point vortex motion
American Physical Society
1999
Title: On the statistical mechanics of planar and spherical point vortex motion. Authors: , Igor; , Paul. Affiliation: AA
On Asymptotic Analysis for Large Amplitude Nonlinear Free Vibration of Simply Supported Laminated Plates
Journal of Vibration and Acoustics
131
5
051010-8
2009
Ananalytical approximation is developed for solving large amplitude nonlinear freevibration of simply supported laminated cross-ply composite thin plates. ApplyingKirchhoff's hypothesis and the nonlinear von Kármán plate theory, aone-dimensional nonlinear second-order ordinary differential equation with quadratic and cubicnonlinearities is formulated with the aid of an energy function.By imposing Newton's method and harmonic balancing to the linearizedgoverning equation, we establish the higher-order analytical approximations for solvingthe nonlinear differential equation with odd nonlinearity. Based on thenonlinear differential equation with odd and even nonlinearities, two newnonlinear differential equations with odd nonlinearity are introduced for constructingthe analytical approximations to the nonlinear differential equation with generalnonlinearity. The analytical approximations are mathematically formulated by combining piecewiseapproximate solutions from such two new nonlinear systems. The third-orderanalytical approximation with better accuracy is proposed here and comparedwith other numerical and approximate methods with respect to theexact solutions. In addition, the method presented herein is applicableto small as well as large amplitude vibrations of laminatedplates. Several examples including large amplitude nonlinear free vibration ofsimply supported laminated cross-ply rectangular thin plates are illustrated andcompared with other published results to demonstrate the applicability andeffectiveness of the approach. \n\t\t\n\t\t\t ©2009 American Society of Mechanical Engineers
approximation theory; laminates; nonlinear differential equations; plates (structures); vibrations
On Universal Mechanics and Superluminal Velocities
Applied Mathematics
05
17
2728-2738
2014
10.4236/am.2014.517260
In this work we continue to set up the theory of universal space and time and derive the Euclidean form of the scaling transformations. Two types of velocities emerge, inertial and universal, with the former bound by the light velocity c whereas the latter is unbound, and may accommodate consistently particles’ velocities possibly exceeding c. The inertial velocity is the ratio of the simultaneous source’s displacement and the corresponding length of the light trip to the observer, whereas the universal velocity has its familiar meaning for motion in a synchronous inertial frame. Defining the momentum as the product of universal velocity and mass, and utilizing the already established mass-energy equivalence, the mechanics constructed on the bases of the new concepts, named universal mechanics, admits superluminal velocities but yet coincides with the relativistic mechanics in its basic dynamical components and their inter-relations. The possibility of superluminal velocities provides a straight forward explanation of the presence of the μ-meson particles abundantly at the sea level despite their generation at high altitude and their short lifetime.
inertial velocity; Inertial Velocity; superluminal speeds; Superluminal Speeds; universal mechanics; Universal Mechanics
Respiratory mechanics of the coatimundi and woodchuck.
Respiration physiology
89
2
147-55
1992
The coatimundi breathes with a large tidal volume and relatively short TE/TTOT while the woodchuck has a relatively long TE/TTOT compared to other mammals. Hence, the respiratory mechanics of the coatimundi and woodchuck were studied to determine whether mechanics play any role in the differences in breathing pattern observed in these two mammals of similar body size. Although static respiratory system compliance was less and lower airway resistance was greater in the woodchuck compared to the coati there was no significant difference in deflationary time constant that could contribute to the difference in expiratory time. Both species exhibit less compliant chest walls than would be predicted for animals this size (4.5 and 5 kg) and the coati lung compliance is greater than that of the woodchuck or the prediction. The large tidal volume in the coati may be attributed in part to the large lung volume of this species (2.2 times the allometric prediction). The differences in breathing pattern are more likely related to differences in the control of breathing (i.e. regulation of expiratory airflow and inspiratory onset) than to differences in respiratory mechanics.
Animals; Carnivora; Humans; Marmota; Respiratory Mechanics; Respiratory Mechanics: physiology; Tidal Volume
Polymer thin films
Lecture
1-20
2008
This lecture is concerned with the formation and properties of polymer thin films (SL) and multilayers (ML)
Thin film growth
Tomei Sankabutsu Kino Zairyo to Sono Oyo
46-53
2006
A review including epitaxy of InGaO3(ZnO)m and NaxCoO2. [on SciFinder (R)]
Epitaxy (thin film growth by epitaxy); review epitaxy
ZnSe thin films by chemical bath deposition method.
Solar Energy Materials & Solar Cells
55
4
379
1998
Describes the deposition of thin films of zinc and selenium onto glass substrates. Application of chemical bath deposition method to deposit thin films; Characteristics of the thin films.
SELENIUM; THIN films; ZINC
Changes in respiratory mechanics during abdominal laparoscopic surgery in children.
Anaesthesia and intensive care
27
3
245-8
1999
We designed this study in order to measure the changes in respiratory mechanics during laparoscopic surgery in children. Ventilation parameters (Flow (Ví) and Peak Pressure (Pmax)) were measured and total respiratory system mechanics (resistance (Rrs) and compliance (Crs)) were derived using multiple linear regression analysis in 11 children aged 8 months to 11 years. The Pmax increased by 26.6% and the Rrs increased by 20.2% whilst the Crs decreased by 38.9% after pneumoperitoneum. These findings suggest that clinically important changes in respiratory mechanics occur as a result of the pneumoperitoneum produced during abdominal laparoscopic surgery.
Abdomen; Abdomen: surgery; Anesthesia, General; Child; Child, Preschool; Female; Humans; Infant; Intraoperative Period; Laparoscopy; Male; Pneumoperitoneum, Artificial; Respiration, Artificial; Respiratory Mechanics
Contact force element of discontinuous deformation computational mechanics model
Dongbei Daxue Xuebao/Journal of Northeastern University
23
11
1112-1115
2002
Relation distance and contact types and their identification criterion\namong bodies were set forth. Control equations of contact mechanics\namong the bodies and transfer of the contact styles were established.\nContact force element was set up on the basis of contact of physical\ncovers of generalized finite elements and Coulomb frictional contact\nlaw. It is shown that bilateral generalized finite elements come\ninto sliding and denoting each other with discontinuity and they\nrespectively correspond to tangential flow and normal flow of plasticity.\nTherefore, the presented contact force element may organically integrate\ntogether continuity and discontinuity, and provides mechanics analysis\nmethod for that discontinuous deformation computational mechanics\nmodel which is appropriately used to deal with contact problem among\nmulti-bodies.
Contacts (fluid mechanics);Deformation;Dynamic mec
Thin-layer chromatography. In
Lipids analysis: a practical approach. Oxford: IRL Press
65-111
1992
Henderson RJ, Tocher DR. Thin-layer chromatography. In: Hamilton RJ, Hamil- ton S, editors.; 1992. p. 65–111
Novel thin film structures.
PCT Int. Appl.
WO2007147947A2
29pp.
2007
A thin film structure, method of producing it and the use thereof are disclosed. The thin film structure comprises a substrate with a thin conductive layer contg. an oxidizing enzyme mixed with an electron transfer mediator. The thin layer is protected against wetting to allow for its storage in dry conditions and further being sufficiently porous to allow for immediate activation of the oxidizing enzyme when contacted with an aq. soln. The thin film can be used as a cathode in electrochem. fuel cells. [on SciFinder(R)]
battery cathode thin film structure; fuel cell cathode thin film structure
SOME MODELS AND METHODS OF PNEUMATIC TIRE MECHANICS
Vehicle System Dynamics
27
sup001
250-571
1997
10.1080/00423119708969659
ABSTRACT Pneumatic tire mechanics is divided into two separate sections, namely external tire mechanics, dealing with the effect of tires on motor-car dynamics, and internal tire mechanics, concerned with the stress and thermal state of tires and their service life depending on loading, structure design and material properties. Connecting links between these two sections are the output characteristics of tires which determine the operational qualities of a car. Since the authors are specialized in the field of internal tire mechanics this paper, for the most part, is concerned with the last section. It shall present a survey of the models and methods, worked out by Russian experts.
3-D finite element modeling of ductile crack growth in thin aluminum materials
Fatigue and Fracture Mechanics: 30th Volume
1360
85-101
2000
This work describes the development and verification of a 3-D model to predict stable, Mode I crack growth in thin, ductile aluminum alloys. The model extends the standard 2-D form of the crack rip opening angle (CTOA) methodology, which determines crack extension based on obtaining a critical angle at the crack tip. When the CTOA reaches the critical value, all the nodes along the current, 3-D crack front are released simultaneously, thereby growing the crack in a self-similar manner. Evaluation of the CTOA occurs at a specified distance behind the crack tip; this decouples CTOA evaluation from mesh refinement. The CTOA-based model also includes adaptive load control strategies to minimize the effects of discrete load increments on the growth response. To evaluate the effectiveness of the described approach, this work describes a validation study using load-crack extension data from 2.3-mm-thick Al 2024-T3 specimens tested at NASA-Langley. The test matrix includes C(T) and M(T) specimens, with varying widths (50 to 600 mm), a/W ratios, and levels of constrains so suppress out-of-plane bending. Comparisons of load-crack extension curves from experiments and analyses of a constrained 150-mm C(T) specimen provide a calibrated critical CTOA value of 5.1 degrees. Analyses using the calibrated CTOA value for constrained and unconstrained specimens provide predictions of peak load in good agreement with the experimental values.
Scattering of water waves by inclined thin plate submerged in finite-depth water
Archive of Applied Mechanics
71
12
827-840
2001
The problem of water wave scattering by an inclined thin plate submerged in water of uniform finite depth is investigated here under the assumption of irrotational motion and linear theory. A hypersingular integral equation formulation of the problem is obtained by an appropriate use of Green's integral theorem followed by utilization of the boundary condition on the plate. This hypersingular integral equation involves the discontinuity in the potential function across the plate, which is approximated by a finite series involving Chebyshev polynomials. The coefficients of this finite series are obtained numerically by collocation method. The quantities of physical interest, namely the reflection and transmission coefficients, force and moment acting on the plate per unit width, are then obtained numerically for different values of various parameters, and are depicted graphically against the wavenumber. Effects of finite-depth water, angle of inclination of the plate with the vertical over the deep water and vertical plate results for these quantities are shown. It is observed that the deep-water results effectively hold good if the depth of the mid-point of the submerged plate below the free surface is of the order of one-tenth of the depth of the bottom.
Thin calcium phosphate coatings on titanium by electrochemical deposition in modified simulated body fluid
J Biomed Mater Res A
76
2
347-355
2006
Adherent and optically semitransparent thin calcium phosphate (CaP) films were electrochemically deposited on titanium substrates in a modified simulated body fluid at 37 degrees C. Coatings deposited by using periodic pulsed potentials showed better adhesion and better mechanical properties than coatings deposited with use of a constant potential. Scanning electron microscopy was used to study the morphology of the coatings. The coatings displayed a polydispersed porous structure with pores in the range of a few nanometers to 1 mum. Furthermore, X-ray diffractometry and the O(1s) satellite peaks in X-ray photoelectron spectroscopy indicated that the coatings possessed a similar surface chemistry to that of natural bone minerals. These results were confirmed by inductively coupled plasma optical emission spectrometry, which yielded a Ca:P ratio of 1.65, close to that of hydroxyapatite. Contact mode atomic force microscopy (AFM) showed the average thickness of the coatings was in the order of 200 nm. Root-mean-square (RMS) roughness values, also derived by AFM, were shown to be much higher on the titanium-CaP surfaces in comparison with untreated titanium substrates, with RMS values of about 300 and 110 nm, respectively. Cell culture experiments showed that the CaP surfaces are nontoxic to MG63 osteoblastic cells in vitro and were able to support cell growth for up to 4 days, outperforming the untreated titanium surface in a direct comparison. These easily prepared coatings show promise for hard-tissue biomaterials.
Adhesiveness; Body Fluids; *Calcium Phosphates; Cell Proliferation; Coated Materials, Biocompatible/*chemistry; Electrochemistry; Materials Testing; Mechanics; Osteoblasts/*cytology; Porosity; Research Support, Non-U.S. Gov't; Surface Properties; *Titanium
New axiomatics for statistical mechanics
Complexity, Metastability and Nonextensivity
965
0-3
2007
10.1063/1.2828757
It is here shown how to use pieces of macroscopic thermodyanamics so as to generate microscopic probability distributions for generalized ensembles, thereby directly connecting macrostate-axiomatics with microscopic results.
equilibrium microscopic probability distribution; maxent; thermodynamics
Arrival time in quantum mechanics
Physics reports
338
2000
The arrival time is a simple classical concept, very common in laboratory practice. This review describes theoretical problems encountered in trying to obtain a quantum mechanical counterpart and the solutions proposed.A summary of current experimental techniques is also included.
Statistical mechanics of complex networks
Rev Mod Phys
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers
Arrival time in quantum mechanics
Phys.\ Rev.\ A
56
5
3425-3435
1997
A self-adjoint operator with dimensions of time is explicitly constructed,\nand it is shown that its complete and orthonormal set of eigenstates\ncan be used to define consistently a probability distribution of\nthe time of arrival at a spatial point.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
1
47-96
2001
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers
QUANTUM MECHANICS
Journal of computer-aided molecular design
25
6
583-97
2011
10.1007/s10822-011-9443-z
The identification of BACE-1, a key enzyme in the production of Amyloid-β (Aβ) peptides, generated by the proteolytic processing of amyloid precursor protein, was a major advance in the field of Alzheimer's disease as this pathology is characterized by the presence of extracellular senile plaques, mainly comprised of Aβ peptides. Hydroxyethylamines have demonstrated a remarkable potential, like candidate drugs, for this disease using BACE-1 as target. Density Functional Theory calculations were employed to estimate interaction energies for the complexes formed between the hydroxyethylamine derivated inhibitors and 24 residues in the BACE-1 active site. The collected data offered not only a general but a particular quantitative description that gives a deep insight of the interactions in the active site, showing at the same time how ligand structural variations affect them. Polar interactions are the major energetic contributors for complex stabilization and those ones with charged aspartate residues are highlighted, as they contribute over 90% of the total attractive interaction energy. Ligand-ARG296 residue interaction reports the most repulsive value and decreasing of the magnitude of this repulsion can be a key feature for the design of novel and more potent BACE-1 inhibitors. Also it was explained why sultam derivated BACE-1 inhibitors are better ones than lactam based. Hydrophobic interactions concentrated at S1 zone and other relevant repulsions and attractions were also evaluated. The comparison of two different theory levels (X3LYP and M062X) allowed to confirm the relevance of the detected interactions as each theory level has its own strength to depict the forces involved, as is the case of M062X which is better describing the hydrophobic interactions. Those facts were also evaluated and confirmed by comparing the quantitative trend, of selected ligand-residue interactions, with MP2 theory level as reference standard method for electrostatic plus dispersion energies.
Quantum mechanics
Journal of computer-aided molecular design
25
6
583-97
2011
10.1007/s10822-011-9443-z
The identification of BACE-1, a key enzyme in the production of Amyloid-β (Aβ) peptides, generated by the proteolytic processing of amyloid precursor protein, was a major advance in the field of Alzheimer's disease as this pathology is characterized by the presence of extracellular senile plaques, mainly comprised of Aβ peptides. Hydroxyethylamines have demonstrated a remarkable potential, like candidate drugs, for this disease using BACE-1 as target. Density Functional Theory calculations were employed to estimate interaction energies for the complexes formed between the hydroxyethylamine derivated inhibitors and 24 residues in the BACE-1 active site. The collected data offered not only a general but a particular quantitative description that gives a deep insight of the interactions in the active site, showing at the same time how ligand structural variations affect them. Polar interactions are the major energetic contributors for complex stabilization and those ones with charged aspartate residues are highlighted, as they contribute over 90% of the total attractive interaction energy. Ligand-ARG296 residue interaction reports the most repulsive value and decreasing of the magnitude of this repulsion can be a key feature for the design of novel and more potent BACE-1 inhibitors. Also it was explained why sultam derivated BACE-1 inhibitors are better ones than lactam based. Hydrophobic interactions concentrated at S1 zone and other relevant repulsions and attractions were also evaluated. The comparison of two different theory levels (X3LYP and M062X) allowed to confirm the relevance of the detected interactions as each theory level has its own strength to depict the forces involved, as is the case of M062X which is better describing the hydrophobic interactions. Those facts were also evaluated and confirmed by comparing the quantitative trend, of selected ligand-residue interactions, with MP2 theory level as reference standard method for electrostatic plus dispersion energies.
Thin film transistors.
U.S. Pat. Appl. Publ.
US20090140237A1
11pp.
2009
A thin film transistor has a semiconducting layer comprising a semiconductor and a mixt. enriched in metallic carbon nanotubes. The semiconducting layer has improved charge carrier mobility. [on SciFinder(R)]
enriched carbon nanotube semiconductor thin film t
Thin, fast, and flexible
Spectrum
2011
Nor are today's thin-film transistors stable enough for displays that use the organic light-emitting diode (OLED), a thin, efficient, high-contrast technology. Stability matters because the ``threshold voltage'' that an amorphous silicon tran- sistor needs to turn on tends to drift as the
Thin film transistors.
U.S. Pat. Appl. Publ.
US20090140236A1
11pp.
2009
A thin film transistor has a semiconducting layer comprising a semiconductor and surface-modified carbon nanotubes. The semiconducting layer has improved charge carrier mobility. [on SciFinder(R)]
thin film transistor semiconductor carbon nanotube
Thin liquid films
Surface Colloid Sci.
3
167-239
1971
A review with 237 refs. Thin liq. films in vapor and liq. media are examd. [on SciFinder (R)]
thin liq film review
Thin, fast, and flexible
Spectrum
2011
Nor are today's thin -film transistors stable enough for displays that use the organic light-emitting diode (OLED), a thin , efficient, high-contrast technology. Stability matters because the “threshold voltage” that an amorphous silicon tran- sistor needs to turn on tends to drift as the ...
Virtual thin client computing
Computing Canada
25
40
8
1999
Boardroom discussions centering around whether an organization should introduce thin clients should not be about reworking the existing system with different hardware and software, but should be about designing applications to work in either fat-client or thin-client mode.
The Role of Mechanics in the Evolution of the Herbaceous Plant Stem
Botanical Gazette
111
3
262-286
1950
1. Eighty-two species, representing forty-one families of plants, characterized, at least in part, by herbaceous stems, were examined to determine the role of mechanics in the evolution of the herbaceous plant stem. 2. There appears to be no definite and sequential line of evolution which can be based on mechanical adaptations in stem structure for the herbaceous type. Many mechanical adaptations occur in primitive genera as well as in the higher groups, and in many of the higher herbaceous orders there are practically no striking structural modifications which indicate an increase or decrease in the mechanical efficiency of the stem. 3. Lianas are plants which have been able by various other adaptations to survive in spite of a habit which is characterized by a length-diameter ratio so large that the mechanical tissues are incapable of supporting the stem without external aid. 4. Stems which at maturity reach a length-diameter ratio at which they approach the form of an Euler column will probably be scrambling, climbing, or prostrate in habit. The stem's ability to support itself is probably doubtful at a length-diameter ratio of 60 plus, and practically impossible at 100 plus. 5. Massive stems, such as the boles of large trees, tend to assume the form of a column of constant strength near the base, a tendency which disappears with reduction in massiveness during the course of evolution. 6. Certain polygonal cross sections in stems, although following no special phylogenetic sequence, represent adaptations which increase the mechanical efficiency of the stem in many cases; others, such as triangular cross sections, may produce the opposite result. 7. Discrete bundles and thin rings of vascular or mechanical tissue in various species, while achieved by different phylogenetic sequences, are essentially similar from a mechanical standpoint when viewed in the light of Hooke's law as applied to composite sections. 8. Two lines of evolution in herbaceous stems are indicated: (a) proliferation of the ray tissue and its congregation into large radial tracts, thereby breaking the xylem cylinder into separate bundles, with an accompanying decrease of rays and vessels in any vascular tissue intervening between the bundles, and (b) thinning of the xylem cylinder through a decrease in cambial activity which is accompanied by a loss of rays and a reduction in the number of vessels in the regions so affected. 9. Hutchinson's inclusion of the genus Phryma in the Verbenaceae is given added support by the similarity in stem anatomy of the genus to that of certain members of the Verbenaceae. 10. The derivation, at least in part, of the Compositae from the Umbelliferae, as suggested by Bessey and Hutchinson, is supported by the anatomical similarities relative to the schizogenous oil ducts which are found in both groups.
Course in mechanics of fluids
Journal of Engineering Education
24
4
299-302
1933
Course for widening field of knowledge and meeting rapidly changing conditions, which is part of larger program initiated for Mechanical Engineering Department of Columbia School of Engineering.
Education; Hydraulics
Numerical methods in rock mechanics
International Journal of Rock Mechanics and Mining Sciences
39
409-427
2002
10.1016/S1365-1609(02)00065-5
The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures built on and in rock masses, and hence for supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating couplings between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized. Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference list, ‘significant’ references are asterisked and ‘very significant’ references are doubly asterisked.
Coupled processes; Design; Numerical modelling; Outstanding issues; Review; Rock mechanics
ON THE QUANTUM MECHANICS OF COLLISIONS
Zeitschrift für Physik
38
11-12
803-827
1926
10.1007/BF01397184
Zusammenfassung Durch eine Untersuchung der Stoßvorgänge wird die Auffassung entwickelt, daß die Quantenmechanik in der Schrödingerschen Form nicht nur die stationären Zustände, sondern auch dieQuantensprünge zu beschreiben gestattet.
Fracture mechanics of notched bodies
Materials Science
34
6
741-759
1998
Fracture mechanics of notched bodies generalizes the concept of classical fracture mechanics dealing with cracks. Cracks are regarded as a special case of notches with zero radius of the notch tip and zero notch angle. Theoretically, the acuity of a crack is infinite. This results in the appearance of singularities of stresses characterized by the stress intensity factors in linear fracture mechanics. In the case of notches, we deal with the highest local stresses near the notch tip and consider a certain physical volume where the (effective) fracture stresses or strains or specific strain energy can be specified as the corresponding values of these quantities on the boundary of the zone of pseudosingularity. This enables one to study fracture by using both global and local criteria. The triaxiality of stresses strongly affects the effective parameters, temperature, and the strain rate responsible for the ductile-brittle transition in the material. © 1999 Kluwer Academic/Plenum Publishers.
Multilayer hybrid-stress finite element analysis of composite laminates with delamination cracks originating from transverse cracking
Engineering Fracture Mechanics
54
713-729
1996
10.1016/0013-7944(95)00118-2
An assumed hybrid-stress finite element model together with a composite multilayer element incorporating the technique of contact analysis is employed to analyze a composite laminate with delamination cracks originating from transverse cracking. Contact without friction on the crack surfaces and three-dimensional interlaminar stresses are taken into account. Once the contact zone exists, the assumed stress field satisfies the traction reciprocity conditions on the contact area and a transformation matrix is employed to deal with the contact conditions for the displacements on the contact zone. The interlaminar stresses and stress intensity factors are calculated accurately. As examples, cross-ply composite laminates with delamination cracks originating from transverse cracking under extension are studied. The influence of ply thickness on the growth of delamination cracks is also evaluated. The comparisons between the present results and referenced solutions show the high accuracy and validity of the present technique. Copyright ?? 1996 Elsevier Science Ltd.
Single-molecule mechanics of heavy-meromyosin and S1 interacting with rabbit or drosophila using optical tweezers
Biophys J.
68
4, Suppl. S
S298-S305
1995
Single-molecule mechanical interactions between rabbit heavy meromyosin\n(HMM) or subfragment 1 (S1) and rabbit actin were measured with an\noptical tweezers piconewton, nanometer transducer. Similar intermittent\ninteractions were observed with HMM and S1. The mean magnitude of\nthe single interaction isotonic displacements was 20 nm for HMM and\n15 nm with S1. The mean value of the force of single-molecule interactions\nwas 1.8 pN for HMM and 1.7 pN with S1. The stiffness of myosin S1\nwas determined by applying a sinusoidal length change to the thin\nfilament and measuring the corresponding force; the mean stiffness\nwas 0.13 pN nm(-1). By moving an actin filament over a long distance\npast an isolated S1 head, we found that cross-bridge attachment occurred\npreferentially at a periodicity of about 40 nm, similar to that of\nthe actin helical repeat. Rate constants for the probability of detachment\nof HMM from actin were determined from histograms of the lifetime\nof the attached state. This gave a value of 8 s(-1) or 0.8 x 10(6)\nM(-1) S-1 for binding of ATP to the rigor complex. We conclude (1)\nthat our HMM-actin interactions involve just one head, (2) that compliance\nof the cross-bridge is not in myosin subfragment 2, although we cannot\nsay to what extent contributions arise from myosin S1 or actin, and\n(3) that the elemental movement can be caused by a change of shape\nof the S1 head, but that this would have to be much greater than\nthe movements suggested from structural studies of S1 (Rayment et\nal., 1993).
The Shockwave Response of Thin Composite Materials
Volume 8: Mechanics of Solids, Structures and Fluids
8
703
2012
10.1115/IMECE2012-88193
Impingement of blast or shock waves on structures is characterized by a substantial transient aerodynamic load that develops over the short time associated with the shock reflection time scale. This mutual interaction between the shock wave and the structure can cause significant deformation of the structure and high strain rates within the material resulting in damage. An experimental investigation was carried out to determine the aeroelastic response of thin flat plates of composite materials during face-on impact with planar shock waves. The experiments were performed in a large-scale shock tube research facility, which had a working section of 12 inches in diameter and a length of 80 ft. Phenolic composite S2-HJ1 plates of 1/8 inch nominal thickness consisting of 12 layers of fibers and epoxy composite S2 plates of 1/8 inch nominal thickness consisting of 10 layers of fibers were tested in the present investigation. Miniature semi-conductor strain-gauges of high frequency response, high speed photography and Digital Image Correlation techniques were employed to measure locally the strain on the exterior side of the plates and high frequency response pressure transducers were used to measure time-dependent wall and total pressure. In order to provide comparison with the response of monolithic material to similar compressive loadings, aluminum and stainless steel plates were also tested under the same conditions. The application of shock loading on the specimen causes significant permanent deformation on the plates which has been measured immediately after the experiment while the specimen is still mounted on the end flange of the shock tube. These experimental data obtained in the present experiments include the measured displacement of the external surface of the plates from their original position in the normal to the plate direction along the radius of the specimen. This displacement is highest at the center of the plate and zero at the location of clamping. The results show that the deformations of the thicker plates are still considerably lower than those obtained in the steel and thinner composite plates although the loading pressure is more than triple in magnitude and the corresponding impulse is about 2.3 times higher. Composite plates were found to suppress several of the modes of the wave patterns while metallic ones demonstrate a rich variety of interacting modes. The frequency content of the strain signals on the surface of composite plates was not always the same with the content of the surface acceleration measured in free vibration experiments. Copyright © 2012 by ASME.
Lecture Notes on Fracture Mechanics
Architectural Engineering
1-8
2006
Fracture mechanics is a vast and growing field. A search of the Cornell Library in winter 2006 uncovered over 181 entries containing fracture mechanics in the subject heading and 10,000 entries in a relevance keyword search. This book is written for students who want to prepare to be able to read some of this vast literature and for those who want to apply fracture mechanics to real world problems. It is assumed the reader is familiar with the theory of linear elasticity, vector calculus, linear algebra and indicial notation. As much as possible I proceed in a linear fashion, but the reader may find that some backtracking is needed. These notes are used in a one semester course at Cornell. There are many approaches to teaching fracture. Here the emphasis is on mechanics models for crack tip fields and energy flows with discussion of how these results affect observed fracture behavior. A brief discussion of computational fracture methods is given along with additional practical aspects such as fracture toughness testing and fracture criteria. The notes do not contain much on the understanding of material behavior or on fracture at the micromechanical level. Both the mechanics and the materials sides of fracture should be studied in order to obtain a balanced and more complete picture of the field. These notes grow out of my experience teaching fracture at Cornell and taking fracture mechanics in graduate school at Caltech with Ares Rosakis. Textbooks consulted include Hutchinsons notes on nonlinear fracture 1, Lawns book on the fracture of brittle materials 2, Suresh on fatigue 3 and texts by Janssen 4, Anderson 5, Sanford 6 and Hellan 7. Topics that could be added include interface fracture, better coverage of computational methods, viscoelastic fracture and more discussion of the physical aspects of fracture. Topics that I hope to work on but have yet to start include: computational cohesive zone, fatigue crack growth model and fracture of plates and shells.
Heat conduction analysis of laminated shells by a sampling surfaces method
Mechanics Research Communications
55
59-65
2014
10.1016/j.mechrescom.2013.10.018
A paper focuses on the use of the method of sampling surfaces (SaS) for the exact three-dimensional (3D) heat conduction analysis of laminated orthotropic and anisotropic shells. This method is based on selecting inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to choose the temperatures of these surfaces as basic variables. Such an idea permits the representation of the proposed thermal laminated shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. As a result, the SaS method can be applied efficiently to exact 3D solutions of the steady-state heat conduction problem for cross-ply and angle-ply composite shells with a specified accuracy using a sufficient number of SaS.
Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory
International Journal of Non-Linear Mechanics
72
42-52
2015
http://dx.doi.org/10.1016/j.ijnonlinmec.2015.02.007
Abstract In this paper, we present an effectively numerical approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of laminated composite plates. The HSDT allows us to approximate displacement field that ensures by itself the realistic shear strain energy part without shear correction factors (SCFs). IGA utilizing basis functions namely B-splines or non-uniform rational B-splines (NURBS) enables to satisfy easily the stringent continuity requirement of the HSDT model without any additional variables. The nonlinearity of the plates is formed in the total Lagrange approach based on the small strain assumptions. Numerous numerical validations for the isotropic, orthotropic, cross-ply and angle-ply laminated plates are provided to demonstrate the effectiveness of the proposed method.
Higher-order shear deformation theory; Isogeometric analysis; Laminated composite plate; Nonlinear analysis
Buckling and vibration of thick laminates on pasternak foundations
Journal of Engineering Mechanics
122
1
54-63
1996
This paper investigates buckling, free vibration, and vibration with initial in-plane loads for moderately thick, simply supported symmetric cross-ply rectangular laminates on Pasternak foundations. The total potential energy functional is derived based on the first-order shear deformation plate theory. The differential equations, which govern the vibration and buckling behavior of the plate are then derived from the potential energy functional. Employing the Navier solution procedure, closed-form buckling and vibration solutions have been obtained and are presented in tables and figures. Extensive parametric studies have been carried out to investigate the effects of plate geometry, in-plane load ratio, and foundation parameters on the buckling and vibration behavior of the plate system. Sets of first-known closed-form buckling and vibration results are presented for simply supported symmetric cross-ply laminates on Pasternak foundations. These results may be useful to engineers in engineering practice and to researchers in checking numerical models.
Thin Film
Nanotechnology
23
4
045604
2012
10.1088/0957-4484/23/4/045604
Oxide nanowires were directly grown on a CuO x thin film deposited by plasma-enhanced atomic layer deposition without additional metal catalysts. Oxide nanowires would exhibit metal-catalyst-free growth on the CuO x thin film with oxide materials diffused on the top. Through a focused ion beam and transmission electron microscopy, we could verify that SnO 2 and ZnO nanowires were grown as single-crystalline structures just above the CuO x thin film. Bottom-gate structural SnO 2 and ZnO nanowire transistors exhibited mobilities of 135.2 and 237.6 cm 2 V -1 s -1 , respectively. We anticipate that a variety of large-area and high-density oxide nanowires can be grown at low cost by using the CuO x thin film.
Hybrid ab initio quantum mechanics molecular mechanics calculations of free energy surfaces for …
Journal Of Physical Chemistry B
1998
An effective approach for ab initio calculations of activation free energies of enzymatic reactions is developed and examined. This approach uses an empirical valence bond (EVB) potential surface as a reference potential for
Thin slicing
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
42
6
112-122
2007
10.1177/0956797610381507
Program slicing systematically identifies parts of a program relevant to a seed statement. Unfortunately, slices of modern programs often grow too large for human consumption. We argue that unwieldy slices arise primarily from an overly broad definition of relevance, rather than from analysis imprecision. While a traditional slice includes all statements that may affect a point of interest, not all such statements appear equally relevant to a human. As an improved method of finding relevant statements, we propose thin slicing. A thin slice consists only of producer statements for the seed, i.e., those statements that help compute and copy avalue to the seed. Statements that explain why producers affect the seed are excluded. For example, for a seed that reads a value from a container object, a thin slice includes statements that store the value into the container, but excludes statements that manipulate pointers to the container itself. Thin slices can also be hierarchically expanded to include statements explaining how producers affect the seed, yielding a traditional slice in the limit. We evaluated thin slicing for a set of debugging and program understanding tasks. The evaluation showed that thin slices usually included the desired statements for the tasks (e.g., the buggy statement for a debugging task). Furthermore, in simulated use of a slicing tool, thin slices revealed desired statements after inspecting 3.3 times fewer statements than traditional slicing for our debugging tasks and 9.4 times fewer statements for our program understanding tasks. Finally, our thin slicing algorithm scales well to relatively large Java benchmarks, suggesting that thin slicing represents an attractive option for practical tools.
can be very hard; complex data structures in; data and; debugging; motivation large-scale object-oriented programs; of this; pervasive use of heap-allocated; program understanding; slicing; these programs causes much; to understand and debug
Thin slicing
Proc. PLDI
42
6
112-122
2007
10.1145/1250734.1250748
Program slicing systematically identifies parts of a program relevant to a seed statement. Unfortunately, slices of modern programs often grow too large for human consumption. We argue that unwieldy slices arise primarily from an overly broad definition of relevance, rather than from analysis imprecision. While a traditional slice includes all statements that may affect a point of interest, not all such statements appear equally relevant to a human. As an improved method of finding relevant statements, we propose thin slicing. A thin slice consists only of producer statements for the seed, i.e., those statements that help compute and copy avalue to the seed. Statements that explain why producers affect the seed are excluded. For example, for a seed that reads a value from a container object, a thin slice includes statements that store the value into the container, but excludes statements that manipulate pointers to the container itself. Thin slices can also be hierarchically expanded to include statements explaining how producers affect the seed, yielding a traditional slice in the limit. We evaluated thin slicing for a set of debugging and program understanding tasks. The evaluation showed that thin slices usually included the desired statements for the tasks (e.g., the buggy statement for a debugging task). Furthermore, in simulated use of a slicing tool, thin slices revealed desired statements after inspecting 3.3 times fewer statements than traditional slicing for our debugging tasks and 9.4 times fewer statements for our program understanding tasks. Finally, our thin slicing algorithm scales well to relatively large Java benchmarks, suggesting that thin slicing represents an attractive option for practical tools.
debugging; program understanding; slicing
Lunar Sample Atlas: Apollo Thin Sections
web pages
2012
The Apollo Thin Sections catalog is a subset of the Lunar Sample Atlas, and includes those samples for which thin-section views are available.
Apollo; thin section
Modale Interpretaties van Quantummerchanica: Filosofie tussen Fysica en Metafysica (Modal Interpretations of Quantum Mechanics)
Algemeen Nederlands Tijdschrift voor Wijsbegeerte
93
2
93-104
2001
Quantum mechanics is a theory about elementary particles that systematically describes the outcomes of measurements on those particles but that doesn't systematically describe the properties of the particles themselves. Interpretations of quantum mechanics try to complete quantum mechanics by adding these descriptions of the properties of particles. The paper firstly introduces the reader in a nontechnical way to the problems addressed by interpretations of quantum mechanics. Secondly, it presents the solutions provided by so-called modal interpretations. Finally, it assesses the tenability of modal interpretations within the frameworks of scientific realism and constructive empiricism.
Modal; Physics; Quantum Mechanics; Realism; Science
The spacetime approach to quantum mechanics
Vistas Astron.
37
569-583
1993
10.1016/0083-6656(93)90097-4
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schr\"odinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. Sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not "at definite moments of time". An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics is the set of the alternatives defined by whether a particle never crosses a fixed spacetime region or crosses it at least once. The general notion of a set of spacetime alternatives is a partition (coarse-graining) of the histories into an exhaustive set of exclusive classes. With this generalization the sum-over-histories formulation can be said to be in fully spacetime form with dynamics represented by path integrals over spacetime histories and alternatives defined as spacetime partitions of these histories. When restricted to alternatives at definite moments of times this generalization is equivalent to Schr\"odinger-Heisenberg quantum mechanics. However, the quantum mechanics of more general spacetime alternatives does not have an equivalent Schr\"odinger-Heisenberg formulation. We suggest that, in the quantum theory of gravity, the general notion of "observable" is supplied by diffeomorphism invariant partitions of spacetime metrics and matter field configurations. By generalizing the usual alternatives so as to put quantum theory in fully spacetime form we may be led to a covariant generalized quantum mechanics of spacetime free from the problem of time.
Preferred conformation of 1-phenyl-2-propanol. Ab initio and molecular mechanics calculations with geometry optimization
Bull. Chem. Soc. Jpn.
58
2713-2714
1985
The most stable conformation of 1-phenyl-2-propanol, optimized by ab initio and molecular mechanics (MM2) calculations, is a phenyl-methyl anti and phenyl-OH gauche conformation with an intramolecular OH-π hydrogen bond.
1-phenyl-2-propanol; ab initio calculation; CH/p interaction; molecular mechanics calculation
ROCK MECHANICS-THEORY AND PRACTICE. PROCEEDINGS 11TH SYMPOSIUM, BERKELEY, CALIF, JUNE 16-19 1969
Soc Mining Engrs, AIME, New York, NY
1970
Proceedings contains 34 papers discussing-geologic factors in rock mechanics; simulation of geologic factors; simulation of rock behavior; field studies; role of fluids in rock mechanics; and recent developments in rock drilling. Selected papers are indexed separately. Author and subject indexes are included.
The Preparation of Thin Sections Using Polyethylene Glycols
Micromorphilogical techniques and Applications. Technical Monograph No.2, Rothamsted Experimental Station.
2
15-24
1970
The properties of polyrthylene glycols are sumarized and details are given for preparing thin sections of soils using Carbowax 6000 as embedding agent. The advantages and limitations of the tecnique are discussed.
application; applications; CARBOWAX; Polyethylene; properties; SECTIONS; soil; SOILS; THIN; thin section; thin sections; THIN-SECTIONS
Glycemic control, reported pain and leakage with a 4[THIN SPACE]mm[THIN SPACE]x[THIN SPACE]32[THIN SPACE]G pen needle in obese and non-obese adults with diabetes: a post hoc analysis
Current Medical Research & Opinion
28
8
1305-1311
2012
Abstract Objective: The shortest pen needle (PN) for subcutaneous insulin therapy is 4[THIN SPACE]mm. Clinicians may hesitate to use it in obese patients. We report a post hoc analysis of a previously published study of the 4[THIN SPACE]mm[THIN SPACE]x[THIN SPACE]32[THIN SPACE]G PN, evaluating responses in obese (>=30[THIN SPACE]kg/m(2)) and non-obese (<30[THIN SPACE]kg/m(2)). Methods: Subjects (BMI 20 to 49[THIN SPACE]kg/m(2), 52% obese) with diabetes used 4[THIN SPACE]mm[THIN SPACE]x[THIN SPACE]32[THIN SPACE]G PNs and either 5[THIN SPACE]mm or 8[THIN SPACE]mm PNs (both 31[THIN SPACE]G) in two, 3-week treatment periods in a randomized noninferiority cross-over trial. Percentage absolute change in fructosamine (%[BOX DRAWINGS LIGHT VERTICAL (present in WGL4)][Greek capital Delta] Fru[BOX DRAWINGS LIGHT VERTICAL (present in WGL4)]) was the primary endpoint. Equivalent glycemic control was defined as %[BOX DRAWINGS LIGHT VERTICAL (present in WGL4)][Greek capital Delta] Fru[BOX DRAWINGS LIGHT VERTICAL (present in WGL4)] within 20% (including 95% CI). The impact of obesity on change in fructosamine, pain and reported insulin leakage from the skin is described. Clinical trial registration: Clinicaltrials.gov - identifier: NCT00928057. Limitations: This report is a post hoc analysis of two BMI subgroups resulting in smaller sample sizes. Results: Of 168 who completed the study, 163 were included in the fructosamine analyses - 83 and 80 in the 4/5[THIN SPACE]mm and 4/8[THIN SPACE]mm groups, respectively. For the 4/5[THIN SPACE]mm group, mean BMI[THIN SPACE]+/-[THIN SPACE]SD in non-obese and obese groups were 25.9[THIN SPACE]+/-[THIN SPACE]2.3 and 35.0[THIN SPACE]+/-[THIN SPACE]4.9[THIN SPACE]kg/m(2), respectively; 4/8[THIN SPACE]mm group 25.2[THIN SPACE]+/-[THIN SPACE]2.6 and 35.6[THIN SPACE]+/-[THIN SPACE]4.2[THIN SPACE]kg/m(2). BMI group was not significant for %[BOX DRAWINGS LIGHT VERTICAL (present in WGL4)][Greek capital Delta] Fru[BOX DRAWINGS LIGHT VERTICAL (present in WGL4)] for either 4/5[THIN SPACE]mm or 4/8[THIN SPACE]mm. Between BMI groups, the difference of the means in %[BOX DRAWINGS LIGHT VERTICAL (present in WGL4)][Greek capital Delta] Fru[BOX DRAWINGS LIGHT VERTICAL (present in WGL4)] was 0.4% (4/5[THIN SPACE]mm) and 0.3% (4/8[THIN SPACE]mm). The 4[THIN SPACE]mm PN was significantly less painful in all subject groups, except non-obese in 4/5[THIN SPACE]mm. Regardless of needle size, obese subjects reported more leakage events. For both BMI groups, there were fewer total reported leakage events when using the 4[THIN SPACE]mm vs 5[THIN SPACE]mm and 8[THIN SPACE]mm needles. Conclusions: The 4[THIN SPACE]mm pen needle provided equivalent glycemic control in both obese and non-obese patients compared to 5[THIN SPACE]mm and 8[THIN SPACE]mm needles with no increase in reports of skin leakage, in this post-hoc analysis. These findings should be confirmed in a prospective randomized controlled trial.
Influence of the patient positioning on respiratory mechanics during pneumoperitoneum
Middle East journal of anesthesiology
16
5
521
2002
The aim of this study was to evaluate the effect of patient positioning during laparoscopic cholecystectomy on respiratory mechanics and arterial blood gases. Thirty patients of ASA I were included. Ventilation was controlled mechanically. Tidal volume and ventilator frequency were kept unchanged throughout the operation. Intra-abdominal pressure was kept constant at 12 mmHg. Ventrak respiratory system was used for measuring respiratory mechanics. The airway resistance (Raw), the dynamic compliance (Cdyn), and the peak inspiratory pressure (PIP) were monitored. Measurements were made in five intervals: "a" after induction of general anesthesia, "b" after insufflation, "c" in the Trendelenburg position of 40 degree, "d" in the Fowler position of 40 degree, and "e" after desufflation. Samples of arterial blood gases were collected while the respiratory mechanics were being recorded. The mean arterial pressure (MAP) and heart rate (HR) were also monitored. In our study, during intervals "c" and "d", PCO2, was increased and pH decreased. With the initiation of insufflation, Cdyn, PIP, and Rawx, were altered (P < 0.05). The patient positioning had a significant effect on respiratory mechanics. After desufflation only Cdyn changed (P < 0.05). Although HR remained in normal limits, MAP increased during pneumoperitoneum (P < 0.05). We conclude that blood gas changes and respiratory mechanics were affected by the duration of pneumoperitoneum and patient positioning. The Fowler position had the least influence on respiratory mechanics.
Display device having a thin glass substrate.
U.S. Pat. Appl. Publ.
US20110255034A1
20pp.
2011
The display device according to the present invention is a display device comprising a thin glass substrate (applied thin glass) and a thin film transistor circuit (TFT circuit layer) formed on the thin glass substrate, wherein the thin glass substrate is gained by forming a transparent resin film (resin thin film) on a support member, applying a glass material to the transparent resin film, baking the glass material, and after that removing the support member. [on SciFinder(R)]
display device glass substrate
Propagation of thin plastic zones in the vicinity of a normally separating crack
Journal of Applied Mechanics and Technical Physics
50
5
901-910
2009
10.1007/s10808-009-0122-y
A problem of the development of a plastic zone in the vicinity of a physical cut in the plain strain and stress states is posed and solved on the basis of a discrete deformation model under the assumption of an ideal elastoplastic medium. The Tresca yield condition and the ultimate plasticity condition are used in studying the plane stress state. The dependence of the plastic zone length on the external load is compared with a similar dependence obtained on the basis of the Leonov-Panasyuk-Dugdale model. In contrast to the Leonov-Panasyuk-Dugdale model, the distributions of stresses and lengths of plastic zones in the plane strain and stress states are found to be substantially different if elastic compressibility and compressive-tensile stresses along the cut direction are taken into account. © MAIK/Nauka 2009.
Boundary integral equation; Boundary integral equations; Characteristic size; Discrete deformation; Dugdale model; Elasticity; Elasto-plastic; External loads; Idealelastoplastic model; Linear elasticity; Plain strain; Plane strains; Plane-stress state; Plastics; Plastic zones; Stress state; Yield conditions
Numerical simulation analysis on porthole dies extrusion of aluminum mini-thin harmonica-shaped tube
Applied Mechanics and Materials
457-458
156-159
2014
This paper describes a 3D-deform simulation of porthole die extrusion process for producing harmonica-shaped tubes used for a cooling system of automobiles. Designing the related structure of the porthole die and observing the simulation results, the study was designed to evaluate the welding effect when the length of bearing exit take different values.The mean pressure and exit velocity at the welding plane are analyzed at the same time. The welding effect is determined by the mean pressure at the welding plane.The behavior of metal flow in the container is analyzed in this paper. Through the above analysis, the best structure and size can be obtained in the process of deformation so as to obtain the better machanical properties. © (2014) Trans Tech Publications, Switzerland.
Exit velocity; Harmonica-shaped tube; Mean pressure; Porthole die
Crack identification in thin plates with anisotropic damage model and vibration measurements
Journal of Applied Mechanics, Transactions ASME
72
6
852-861
2005
Many approaches on modeling of cracks in structural members have been reported in the literatures. However, most of them are explicitly developed for the purpose of studying the changes in static and dynamic responses of the structure due to the crack damage, which is a forward problem mathematically. Thereby the use of these models is inconvenient or even impossible for detecting damage in structures from vibration measurements, which is usually an inverse problem. An anisotropic damage model is proposed for a two-dimensional plate element with an edge-parallel crack. The cracked plate element is represented by a plate element with orthotropic anisotropic material expressed in terms of the virgin material stiffness and a tensor of damage variables. Instead of using the effective stress concept, strain equivalence, or strain energy equivalence principles, the vector of damage variables is identified based on the principle of equivalent static and dynamic behaviors. A nonmodel-based damage identification approach is developed incorporating the proposed anisotropic model and the estimated uniform load surface curvature (ULSC) from vibration measurements. The actual length of the crack is then predicted from the identified variables based on conservation law of potential energy for crack growth. The validity of the methodology is demonstrated by numerical examples and experiment results with comparison to results from existing strain energy equivalence theory. Copyright © 2005 by ASME.
On the oscillations of a thin-walled structure containing a fluid, in the presence of a hydrodynamic damper
Journal of Applied Mathematics and Mechanics
43
6
1185-1192
1979
10.1016/0021-8928(79)90045-5
A model of a hydrodynamic oscillation damper is proposed. The model is used to obtain the equations describing longitudinal oscillations of a structure which includes a shell partially filled with fluid, and contains a hydrodynamic damper. It is shown that the use of the damper leads to considerable increase in the damping of the oscillations of specified frequencies within the structure. In modern technology one encounters various types of problems connected with restricting the amplitudes of the axisymmetric vibrations of shells and of the longitudinal oscillations of structures consisting of shells partially filled with fluid. Various devices have been proposed [1] for solving these problems. All these devices have a common feature, namely an elastic shell filled with gas and placed in the fluid. The natural frequency of oscillations of such a shell in a fluid can be tuned to required frequency. The effect of such a device is analogous to the effect of a dynamic vibration damper in mechanical systems [2]. A part of the fluid contained in the shell serves as the active mass of the dynamic damper, and for this reason we shall call such devices the hydrodynamic vibration dampers.
Effect of Deposition and Storage Conditions on the Gas Permeability of SiOx Thin Films
Applied Mechanics and Materials
378
248-252
2014
SiOx films (80 nm thick) were vacuum deposited onto a 25-μm-thick polyethylene terephthalate (PET) substrate under various conditions. The effects of chamber pressure, evaporating temperature, and chamber gas composition on the time evolution of the oxygen transmission rate (OTR) were investigated together with changes in the films composition. It was found that the OTR decreases over time when the films are left in air, the rate of the decrease being greater at higher pressures during the formation of the films. However, if the pressure is too high, the OTR immediately reaches a high value after evaporation and does not decrease over time, not even if the films are left in air for a week. It is possible to obtain acceptable low OTR values by employing a moderate operating pressure, a suitable evaporating temperature, and an aging treatment after deposition without using a high-capacity vacuum system and without heat damage of the plastic film substrate.
Gas Permeability; Plastic Substrate; SiOx Films; Vacuum Deposition; Web Coater
Film Drainage between Two Drops: Vortex Formation in Thin Liquid Films
Interciencia
34
6
380-384
2009
In this study, a mathematical formalism that takes into account the surfactant effect on the drainage of the interfacial film between two drops is considered. The effects of thermal perturbations and van der Waals forces are neglected. In the mathematical formalism the Navier-Stokes equations within the lubrication approximation are coupled to a diffusion - convection equation leading to an evolution equation for the interfacial film. This last equation is solved by using the numerical method of lines coupled with an implicit Runge-Kutta method for the integration with respect to time. As a result of the inclusion of interfacial tension gradients a non oscillating dimple arises, even beginning with an initial condition corresponding to a plane interfacial film.
coalescence; dimple; drops; emulsion films; fluid mechanics; interfacial film; marangoni effect; mechanism; rupture; stability; surfactant mass-transfer; thickness; time
Making Fast Cordage
Bulletin of Primative Technology
17
Spring
37-42
1999
An overview of thigh spinning one ply and two ply cordage using inner bark or bast fibres.
bast fibre; cordage; Spinning
Elastic-plastic crack growth simulation and residual strength prediction of thin plates with single and multiple cracks
ASTM Special Technical Publication
1332
97-113
1999
This paper presents numerical simulations of elastic-plastic, Mode I crack growth in thin aluminum plates. Two series of tests are simulated, M(T) specimens, and specimens containing multiple co-planar cracks. Elastic-plastic, shell finite element analysis is used to predict the residual strength of the tested plates. The crack tip opening angle (CTOA) measured at a specific distance behind the crack tip is the fracture criterion to characterize stable crack growth under conditions of general yielding. For small M(T) specimens, the limit load is attained due to net section yielding after the plastic zone reaches a free edge. In contrast, the residual strength of large specimens is achieved after some amount of crack growth with the plastic zone well-confined by the elastic region. Results of predicted residual strength are comparable to experimental measurements. However, as the width of the panel increases, the relative difference between experimental measurements and numerical predictions increases. The same CTOA fracture criterion is used to simulate crack growth and link-up in the multiple crack specimens. Predicted link-up load and residual strength are in good agreement with experimental measurements. A loss of residual strength due to the presence of multiple small cracks is observed.
Aluminum; Crack propagation; Cracks; Crack tip opening angle; Elasticity; Finite element method; Fracture mechanics; Loads (forces); Mathematical models; Numerical simulation; Plasticity; Plastic zone; Plates (structural components); Residual strength; Strength of materials
Lung injury and respiratory mechanics in rugby union
J Sports Med Phys Fitness
ePub
ePub
ePub-ePub
2014
Rugby is a highly popular team contact sport associated with high injury rates. Specifically, there is a chance of inducing internal lung injuries as a result of the physical nature of the game. Such injuries are only identified with the use of specific invasive protocols or equipment. This study presents a model--based method to assess respiratory mechanics of N=11 rugby players that underwent a low intensity experimental mechanical ventilation (MV) test before and after a rugby game. Participants were connected to a ventilator via a facemask and their respiratory mechanics estimated using a time--varying elastance model. All participants had a respiratory elastance <10 cmH2O/L with no significant difference observed between pre and post--game respiratory mechanics (P>0.05). Model--based respiratory mechanics estimation has been used widely in the treatment of the critically ill in intensive care. However, the application of a ventilator to assess the respiratory mechanics of healthy human beings is limited. This is the first study to conceptualize the assessment of respiratory mechanics in healthy athletes as a means to monitor post exercise stress and therefore manage recovery.
Brownian Motion and the Stochastic Theory of Quantum Mechanics
Irreversibility in the Many-Body Problem
457-470
1972
10.1007/978-1-4899-2669-2
The purpose of this lecture is to give the principles of the simplest stochastic mechanics in configuration space. The work simplest will be explained later; configuration space is the space of the position coordinates of the particles and stochastic mechanics is defined as follows: We call stochastic mechanics to any dynamical theory in which the equations of motion are not fully known. The partial ignorance about the equations of motion is taken into account by introducing stochastic parameters in it. The typical example of stochastic mechanics is the theory of Brownian motion. We distinguish stochastic from statistical mechanics by defining statistical mechanics as a theory in which the differential equations of motion are in principle known even though the initial conditions are not completely specified. Irreversibility in the Many-Body Problem Irreversibility in the Many-Body Problem Look Inside Chapter Metrics Downloads 12 Provided by Bookmetrix Other actions Reprints and Permissions Export citation About this Book Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn
Kalker's method applied to some improper integrals in fracture mechanics
Engineering Fracture Mechanics
54
2
229-237
1996
10.1016/0013-7944(95)00197-2
This paper discusses some methods of contact mechanics, which can be applied to fracture problems. First, improper integrals with a singularity of the order r−3 are treated, which some authors call hypersingular integrals. Compared with other publications, a simplified formulation is achieved by application of Kalker's analytical method for singularities of the order r−1. The result is written in terms of hypergeometric functions, which are recursively reduced to standard elliptic integrals. Similar to the superposition of single forces in contact mechanics, a superposition of single displacements is used in fracture mechanics and the methods of contact mechanics are applied to fracture mechanics. In contrast to the modelling of the crack surface as a polynomial in x and y, a discrete displacement function with constant values on an equidistant rectangular mesh is more promising. The integration is performed as a matrix product and the cyclic structure of this matrix is used to reduce the required computer memory.
Mechanics of interface with applications in electronic packaging
IEEE Transactions on Device and Materials Reliability
3
4
129-143
2003
10.1109/TDMR.2003.820623
The purpose of this paper is to present a brief review of the mechanics of interface fracture, with a focus on applications in electronic packaging. From a structural mechanics perspective, electronic devices can be thought of as composite structures fabricated from highly dissimilar materials. Often, the interfaces between these materials are where failure is most likely to occur when the device is subjected to thermomechanical loading. The mechanics of interface fracture is a specialized subtopic within the discipline of fracture mechanics and the nonspecialist may be unaware of some of the subtle differences encountered in applying interface fracture concepts. The mechanics associated with interface fracture introduces certain mathematical concepts that may seem to be unnecessarily complicated, but are essential for its proper application. It is important that the electronic packaging reliability engineer be aware of these concepts, understanding the most important implications. This review will focus on the mechanics and computational aspects of interface fracture in electronic structures, with a particular emphasis on some details that the nonexpert could only obtain after an extensive review of the available literature. Numerical results are presented for the important problem of corner cracking between silicon and epoxy materials subjected to thermomechanical loading. These new results provide insight into the three-dimensional nature of interfacial crack propagation at bimaterial corners.
Influence of the patient positioning on respiratory mechanics during pneumoperitoneum.
Middle East journal of anesthesiology
16
5
521-528
2002
The aim of this study was to evaluate the effect of patient positioning during laparoscopic cholecystectomy on respiratory mechanics and arterial blood gases. Thirty patients of ASA I were included. Ventilation was controlled mechanically. Tidal volume and ventilator frequency were kept unchanged throughout the operation. Intra-abdominal pressure was kept constant at 12 mmHg. Ventrak respiratory system was used for measuring respiratory mechanics. The airway resistance (Raw), the dynamic compliance (Cdyn), and the peak inspiratory pressure (PIP) were monitored. Measurements were made in five intervals: "a" after induction of general anesthesia, "b" after insufflation, "c" in the Trendelenburg position of 40 degree, "d" in the Fowler position of 40 degree, and "e" after desufflation. Samples of arterial blood gases were collected while the respiratory mechanics were being recorded. The mean arterial pressure (MAP) and heart rate (HR) were also monitored. In our study, during intervals "c" and "d", PCO2, was increased and pH decreased. With the initiation of insufflation, Cdyn, PIP, and Rawx, were altered (P < 0.05). The patient positioning had a significant effect on respiratory mechanics. After desufflation only Cdyn changed (P < 0.05). Although HR remained in normal limits, MAP increased during pneumoperitoneum (P < 0.05). We conclude that blood gas changes and respiratory mechanics were affected by the duration of pneumoperitoneum and patient positioning. The Fowler position had the least influence on respiratory mechanics.
Teaching Research and Practice on Material Mechanics with the core of Practical cases
Procedia Engineering
15
4256-4260
2011
10.1016/j.proeng.2011.08.798
During the teaching of material mechanics, with the core of practical cases can not only retain the original advantages, but also overcome its disadvantages at a maximum level. This article clarified such advantages of this kind of teaching and the methodology to carry on. Proofed by practice that the teaching of material mechanics with a core of practical cases is one kind of very effective teaching model.
material mechanics; Practical cases; teaching practice; teaching research
Dynamic versus static respiratory mechanics in acute lung injury and acute respiratory distress syndrome.
Critical care medicine
34
8
2090-8
2006
10.1097/01.CCM.0000227220.67613.0D
It is not clear whether the mechanical properties of the respiratory system assessed under the dynamic condition of mechanical ventilation are equivalent to those assessed under static conditions. We hypothesized that the analyses of dynamic and static respiratory mechanics provide different information in acute respiratory failure.
adult; critical care; lung compliance; mechanical stress; respiratory distress syndrome; respiratory mechanics
Mechanics of the nucleus in differentially uncommitted cells
ProQuest Dissertations and Theses
113
2010
When present, the nucleus occupies a large volume of the cell and its structures play a strong role in nuclear and cell mechanics. Mechanical properties are pivotal for cells to sense and internalize external forces, which may lead to alteration of function. Evidence suggests that function of differentially uncommitted cell types--cancer and stem cells--may be correlated to mechanics. Differentially uncommitted cells present the ability to differentiate, or transform in the case of cancer, the potential to invade tissues, away from their original niches, or tumors in the case of cancer, and present very similar organizations of chromatin and lamina structures. The aim here is to address how cell mechanics correlates to the functions of differentially uncommitted cells. We mechanically characterized 3 cancer cell models with micropipette aspiration--fibrosarcoma and melanoma lines--and 3 stem cell models--hematopoietic, mesenchymal and perivascular stem cells. In the fibrosarcoma, the variation of expression in one oncogene was enough to generate drastic alterations in structure and mechanics of the nucleus, while two melanoma cell lines in very different stages of transformation presented considerably different mechanical reactions to aspiration associated with different nuclear morphologies. Mechanics seems to vary considerably among stem cells with different origins and culture conditions, where different applications may be more efficient with specific stem cell types relatively to others based on mechanical properties. This study was associated with the analysis of nuclear and cytoplasmic structures, where special attention was given to A-type lamins as a possible component to be manipulated in order to tune nuclear and consequently cell mechanics. Structural changes were observed and analyzed in HeLa cells after regulating the expression and altering specific molecular properties of A-type lamins. Lamin AΔ50--a mutated form of A-type lamins--was expressed in metastatic melanoma cells and nuclear deformation was considerably reduced. Mechanics of the nucleus seems to play a strong role in defining the properties of differentially uncommitted cells. However, different mechanisms of nuclear mechanics were observed among the tested cells, suggesting the existence of more possible scenarios of structural organization in other differentially uncommitted cells.
0541:Biomedical engineering; 0648:Biomechanics; Applied sciences; Biological sciences; Biomechanics; Biomedical engineering; Cell nuclei; Lamin A; Stem cells; Uncommitted cells
Mechanics of an educational exchange
Aust J Rural Health
8
4
218-221
2000
Rural general practitioners occasionally exchange practices internationally. The process of exchanging is a complicated one, which involves multiple bureaucarcies. Exchanging is not for the anxious or impatient. We exchanged with a family physician in Canada and had to arrange registration, provider numbers and immigration for our Canadian colleague, as well as for ourselves in Canada. In addition, there are many personal details (cars, house, etc.) that must also be sorted out.
Alberta; Credentialing; Emigration and Immigration; Family Practice/*education; Financial Management; Humans; *International Educational Exchange; *Rural Health Services; Victoria
Quantum Mechanics on the Hypercube
Representations
8
2000
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this representation acts in a natural way on the coordinates of the non-commutative 2-torus,T^2, and thus is relevant for noncommutative field theories as well as theories of quantum space-time.
Chaotic Dynamics; High Energy Physics - Theory; Quantum Algebra; Quantum Physics
The Mechanics of Rationality
Southern Journal of Philosophy
28(3) 343-366
1990
The paper examines the relation between rationality and mechanism. What is contested is the thesis that, if at base our functioning were mechanical, we could not be genuinely rational, we could not believe or act for a reason. It is argued that on the contrary, not only can the rational and mechanical coincide, more strongly the operation of reason requires a mechanism of a certain sort; for the mechanical system enables the operation of reason.
Dennett, D; Metaphysics; Rationality
CLASSICAL AND COMPUTATIONAL MECHANICS.
Molecules (Basel, Switzerland)
15
8
952
2010
10.3390/molecules15085692
An efficient route for the synthesis of the phosphoramidite derivative of 5-methylcytosine bearing a tert-butylsulfanyl group protected thiol is described. This building block is used for the preparation of oligonucleotides carrying a thiol group at the nucleobase at the internal position of a DNA sequence. The resulting thiolated oligonucleotides are useful intermediates to generate oligonucleotide conjugates carrying molecules of interest at internal positions of a DNA sequence.
Chiral Symmetry Breaking in Magnetic Thin Films and Multilayers
Physical Review Letters
87
3
37203
2001
A phenomenological theory of chiral symmetry breaking in magnetic nanostructures is developed considering induced, inhomogeneous chiral interactions (Dzyaloshinsky-Moriya-type). Application of the theory to films and multilayers with in-plane and out-of-plane magnetization predicts modulated and two-dimensional localized patterns (vortices). These new classes of magnetic patterns are intrinsically stable and localized on nanometer scale. Various experimental observations agree qualitatively with structures derived from this theory.
Films; MAGNETIC; magnetic thin film; magnetic thin films; Multilayer structure; Symmetry; THIN; Thin Film; THIN-FILM; Thin Films; Thin-Films
The History of Quantum Mechanics as a Decisive Argument Favoring Einstein over Lorentz
Philosophy of Science
52
44
1985
Einstein's papers on relativity, Quantum theory, And statistical mechanics were all part of a single research program; the aim was to unify mechanics and electrodynamics. It was this broader program-Which eventually split into relativistic physics and quantum mechanics-That superseded lorentz's theory. The argument of this paper is partly historical and partly methodological. A notion of "crossbred objects"-Theoretical objects with contradictory properties which are part of the domain of application of two different research programs-Is developed that explains the dynamics of revolutionary theory change.
Studies of mechanics property of discontinuity of engineering rockmass under three-dimensional stress
Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering
20
SUPPL.
1734-1738
2001
Based on lots of testing results of rocks obtained from lab and site,\nthe mechanics property of discontinuity of engineering rockmass under\nthree-dimensional stress is studied. Especially, the strength and\ndeformation of jointed rocks are analyzed. And the failure mechanism\nand failure principle of engineering rocks are discussed.
Deformation;Failure analysis;Rock mechanics;Stress
Probability and quantum mechanics. The conceptual foundations of stochastic mechanics
Quantum Probability and Applications to the Quantum Theory of Irreversible Processes
1055
1984
10.1007/BFb0071705
We analyze the peculiar features of probabilistic concepts in quantum mechanics, with particular enphasis on the role of coherence properties of the quantum-mechanical description. It is recognized that the paradoxical aspects of quantum mechanics can be interpreted as having rise from improper use of classical probabilistic concepts, in particular the definition of conditional expectations. Then the program of stochastic quantization is presented from the point of view of avoiding these difficulties. Here the kinematics of the system is described through stochastic differential equations, thus employing standard concepts of classical probability theory. On the other hand the dynamics is specified through stochastic variational principles, based on dynamical actions containing averages with respect to all possible initial configurations of the system. In this way, the resulting programming equation is of the Hamilton-Jacobi type with additional terms depending on the density. As a consequence we find a peculiar organization of the probabilistic content of the theory, fully equivalent to quantum coherence. In fact the programming equation leads to Schrödinger equation and one can observe typical "interference" of probabilities, according to standard (even if improper) quantum mechanical terminology. Finally we show that a more refined concept of conditional expectation is needed in a probabilistic frame employing dynamical conditions based on averaged stochastic actions, as here. In fact the physical processes correspond to probability measures which make extremal the action. It is easy to check that extremalization followed by standard mathematical conditioning is not equivalent to extremalize over conditioned trajectories. The first pattern is spontaneously followed by researchers led by the primarily philosophical interest of giving realistic interpretations to quantum mechanics. Then paradoxical aspects arise. But it is the second pattern which is really involved in the quantum measurement problem. Our general conclusion is that classical probability theory can be employed for the description of quantum systems, but the dynamical structure must take into account the peculiar features of quantum mechanics, well incorporated in the form of stochastic variational principles. The resulting general probabilistic scheme may well merge in the future with the approach based on the development of the new theory, called quantum probability, the main topic of this Conference.
The subject matter of quantum mechanics
International Journal of Theoretical Physics
31
9
1615-1625
1992
10.1007/BF00671776
This is a philosophical paper. It deals with the interpretation of quantum mechanics, i.e., with reality, the objects of quantum mechanics, probabilities, etc. It is important to distinguish between real things and physical systems. A physical theory is a collection of rules for predictions on the outcome of measurements. Contrary to general belief “prediction” and “possible and actual” are key concepts in physics, as well as the concept of probability, being the most general empirically testable prediction. The Copenhagen interpretation is nothing but a “minimal semantics” of quantum mechanics, dealing with possibilities rather than with facts. Quantum mechanical realism is the futile attempt to confine physics to the description of facts. We answer the old question whether probability is about single events or about series of events: it can be about either, if it is correctly interpreted as a representative of the abstract ensemble. Quantum mechanics is only interesting if it is the most general theory of all possible systems. But this is where the hard problems arise: measurement, reality, indeterminism, etc. These problems can be solved if we accept seriously the key role of prediction and possibility, and abandon the ontology of classical physics.
{F}luid mechanics of heart valves.
Annu Rev Biomed Eng
6
331-362
2004
Valvular heart disease is a life-threatening disease that afflicts\nmillions of people worldwide and leads to approximately 250,000 valve\nrepairs and/or replacements each year. Malfunction of a native valve\nimpairs its efficient fluid mechanic/hemodynamic performance. Artificial\nheart valves have been used since 1960 to replace diseased native\nvalves and have saved millions of lives. Unfortunately, despite four\ndecades of use, these devices are less than ideal and lead to many\ncomplications. Many of these complications/problems are directly\nrelated to the fluid mechanics associated with the various mechanical\nand bioprosthetic valve designs. This review focuses on the state-of-the-art\nexperimental and computational fluid mechanics of native and prosthetic\nheart valves in current clinical use. The fluid dynamic performance\ncharacteristics of caged-ball, tilting-disc, bileaflet mechanical\nvalves and porcine and pericardial stented and nonstented bioprostheic\nvalves are reviewed. Other issues related to heart valve performance,\nsuch as biomaterials, solid mechanics, tissue mechanics, and durability,\nare not addressed in this review.
15255773; Animals; Biomechanics; Bioprosthesis; Computer Simulation; Constriction; Heart Valve Prosthesis; Heart Valves; Humans; Mitral Valve; Pathologic; P.H.S.; Prostheses and Implants; Prosthesis Design; Research Support; Software; Thrombosis; U.S. Gov't
Computaional fracture mechanics: research and application
Engineering Fracture Mechanics
50
5
653-670
1995
10.1016/0013-7944(94)E0051-H
This paper focuses on the impact of computational methodology on furthering the understand- ing of fundamental fracture phenomena. The current numerical approaches to the solution of fracture mechanics problems, e.g. finite element (FE) methods, finite difference methods and boundary element methods, are reviewed. The application of FE methods to the problems of linear elastic fracture problems is discussed. Particular emphases are placed on the stress intensity factors, energy release rate in mixed mode fracture and dynamic crack propagation. Numerical solutions of ductile fracture problems are surveyed. A special focus is placed on stable crack growth problems. The need for further research in this area is emphasized. The importance of large strain phenomena and accurate modeling of non-linearities is highlighted. An expanded version of fracture mechanics methodology is given by Liebowitz [Advances in Fracture Research 3. Pergamon Press, Oxford (1989)]; additional treatment is given in this paper to numerical results incorporating error estimates and algorithms for mesh design into the FE code. The adaptive method involves various stages which includes FE analysis, error estimation/indication, mesh refinement and fracture/failure analysis iteratively. Reference is made to integrate expert knowledge and a hierarchial, rule-based, decision process to fracture mechanics for the purpose of designing practical fracture-proof engineering products. Some further areas of research in adaptive finite element analysis are discussed.
Inertia-free mechanics and the bi-metric procedure
Astronomische Nachrichten
302
127
1981
The failure of various attempts to formulate a generally\napplicable principle of relative motion in the context of\ngeneral relativity led to a project to construct first, on\nthe basis of classical mechanics, a new mechanics in the\nsense of Poincare, and to conduct, as a second step, an\ninvestigation related to the formulation of generalizations\ncompatible with experience regarding the gravitational\ncoupling of nongravitational matter via the equivalence\nprinciple. The considered study is concerned with this\nsecond step. The proposed bimetric procedure is applicable\nalso to other kinds of inertia-free mechanics, such as\nstudied by Barbour (1975), Barbour and Bertotti (1977),\nBarbour and Easthope (1979), or Bertotti and Easthope\n(1979). It is pointed out that the procedure represents\nonly the trivial way of avoiding the obstacles and that it\nis open to be challenged by deeper and more elegant laws\nstill to be found.
BIMETRIC THEORIES; CELESTIAL MECHANICS; DYNAMIC MODELS; FIELD THEORY (PHYSICS); GRAVITATION THEORY; INERTIA; NEWTON THEORY; RELATIVITY; SPACE-TIME FUNCTIONS; UNIVERSE
Some Mining Applications of Unsaturated Soil Mechanics
Geotechnical Engineering Journal of the SEAGS & AGSSEA
43
1
83-98
2012
Unsaturated soil mechanics continues to play poor relation to saturated soil mechanics, although an unsaturated soil at a given density is stronger, less compressible and less permeable (i.e. performs better) than the same soil in a saturated state. There are many examples of unsaturated conditions in the mining field, including the wetting-up and drain-down of initially dry surface waste rock dumps; the irrigation and drain-down of heap leach materials; the drain-down, desiccation and rewetting of mine tailings; the dewatering of mineral products such as coal; the shear strength and compressibility of stored mine wastes; and the performance of geo-covers placed on mine wastes on rehabilitation. This paper highlights the key unsaturated soil mechanics parameters, overviews the nature of mining and processing wastes, and some products, and discusses the issues involved. Some applications of unsaturated soil mechanics addressing the shear strength, compressibility and permeability of mine wastes, and mineral products, are presented, together with data to highlight them.
Quantum mechanics in structure-based drug design
Current opinion in drug discovery & development
9
3
370-379
2006
In principle, quantum mechanics provides a more accurate representation of molecular systems than other modeling approaches. While this notion is not a matter of dispute, it has not yet been definitively demonstrated within the realm of structure-based drug design that the use of quantum mechanical methods over the use of classical modeling approaches is justified in consideration of the increase in expense associated with quantum mechanical methods. Demonstrating that quantum mechanics-based methods can be superior to simpler models, and resolving problems relating to estimating the effects of conformational entropy, will provide key areas of interest in the coming years for in silico structure-based drug design. Recent applications using quantum mechanical methods in structure-based drug design are reviewed herein, and applications ranging from scoring receptor-ligand interactions using quantum mechanics to the generation of quantitative structure-activity relationships using quantum mechanics-derived descriptors are discussed.
The symmetry principle in continuum mechanics
Journal of Applied Mathematics and Mechanics
71
1
20-29
2007
10.1016/j.jappmathmech.2007.03.008
For problems of the mechanics of an anisotropic inhomogeneous continuum, theorems are given concerning the uninterrupted symmetrical and antisymmetrical analytical continuation of the solution through the plane part of the boundary surface of the medium. Theorems are given for two types of mechanics problem; in the first of these both symmetrical and antisymmetrical continuations of the solution are allowed, while in the second only symmetrical continuation of the solution is allowed. Problems of the first type include problems which are reduced to linear thermoelastic dynamic differential equations of motion of an inhomogeneous anisotropic medium possessing a plane of elastic symmetry, to linear thermoelastic dynamic differential equations of motion of an inhomogeneous Cosserat medium, to non-linear differential equations describing the static elastoplastic stress state of a plate, etc. The second type includes problems which are reduced to non-linear differential equations describing geometrically non-linear strains of shells, to Navier-Stokes equations, etc. These theorems extend the principle of mirror reflection (the Riemann-Schwartz principle of symmetry) to linear and non-linear equations of continuum mechanics. The uninterrupted continuation of the solutions is used to solve problems of the equilibrium state of bodies of complex shape. ?? 2007 Elsevier Ltd. All rights reserved.
Ergodic theorem, ergodic theory, and statistical mechanics.
Proceedings of the National Academy of Sciences of the United States of America
112
7
1907-11
2015
10.1073/pnas.1421798112
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.
Remarks on the application of design sensitivity analysis in fracture mechanics
ICF11
2005
Kinematics in structural optimisation and configurational mechanics coincide as long as sufficiently smooth design variations of the material bodies are considered. Thus, variational techniques from design sensitivity analysis can be used to derive the well-known Eshelby tensor and hence the energy release rate. Furthermore, second variations can be derived to solve inverse problems within configurational mechanics. A numerical scheme for computing the maximal energy release rate and its sensitivities is formulated in order to highlight the challenges of sensitivity analysis and optimisation. 1
Nos[e-acute]--Hoover nonequilibrium dynamics and statistical mechanics
Molecular Simulation
33
1-2
13-19
2007
10.1080/08927020601059869
At equilibrium Nos{é}'s 1984 revolutionary thermostat idea linked Newton's mechanics with Gibbs' statistical mechanics. His work expanded the scope of isothermal and isobaric simulations. Nos{é}--Hoover dynamics has subsequently facilitated the simulation and detailed understanding of nonequilibrium problems. The fractal phase-space distributions, and their close link to the Lyapunov spectrum, provide a novel explanation of irreversibility and a rich field for exploration.
Teaching molecular mechanics in the chemistry curriculum. Part 1: Concepts
Actualite Chimique
7
24-33
1997
The concepts are simple, software and hardware more and more available, chemistry on the computer is attractive, practical applications are numerous, the field is growing in academic research as well as in the industry : these are the reasons why we should incorporate molecular modeling in our chemistry curriculum. This article presents molecular mechanics, the classical basis of molecular modeling, to the chemistry teacher. In this first part, the concepts are introduced. In a second part, the possibilities of including molecular mechanics in a chemistry are discussed.
On the origins of the journal of applied mathematics and mechanics
Journal of Applied Mathematics and Mechanics
51
2
i-ii
1987
http://dx.doi.org/10.1016/0021-8928(87)90053-0
It so happens that the year 1988 serves as the occasion of celebrating not only the 40th anniversary of the founding of Pergamon Press, and the 65th birthday of its founder, Robert Maxwell, but is also the 30th anniversary year of the Journal of Applied Mathematics and Mechanics. It is thus a particular pleasure for me to set down here a few remarks concerning the origins of this journal, which represents a cover-to-cover translation of the Soviet Journal PMM (Prikladnaia Matematika i Mekhanika).
LINNThe structure of time and inertial forces in Lagrangian mechanics
0801.4151
2008
Classically time is kept fixed for infinitesimal variations in problems in mechanics. Apparently, there appears to be no mathematical justification in the literature for this standard procedure. This can be explained canonically by unveiling the intrinsic mathematical structure of time in Lagrangian mechanics. Moreover, this structure also offers a general method to deal with inertial forces.
Review of Compressible Plasticity Mechanics in Metal Foams
RARE METAL MATERIALS AND ENGINEERING
38
293-296
2009
The continuous constitutive models and compressible plastic mechanics\nin metal cellular materials is reviewed. On the basis of J2 flow\ntheory a constitutive relation of compressible plastic mechanics\nis obtained. This constitutive relation is used for plane stress\nmode-I crack growth in the nonlinear crack problems of metallic cellular\nmaterials, and the obtained result is compared with the corresponding\nresult of a power-law hardening material 20240T3 aluminum.
The diatomic anharmonic oscillator according to matrix mechanics
Mathematics and Computers in Simulation
49
3
221-234
1999
We determine the energies of states of the diatomic anharmonic oscillator by matrix mechanics in its original form as developed by Heisenberg, Born and Jordan using perturbation theory in successive orders. We present exact formulae for the second-, fourth-, and sixth-order contributions to the energy that were computed with Maple. The calculations involve matrices of finite rank with symbolic entries. We include the Maple programs. © 1999 IMACS/Elsevier Science B.V. All rights reserved.
Anharmonic oscillator; Maple programs; Matrix mechanics
Probabilistic foundations of quantum mechanics and quantum information
Arxiv preprint
239
462
2003
This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.
Quantum mechanics in structure-based drug design
Curr. Opin. Drug Discov. Devel.
9
3
370-379
2006
In principle, quantum mechanics provides a more accurate representation of molecular systems than other modeling approaches. While this notion is not a matter of dispute, it has not yet been definitively demonstrated within the realm of structure-based drug design that the use of quantum mechanical methods over the use of classical modeling approaches is justified in consideration of the increase in expense associated with quantum mechanical methods. Demonstrating that quantum mechanics-based methods can be superior to simpler models, and resolving problems relating to estimating the effects of conformational entropy, will provide key areas of interest in the coming years for in silico structure-based drug design. Recent applications using quantum mechanical methods in structure-based drug design are reviewed herein, and applications ranging from scoring receptor-ligand interactions using quantum mechanics to the generation of quantitative structure-activity relationships using quantum mechanics-derived descriptors are discussed.
Unsaturated Soil Mechanics in Engineering Practice
Journal of Geotechnical and Geoenviromental Engineering
132
March
286-321
2006
10.1061/ASCE1090-0241 2006 132:3 286 CE
Unsaturated soil mechanics has rapidly become a part of geotechnical engineering practice as a result of solutions that have emerged to a number of key problems ?or challenges?. The solutions have emerged from numerous research studies focusing on issues that have a hindrance to the usage of unsaturated soil mechanics. The primary challenges to the implementation of unsaturated soil mechanics can be stated as follows: ?1? The need to understand the fundamental, theoretical behavior of an unsaturated soil; ?2? the formulation of suitable constitutive equations and the testing for uniqueness of proposed constitutive relationships; ?3? the ability to formulate and solve one or more nonlinear partial differential equations using numerical methods; ?4? the determination of indirect techniques for the estimation of unsaturated soil property functions, and ?5? in situ and laboratory devices for the measurement of a wide range of soil suctions. This paper explains the nature of each of the previous challenges and describes the solutions that have emerged from research studies. Computer technology has played a major role in achieving practical geotechnical engineering solutions. Computer technology has played an important role with regard to the estimation of unsaturated soil property functions and the solution of nonlinear partial differential equations. Breakthroughs in the in situ and laboratory measurement of soil suction are allowing unsaturated soil theories and formulations to be verified through use of the “observational method.”
Geotechnical engineering; soil mechanics; unsaturated soil
Some Mining Applications of Unsaturated Soil Mechanics
Geotechnical Engineering Journal of the SEAGS & AGSSEA
43
1
83-98
2012
Unsaturated soil mechanics continues to play poor relation to saturated soil mechanics, although an unsaturated soil at a given \ndensity is stronger, less compressible and less permeable (i.e. performs better) than the same soil in a saturated state. There are many \nexamples of unsaturated conditions in the mining field, including the wetting-up and drain-down of initially dry surface waste rock dumps; \nthe irrigation and drain-down of heap leach materials; the drain-down, desiccation and rewetting of mine tailings; the dewatering of mineral \nproducts such as coal; the shear strength and compressibility of stored mine wastes; and the performance of geo-covers placed on mine \nwastes on rehabilitation. This paper highlights the key unsaturated soil mechanics parameters, overviews the nature of mining and \nprocessing wastes, and some products, and discusses the issues involved. Some applications of unsaturated soil mechanics addressing the \nshear strength, compressibility and permeability of mine wastes, and mineral products, are presented, together with data to highlight them.
Computational Mechanics Solvers Based on Object-Oriented Design Principles
Winter Simulation Conference
486-489
1990
In this paper the methods of object-oriented programming are compared with the software needs of the field of computations mechanics and then assessed. It appears that object-oriented programming techniques can enable computational mechanics software structures with desirable characteristics not easily obtained within a conventional software perspective: (1) they can function more easily with different coordinate types; (2) they facilitate the construction of larger system models from proven (relocatable) sub-system models, and (3) they easily support multi-resolution computational processes.
A review of the Statistical Mechanics approach to Random Optimization Problems
Handbook of Satisfiability
2008
We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these problems, starting from basic concepts. We also discuss how statistical mechanics methods can be used to investigate the behavior of local search and decimation based algorithms.
Non-linear evaluation of respiratory mechanics during laparoscopic cholecystectomy.
Hepato-gastroenterology
50
52
934-938
2003
Laparoscopic cholecystectomy is accompanied by significant increase of the respiratory system elastic and resistive properties. These changes are completely abolished after peritoneal deflation. In the present study we examine the volume and flow dependence of respiratory mechanics during four operation phases.
Aged; Cholecystectomy; Artificial; Respiratory Mechanics; Laparoscopic; Female; Head-Down Tilt; Humans; Int
Quantum mechanics and elements of reality inferred from joint measurements
Journal of Physics A: Mathematical and General
30
2
725
1997
The Einstein - Podolsky - Rosen argument on quantum mechanics incompleteness is formulated in terms of elements of reality inferred from joint (as opposed to alternative) measurements, in two examples involving entangled states of three spin- ##IMG## [http://ej.iop.org/images/0305-4470/30/2/032/img1.gif] particles. The same states allow us to obtain proofs of the incompatibility between quantum mechanics and elements of reality.
Violation of the Robertson-Schrodinger uncertainty principle and noncommutative quantum mechanics
Physical Review D
86
10
105030
2012
10.1103/PhysRevD.86.105030
We show that a possible violation of the Robertson-Schrodinger uncertainty\nprinciple may signal the existence of a deformation of the Heisenberg-Weyl\nalgebra. More precisely, we prove that any Gaussian in phase space\n(even if it violates the Robertson-Schrodinger uncertainty principle)\nwill always be a quantum state of an appropriate noncommutative extension\nof quantum mechanics. Conversely, all canonical noncommutative extensions\nof quantum mechanics display states that violate the Robertson-Schrodinger\nuncertainty principle.
On the geometry of the energy operator in quantum mechanics
International Journal of Geometric Methods in Modern Physics
11
07
1460027
2014
10.1142/S0219887814600275
We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or added with an arbitrary constant factor, both in the mainstream Geometric Quantization and in the Covariant Quantum Mechanics, developed by Jadczyk and Modugno with several contributions from many authors.
Measurement and the interpretation of quantum mechanics and relativity theory
Synthese
102
293-318
1995
10.1007/BF01089804
The axiomatic approaches of quantum mechanics and relativity theory are compared with approaches in which the theories are thought to describe readings of certain measurement operations. The usual axioms are shown to correspond with classes of ideal measurements. The necessity is discussed of generalizing the formalisms of both quantum mechanics and relativity theory so as to encompass more realistic nonideal measurements. It is argued that this generalization favours an empiricist interpretation of the mathematical formalisms over a realist one.
A review of the Statistical Mechanics approach to Random Optimization Problems
arXiv
cs.CC
2008
We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these problems, starting from basic concepts. We also discuss how statistical mechanics methods can be used to investigate the behavior of local search and decimation based algorithms.
cs.CC
Relationships between power-law long-range interactions and fractional mechanics
Physica A: Statistical Mechanics and its Applications
391
23
5827-5838
2012
10.1016/j.physa.2012.06.055
We investigate the relationships between models of power-law long-range interactions and mechanics based on fractional derivatives. We present the fractional Lagrangian density which gives the Euler-Lagrange equation that serves as the equation of motion for fractional-power-law long-range interactions. We derive this equation by the fractional variational method. In addition, we derive a Noether-like current from the fractional Lagrangian density. © 2012 Elsevier B.V. All rights reserved.
European Journal of Computational Mechanics / Revue Européenne de Mécanique Numérique The sensitivity equation method in fluid mechanics The sensitivity equation method in fluid mechanics
European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique
17
1-2
31-61
2008
10.3166/REMN.17.31-61
We present the sensitivity Equation Method (SEM) as a complementary tool to adjoint based optimisation methods. Flow sensitivities exist independently of a design problem and can be used in several non-optimization ways: characterization of complex flows, fast evaluation of flows on nearby geometries, and input data uncertainties cascade through the CFD code to yield uncertainty estimates of the flow field. The Navier-Stokes and sensitivity equationssensitivity are solved by an adaptive finite element method.
Computed tomography and associations to lung mechanics "the evaluation of COPD longitudinally to identify predictive surrogate endpoints" (ECLIPSE) study
AMERICAN JOURNAL OF RESPIRATORY AND CRITICAL CARE MEDICINE
181 (1 Mee
2010
Rationale: Chronic obstructive pulmonary disease (COPD) is characterized by the presence of airflow limitation measured physiologically. It is thought airflow limitation is caused by some combination of emphysematous destruction of the lung parenchyma and airway remodeling. One of the goals of the ECLIPSE study is to determine the contribution of these anatomic changes on lung physiology. Methods: The current analysis was performed on a subset (N=515) of the entire cohort (N=2747) that underwent lung volume measurements using body plethysmography, spirometry, and CT scans. Spirometry was post-bronchodilator following ATS criteria (FEV<sub>1</sub> %predicted calculated from ECCS). Body plethysmography was post-bronchodilator for measuring static lung volumes. Multi-slice CT scans were obtained at suspended inspiration using a thin slice (1 or 1.25 mm) low dose (40mAs) protocol. CT scans were analyzed by radiologist consensus read and by Pulmonary Workstation 2.0 software (VIDA Diagnostics) to determine extent of CT emphysema (<-950HU, %low attenuation areas; %LAA) and airways thickening (wall area % of RB1 and airway wall area at 10mm; Pi10). Strength of associations were determined between all physiological variables and the extent of emphysema and airways thickening. Results: In this cohort, LAA% correlated significantly with FEV<sub>1</sub>/FVC (r = -0.70), FEV<sub>1</sub> %predicted (r = -0.55), RV %predicted (r = 0.49), TLC %predicted (r = 0.46), IC/TLC (r = -0.44), and RV/TLC (r = 0.36). There was no association between airway wall measurements and any of the physiological variables (r <= 0.2). The association between %LAA and FEV<sub>1</sub>/FVC showed consistent and moderate associations in all GOLD stages with most subjects exhibiting a high degree of emphysema and a low FEV<sub>1</sub>/FVC in GOLD IV (Table 1). (Figure presented) Conclusion: The results of this study show that the correlation of the FEV<sub>1</sub>/FVC ratio, which can be regarded as a surrogate of elastic recoil, was more strongly associated with the extent of emphysema than the traditional FEV<sub>1</sub>. We believe that the FEV<sub>1</sub>/FVC ratio is an important measurement and provides reassurance that its correlation with extent of emphysema will be observed in much smaller cohorts. Funded by GlaxoSmithKline (Clinicaltrials.gov identifier NCT00292552; GSK Code SCO104960).
airflow; airway; airway remodeling; attenuation; body plethysmography; bronchodilating agent; chronic obstructive lung disease; computer assisted tomography; computer program; consensus; diagnosis; emphysema; human; low drug dose; lung; lung mechanics; lung parenchyma; lung volume; multidetector computed tomography; physiology; radiologist; reassurance; society; spirometry; thin layer chromatography
Modeling and nonlinear FE analysis of composite shells at finite \t\t\t\t\trotations
Research and Applications in Structural Engineering, Mechanics and Computation
907-910
2013
doi:10.1201/b15963-166
This paper presents a numerical study on static and stability analysis of layered composite structures. The shell element is based on the Reissner-Mindlin first-order shear deformation theory and strain-displacement relations are valid for small strains but finite rotations. Finite rotations are treated by Rodrigues parameterization. Two types of examples, static analysis of a composite laminated plate with hinged edges and stability analysis of a layered cross-ply cylindrical shell are carried out in the range of geometrically nonlinear deformation. The present simulations are compared with those obtained by finite element analyses based on first-order transverse shear deformation moderate or large rotation or refined von Kármán-type theories in earlier literature.
Analysis of a crack approaching two circular holes in [ laminates
Engineering Fracture Mechanics
46
2
235-244
1993
10.1016/0013-7944(93)90284-Y
The problem of a crack approaching two circular holes in [0n90m]s laminates is investigated. The stress intensity factors are obtained by using the modified mapping-collocation method which is based on analytic function theory of complex variables. The present results show excellent agreement with existing solutions for a crack approaching two circular holes in an isotropic infinite plate. In the numerical calculations, various types of cross-ply laminated composites are considered. To investigate the effect of orthotropy and geometry [dR and a(d−R)] on crack tip singularity, stress intensity factors are considered as functions of the normalized crack length. It is expected that the modified mappingcollocation method can be applied to the analysis of various kinds of cracks existing around the areas of stress concentrations of composite laminates.
Design of composite laminates by a genetic algorithm with memory
Mechanics of Advanced Materials and Structures
1
1
95–117
1994
This paper describes the use of a genetic algorithm with memory for the design of minimum thickness composite laminates subject to strength, buckling and ply contiguity constraints. A binary tree is used to efficiently store and retrieve information about past designs. This information is used to construct a set of linear approximations to the buckling load in the neighborhood of each member of the population of designs. The approximations are then used to seek nearby improved designs in a procedure called local improvement. The paper demonstrates that this procedure substantially reduces the number of analyses required for the genetic search. The paper also demonstrates that the use of genetic algorithms helps find several alternate designs with similar performance, thus giving the designer a choice of alternatives.
Growth optimization of zinc phthalocyanine thin films fo high performance thin film transistor
AIP Conference Proceedings
1349
PART A
687-688
2011
10.1063/1.3606044
The morphology of thermally evaporated zinc phthalocynine (ZnPc) organic thin films were engineered for obtaining high performance organic thin film transistor(OTFT) by varying substrate temperature and fixed deposition rate 0.1 Å/sec. ZnPc thin films were characterized by X-ray diffraction (XRD) and atomic force microscopy. The output characteristic of organic thin film transistor shows the highest mobility in the device with the thin film grown at 90°C by reducing the effect of grain boundaries. © 2011 American Institute of Physics.
Design of composite laminates by a genetic algorithm with memory
Mechanics of Advanced Materials and Structures
1
1
95–117
1994
This paper describes the use of a genetic algorithm with memory for the design of minimum thickness composite laminates subject to strength, buckling and ply contiguity constraints. A binary tree is used to efficiently store and retrieve information about past designs. This information is used to construct a set of linear approximations to the buckling load in the neighborhood of each member of the population of designs. The approximations are then used to seek nearby improved designs in a procedure called local improvement. The paper demonstrates that this procedure substantially reduces the number of analyses required for the genetic search. The paper also demonstrates that the use of genetic algorithms helps find several alternate designs with similar performance, thus giving the designer a choice of alternatives.
Simultaneous optimization of fiber distribution and layup for maximum stiffness of composite laminates using lamination parameters
Jisuan Lixue Xuebao/Chinese Journal of Computational Mechanics
29
4
475-480
2012
Elastic properties of fiber reinforced composite laminates depend on fiber volume fraction and lay-up configuration (number of layers, ply angles and thicknesses). In this paper, the stiffness of fiber reinforced laminates with limited fiber volume fraction used is maximized by optimizing the lay-up and fiber distribution. In the formulation of this optimization problem, the design variables are the lamination parameters which are used to describe the layup of laminates and the characterization parameters which describe fiber volume fraction distribution in layers, the objective is the minimum compliance of laminates. Several design examples are shown for different rules of lay-up and fiber volume distribution.
Vibration of laminated plates having elastic edge flexibilities
Journal of Engineering Mechanics
123
10
1012-1019
1997
The first known investigation on the problem of free vibration of symmetric cross-ply laminated plates having elastically restrained edges is considered. The Ritz method is used in combination with a variational formulation and a first-order transverse shear deformation theory. The Ritz functions consist of polynomials that include a basic function that imposes the free edge boundary conditions. The elastic edge flexibilities are considered by both the linear elastic rotational and translational supports to act simultaneously. Numerical results are obtained to investigate the effects of elastic restraint stiffness, material properties, and geometric parameters upon the natural frequencies of flexural vibration.
Chest wall mechanics during pressure support ventilation.
Critical care (London, England)
10
2
R54
2006
10.1186/cc4867
During pressure support ventilation (PSV) a part of the breathing pattern is controlled by the patient, and synchronization of respiratory muscle action and the resulting chest wall kinematics is a valid indicator of the patient's adaptation to the ventilator. The aim of the present study was to analyze the effects of different PSV settings on ventilatory pattern, total and compartmental chest wall kinematics and dynamics, muscle pressures and work of breathing in patients with acute lung injury.
Adult; Aged; Female; Humans; Male; Middle Aged; Positive-Pressure Respiration; Positive-Pressure Respiration: methods; Positive-Pressure Respiration: statistics & numeri; Respiratory Insufficiency; Respiratory Insufficiency: physiopathology; Respiratory Insufficiency: therapy; Respiratory Mechanics; Respiratory Mechanics: physiology; Respiratory Muscles; Respiratory Muscles: physiology; Thoracic Wall; Thoracic Wall: physiology
Statistical Mechanics of a Discrete Nonlinear System
Physical Review Letters
84
17
3740-3743
2000
10.1103/PhysRevLett.84.3740
Statistical mechanics of the discrete nonlinear Schrödinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = ∞, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.
Knowledge mechanics and its temporal nature
ACM Ubiquity
9
15
2008
Wordnet defines knowledge as the psychological result of perception, learning and reasoning. Like mechanics is the study o fthe way matter and force interact with each other, knowledge mechanics refers to the study if intermingling between two facets of knowledge - tacit and explicit. Tacit knowledge is personal knowledge which is difficult to express and communicate. On the other hand, explicit knowledge has been or can be articulated, codified and stored in certain media. The transformation of knowledge among these two facets has been the main topic of study among the researchers. This paper also explores the temporal nature of knwoledge, ie how time relates to knowledge and the factors involved in the natural decay of knowledge.
Statistical Mechanics Model for Protein Folding
arXiv
physics.bi
2010
We present a novel statistical mechanics formalism for the theoretical description of the process of protein folding$\leftrightarrow$unfolding transition in water environment. The formalism is based on the construction of the partition function of a protein obeying two-stage-like folding kinetics. Using the statistical mechanics model of solvation of hydrophobic hydrocarbons we obtain the partition function of infinitely diluted solution of proteins in water environment. The calculated dependencies of the protein heat capacities upon temperature are compared with the corresponding results of experimental measurements for staphylococcal nuclease and metmyoglobin.
cond-mat.stat-mech; physics.bio-ph; physics.chem-ph; q-bio.BM
Biomechanics: applications of engineering mechanics
Mechanics in Engineering
53-82
1976
INTRODUCTION The purpose of the present paper is primarily to give a historical perspective of the field of biomechanics. It will also attempt to describe the nature and status of some of the principal areas of current interest and to conjecture on the future interests and utility of biomechanics. It may be useful to start with a definition: Biomechanics is the application of mechanics to biological problems. A wide variety of aspects of mechanics have found applications in biology and medicine including rigid body dynamics, solid mechanics, fluid mechanics, finite deformation as well as linear elasticity, inelasticity, rheology, electromagnetic interactions, material science, structural analysis and most everything else that is usually included in engineering mechanics. Biomechanics is here regarded as a subdivision of bioengineering which is broader in that it includes, in addition, applications of chemical, thermodynamic, and electrical theories and technologies. It may also involve considerations of such matters as the design of hospitals, artificial organs, instrumentation and documentation systems, and health care delivery systems. There is another dimension to biomechanics and bioengineering which will not be treated here. This concerns organizational and educational aspects. Should biomechanics be regarded as a part of physiology or of engineering mechanics or of neither? Should we educate bioengineers or applied mechanicians? These questions will not be answered here, but some comments on how it seems best to conduct research will be developed. For this purpose the recent history of biomechanics may be of some guidance. At least for the immediate future, the close cooperation of engineering mechanicians with their counterparts in biology and medicine seems essential to further progress. The historical view proposed herein may be summarized in several stages. In ancient civilizations there was an extensive empirical knowledge for example, that blood flow through the heart valved was only in one direction although they did not realize that the blood circulated in a closed loop. But as there was very little knowledge of engineering mechanics, there was very little that could be called biomechanics. This applies to the middle ages as well. During the renaissance and up to about 1900, the growth of science, mathematics, physics, mechanics and biomechanics was, on the whole, intertwined. There was a smaller sum total of existing knowledge and outstanding individuals integrated concepts and applications over a wide range of both physical and biological subjects. Euler, Thomas Young and Helmholtz are outstanding examples. Poiseuille's experiments on capillary flow in 1840 were soon followed by analytical solutions by engineers and physicists. In the first half of the twentieth century, engineering methods and technology grew very rapidly in theoretical sophistication and practice. This was a period in which the possible applications of methods of analysis developed for engineering purposes were not carried over to similar problems in biology to which they would be applicable and illuminating. By 1950, theory and experimental data on the aerodynamics of aircraft was much more highly developed that data and explanations of the flight of birds and insects. Control theory was at a sophisticated theoretical level in engineering, but had not yet been applied to the control and mechanics of breathing. Large strain elasticity had ben developed for analysis of rubber tires, but was not yet applied to skin, muscles, arteries or red blood cells. Starting in the 1950's, a new dialogue sprang up between the engineering and biological communities and led to a rapid acceleration of research in biomechanics. The available engineering method of analysis and design were applied to biological problems over a broad spectrum of topics. Current work in biomechanics is making use not only of classical fluid and solid mechanics, but also of more recent developments such as fracture theory, finite deformation elasticity, finite element methods and network analysis. Moreover, rapid progress is being made in research for the sake of understanding biological phenomena on one hand as well as in design or application oriented research. A good example of the former is the very recent expansion of analysis of swimming, flying and other forms of locomotion by the full gamut of animals from microorganisms to whales. More directly applied efforts are the extensive studies of the mechanics of head and spinal injuries. These aim to understand and then to alleviate the injuries and fatalities in automobile accidents. In the near future, both exploratory and applied research in biomechanics are likely to continue to expand. This is an estimate of the momentum generated during the last twenty years. There have been set into mtion currents leading to the diffusion of physical and biological viewpoints into each other through individuals, applications, societies, books and journals. It does not seem likely that these fields will separate again.
Ram
Mechanics and dynamics of the cytoskeleton: a special issue stemming from the 2008 ECF Meeting/FEBS Workshop (Mechanics and Dynamics of the Cytoskeleton) in Potsdam, Germany.
Cell motility and the cytoskeleton
66
10
769-70
2009
10.1002/cm.20415
Note that Part II of this special issue will appear in the following issue: Volume 66, Issue 11, 2009.
Animals; Biomechanics; Cytoskeleton; Humans
Combining Quantum Mechanics Methods with Molecular Mechanics Methods in ONIOM
Journal of Chemical Theory and Computation
2
815-826
2006
The purpose of this paper is 2-fold. First, we present several extensions to the ONIOM(QM:MM) scheme. In its original formulation, the electrostatic interaction between the regions is included at the classical level. Here we present the extension to electronic embedding. We show how the behavior of ONIOM with electronic embedding can be more stable than QM/ MM with electronic embedding. We also investigate the link atom correction, which is implicit in ONIOM but not in QM/MM. Second, we demonstrate some of the practical aspects of ONIOM(QM:MM) calculations. Specifically, we show that the potential surface can be discontinuous when there is bond breaking and forming closer than three bonds from the MM region.
Combining Quantum Mechanics Methods with Molecular Mechanics Methods in ONIOM
JCTC
2
3
815-826
2006
10.1021/ct050289g
The purpose of this paper is 2-fold. First, we present several extensions to the ONIOM(QM:MM) scheme. In its original formulation, the electrostatic interaction between the regions is included at the classical level. Here we present the extension to electronic embedding. We show how the behavior of ONIOM with electronic embedding can be more stable than QM/MM with electronic embedding. We also investigate the link atom correction, which is implicit in ONIOM but not in QM/MM. Second, we demonstrate some of the practical aspects of ONIOM(QM:MM) calculations. Specifically, we show that the potential surface can be discontinuous when there is bond breaking and forming closer than three bonds from the MM region.
Combining Quantum Mechanics Methods with Molecular Mechanics Methods in ONIOM
Journal of Chemical Theory and Computation
2
3
815-826
2006
Abstract: The purpose of this paper is 2-fold. First, we present several extensions to the ONIOM(QM:MM) scheme. In its original formulation, the electrostatic interaction between the regions is included at the classical level. Here we present the extension to electronic embedding. We show how the behavior of ONIOM with electronic embedding can be more stable than QM/MM with electronic embedding. We also investigate the link atom correction, which is implicit in ONIOM but not in QM/MM. Second, we demonstrate some of the practical aspects of ONIOM(QM:MM) calculations. Specifically, we show that the potential surface can be discontinuous when there is bond breaking and forming closer than three bonds from the MM region.
Mechanics of wool fibers and structures.
Textile Asia
22
2
39-40,49-52
1991
The micro- and macromechanical properties of wool fibers and structures are investigated in order to provide insight into wool fabric testing and measurement, fiber and fabric property database development, fabric structures, process control, and quality assurance. The micromechanisms of knitted structures, the role of mechanical properties in carpet wear, fabric deformation, and clothing mechanics are considered. The continuing development of reliable, objective fabric measurement techniques is discussed. A theoretical basis for future studies of fiber and fabric mechanical properties is established by a continuum mechanical model of wool fiber bundles.
cloth; deformation; fiber; historic monuments; measuring; mechanical properties; mechanics; quality control; wool (fiber)
Tape mechanics over a flat recording head
JSME-IIP/ASME-ISPS Joint Conference on Micromechatronics for Information and Precision Equipment (MIPE)
3-4
2003
Tape mechanics over a flat-head is investigated. As a first order of approximation, a simplified system is analyzed; where a uniform subambient pressure is assumed to be acting on the tape, over the head region. This allows a closed form solution for the tape mechanics by itself. Tape and head-wear at the corners of the head, and wear of the magnetically active regions located at the central part of the flat-head are critical issues to be considered in designing a flat-head/tape interface. The closed-form solution, presented here, is particularly useful in obtaining estimates of the magnitudes of the reaction forces at the corners.
Dependence on a parameter in continuum mechanics
Rendiconti di Matematica, Serie VII
20
281-291
2000
In this paper is pointed out the special meaning of some parameters which are present in the constitutive relations of Continuum Mechanics. They make possible to characterize some important properties such as incompressibility and rigidity. Furthermore, it seems convenient to take into consideration in the constitutive relations the greatest dimension of the elementary particles of the physical corpuscular hypothesis of matter. Its presence leads to a more refined continuum model which, among other things, requires more physically acceptable conditions on the boudary than the usual ones.
Relativistic Quantum Mechanics through Frame‐Dependent Constructions
Philosophy of Science
72
5
802-813
2005
10.1086/508948
This paper is concerned with the possibility and nature of relativistic hidden‐variable formulations of quantum mechanics. Both ad hoc teleological constructions and frame‐dependent constructions of spacetime maps are considered. While frame‐dependent constructions are clearly preferable, a many‐maps theory based on such constructions fails to provide dynamical explanations for local quantum events. Here the hidden‐variable dynamics used in the frame‐dependent constructions is just a rule that serves to characterize the set of all possible spacetime maps. While not having dynamical explanations of the values of quantum‐mechanical measurement records is a significant cost, it may prove too much to ask for dynamical explanations in relativistic quantum mechanics.
Combined quantum and molecular mechanics (QM/MM)
Drug Discovery Today: Technologies
1
3
253-260
2004
10.1016/j.ddtec.2004.11.008
We describe the current state of the art of mixed quantum mechanics/molecular mechanics (QM/MM) methodology, with a particular focus on modeling of enzymatic reactions. Over the past decade, the effectiveness of these methods has increased dramatically, based on improved quantum chemical methods, advances in the description of the QM/MM interface, and reductions in the cost/performance of computing hardware. Two examples of pharmaceutically relevant applications, cytochrome P450 and class C ??-lactamase, are presented. ?? 2004 Elsevier Ltd. All rights reserved.
On Everett's Formulation of Quantum Mechanics
The Monist
80
1
70-96
1997
Everett wanted a formulation of quantum mechanics that (i) took the linear dynamics to be a complete and accurate description of the time-evolution of all physical systems and (ii) logically entailed the same subjective appearances predicted by the standard formulation of quantum mechanics. While most everyone would agree with this description of Everett's project, there is little agreement on exactly how his relative-state formulation was supposed to work. In this paper, I consider two very different readings of Everett: the bare reading and the splitting-worlds reading. What distinguishes these is their interpretation of the wave function and how one accounts for the experiences of observers. The difficulty in interpreting Everett, however, is illustrated by the fact that neither reading is entirely compatible with his own description of his project.
ON UNIFIED APPROACHES TO TWISTED YARN MECHANICS.
Appl Polym Symp
27
253-273
1975
General considerations of twisted yarn mechanics are followed by a detailed discussion of the subject under the following main headings - the simplest models and basic relations; development of the energy method; force and moment equilibrium methods (continuous filament yarns and fiber slippage in staple fiber yarns); and conclusions. It is demonstrated that the most straightforward problem in yarn mechanics had been ″solved″ by the energy method, and the development given in this paper extend the range of application of the method. The energy method gives the framework of a unified approach to the problems of real yarns provided the yarn is adequately characterized.
Nanoscience and engineering in mechanics and materials
Journal of Physics and Chemistry of Solids
65
8-9
1501-1506
2004
10.1016/j.jpcs.2003.09.032
The transcendent technologies include nanotechnology, microelectronics, information technology and biotechnology as well as the enabling and supporting civil infrastructure systems and materials. These technologies are the primary drivers of the 21st century and the new economy. Mechanics and materials are essential elements in all of the transcendent technologies. Research opportunities, education and challenges in mechanics and materials, including nanomechanics, carbon nanotubes, bioinspired materials, coatings, fire-resistant materials as well as improved engineering and design of materials are presented and discussed in this paper.
Smallest Relational Mechanics Model of Quantum Cosmology
arXiv
gr-qc
2009
Relational particle mechanics are models in which there is, overall, no time, position, orientation (nor, sometimes, scale). They are useful for whole-universe modelling - the setting for quantum cosmology. This note concerns 3 particles in 1d in shape-scale split variables. The scale part parallels certain Friedmann equations, while in this note the shape part involves functions on the circle. The scale part is taken to be `heavy' and `slow' so the semiclassical approach applies and scale provides an approximate timestandard with repect to which the light physics runs. Relational particle mechanics moreover provide conceptual models of inhomogeneity, structure formation and nontrivial linear constraints (minisuperspace models do not and midisuperspace models only do at the cost of substantial complications).
Fluid mechanics in membrane filtration: Recent developments
Journal of Membrane Science
40
2
123-147
1989
http://dx.doi.org/10.1016/0376-7388(89)89001-5
Recent developments of the role of fluid mechanics in membrane filtration are presented. Understanding of membrane polarization and fouling is intimately related through mass transfer to fluid mechanics in membrane modules. After discussing the behavior of dissolved ions, macromolecules and collodial particles in cross-flow filtration, we describe several attempts to model both steady one and two phase flows and unsteady flows. For the latter, we consider both oscillating flows and flows with centrifugal instabilities. Moving cake and surface reaction models are also included. Several examples using these principles are taken from biotechnology and industrial effluent treatment.
ON A GEOMETRICAL DESCRIPTION OF QUANTUM MECHANICS
International Journal of Geometric Methods in Modern Physics
08
01
87
2011
10.1142/s0219887811004987
We show that Quantum Mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular Weyl affine space which we call Q-wis. This is proved using the Bohm-de Broglie causal formulation of Quantum Mechanics. In the Q-wis geometry, the length of extended objects changes from point to point. In our proposed geometrical formulation, deformation of the standard rulers used to measure physical distances are in the core of quantum effects.
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Quantum Physics
Can quantum mechanics be an emergent phenomenon?
Journal of Physics: Conference Series
174
012034
2009
10.1088/1742-6596/174/1/012034
We raise the issue whether conventional quantum mechanics, which is not a hidden variable theory in the usual Jauch-Piron's sense, might nevertheless be a hidden variable theory in the sense recently conjectured by G. 't Hooft in his pre-quantization scheme. We find that quantum mechanics might indeed have a fully deterministic underpinning by showing that Born's rule naturally emerges (i.e., it is not postulated) when 't Hooft's Hamiltonian for be-ables is combined with Koopmann–von Neumann operatorial formulation of classical physics.
Soil mechanics aspects of soft ground tunnelling
Ground Engineering
14
5
20-24,26,38
1981
Recently a number of calculations have been developed which deal with the stability of tunnels and tunnel headings and with settlements caused by tunnelling. These calculations always consider quite separately drained cases and undrained cases in accordance with the basic principles of soil mechanics but it is not always obvious which calculation is applicable for a particular tunnelling problem. This paper considers the stresses and pore pressures in soft ground due to tunnelling and it discusses the calcuations appropriate for estimating the stability of the tunnel and its heading and the settlements caused by tunnelling.
pore pressures; soil mechanics; stress analysis
From Lagrangian to Quantum Mechanics with Symmetries
Journal of Physics: Conference Series
380
012008
2012
10.1088/1742-6596/380/1/012008
We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.
classi-; jacobi last multiplier; lagrangian; lie symmetry; noether symmetry
Mécanique des roches: Généralités= Rock mechanics: Generalities
Techniques de l'ingénieur
1-7
1997
Il est courant d'affirmer que le matériau rocheux est un matériau de qualité, rigide et résistant, et que les massifs rocheux sont de «bons terrains» pour les travaux de génie civil. Cependant, l'optimisation des travaux au rocher nécessite une connaissance du comportement mécanique des roches, et les grands ouvrages de génie civil, tels que tunnels profonds, barrages, centrales nucléaires, ou viaducs de grande portée, sollicitent le massif rocheux parfois à la limite de ses capacités. La mécanique des roches, science de l'ingénieur qui s'est individualisée depuis une trentaine d'années, possède quelques spécificités que nous présentons sommairement ci-après.
Application; Civil engineering; Definition; Geotechnics; Modeling; Propagation velocity; Rock mass; Rock mechanics; Scale effect; Shear strength; Soil mechanics; Strength of materials; Wave propagation
Mechanics of ball end milling process
Proceedings of the 1993 ASME Winter Annual Meeting, November 28, 1993 - December 3
64
543-552
1993
Mechanics of cutting with ball ended cutters are modeled. The model is based on the analytic representation of ball shaped helical flute geometry, and its rake and clearance surfaces. It is assumed that friction and pressure loads on the rake face are proportional to the uncut chip thickness area. The load on the flank contact face are concentrated on the in cut portion of the cutting edge. The pressure and friction coefficients are identified from a set slot milling tests at different feeds and axial depth of cuts, and are used to predict the cutting forces for any condition. The experimentally verified model accurately predicts the cutting forces in three cartesian directions.
Ball milling; Ball mills; Cutting tools; Forecasting; Friction; Loads (forces); Mathematical models; Mechanics; Metal cutting; Pressure; Surfaces
Stochastic reduction in nonlinear quantum mechanics
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
458
2021
1117-1127
2002
10.1098/rspa.2001.0914
Stochastic extensions of the Schrodinger equation have attracted attention recently as plausible models for state reduction in quantum mechanics. Here we formulate a general approach to stochastic Schrodinger dynamics in the case of a nonlinear state space of the type proposed by Kibble. We derive a number of new identities for observables in the nonlinear theory, and establish general criteria on the curvature of the state space sufficient to ensure collapse of the wave function.
di; erential geom etry; holom orphic sectional curvature; kahler di; nonlinear quantum mechanics; quantum measurem ent; stochastic; usion
Relativistic quantum mechanics of a Dirac oscillator
European Journal of Physics
16
3
135-141
1995
10.1088/0143-0807/16/3/008
The Dirac oscillator is an exactly soluble model recently introduced in the context of many particle models in relativistic quantum mechanics. The model has been also considered as an interaction term for modelling quark confinement in quantum chromodynamics. These considerations should be enough for demonstrating that the Dirac oscillator can be an excellent example in relativistic quantum mechanics. In this paper we offer a solution to the problem and discuss some of its properties. We also discuss a physical picture for the Dirac oscillator's non-standard interaction, showing how it arises on describing the behaviour of a neutral particle carrying an anomalous magnetic moment and moving inside an uniformly charged sphere.
Physica A: Statistical Mechanics and its Applications
Physica A: Statistical Mechanics and its Applications
330
1-2
-
2003
10.1016/j.physa.2003.11.006
The proceedings contains 35 papers from the conference on Physica\nA: statistical mechanics and its applications. Topics discussed include:\nhuman waves in stadiums; competition between Levy jumps and continuous\ndrift; fundamental problems in statistical physics of jammed packings;\na thermodynamic approach to slowly sheared granular matter; unity\nand discord in opinion dynamic; and the effect of long-term correlations\non the return periods of rare events.
Wave Mechanics Applied to Semiconductor Heterostructures
Journal of Modern Optics
38
6
1211-1212
1991
10.1080/09500349114551351
Examines the basic electronic and optical properties of two- dimensional semiconductor heterostructures based on III-V and II-VI compounds. Explores various consequences of one-dimensional size-quantization on the most basic physical properties of heterolayers. Beginning with basic quantum mechanical properties of idealized quantum wells and superlattices, it discusses the occurrence of bound states when the heterostructure is imperfect or when it is shone with near bandgap light.
From classical to quantum mechanics through optics
European Journal of Physics
31
1
171-192
2010
Doi 10.1088/0143-0807/31/1/016
In this paper, we revise the main aspects of the 'Hamiltonian analogy': the fact that optical paths are completely analogous to mechanical trajectories. We follow Schrodinger's original idea and go beyond this analogy by changing over from the Hamilton's principal function S to the wavefunction Psi. We thus travel from classical to quantum mechanics using optics as a guide. Unfortunately, and despite its mathematical beauty and simplicity, the connection between classical and quantum mechanics through optics is nowadays hardly known and mostly ignored in university education. The present work tries to fill this gap.
Altered alveolar mechanics in the acutely injured lung.
Critical care medicine
29
5
1049-1055
2001
10.1097/00003246-200105000-00036
OBJECTIVES: Alterations in alveolar mechanics (i.e., the dynamic change in alveolar size during tidal ventilation) are thought to play a critical role in acute lung injuries such as acute respiratory distress syndrome (ARDS). In this study, we describe and quantify the dynamic changes in alveolar mechanics of individual alveoli in a porcine ARDS model by direct visualization using in vivo microscopy. DESIGN: Prospective, observational, controlled study. SETTING: University research laboratory. SUBJECTS: Ten adult pigs. INTERVENTIONS: Pigs were anesthetized and placed on mechanical ventilation, underwent a left thoracotomy, and were separated into the following two groups post hoc: a control group of instrumented animals with no lung injury (n = 5), and a lung injury group in which lung injury was induced by tracheal Tween instillation, causing surfactant deactivation (n = 5). Pulmonary and systemic hemodynamics, blood gases, lung pressures, subpleural blood flow (laser Doppler), and alveolar mechanics (in vivo microscopy) were measured in both groups. Alveolar size was measured at peak inspiration (I) and end expiration (E) on individual subpleural alveoli by image analysis. Histologic sections of lung tissue were taken at necropsy from the injury group. MEASUREMENTS AND MAIN RESULTS: In the acutely injured lung, three distinct alveolar inflation-deflation patterns were observed and classified: type I alveoli (n = 37) changed size minimally (I - EDelta = 367 +/- 88 microm2) during tidal ventilation; type II alveoli (n = 37) changed size dramatically (I - EDelta = 9326 +/- 1010 microm2) with tidal ventilation but did not totally collapse at end expiration; and type III alveoli (n = 12) demonstrated an even greater size change than did type II alveoli (I - EDelta = 15,418 +/- 1995 microm2), and were distinguished from type II in that they totally collapsed at end expiration (atelectasis) and reinflated during inspiration. We have termed the abnormal alveolar inflation pattern of type II and III alveoli "repetitive alveolar collapse and expansion" (RACE). RACE describes all alveoli that visibly change volume with ventilation, regardless of whether these alveoli collapse totally (type III) at end expiration. Thus, the term "collapse" in RACE refers to a visibly obvious collapse of the alveolus during expiration, whether this collapse is total or partial. In the normal lung, all alveoli measured exhibited type I mechanics. Alveoli were significantly larger at peak inspiration in type II (18,266 +/- 1317 microm2, n = 37) and III (15,418 +/- 1995 microm2, n = 12) alveoli as compared with type I (8214 +/- 655 microm2, n = 37). Tween caused a heterogenous lung injury with areas of normal alveolar mechanics adjacent to areas of abnormal alveolar mechanics. Subsequent histologic sections from normal areas exhibited no pathology, whereas lung tissue from areas with RACE mechanics demonstrated alveolar collapse, atelectasis, and leukocyte infiltration. CONCLUSION: Alveolar mechanics are altered in the acutely injured lung as demonstrated by the development of alveolar instability (RACE) and the increase in alveolar size at peak inspiration. Alveolar instability varied from alveolus to alveolus in the same microscopic field and included alveoli that changed area greatly with tidal ventilation but remained patent at end expiration and those that totally collapsed and reexpanded with each breath. Thus, alterations in alveolar mechanics in the acutely injured lung are complex, and attempts to assess what may be occurring at the alveolar level from analysis of inflection points on the whole-lung pressure/volume curve are likely to be erroneous. We speculate that the mechanism of ventilator-induced lung injury may involve altered alveolar mechanics, specifically RACE and alveolar overdistension.
Statistical Mechanics of the Dislocation System in a Crystal
J. Phys. Soc. Jpn
57
11
3742-3752
1988
10.1143/JPSJ.57.3742
The statistical mechanics of the assembly of the dislocation lines\nin a three dimensional crystal is developed. Using the transfer matrix\nmethod, the statistical mechanics of the dislocations is transformed\ninto the ground state problem of the two dimensional Fermion-Boson\nsystem. This approach gives a convincing proof for the free energy\nexpression: \[ f(ρ) = -F_1 ρ\ln C ρ+ F_2 ρ+ F_3 ρ^2,\n\] where ρ is the dislocation density, F_1 and F_3 are positive\nconstants, and C is a constant of the order a^2 (a being the\nlattice spacing). The constant F_2 is positive at low temperatures\nbut is negative at high temperatures.
Mechanics of Crack Arrest in Concrete
Proceedings of the ASCEJ of Engineering Mechanics Division
89
3, May/June
147-168
1963
The application of linear-elastic fracture mechanics reveals that the strength of concrete in tension is limited by internal holes and micro-cracks. Fracture arrest can be achieved by reducing the spacing of reinforcement to a suitable scale. Reinforcement diameter decreases in proportion to reduction in spacing in order to maintain steel percentage. Theoretical results indicate that the tensile cracking strength of concrete increases in proportion to the inverse square root of the reinforcing spacing. Tests on closely spaced wire reinforced beams support the theoretical calculations.
Finite element methods in fracture mechanics
Computers & Structures
31
1
1-9
1989
Finite element methodology specific to the analysis of fracture mechanics problems is reviewed. Primary emphasis is on the important algorithmic developments which have enhanced the numerical modeling of fracture processes. Methodologies to address elasto-static problems in two- and three-dimensions, elasto-dynamic problems, elasto-plastic problems, special considerations for three-dimensional nonlinear problems and the modeling of stable crack growth are reviewed. In addition, the future needs of the fracture community are discussed and open questions are identified. The need for theoretical advancements in continuum mechanics and constitutive fracture laws coupled with improved numerical algorithms is emphasized. Extensive reference is made to the open literature base for further details.
Engineering problems and rock mechanics: some examples
Engineering Geology
7
333-358
1973
10.1016/0013-7952(73)90014-8
The purpose of this paper is to show how rock mechanics interprets geologic informa- tion and helps to adapt engineering design to rock conditions. The paper analyses eight case histories of large engineering projects. In five cases the designers took careful account of the conditions prevailing in the rock masses, the rock characteristics, the strength of the rock and the modified stress---strain pattern created by the new structure. The intrinsic curve of the rock mass, the Coulomb condition, the residual stresses and the E-modulus in the families of joints are among the more important characteristics of the rock mass. In two case histories, it is shown how an erroneous estimate of the cleft-water pressures caused disaster. Rock mechanics is a necessary link between engineering and geology. APPROACH
Variational methods, multisymplectic geometry and continuum mechanics
Journal of Geometry and Physics
38
3-4
253-284
2001
10.1016/S0393-0440(00)00066-8
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic reduction and for the further development of Veselov-type multisymplectic discretizations and numerical algorithms. The latter will be the subject of a companion paper. © 2001 Elsevier Science B.V.
53C15; 76A02; 76M30; Classical field theory; Continuum mechanics; Multisymplectic geometry; Variational methods
DNA under Force: Mechanics, Electrostatics, and Hydration
Nanomaterials
5
1
246-267
2015
10.3390/nano5010246
Quantifying the basic intra- and inter-molecular forces of DNA has helped us to better understand and further predict the behavior of DNA. Single molecule technique elucidates the mechanics of DNA under applied external forces, sometimes under extreme forces. On the other hand, ensemble studies of DNA molecular force allow us to extend our understanding of DNA molecules under other forces such as electrostatic and hydration forces. Using a variety of techniques, we can have a comprehensive understanding of DNA molecular forces, which is crucial in unraveling the complex DNA functions in living cells as well as in designing a system that utilizes the unique properties of DNA in nanotechnology.
dna; DNA; electrostatics; hydration; mechanics
Path Integrals in Noncommutative Quantum Mechanics
Theoretical and Mathematical Physics
140
3
9
2003
10.1023/B:TAMP.0000039834.84359.f8
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated. Our approach is based on the fact that a quantum-mechanical system with a noncommutative configuration space may be regarded as another effective system with commuting spatial coordinates. Since path integral for quadratic Lagrangians is exactly solvable and a general formula for probability amplitude exists, we restricted our research to this class of Lagrangians. We found general relation between quadratic Lagrangians in their commutative and noncommutative regimes. The corresponding noncommutative path integral is presented. This method is illustrated by two quantum-mechanical systems in the noncommutative plane: a particle in a constant field and a harmonic oscillator.
feynman path integral; noncommutative quantum mechanics; systems with quadratic la
Chapter One – Mechanics of Material Mutations
Advances in Applied Mechanics
47
1-91
2014
10.1016/B978-0-12-800130-1.00001-1
Mutations in solids are defined here as dissipative reorganizations of the material texture at different spatial scales. We discuss possible views on the description of material mutations with special attention to the interpretations of the idea of multiple reference shapes for mutant bodies. In particular, we analyze the notion of relative power—it allows us to derive standard, microstructural, and configurational actions from a unique source—and the description of crack nucleation in simple and complex materials in terms of a variational selection in a family of bodies differing from one another by the defect pattern, a family parameterized by vector-valued measures. We also show that the balance equations can be derived by imposing structure invariance on the mechanical dissipation inequality.
15A15; 15A18; Complex materials; Continuum mechanics; Covariance; Defects; Primary 05C38; Relative power; Secondary 05A15
Molecular mechanics (MM3) parameterization for oxocarbenium ions
Journal of Computational Chemistry
21
5
329-339
2000
http://dx.doi.org/10.1002/(SICI)1096-987X(20000415)21:5<329::AID-JCC1>3.0.CO;2-0
The physical properties of a diverse group of 12 oxocarbenium ions have been studied with ab initio calculations at the MP2/6-31+G* level of theory. Based on theoretically derived properties such as molecular equilibrium geometry, dipole moment, and vibrational frequencies, a molecular mechanics (MM3) force field has been developed with the assistance of the programs TORSMART and MPMSR, components of our artificial parameter development and refinement method. The MM3 force field is now able to reproduce bond lengths, bond angles, moments of inertia, dipole moments, torsional energy profiles, and vibrational frequencies of oxocarbenium ions, which will allow further studies of glycoside hydrolysis and their rates of reaction. (C) 2000 John Wiley & Sons, Inc.
molecular mechanics MM3 force field parameterizati
Quantum mechanics from five physical assumptions
Time
14
2011
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions concern fundamental symmetries of physical interactions. The third concerns the Hilbert-space dimensions and the fourth and fifth the self-interaction Hamiltonians of the systems that function as "observers" within the theory. These assumptions are shown to provide a sufficient motivation for the usual Hilbert-space formalism, and to obviate the observation-related axioms and most interpretative assumptions with which minimal quantum mechanics is typically supplemented.
Quantum Physics
Quantum mechanics as a consequence of discrete interactions
Physics
11973
2007
Quantum mechanics is usually presented starting from a series of postulates\nabout the mathematical framework. In this work we show that those same\npostulates can be derived by assuming that measurements are discrete\ninteractions: that is, that we measure at specific moments in time (as opposed\nto a continuous measurement that spans a long time interval) and that the\nsystem is in general affected by our measurement. We believe that this way of\npresenting quantum mechanics would make it easier to understand by laying out a\nmore cohesive view of the theory and making it resonate more with our physics\nintuition.
Quantum Physics
Computational Mechanics of Solids with Boundary Potentials
2nd South-East European Conference on Computational Mechanics
June
22-24
2009
Common modeling in continuum mechanics takes exclusively the bulk into account, nevertheless, neglecting possible contributions from the boundary. However, boundary effects sometimes play a dominant role in the material behavior, the most prominent example being surface tension. Within this contribution boundary potentials are allowed, in general, to de- pend not only on the boundary deformation but also on the boundary deformation gradient. Motivated by this idea, a suitable finite element framework based on rank deficient deformation gradients is established. In essence, the total potential energy functional that we seek to mini- mize with respect to all admissible spatial variations at fixed material placement is consisting of both contributions from the bulk and the boundary.
boundary potentials; surface tension
Advances in the fracture mechanics of cortical bone.
Journal of biomechanics
20
11-12
1071-1081
1987
10.1016/0021-9290(87)90025-X
As cortical bone is a semi-brittle solid, its fracture is dependent not only on the magnitude of the applied stress, but also on the nature of any intrinsic or introduced cracks. Consequently a variety of fracture mechanics techniques have been utilised to evaluate the fracture toughness of cortical bone, including the single edge notched, centre notched cylindrical and compact tension methods, and values have been established for the critical stress intensity factor (Kc) and the critical strain energy release rate (Gc). The Kc and Gc values obtained depend on the orientation of the cortical bone, as well as on bone density, the velocity of crack propagation and specimen geometry. The significance of these fracture mechanics parameters for cortical bone is critically reviewed.
Online heat transfer and fluid mechanics laboratory
Computer Applications in Engineering Education
13
1
1-9
2005
This paper presents, how multimedia technology can be implemented over the web to enhance the learning experience of students at the University of Oklahoma in a heat transfer and fluid mechanics laboratory. This course module not only introduces fundamental theories about measurement, but also details the experimental setup and procedure for each laboratory assignment. in addition, it has a unique component called "virtual laboratory" in which students can learn the operation of advanced and sophisticated instruments that are not normally available in an undergraduate teaching laboratory. The implementation of "virtual laboratory" can better utilize the resources available while providing an excellent opportunity of learning for students. (c) 2005 Wiley Periodicals, Inc.
fluid mechanics; heat transfer; online laboratory courseware; virtual laboratory
Part 2: introduction to continuum mechanics
Continuum
51
3
171-186
1984
10.1115/1.3167763
This book presents an introduction to the classical theories of continuum mechanics; in particular, to the theories of ideal, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. These theories are important, not only because they are applicable to a majority of the problems in continuum mechanics arising in practice, but because they form a solid base upon which one can readily construct more complex theories of material behavior. Further, although attention is limited to the classical theories, the treatment is modern with a major emphasis on foundations and structure
Statistical Mechanics of Games - Evolutionary Game Theory -
Progress of Theoretical Physics Supplement
179
216-226
2009
This paper formulates evolutionary game theory with a new concept using statistical mechanics. This study analyzes the following situations: each player on the lattice plays a game with its nearest neighbor or with a randomly matched player. These situations are formulated using an analogy with the Ising model and the Sherrington-Kirkpatrick model, the simplest models in statistical mechanics. As a result, theoretical calculations agree with classical evolutionary game theory in terms of the parameter size. This paper shows that bifurcations occur in a quenched system with externalities, hence, this system has multiple equilibria. This paper discusses the simplified Cont and Bouchaud model through our models. We extend the player's behavior and matching in Cont and Bouchaud model.
equilibria; model
Fracture mechanics of a composite with ductile fibers
Journal of the Mechanics and Physics of Solids
19
2
71-87
1971
10.1016/0022-5096(71)90019-6
Fracture mechanics of a metal-matrix composite containing ductile-metallic fibers is described. Experimental verification of the proposed descriptions has been established with an aluminum-base composite containing uni-directional stainless-steel fibers. Theoretical description of the plastic energy dissipation shows that crack propagation across fibers is very difficult because of the high energy density represented by the fiber. The fiber contribution is an increasing function of volume fraction which results in the critical stress-intensity factor increasing with fiber content. On the other hand, crack propagation between fibers is very easy because the inter-fiber spacing limits the plastic energy dissipation in the matrix. The critical stress intensity for crack propagation between fibers is a decreasing function of volume fraction. © 1971.
Foundations of Quantum Mechanics and Quantum Computation
Proceedings of the 25th Conference on Physics. The Theory of the Quantum World
21-90
2013
I ask the question: What can we infer about the nature and structure of the physical world (a) from experiments already done to test the predictions of quantum mechanics (b) from the assumption that all future experiments will agree with those predictions? I discuss existing and projected experiments related to the two classic paradoxes of quantum mechanics, named respectively for EPR and Schrodinger's Cat, and show in particular that one natural conclusion from both types of experiment implies the abandonment of the concept of macroscopic counterfactual definiteness.
Molecular mechanics modeling of carbon nanotube fracture
Carbon
45
9
1769-1776
2007
10.1016/j.carbon.2007.05.009
The fracture of carbon nanotubes (CNTs) is studied in this paper. Molecular mechanics models that incorporate the modified Morse potential and reactive empirical bond-order potential are developed to envisage the fracture behavior of perfect CNTs. The tensile strength, fracture strain, and fracture angle under tension are discussed, and special attention is paid to the effects of tube chirality. Explicit expressions for the fracture solutions for achiral carbon nanotubes are presented, but only numerical results are available for chiral carbon nanotubes. The predicted results of the present model are in good agreement with existing data and those of molecular mechanics simulations via the Materials Studio software package, which indicates the effectiveness of the developed models. ?? 2007 Elsevier Ltd. All rights reserved.
Symmetry as a foundational concept in Quantum Mechanics
arXiv
1-8
2015
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a fundamental concept in the construction of physical systems. Based on this idea, we propose a series of postulates for describing quantum systems, and establish their relation and correspondence with axioms of standard quantum mechanics. Through some examples we show that this reformulation helps better understand some of ambiguities of standard description. Nonetheless its application is not limited to explaining confusing concept and it may be a necessary step toward a consistent model of quantum cosmology and gravity.
Smallest Relational Mechanics Model of Quantum Cosmology
Quantum
gr-qc
4-7
2009
Relational particle mechanics are models in which there is, overall, no time, position, orientation (nor, sometimes, scale). They are useful for whole-universe modelling - the setting for quantum cosmology. This note concerns 3 particles in 1d in shape-scale split variables. The scale part parallels certain Friedmann equations, while in this note the shape part involves functions on the circle. The scale part is taken to be `heavy' and `slow' so the semiclassical approach applies and scale provides an approximate timestandard with repect to which the light physics runs. Relational particle mechanics moreover provide conceptual models of inhomogeneity, structure formation and nontrivial linear constraints (minisuperspace models do not and midisuperspace models only do at the cost of substantial complications).
Multiscale thermodynamics and mechanics of heat.
Physical Review E - Statistical, Nonlinear and Soft Matter Physics
83
6 Pt 1
061134
2011
10.1103/PhysRevE.83.061134
Heat transfer is investigated on three levels of description: Fourier, Cattaneo, and Peierls. The microscopic nature of the heat that becomes important, in particular in nanoscale systems, is characterized by a vector field related to the heat flux on the Cattaneo level and by the phonon distribution function on the Peierls level. All dynamical theories discussed in the paper are fully nonlinear and all are proven to be compatible among themselves, with equilibrium thermodynamics, and with mechanics. An investigation of the first two compatibilities gives rise to potentials having the physical interpretation of nonequilibrium entropies. The compatibility with mechanics is manifested by the Hamiltonian structure of the time-reversible part of the time evolution.
Mechanics in biology: cells and tissues.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
367
3335-3337
2009
10.1098/rsta.2009.0122
Biology is becoming the most important interdisciplinary field where physics and mathematics meet. The discoveries that have characterized biological sciences in the last few decades, and the insight made possible at the cellular and subcellular scales, offer fertile grounds on which to develop a formal description of biology using the quantitative methods of physics. One important goal in this effort is to understand the complex rules that govern living matter within the precise formal framework provided by the balance laws of mechanics.
Second quantization in nonrelativistic quantum mechanics
American Journal of Physics
51
4
312
1983
10.1119/1.13259
Second quantization in nonrelativistic quantum mechanics is given in a simplified way using eigenstates of the number operator. The field creation operator is shown to be the operator which adds a particle with a delta‐function wave function to the system, while the field annihilation operator removes a particle with a delta‐function wave function from the system. The field creation operator is proved to be the Hermitian conjugate of the annihilation operator. The commutation (anticommutation) relations for boson (fermion) field operators are proved from the symmetry (antisymmetry) of the many‐particle wave function. The second quantized form of one‐ and two‐particle operators is obtained from their form in wave mechanics using the definition of the field creation and annihilation operators.
Generalized statistical mechanics for superstatistical systems.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
369
453-465
2011
10.1098/rsta.2010.0280
Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex system onto a system of ordinary statistical mechanics with modified energy levels. We also briefly review recent examples of applications of the superstatistics concept for three very different subject areas, namely train delay statistics, turbulent tracer dynamics and cancer survival statistics.
cancer; complex system; fluctuating environment; keywords; namely train delay statistics; superstatistics; survival statistics; turbulent tracer dynamics and
Some recent advances in classical statistical mechanics
Dynamics of dissipation
7-33
2002
Two recent developments, each introducing a new, not previously available basic aspect of classical statistical mechanics, are discussed. The presentations concern a new distribution function describing a system in a nonequilibrium stationary state, which leads in turn to a Fluctuation Theorem for large deviations, possibly far away from equilibrium. Furthermore an attempt is made to place the statistics introduced by Tsallis some time ago, in the general context of statistical mechanics. This is based on a remark by Einstein and the consistency of this statistics with some recent experiments on fully developed turbulence.
Mechanics of Dynamic Debonding
Proceedings of the Royal Society: Mathematical and Physical Sciences (1990-1995)
433
1889
679-697
1991
10.1098/rspa.1991.0070
Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined. Emphasis is placed on extending an established framework for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response. For a crack running at non-uniform speed, the crack tip behaviour is governed by an instantaneous steady-state, two-dimensional singularity. This simplifies the problem, rendering the Stroh techniques applicable. In general, the singularity oscillates, similar to quasi- static cracks. The oscillation index is infinite when the crack runs at the Rayleigh wave speed of the more compliant material, suggesting a large contact zone may exist behind the crack tip at high speeds. In contrast to a crack in homogeneous materials, an interface crack has a finite energy factor at the lower Rayleigh wave speed. Singular fields are presented for isotropic bimaterials, so are the key quantities for orthotropic bimaterials. Implications on crack branching and substrate cracking are discussed. Dynamic stress intensity factors for anisotropic bimaterials are solved for several basic steady state configurations, including the Yoffe, Goldshtein, and Dugdale problems. Under time-independent loading, the dynamic stress intensity factor can be factorized into its equilibrium counterpart and the universal functions of crack speed.
Nano and Cell Mechanics
Nano and Cell Mechanics: Fundamentals and Frontiers
191-226
2013
10.1002/9781118482568
The emergence of one-dimensional nanostructures as fundamental constituents of advanced materials and next-generation electronic and electromechanical devices has increased the need for their atomic-scale characterization. Given its spatial and temporal resolution, coupled with analytical capabilities, transmission electron microscopy (TEM) has been the technique of choice in performing atomic structure and defect characterization. A number of approaches have been recently developed to combine these capabilities with in-situ mechanical deformation and electrical characterization in the emerging field of in-situ TEM electromechanical testing. This has enabled researchers to establish unambiguous synthesis-structure-property relations for one-dimensional nanostructures. In this article, the development and latest advances of several in-situ TEM techniques to carry out mechanical and electromechanical testing of nanowires and nanotubes are reviewed. Through discussion of specific examples, it is shown how the merging of several microsystems and TEM has led to significant insights into the behavior of nanowires and nanotubes, underscoring the significant role in-situ techniques play in the development of novel nanoscale systems and materials.
Electromechanical testing; In-situ testing; Nanotubes; Nanowires; TEM
Mechanics of Flow Forming
CIRP Annals - Manufacturing Technology
30
1
159-162
1981
10.1016/S0007-8506(07)60915-9
One of the applications of large scale deformation using point loads (Compressive) is in spinning and flow forming. This technique has been utilised in developing a flow forming machine at CMTI for manufacture of axisysmetric components like, cylindrical utensils, pressure cooker bodies, etc out of aluminium as raw material. The paper describes the mechanics of flow forming process, wherein the material flow follows the law of equal volume and is informative regarding the following aspects: 1) The complex state of material at deformation zone, 2) The forces required to flow form the material, 3) The effect of the process on material i.e., strength, elongation characteristics and hardness, and 4) The variance in product geometry with respect to various process parameters like percentage reduction feed rate and peripheral speeds. The above mentioned points are supported with experimental results along with a comparison of various experimental results of force data with values from empirical formulae established by earlier researchers and discussion of their validity.
Unsaturated soil mechanics
Engineering Geology
106
1-2
26-39
2009
10.1016/j.enggeo.2009.02.010
Most constitutive models for unsaturated soils are based on identification of soil-water suction with the capillary component of the matrix potential, ignoring the contribution of adsorption to this potential. Identification of potential (energy per unit volume) with stress (or suction), is questioned, since these quantities have different physical significance despite their common dimensions. It is suggested that the identification of matrix potential with (ua−uw) results from neglecting the adsorption potential, and adopting an unrealistic pore space model. This identification was probably motivated by the laboratory axis translation technique, but it is not valid under normal field conditions where the air pressure is usually atmospheric, and soil water cannot develop high tension without cavitating. Axis translation alters soil behavior by preventing cavitation, thus casting doubt on the relevance of laboratory results obtained from these tests to actual field conditions. Specifically, in soils having large specific surface areas, there is a range of conditions, relevant to geotechnical engineering, in which capillary potential appears to account for only a small part of matrix potential, the major contribution resulting from water adsorption onto the soil particles. Consideration of a double porosity model and cavitation of water under the tension generated by capillary mechanism appear indispensable for the interpretation of unsaturated soil behavior.
Cavitation; Matrix potential; Soil physics; Suction; Unsaturated soil mechanics
Mach and Hertz's mechanics
Studies in History and Philosophy of Science
39
91-101
2008
10.1016/j.shpsa.2007.11.007
The place of Heinrich Hertz’s The principles of mechanics in the history\nof the philosophy of science is disputed. Here I critically assess\npositivist interpretations, concluding that they are inadequate.\n\n\nThere is a group of commentators who seek to align Hertz with positivism,\nor with specific positivists such as Ernst Mach, who were enormously\ninfluential at the time. Max Jammer is prominent among this group,\nthe most recent member of which is Joseph Kockelmans. I begin by\ndiscussing what Hertz and Mach had to say about one another, and\nI specify certain respects in which their views are indeed similar.\nI then go on to detail their differences, looking at Hertz’s attitude\nto the atomic theory, to the mechanical world-view, to simplicity,\nto unobservables and metaphysics, and his objections to Newtonian\nforces. I conclude that the positivist interpretation of Hertz’s\nmechanics significantly overplays its similarities to Mach’s views.
Experimental and Applied Mechanics
Experimental and Applied Mechanics
6
393-398
2011
10.1007/978-1-4614-0222-0
Composite sandwich structures find applications in many aerospace systems due to their lightweight and high strength. However, these structures are susceptible to low energy impact damage. Our studies of the damage resistance and tolerance of honeycomb core sandwich structures shows that the performance of the core plays a key role. Thus we have undertaken a study of the compressive and shear behavior of the aluminum honeycomb cores used in several space systems. The study consists of uniaxial and compression/shear tests of the core. Using a novel ring specimen loaded in compression and torsion, we can load along any line in compression/shear stress space in order to map out the core’s yield surface and its evolution. Results from the experiments are used to validate computational models that are part of a larger simulation of the compression after impact strength of honeycomb core composites.
Intelligence by mechanics.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
365
1850
199-220
2007
10.1098/rsta.2006.1911
Research on the biomechanics of animal and human locomotion provides insight into basic principles of locomotion and respective implications for construction and control. Nearly elastic operation of the leg is necessary to reproduce the basic dynamics in walking and running. Elastic leg operation can be modelled with a spring-mass model. This model can be used as a template with respect to both gaits in the construction and control of legged machines. With respect to the segmented leg, the humanoid arrangement saves energy and ensures structural stability. With the quasi-elastic operation the leg inherits the property of self-stability, i.e. the ability to stabilize a system in the presence of disturbances without sensing the disturbance or its direct effects. Self-stability can be conserved in the presence of musculature with its crucial damping property. To ensure secure foothold visco-elastic suspended muscles serve as shock absorbers. Experiments with technically implemented leg models, which explore some of these principles, are promising.
Mechanics of the left ventricle.
Biophysical journal
39
3
279-88
1982
10.1016/S0006-3495(82)84518-9
A theory is presented for the mechanics of the left ventricle. A linear continuum description of the myocardium is developed, which incorporates anisotropic elastic effects due to the fiber direction field. The relation between fiber tension and fiber strain contains a time-dependent activation function that drives the ventricle around its cycle. The theory is applied to a simplified geometry consisting of a thick-walled finite cylinder in which fibers spiral on helical paths and terminate on planar end surfaces. The helix pitch angle varies continuously through the wall. The ventricular cycle is analyzed by specifying the pressures at which the aortic and mitral valves open and close. Key quantities are tabulated which permit a simple determination of the properties of the model under changes of wall thickness, fiber angles, muscle parameters, preload, afterload, etc. It is shown how the active muscle parameters can be inferred from a measurement of the end systolic pressure-volume line.
Animals; Elasticity; Heart; Heart: anatomy & histology; Humans; Mathematics; Models, Biological; Stress, Mechanical; Ventricular Function
Asynchronous contact mechanics
Communications of the ACM
55
102
2012
10.1145/2133806.2133828
We develop a method for reliable simulation of elastica in com- plex contact scenarios. Our focus is on firmly establishing three parameter-independent guarantees: that simulations of well- posed problems (a) have no interpenetrations, (b) obey causality, momentum- and energy-conservation laws, and (c) complete in fi- nite time. We achieve these guarantees through a novel synthe- sis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two- and three- dimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geome- tries, sharp features, and sliding during extremely tight contact.
and engineering; collision; contact; contact scenarios is critical; entertainment; ing; product design; robust simulation of complex; simulation; symplectic; to applications spanning graphics; train-; variational; virtual worlds
Mechanics of reversible adhesion
SOFT MATTER
7
18
8657-8662
2011
10.1039/c1sm05915g
By pressure-controlled surface contact area, reversible adhesion can be achieved with strengths tunable by 3 orders of magnitude. This capability facilitates robust transfer printing of active materials and devices onto any surface for the development of stretchable and/or curvilinear electronics. The most important parameter in designing the surfaces of stamps for this process is the height of the microtips relief: tall microtips may fail to pick up electronics from their growth substrate, while short ones may fail to print electronics on the receiver substrate. Mechanics models are developed to determine the range of the microtip height for successful transfer printing. Analytical expressions for the minimum and maximum heights are obtained, which are very useful for stamp design.
Time in Quantum Mechanics
arXiv
1
1-39
2013
10.1007/978-3-540-73473-4
The failure of conventional quantum theory to recognize time as an observable and to admit time operators is addressed. Instead of focusing on the existence of a time operator for a given Hamiltonian, we emphasize the role of the Hamiltonian as the generator of translations in time to construct time states. Taken together, these states constitute what we call a timeline, or quantum history, that is adequate for the representation of any physical state of the system. Such timelines appear to exist even for the semi-bounded and discrete Hamiltonian systems ruled out by Pauli's theorem. However, the step from a timeline to a valid time operator requires additional assumptions that are not always met. Still, this approach illuminates the crucial issue surrounding the construction of time operators, and establishes quantum histories as legitimate alternatives to the familiar coordinate and momentum bases of standard quantum theory.
Stochastic Quantum-Mechanics
Lecture Notes in Economics and Mathematical Systems
370
82-98
1991
The need for answering the question whether quantum mechanics is complete by itself and whether quantum fluctuations and thermal fluctuations are of the same genus, is discussed in this report. The hydrodynamic Hamilton Jacobi equations for the quantum Madelung fluid reveal the existence Df a quantum potential which corresponds to the mysterious dependence of the individual on the statistical ensemble of which it is a member. Nelson's analysis, starting from the Brownian motion of a particle moving in the field of a background white noise, leads to coupled equations for the velocity fields under certain conditions; these are described in the first three sections. Section 4 deals with indeterminacy relation in a novel way based on the two velocities envisaged in Nelson's work and some examples are given. The concluding section deals with the criticism of these two approaches and promises the unification of the three approaches including the derivation of the Feynman's path formalism obtained by complexifying the phase accumulation and assigning a proper measure for it. The extension of this approach to relativistic and spinning particles will form the content of part II of this article to be published elsewhere.
Nuclear mechanics in disease
Annu Rev Biomed Eng
13
397-428
2011
10.1146/annurev-bioeng-071910-124736
Over the past two decades, the biomechanical properties of cells have emerged as key players in a broad range of cellular functions, including migration, proliferation, and differentiation. Although much of the attention has focused on the cytoskeletal networks and the cell's microenvironment, relatively little is known about the contribution of the cell nucleus. Here, we present an overview of the structural elements that determine the physical properties of the nucleus and discuss how changes in the expression of nuclear components or mutations in nuclear proteins can not only affect nuclear mechanics but also modulate cytoskeletal organization and diverse cellular functions. These findings illustrate that the nucleus is tightly integrated into the surrounding cellular structure. Consequently, changes in nuclear structure and composition are highly relevant to normal development and physiology and can contribute to many human diseases, such as muscular dystrophy, dilated cardiomyopathy, (premature) aging, and cancer.
Adaptation; Animals; Biomechanics/physiology; Cell Nucleus/*physiology/ultrastructure; Cell Physiological Processes/*physiology; Disease/*etiology; Humans; Nuclear Lamina/*physiology/ultrastructure; Nuclear Proteins/*metabolism/ultrastructure; Physiological/physiology
Mechanics of Offshore Pipelines
Mechanics of Offshore Pipelines
59-88
2007
10.1016/B978-008046732-0/50003-9
This chapter briefly describes the process of steel making for line pipes. This is followed by outlines of the main steps that comprise the five major manufacturing processes. The effect of these processes on the mechanical properties and the geometric characteristics of the finished pipe are given particular emphasis because they affect their mechanical behavior. Steel production starts with the melting of iron ore, coke, limestone, and manganese ore in a blast furnace. Hot metal is delivered from the blast furnaces to the steel mill in "torpedo" ladles. Steel is a polycrystalline material. The small crystals, or grains, contain lattice defects known as dislocations, which limit their strength and, consequently, that of the material. Motions of dislocations causes plastic deformation of crystals. Macroscopic plastic strain is the cumulative effect of grain-level plastic deformation. Additional deformation can take place because of the interaction of grains at their boundaries. Steel is strengthened in many ways, which increase the resistance to dislocation mobility.
Critical State Soil Mechanics
Soil Use and Management
25
3
128-105
1968
10.1111/j.1475-2743.1987.tb00718.x
This book is about the mechanical properties of saturated remoulded soil. It is written at the level of understanding of a final-year undergraduate student of civil engineering; it should also be of direct interest to post-graduate students and to practising civil engineers who are concerned with testing soil specimens or designing works that involve soil. Our purpose is to focus attention on the critical state concept and demonstrate what we believe to be its importance in a proper understanding of the mechanical behaviour of soils. We have tried to achieve this by means of various simple mechanical models that represent (with varying degrees of accuracy) the laboratory behaviour of remoulded soils. We have not written a standard text on soil mechanics, and, as a consequence, we have purposely not considered partly saturated, structured, anisotropic, sensitive, or stabilized soil. We have not discussed dynamic, seismic, or damping properties of soils; we have deliberately omitted such topics as the prediction of settlement based on Boussinesq's functions for elastic stress distributions as they are not directly relevant to our purpose. The material presented in this book is largely drawn from the courses of lectures and associated laboratory classes that we offered to our final year civil engineering undergraduates and advanced students in 1965/6 and 1966/7. Their courses also included material covered by standard textbooks such as Soil Mechanics in Engineering Practice by K. Terzaghi and R. B. Peck (Wiley 1948), Fundamentals of Soil Mechanics by D. W. Taylor (Wiley 1948) or Principles of Soil Mechanics by R. F. Scott (Addison-Wesley 1963). In order to create a proper background for the critical state concept we have felt it necessary to emphasize certain aspects of continuum mechanics related to stress and strain in chapter 2 and to develop the well-established theories of seepage and one-dimensional consolidation in chapters 3 and 4. We have discussed the theoretical treatment of these two topics only in relation to the routine experiments conducted in the laboratory by our students, where they obtained close experimental confirmation of the relevance of these theories to saturated remoulded soil samples. Modifications of these theories, application to field problems, three-dimensional consolidation, and consideration of secondary effects, etc., are beyond the scope of this book. In chapters 5 and 6, we develop two models for the yielding of soil as isotropic plastic materials. These models were given the names Granta-gravel and Cam-clay from that river that runs past our laboratory, which is called the Granta in its upper reaches and the Cam in its lower reaches. These names have the advantage that each relates to one specific artificial material with a certain distinct stress - strain character. Granta-gravel is an ideal rigid/plastic material leading directly to Cam-clay which is an ideal elastic/plastic material. It was not intended that Granta-gravel should be a model for the yielding of dense sand at some early stage of stressing before failure: at that stage, where Rowe's concept of stress dilatancy offers a better interpretation of actual test data, the simple Granta-gravel model remains quite rigid. However, at peak stress, when Granta-gravel does yield, the model fits our purpose and it serves to introduce Taylor's dilatancy calculation towards the end of chapter 5. Chapter 6 ends with a radical interpretation of the index tests that are widely used for soil classification, and chapter 7 includes a suggested computation of `triaxial' test data that allows students to interpret much significant data which are neglected in normal methods of analysis. The remainder of chapter 7 and chapter 8 are devoted to testing the relevance of the two models, and to suggesting criteria based on the critical state concept for choice of strength parameters in design problems. Chapter 9 begins by drawing attention to the actual work of Coulomb - which is often inaccurately reported - and its development at Gothenberg; and then introduces Sokolovski's calculations of two-dimensional fields of limiting stress into which we consider it appropriate to introduce critical state strength parameters. We conclude in chapter 10 by demonstrating the place that the critical state concept has in our understanding of the mechanical behaviour of soils. We wish to acknowledge the continual encouragement and very necessary support given by Professor Sir John Baker, O.B.E., Sc.D., F.R.S., of all the work in the soil mechanics group within his Department. We are very conscious that this book represents only part of the output of the research group that our teacher, colleague, and friend, Ken Roscoe, has built up over the past twenty years, and we owe him our unbounded gratitude. We are indebted to E. C. Hambly who kindly read the manuscript and made many valuable comments and criticisms, and we thank Mrs Holt-Smith for typing the manuscript and helping us in the final effort of completing this text.
Mechanics of ureteral dilatation
Canadian Journal of Surgery
15
1
4-14
1972
The ureter has only 1 muscular coat whose individual muscle bundles have an irregular helical arrangement. Increased intraluminal volumes stretch these muscle bundles equally in every direction, leading to dilatation and lengthening. Several physiologic states lead to ureteral dilatation: increased urine volume (diuresis); increased normal resistance at the ureterovesical junction (bladder filling); and muscular atony (pregnancy and contraceptive pills). Pathologic ureteral dilatation is due to: mechanical obstruction (stones, tumors); vesicoureteral reflux owing to the impact of repeated overstretching, high pressures, increased volumes, and congenital muscular weakness; infravesical obstruction or neurogenic vesical dysfunction because of trigonal hypertrophy aggravated by trigonal stretching due to variable residual urine; trigonal irritation and spasm; and functional ureteral obstruction due to derangement in muscle fiber orientation, commonly in the juxtavesical ureter. The ureter has a remarkable capacity for recovery unless its musculature is congenitally deficient or pathologically fibrosed.
bladder filling; diuresis; hyperbarism; hypertrophy; *mechanics; muscle; muscle cell; muscle spasm; muscle weakness; neurogenic bladder; obstruction; oral contraceptive agent; pregnancy; residual urine; stretching; tumor; ureter; *ureter dilatation; ureter obstruction; urine volume; vesicoureteral reflux
Mechanics of discrete contact
Tribology International
39
5
381-386
2006
10.1016/j.triboint.2005.04.020
An approach based on the method of averaging is proposed to solve the discrete contact problems for bodies with given macro- and microgeometry. It divides the problem analysis into two scales of sizes. In macroscale the nominal (continuous) contact region is considered, and the integral equation to determine the nominal contact pressure is reduced. This equation includes the additional displacement function which depends on the nominal contact pressure and the microgeometry parameters at the fixed point of the nominal contact region. This function can be determined from the consideration of the discrete contact problem in the microscale for the particular models of surface microgeometry. The periodic contact problem for an elastic half-space has been solved to find the additional displacement function taken into account the interaction between contact spots. The analysis of the system of equations obtained for the periodic problem makes it possible to state the principle of localization which is used to solve the problems in micro- and in macroscale. The influence of the microgeometry parameters on the real and nominal contact characteristics is analyzed. © 2005 Elsevier Ltd. All rights reserved.
Contact pressure; Discrete contact; Rough surface
Mechanics of basin inversion
Tectonophysics
305
1-3
109-120
1999
10.1016/s0040-1951(99)00023-2
The long-term consequences of rifting for the thermal state of the deep crust and upper mantle reflect, in part, cooling induced by the reduction in heat production in the attenuated lithosphere and heating due to the burial of this heat production beneath the basin. Provided that the heat production is largely concentrated in the upper half of the crust, these factors result in significant increases in temperature at deep crustal and upper mantle levels. Because the Moho depth is likely to be reduced in the long-term limit of an isostatically balanced basin, these same factors may lead to slight cooling or slight heating of the Moho, depending on the nature of the basin-fill. For a Brace-Goetze lithospheric rheology (i.e. a rheology governed by a combination of frictional sliding and power-law creep), significant long-term lithospheric weakening (up to 5% per kilometre of basin-fill) accompanies basin formation when the lower crust is initially relatively strong and the basin fill is characterised by appreciable heat production and low thermal conductivity. In contrast, initially weak lower-crustal rheologies may result in long-term lithospheric strengthening. Evidence for basin-inversion in the geological record may therefore imply that heat production is strongly concentrated in the upper half of the crust and, under normal continental thermal regimes, the lower crust is strong.
basin inversion; extensional basins; lithosphere; mechanics; rheology
Mechanics of Composite Plates
Solid Mechanics and Its Applications
178
173-223
2011
Composite plates are increasingly used in engineering applications where they provide enhanced strength and stiffness without incurring additional weight compared to metallic counterparts or alternatively, enable a designer to reduce the weight, without sacrificing strength and stiffness. This is reflected in Fig. 5.1 where both specific strength as well as specific stiffness of composite materials are shown to be remarkable superior to typical alloys (specific strength and specific stiffness are strength per unit weight and elastic modulus per unit weight, respectively). Potential advantages of composite plates are related to the opportunity to tailor the response by orienting stiff high-strength fibers in the direction of maximum stresses. In other words, such plates utilize the principal difference of composites from isotropic materials, i.e. their anisotropic direction-dependent properties. A further enhancement in the response may be achieved by using sandwich plates where a light and relatively compliant core joins two stiff opposite facings and whose concept can be traced back to the classical I-beam.
Engineering
Particle scale reservoir mechanics
Oil and Gas Science and Technology
57
5
525-538
2002
10.2516/ogst:2002035
This paper summarizes some developments and applications of discrete particle modelling based on the commercial code PFC (Particle Flow Code), The following examples with relevance to geomechanical reservoir behaviour are described: - Numerical and experimental results are shown illustrating nonlinear evolution of depletion-induced compaction and stress path for simulated reservoir rock, i.e. materials that are formed under stress. This nonlinearity is often lost in core measurements, as a result of stress release during coring (core damage). - Angular and breakable superparticles have been implemented in the particle model and applied to simulate the formation of a compaction band at high stress level. The model is also used to investigate the formation of a shear band at lower confinement. - Numerical scheme of fluid coupling has been developed in both 2D and 3D models and applied to study stress-dependent permeability. - Stress-dependency of the acoustic properties of a bonded particle assemblage has been studied. The preliminary results of the simulations with various developments show qualitative and also quantitative consistence with experiments. It proves the feasibility of applying a discrete particle model as a numerical laboratory to study particle scale reservoir mechanics.
Computational Cardiovascular Mechanics
Computational Cardiovascular Mechanics: Modeling and Applications in Heart Failure
277-295
2010
10.1007/978-1-4419-0730-1
Coronary artery bypass graft (CABG) is a major therapy for ischemic heart disease which if left untreated can progress to failure of the heart. Restenosis, a leading cause of CABG, can be correlated with the geometric configuration and the hemodynamics of the graft. In this chapter we use computational fluid dynamics (CFD) to investigate the hemodynamics in a 3D out-of-plane sequential bypass graft model. Using a finite volume approach, quasi-steady flow simulations are performed at mid-ejection and at mid-diastole. Plots of velocity vectors, wall shear stress (WSS), and spatial WSS gradient (WSSG) distribution are presented in the aorto-left coronary bypass graft domain. Simulation results reveal a more uniform WSS and spatial WSSG distribution in the side-to-side (sequential graft) anastomosis configuration over the end-to-side (multiple graft) anastomosis. Results for the multiple bypass graft model show the peak magnitudes of the spatial WSSG are higher compared to the sequential bypass graft model. These findings suggest that sequential bypass grafting may be preferable over multiple bypass grafting to avoid non-uniformities of WSS. © 2010 Springer-Verlag US.
Mechanics of the Cell
Cell
109
6
685-686
2002
10.1016/S0092-8674(02)00789-4
Biological physics, the application of physics to provide an understanding of biological phenomenas, is a burgeoning, new inter-disciplinary subject. This text explores the physics behind the architecture of a cell's envelope and internal scaffolding, as well as the properties of its soft components. The analysis is performed within a consistent mathematical framework, although readers can navigate from the introductory material to biological applications without working through the intervening mathematics. The book includes applications and extensions handled through problems at the end of each chapter. This text is aimed at senior undergraduates and graduate students in science and biomedical engineering.
Mechanics of Automobiles
Mechanics of Automobiles
25-58
1964
10.1016/B978-0-08-010303-7.50006-1
This chapter focuses on vehicle braking and brakes. The forces that are responsible for the performance—positive as in acceleration or negative as in braking—of a vehicle are those developed between the tyres and the road. The forces generated by the road and tyre interaction depend upon many characteristics of both the road and tyres. The maximum tractive—or braking—effort depends upon the normal thrust between the tyres and the road. The ratio of the total maximum tractive—or braking—effort to the normal thrust is a constant called the coefficient of friction or coefficient of adhesion. When a vehicle moving round a curve is braked, the frictional forces between the tyres and road become more complex than in straight line motion because of the necessary side forces acting on the wheels. The braking capacity of a vehicle is reduced when moving in a flat turn. If the coefficient of adhesion is sufficiently high, the vehicle can, above a certain speed, overturn before sliding sideways. Internal expanding shoe brakes, used extensively on motor vehicles, essentially consist of curved shoes to which a lining of friction material is rigidly attached.
Mechanics of biological tissue
Mechanics of Biological Tissue
1-522
2006
10.1007/3-540-31184-X
Diverse reports over the last three decades reveal the ubiquitous role of mechanical factors in controlling many aspects of vascular growth and re- modeling. Examples include vascular adaptations during normal development, those due to altered loads ranging from exercise to a microgravity envi- ronment, those due to interventional procedures such as stenting or bypass surgery, and those incurred during the development of diseases ranging from hypertension to atherosclerosis or the formation of aneurysms. Concurrently, there has been an increased realization that mathematical modeling must play a central role in our attempts to understand and better predict vascular growth and remodeling. Models will help guide the identification and inter- pretation of revealing experiments and will allow an efficient exploration of the consequences of competing hypotheses.
Mechanics of respiratory muscles.
Respiratory Physiology & Neurobiology
163
1-3
82-9
2008
10.1016/j.resp.2008.04.019
Lung ventilation is a mechanical process in which the respiratory muscles are acting in concert to remove air in and out of the lungs. Any alteration in the performance of the respiratory muscle may reduce the effectiveness of ventilation. Thus, early diagnosis of their weakness is vital for treatment and rehabilitation. Different techniques, which are based on different measurement protocols, can be utilized for evaluation of respiratory muscle strength. Respiratory muscle strength can be assessed using pressure measurement either from the mouth or from the nostril during quasi-static breathing. However, it estimates only global performance of respiratory muscles. Techniques that are based on electromyography measurements during muscle contraction (EMG) enable the differentiation between the different respiratory muscles. Along with the above clinical and physiological techniques for assessment of respiratory muscle strength and endurance, mechanical and mathematical models of the chest wall were developed in the last few decades for analysis of chest wall movements and the contribution of its components to respiration. In this review, the different methods and the models utilized for evaluation of respiratory muscles function will be discussed.
Animals; Biological; Humans; Models; Muscle Contraction; Muscle Contraction: physiology; Muscle Strength; Muscle Strength: physiology; Respiratory Mechanics; Respiratory Muscles; Respiratory Muscles: anatomy & histology; Respiratory Muscles: physiology
Multiresolution molecular mechanics: Statics
Computer Methods in Applied Mechanics and Engineering
258
26-38
2013
10.1016/j.cma.2013.01.014
This paper presents a new concurrent atomistic-continuum coupling method called the multiresolution molecular statics (MMS). By introducing a novel energy sampling framework, MMS aims at accurately and efficiently approximating the atomic energy of the system at different resolutions without the cumbersome interfacial treatment in existing methods. The key features of the MMS method are: (1) consistency with the atomistics framework, (2) consistency with the order of shape functions introduced, and (3) flexibility in energy approximation with respect to accuracy and efficiency. Under the energy sampling framework, several sampling schemes have been devised and tested for interface compatibility, and compared to existing methods. Sources of errors in the different approximations have been identified. The proposed MMS method demonstrates very good accuracy in solving crack propagation and surface relaxation problems when compared to full molecular statics. ?? 2013 Elsevier B.V.
Crack propagation; Interface compatibility; Molecular statics; Multiscale modeling; Surface relaxation
Fluid Mechanics of Microrheology
Annual Review of Fluid Mechanics
42
1
413-438
2010
10.1146/annurev-fluid-121108-145608
In microrheology, the local and bulk mechanical properties of a complex fluid are extracted from the motion of probe particles embedded within it. In passive microrheology, particles are forced by thermal fluctuations and probe linear viscoelasticity, whereas active microrheology involves forcing probes externally and can be extended out of equilibrium to the nonlinear regime. Here we review the development, present state, and future directions of this field. We organize our review around the generalized Stokes-Einstein relation (GSER), which plays a central role in the interpretation of microrheology. By discussing the Stokes and Einstein components of the GSER individually, we identify the key assumptions that underpin each, and the consequences that occur when they are violated. We conclude with a discussion of two techniques—multiple particle-tracking and nonlinear microrheology—that have arisen to handle systems in which the GSER breaks down.
fluctuation; mobility; rheology; stokes-einstein relation; viscoelasticity
Geomorphological Fluid Mechanics
Lecture Notes in Physics
582
319-338
2001
10.1007/3-540-45670-8
Over the last century, mountain ranges in Europe and North America have seen substantial development due to the increase in recreational activities, transportation, construction in high altitude areas, etc. In these mountain ranges, avalanches often threaten man's activities and life. Typical examples include recent disasters, such as the avalanche at Val d'Isère in 1970 (39 people were killed in a hostel) or the series of catastrophic avalanches throughout the Northern Alps in February 1999 (62 residents killed). The rising demand for higher safety measures has given new impetus to the development of mitigation technology and has given rise to a new scientific area entirely devoted to snow and avalanches. This paper summarises the paramount features of avalanches (formation and motion) and outlines the main approaches used for describing their movement. We do not tackle specific problems related to snow mechanics and avalanche forecasting. For more information on the subject, the reader is referred to the main textbooks published in Alpine countries 1-8.
Statistical fluid mechanics
European Journal of Mechanics - B/Fluids
17
679-681
1998
10.1016/S0997-7546(98)80021-6
PURPOSE: The purposes of this qualitative/descriptive study were to (a) explore experiences and decision-making behaviors associated with adoption of a sodium-restricted diet (SRD) among older women with hypertension or heart failure and (b) identify healthcare system and contextual factors that facilitate or impede adherence to SRD. DATA SOURCES: Participants were 33 single older women, aged 65-98 years, residing in three congregate living facilities in the high-risk "coronary valley" area of the United States. A semistructured interview format was employed with three focus groups. The audio-taped transcribed data were content analyzed for themes by the researchers with the assistance of ATLAS.Ti computer software. CONCLUSIONS: Predominant themes were lack of SRD education by healthcare providers, a desire for more information about sodium, including the use of alternative herbal seasonings, and large-print informational materials. Eating alone with no motivation to cook and share meals was a contextual barrier to healthy nutrition. IMPLICATIONS FOR PRACTICE: To prevent costly hospitalizations and rehospitalization from nonadherence to SRD, clinicians need to provide more structured SRD education supplemented with printed brochures. Exploring the client's nutritional social setting may improve SRD adherence.
Mechanics of Mammalian Swimming
Bulletin of the American …
2008
Propulsion of large mammals ($i.e.$ dolphins and humans) has been of great interest for both technological and athletic reasons. The foundational question is how fast can a mammal swim? Digital Particle Image Velocimetry (DPIV) has been modified to be safely used on swimmers and dolphins. Experiments of dolphins performing various swimming behaviors were performed at the Long Marine Laboratory, University of California, Santa Cruz. Vortices generated by the dolphins' tail motions were used to estimate thrust production. Also, a two-dimensional dynamic force balance was constructed to study and improve the mechanics of elite swimmers. Paired with an underwater video camera, the forces seen could be directly related to the motion of the swimmer. These force measurements could be correlated to time resolved DPIV measurements of flow around the swimmers. Measurements made with swimmers, Megan Jendrick (2000 Olympic gold medalist) and Ariana Kukors (4x US National Champion), as well as data from trials with two dolphins will be presented.
Priciples of Quantum Mechanics
Adolescence education newsletter
2
2
7
1999
10.1119/1.1933288
Currently being developed by the Thoughtshop Foundation in collaboration with the Child In Need Institute in West Bengal, this kit is intended to help peer educators in generating awareness about reproductive health issues among rural adolescent boys and men through discussions and other activities. The central theme is men's responsibility for their sexual behavior and the reproductive and sexual health of their partners. In five modules, the kit tells the story of Shankar, a boy 13 years old. Each module consists of a flip chart and accompanying visual aids/activities. The modules are as follows: 1) Puberty, self-esteem, responsibility; 2) Knowledge of changes which girls experience during puberty; 3) Childbirth; 4) Contraception--why/how; 5) Safer sex, hygiene, STD/HIV/AIDS.
Adolescent; Age Factors; Asia; Behavior; Demography; Developing Countries; Education; Health; India; Population; Population Characteristics; Reproductive Medicine; Research; Sex Education; Sexual Behavior; Sexual Partners; Teaching Materials
Fracture Mechanics Ch08
Fracture Mechanics
189-225
2012
10.1016/B978-0-12-385001-0.00008-0
For homogeneous materials, the crack tip stress and displacement fields play a central role in establishing fracture parameters for investigating interface fracture. The asymptotic eigenfunction expansion method is used to analyze the interface crack tip fields but the characteristic equations for determining the eigenvalue or the stress singularity index is much more complex due to the material property mismatch along the interface. In analyzing the asymptotic crack tip stress and displacement fields, it is sufficient to consider a semi-infinite crack lying at the interface between two dissimilar homogeneous materials. The crack surface contact zone and the stress oscillation zone near an interface crack tip are analyzed using the oscillatory crack tip fields. In addition, the oscillatory nature of stress and displacement fields near the tip of an interfacial crack implies contact of the crack surfaces. When the contact zone size is smaller than the crack length and other in-plane dimensions, such as in bimaterial cracks under Mode I loading, the oscillatory crack tip fields is used to predict interfacial fracture.
complex stress intensity factor; crack surface contact; Dundurs' parameters; energy release rate; interface crack; phase angle; stress oscillation
Superconductivity of niobium thin films
Thin Solid Films
61
3
27-30
1979
10.1143/JPSJ.26.347
Examines some of the parameters for making superconducting niobium thin films and the effects variations in these parameters have on the critical temperature. The I-V characteristics across the current-induced transition are presented and two values of critical temperature, 4.7K and 7.7K, were obtained for two film thicknesses
critical currents; niobium; superconducting thin f
Introduction to Thin-Film Photovoltaics
Advanced Characterization Techniques for Thin Film Solar Cells
1-32
2011
10.1002/9783527636280.ch1
This chapter contains sections titled:\n\n* Introduction * The Photovoltaic Principle * Functional Layers in\nThin-Film Solar Cells * Comparison of Various Thin-Film Solar-Cell\nTypes * Conclusions * References
Band-gap energy; Chemical bath deposition (cbd); Photogenerated carriers; Solar cells; Thin-film photovoltaics
The classical roots of wave mechanics: Schrodinger's transformations of the optical-mechanical analogy
Studies in History and Philosophy of Modern Physics
40
4
338-351
2009
DOI 10.1016/j.shpsb.2009.06.007
In the 1830s, W. R. Hamilton established a formal analogy between optics and mechanics by constructing a mathematical equivalence between the extremum principles of ray optics (Fermat's principle) and corpuscular mechanics (Maupertuis's principle). Almost a century later, this optical-mechanical analogy played a central role in the development of wave mechanics. Schrodinger was well acquainted with Hamilton's analogy through earlier studies. From Schrodinger's research notebooks, we show how lie used the analogy as a heuristic tool to develop de Broglie's ideas about matter waves and how the role of the analogy in his thinking changed from a heuristic tool into a formal constraint on possible wave equations. We argue that Schrodinger only understood the full impact of the optical-mechanical analogy during the preparation of his second communication on wave mechanics: Classical mechanics is an approximation to the new undulatory mechanics, just as ray optics is an approximation to wave optics. This completion of the analogy convinced Schrodinger to stick to a realist interpretation of the wave function, in opposition to the emerging mainstream. The transformations in Schrodinger's use of the optical-mechanical analogy can be traced in his research notebooks, which offer a much more complete picture of the development of wave mechanics than has been previously thought possible. (C) 2009 Published by Elsevier Ltd.
eigen-value-problem; equation; hamilton, w. r.; optical-mechanical analogy; quantization; quantum mechanics; schrodinger, e.; wave mechanics
Hilbert space quantum mechanics is noncontextual
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
44
3
174-181
2013
10.1016/j.shpsb.2013.02.001
It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an appropriately constructed apparatus can be shown to reveal the value of an observable A possessed by the measured system before the measurement took place, whatever other compatible ([B,A]=0) observable B may be measured at the same time.
Contextual; Hilbert space; Quantum mechanics
Empirical Force Field Models: Molecular Mechanics
Molecular Modelling: Principles and Applications
165-252
2001
This book provides a detailed description of the techniques employed in molecular modeling and computational chemistry. The first part of the book covers the two major methods used to describe the interactions within a system (quantum mechanics and molecular mechanics). The second part then deals with techniques that use such energy models, including energy minimization, molecular dynamics, Monte Carlo simulations and conformational analysis. The author also discusses the use of more advanced modeling techniques such as the calculation of free energies and the simulation of chemical reactions. In addition he considers aspects of both chemoinformatics and bioinformatics and techniques that can be used to design new molecules with specific properties. Many of the topics are treated in considerable depth but the student is assumed to have only a basic knowledge of the relevant physical and chemical principles.
The molecular mechanics of eukaryotic translation.
Annual review of biochemistry
73
657-704
2004
10.1146/annurev.biochem.73.030403.080419
Great advances have been made in the past three decades in understanding the molecular mechanics underlying protein synthesis in bacteria, but our understanding of the corresponding events in eukaryotic organisms is only beginning to catch up. In this review we describe the current state of our knowledge and ignorance of the molecular mechanics underlying eukaryotic translation. We discuss the mechanisms conserved across the three kingdoms of life as well as the important divergences that have taken place in the pathway.
Archaeal Proteins; Archaeal Proteins: biosynthesis; Archaeal Proteins: genetics; Biological; Codon; Eukaryotic Cells; Eukaryotic Initiation Factors; Eukaryotic Initiation Factors: metabolism; Fungal Proteins; Fungal Proteins: biosynthesis; Fungal Proteins: genetics; Initiator; Messenger; Messenger: genetics; Messenger: metabolism; Models; Peptide Chain Initiation; Peptide Chain Termination; Protein Biosynthesis; Proteins; Proteins: genetics; RNA; Translational
Damage mechanics in the post-failure regime
Mechanics of Materials
4
2
149-160
1985
10.1016/0167-6636(85)90013-4
A continuum damage model for the deformation of brittle materials, based on the mechanics of microcrack nucleation and growth, is extended to include the effect of interaction among neighboring microcracks on the evolution of damage. As a result, the range of validity of the model is extended to include a limited region of homogeneous softening just beyond the point of maximum stress. With the inclusion of interaction effects, a variety of non-linear, time-dependent behavior can be realistically modeled. Examples of the response of rock subjected to a variety of deformation histories such as constant stress rate loading, creep, and uniaxial strain are presented and the results are compared to experimental results where possible.
Modelling materials for engineering rock mechanics
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts
7
1
77-121
1970
10.1016/0148-9062(70)90029-X
Information on modelling materials is disseminated throughout the literature. Based on a simple, quaalitative classification, a representative cross section of this information has been assembled, so that most materials of any prominence have been documented. In addition to practical information, including mechanical and physical properties, some of these materials are critically assessed in relation to the problem of simulating rock. Reference is also made to modelling materials used in other disciplines where this has seemed relevant to rock mechanics. Finally, brief consideration is given to the important problems of modelling anisotropy and joint behaviour. A full bibliography is appended.
A theory of smeared continuum damage mechanics
Journal of Mechanical Science and Technology
12
2
233-243
1998
10.1007/BF02947168
This paper considers smeared continuum damage mechanics based on the equivalent elliptical crack representation of a local damage. This approach provides a means of utilizing the crack energies derived in fracture mechanics, and of identifying the local damage state from local stress and strain information. The strain energy equivalence principle is used to derive the effective continuum elastic properties of a damaged solid in terms of the undamaged elastic properties and a scalar damage variable. The scalar damage variable is used to develop a consistent damage evolution equation. The combination of representing local damage as an equivalent elliptical crack, the determination of effective elastic properties using a strain energy equivalence principle, and a consistent damage evolution equation yields a simple, yet powerful local approach for continuum damage analysis
Engineering
The Modal Interpretation of Quantum Mechanics
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
1976
82-103
1976
This paper presents a general formal semantic scheme for the interpretation of quantum mechanics, in terms of which van Fraassen's Copenhagen and anti-Copenhagen variants of the modal interpretation are examined. The general character of the modal interpretation is motivated in a discussion of classical statistical mechanics, the distinction being made between statistical states and micro-states. The notion of a quasi-classical (micro) state is introduced in a discussion of the theorem of Gleason and Kochen and Specker. It is shown that, according to the anti-Copenhagen variant, the class of micro-states coincides with a special class of quasi-classical states. The paper concludes with two general criticisms of the anti-Copenhagen variant.
Structure and mechanics of coated textile fabrics
Structure and Mechanics of Textile Fibre Assemblies
213-241
2008
Doi 10.1533/9781845695231.213
Coated fabrics are an important family of textile structures and have a wide range of applications. Geometry and manufacturing methods of coated fabrics along with fibers and fabrics used in the reinforcement structures are explained. Polymers and additives used in coated fabrics are included. Adhesion between coatings and fabrics is critical for the high performance expected of coated fabrics. The behavior of coated fabrics in tensile, tear, bending and shear loading is analyzed. Models to simulate the mechanics of coated fabrics are discussed. Recycling techniques of coated fabrics are included.
additives; coated fabrics; mechanical behavior; modeling; polymers; recycling
Tetrahexylsexithiophene: crystal structure and molecular mechanics calculations
Macromolecular Chemistry and Physics
199
9
1973-1979
1998
The synthesis, crystal structure and detailed molecular mechanics calculations, including crystal packing interactions, of tetrahexylsubstituted sexithienylene are presented. Unexpectedly the molecule, which arranges in the P-1space group, displays no herringbone arrangement, thienylenic rings are far from coplanarity and the alkylic side chains present different conformations. Molecular mechanics fully accounts for these findings. From crystal packing computations it is derived that different arrangements are unable to lower the packing energy, due to the closeness of two alkyl chains on the same side of the thienylenic backbone, which prevents interspersion of non-parallel molecules.
Learning engineering mechanics through video production
34th Annual Frontiers in Education, 2004. FIE 2004.
7-12
2004
10.1109/FIE.2004.1408659
This paper presents an approach to integrating student-produced videos into an engineering mechanics class. Each student worked in a production team to produce a two- to three-minute educational video investigating a combined translational/rotational motion. Through this experience students expanded their communication skills by becoming familiar with the technical and creative skills of video production. They also expanded their understanding of mechanics by studying real-world applications and communicating their results. Throughout the project, students received extensive assistance from the college's media services staff- including workshops on managing and planning production, shooting and editing. Once the videos were completed, students were encouraged to reflect upon their experience through peer reviews and group reflections. Student feedback is presented and supports the success of the activity.
Quantum Mechanics and Travel to the Stars
Nexus
21
5
43-48
2014
This article outlines a view of the quantum mechanical wave-function as the limit of classical mechanics. It argues that the region inside the wave-function is physically unrelated to that outside and represents a fundamentally different reality. A review of published evidence for this view is presented and it is argued that these ideas (and indeed more traditional physics and mathematics, even if the interpretation is incorrect) lead logically to the possibility of interstellar travel and teleportation though quantum mechanisms. Some of the practical implications of this are also explored.
interstellar travel; propulsion; Quantum Mechanics; relativity; space travel; teleportation
Scheduling reefer mechanics at container terminals
Transportation Research Part E: Logistics and Transportation Review
51
17-27
2013
10.1016/j.tre.2012.12.007
This paper discusses the scheduling of reefer mechanics at container terminals. Reefer mechanics plug and unplug reefer containers such that due times are met. We outline the resulting scheduling problem and two simple heuristics. Subsequently, we present a simulation model to analyze the scheduling methods and the reefer-related processes in a realistic dynamic framework. Some results from the simulation experiments are also presented. They demonstrate the applicability of the heuristic and the use of the simulation model in practice. The simulation study was carried out for a real container terminal in the port of Hamburg, Germany. © 2012 Elsevier Ltd.
Case study; Container terminal; Heuristic; Reefer; Scheduling; Simulation
Finite element methods in fracture mechanics
Finite Element Methods in Engineering: Proceedings of the Fifth International Conference in Australia on Finite Element Methods
31
1
1
1989
10.1016/0045-7949(89)90160-0
Finite element methodology specific to the analysis of fracture mechanics problems is reviewed. Primary emphasis is on the important algorithmic developments which have enhanced the numerical modeling of fracture processes. Methodologies to address elasto-static problems in two- and three-dimensions, elasto-dynamic problems, elasto-plastic problems, special considerations for three-dimensional nonlinear problems and the modeling of stable crack growth are reviewed. In addition, the future needs of the fracture community are discussed and open questions are identified. The need for theoretical advancements in continuum mechanics and constitutive fracture laws coupled with improved numerical algorithms is emphasized. Extensive reference is made to the open literature base for further details.
Schrodinger and the Interpretation of Quantum Mechanics
Foundations of Physics
17
12
1205-1220
1987
On the occasion of the centennial of his birth, Schr6dinger's life and views are sketched and his critique of the interpretation of quantum mechanics accepted at his time is examined. His own interpretation, which he had to abandon after a short time, provides a prime example of the way in which the tentative meaning of central theoretical terms in a new and revolutionary theory often fails. Schrfdinger's strong philosophical convictions have played a key role in his refusal to break with many of the notions of classical physics. At the same time, they made him into a keen and incisive critic of the Copenhagen interpretation. His criticism is compared with present views on quantum mechanics.
A historical review on nonholomic mechanics
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
106
1
191-224
2012
10.1007/s13398-011-0046-2
The aim of this paper is to present a short historical/scientific review on nonholonomic mechanics, with special emphasis on the latest developments. Indeed, the use of differential geometric tools has permitted in the last 25 years a fast and unsuspected advance in the theory, particularly in a better understanding of symmetries and reduction, Hamilton–Jacobi theory and integrability characterizations, and the construction of suitable geometric integrators. The last part of the paper is devoted to discuss the latest results in Hamilton–Jacobi theory for nonholonomic dynamics using our own approach.
Invariants and stability in classical mechanics
Reports on Progress in Physics
40
9
1033
1977
10.1088/0034-4885/40/9/002
In the last 20 years there have been discoveries in classical mechanics that have made an impact on several other branches of physics. The important result from which these developments stem has become known as the KAM theorem. This relates to a situation in which a simple integrable dynamical system is subjected to perturbations. Whereas before perturbation the motion could be described as regular, after perturbation the phase space is sharply divided into regions of regular and highly irregular motion. Computer calculations have made it possible to appreciate both the complexity and the detailed structure of the situation. Examples of this behaviour have been found in plasma physics, statistical mechanics and astronomy. A qualitative review is given of the KAM theorem, the work that led up to it and its application to various branches of physics.
Is standard quantum mechanics technologically inadequate?
British Journal for the Philosophy of Science
58
3
595-604
2007
10.1093/bjps/axm027
In a recent issue of this journal, P.E. Vermaas ([2005]) claims to have demonstrated that standard quantum mechanics is technologically inadequate in that it violates the technical functions condition'. We argue that this claim is false because based on a narrow' interpretation of this technical functions condition that Vermaas can only accept on pain of contradiction. We also argue that if, in order to avoid this contradiction, the technical functions condition is interpreted widely' rather than narrowly', then Vermaas, argument for his claim collapses. The conclusion is that Vermaas' claim that standard quantum mechanics is technologically inadequate evaporates. 1 Introduction 2 The Narrow Interpretation 3 The Wide Interpretation 4 The Teleportation Scheme 5 Conclusions
Interpretations of Quantum Mechanics: a critical survey
Arxiv preprint arXiv08113877
17
2008
This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. In the same time, there are implicit and hidden assumptions about his role. In fact, most interpretations taking as ontic level one of these fundamental concepts as information, physical law and matter bring us to new problematical questions. We think, that no interpretation of the quantum theory can avoid this intrusion until we do not clarify the nature of observer.
Statistical mechanics of budget-constrained auctions
Journal of Statistical Mechanics: Theory and Experiment
2009
07
P07002
2009
10.1088/1742-5468/2009/07/P07002
Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). Based on the cavity method of statistical mechanics, we introduce a message passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.
The molecular mechanics of eukaryotic translation.
Ann Rev Biochem
73
657-704
2004
10.1146/annurev.biochem.73.030403.080419
Great advances have been made in the past three decades in understanding the molecular mechanics underlying protein synthesis in bacteria, but our understanding of the corresponding events in eukaryotic organisms is only beginning to catch up. In this review we describe the current state of our knowledge and ignorance of the molecular mechanics underlying eukaryotic translation. We discuss the mechanisms conserved across the three kingdoms of life as well as the important divergences that have taken place in the pathway.
Archaeal Proteins; Archaeal Proteins: biosynthesis; Archaeal Proteins: genetics; Biological; Codon; Eukaryotic Cells; Eukaryotic Initiation Factors; Eukaryotic Initiation Factors: metabolism; Fungal Proteins; Fungal Proteins: biosynthesis; Fungal Proteins: genetics; Initiator; Messenger; Messenger: genetics; Messenger: metabolism; Models; Peptide Chain Initiation; Peptide Chain Termination; Protein Biosynthesis; Proteins; Proteins: genetics; RNA; Translational
The mechanics of quasi-static crack growth
US National Congress of Applied Mechanics
June 1978
191-216
1979
Results on the mechanics of quasi-static crack growth are reviewed. These include recent studies on the geometry and stability of crack paths in elastic-brittle solids, and on the thermodynamics of Griffith cracking, including environmental effects. The relation of crack growth criteria to non-elastic rheological models is considered and paradoxes with energy balance approaches, based on singular crack models, are discussed for visco-elastic, diffuso-elastic, and elastic-plastic materials. Also, recent approaches to prediction of stable crack growth in ductile, elastic-plastic solids are discussed.
Entangled state representations in noncommutative quantum mechanics
Science And Technology
1-16
2005
10.1088/0305-4470/38/39/008
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called entangled state representations. Furthermore, we derive unitary transformations between the new representations and the ordinary one used in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of some basic operators in these representations. To show the potential applications of the entangled state representations, a two-dimensional harmonic oscillator on the noncommutative plane with both coordinate-coordinate and momentum-momentum couplings is exactly solved.
High Energy Physics - Theory
Muscle Mechanics and Dynamics of Ocular Motion
Journal of Mathematical Systems, Estimation, and Control
8
2
1-15
1998
A model of the neuromuscular mechanics of horizontal eye motion is developed. The model of the oculomotor system that is presented incorporates known physiological dynamics and geometry of the musculotendon complex. Muscle force development is a described by a two-component version of Hill's model and consists of a passive and active contractile component. The active component includes the force-velocity and force-length characteristics of the muscle. The passive component accounts for elastic and viscous effects. Activation dynamics couple the neural controls that are appropriate for saccadic movements to the muscle mechanics. Numerical simulations illustrate that the model successfully simulates saccadic movements and accurately depicts eye position and velocity and muscle tension.
Information measures and classicality in quantum mechanics
Physical Review D
59
4
045001
1998
10.1103/PhysRevD.59.045001
We study information measures in quantum mechanics, with the particular emphasis on providing a quan- tification of the notion of predictability and classicality. Our primary tool is the Shannon-Wehrl entropy I. We give a precise criterion for phase space classicality of states and argue that in view of this a I provides a good measure for the degree of deviation from classicality in closed systems and b IS (S the von Neumann entropy plays the same role in open quantum system. We examine particular examples in nonrelativistic quantum mechanics. Finally we generalize the discussion into the field theory case, and this being one of our main motivations we comment on the field classicalization in early universe cosmology.
Modern Optical Techniques in Fluid Mechanics
Annual Review of Fluid Mechanics
16
1
223-244
1984
10.1146/annurev.fluid.16.1.223
Optical techniques are widely used in fluid mechanics to observe and measure properties of flow fields such as velocities or densities. Many of these techniques are qualitative but of great value in guiding intuition for further research by quantitative means. Flow-visualization techniques use light as an information carrier where the information is impressed on the light beam by the fluid flow. Flow-generation techniques use light as an energy carrier to initiate fluid flow by radiation pressure, heating, or optical breakdown. The application of phase tomography and computers for monitoring are discussed.
Debris Flow: Mechanics, Prediction and Countermeasures
Annual Review of Fluid Mechanics
13
1
57-77
2007
10.1007/s00024-008-0342-8
A comprehensive account, treating both theoretical and applied aspects of debris flow, this text begins with a discussion of fundamental mechanical aspects, such as flow characteristics, type classification, mechanics, occurrence and development, fully-developed flow and deposition processes. It sheds light on the application of theory in relation to computer-simulated reproductions of real disasters. Attention is paid to debris flow controlling structures, design effectiveness and performance, soft countermeasure problems, such as identification of debris flow prone ravines and the prediction of occurrence by the concept of precipitation threshold.
Mechanics of coiled nanotubes in uniaxial tension
Materials Science and Engineering: A
408
1-2
136-140
2005
10.1016/j.msea.2005.07.047
The mechanics of coiled nanotubes in uniaxial tension is presented in\nsimple explicit expressions. The estimations for double coils are\nobtained. Given the initial geometry, good agreement in the whole\nstretching process (about 30% elongation) is observed in comparison\nwith the experimental result. In addition, it is found that as an\nalternative, the shear modulus of the tube can be determined by the\nuniaxial tensile test. However, the analysis reveals that it is\ndifficult to precisely determine the Poisson ratio. (c) 2005 Elsevier\nB.V. All rights reserved.
mechanical properties; nanocoil; nanospring; poisson ratio; shear modulus; s modulus; young
Clifford Algebra and the Interpretation of Quantum Mechanics
Clifford Algebras and their Applications in Mathematical Physics
321–346
1986
The Dirac theory has a hidden geometric structure. This talk traces the concep- tual steps taken to uncover that structure and points out significant implications for the interpre- tation of quantum mechanics. The unit imaginary in the Dirac equation is shown to represent the generator of rotations in a spacelike plane related to the spin. This implies a geometric interpreta- tion for the generator of electromagnetic gauge transformations as well as for the entire electroweak gauge group of theWeinberg-Salam model. The geometric structure also helps to reveal closer con- nections to classical theory than hitherto suspected, including exact classical solutions of the Dirac equation.
The Fluid Mechanics of Carbon Dioxide Sequestration
Annual Review of Fluid Mechanics
46
255-272
2013
10.1146/annurev-fluid-011212-140627
Humans are faced with a potentially disastrous global problem owing to the current emission of 32 gigatonnes of carbon dioxide (CO2) annually into the atmosphere. A possible way to mitigate the effects is to store CO2 in large porous reservoirs within the Earth. Fluid mechanics plays a key role in determining both the feasibility and risks involved in this geological sequestration. We review current research efforts looking at the propagation of CO2 within the subsurface, the possible rates of leakage, the mechanisms that act to stably trap CO2, and the geomechanical response of the crust to large-scale CO2 injection. We conclude with an outline for future research.
convective dissolution; geomechanics; gravity currents; leakage; residual trapping
Non-local continuum mechanics and fractional calculus
Mechanics Research Communications
33
6
753-757
2006
10.1016/j.mechrescom.2006.05.001
The present work introduces fractional calculus into the continuum mechanics area describing non-local constitutive relations. Considering a one-dimensional body and assuming total stored energy depending not only upon the local strain but also upon a fractional derivative of the stain, an elastic model with non-local stress-strain behavior is introduced. Fractional calculus provides a natural framework for describing non-local constitutive relations and requires no assumptions for the interval of non-local influence. Furthermore, the proposed method works in finite intervals contrary to the existing theories requiring infinite domains. ?? 2006 Elsevier Ltd. All rights reserved.
Coexistence of phases; Elasticity; Fractional calculus; Non-local strain energy density
AdS2/CFT1, canonical transformations and superconformal mechanics
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
555
1-2
99-106
2003
10.1016/S0370-2693(03)00040-6
We propose a simple conformal mechanics model which is classically equivalent to a charged massive particle propagating near the AdS2 × S2 horizon of an extreme Reissner-Nordström black hole. The equivalence holds for any finite value of the black hole mass and with both the radial and angular degrees of freedom of the particle taken into account. It is ensured by the existence of a canonical transformation in the Hamiltonian formalism. Using this transformation, we construct the Hamiltonian of a N = 4 superparticle on AdS2 × S2 background. © 2003 Published by Elsevier Science B.V.
AdS/CFT; Canonical transformation; Conformal mechanics
Statistical Mechanics and Quantum Fields on Fractals
Contemporary Mathematics
924
21
2012
Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the corresponding absence of Fourier mode decomposition. Moreover, the existence of a set of distinct dimensions characterizing the physical properties (spatial or spectral) of fractals make them a useful testing ground for dimensionality dependent physical problems. This paper addresses specific problems including the behavior of the heat kernel and spectral zeta functions on fractals and their importance in the expression of spectral properties in quantum physics. Finally, we apply these results to specific problems such as thermodynamics of quantum radiation by a fractal blackbody.
09; 924; and phrases; fractals; in part by the; israel science foundation grant; no; quantum field theory; statistical mechanics; the author was supported
A toy model for quantum mechanics
0705.2742
2007
doi:10.1007/s10701-007-9171-3
The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.
The Molecular Mechanics of Quantized Valence Bonds
J. Mol. Model.
3
3
124-141
1997
10.1007/s008940050026
A new force field, Quantized Valence Bonds' Molecular Mechanics (QVBMM)\nhas been included in the molecular modeling program STR3DLEXE. The\nQVBMM force field successfully embraces and implements all of the\npivotal concepts in VSEPR theory and uniquely integrates lone pairs\ninto molecular mechanics. QVBMM facilitates a detailed analysis of\nthe stereo-electronic effects that contribute to the structural and\nconformational preferences of organic molecules in their ground states,\nincluding those molecules that possess the common heteroatoms. The\ndesign, parameterization and application of the force field to a\nfew representative molecules is discussed. The anomeric effect is\nalso briefly examined.
Mechanics model for actin-based motility
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
79
November 2008
1-10
2009
10.1103/PhysRevE.79.021916
We present here a mechanics model for the force generation by actin polymerization. The possible adhesions between the actin filaments and the load surface, as well as the nucleation and capping of filament tips, are included in this model on top of the well-known elastic Brownian ratchet formulation. A closed form solution is provided from which the force-velocity relationship, summarizing the mechanics of polymerization, can be drawn. Model predictions on the velocity of moving beads driven by actin polymerization are consistent with experiment observations. This model also seems capable of explaining the enhanced actin-based motility of Listeria monocytogenes and beads by the presence of Vasodilator-stimulated phosphoprotein, as observed in recent experiments.
Homogeneous Rigid Body Mechanics with Elastic Coupling
Applications of Geometric Algebra in Computer Science and Engineering
197-212
2002
10.1007/978-1-4612-0089-5_19
Geometric algebra is used in an essential way to provide a coordinate-free approach to Euclidean geometry and rigid body mechanics that fully integrates rotational and translational dynamics. Euclidean points are given a homogeneous representation that avoids designating one of them as an origin of coordinates and enables direct computation of geometric relations. Finite displacements of rigid bodies are associated naturally with screw displacements generated by bivectors and represented by twistors that combine multiplicatively. Classical screw theory is incorporated in an invariant formulation that is less ambiguous, easier to interpret geometrically, and manifestly more efficient in symbolic computation. The potential energy of an arbitrary elastic coupling is given an invariant form that promises significant simplifications in practical applications.
What quantum mechanics describes is discontinuous motion
cds.cern.ch
10
1-13
2000
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies what quantum mechanics describes is discontinuous motion of particles. Considering the fact that space-time may be essentially discrete when considering gravity, we further present a theory of discontinuous motion of particles in discrete space-time. We show that its evolution will naturally result in the dynamical collapse process of the wave function, and this collapse will bring about the appearance of continuous motion of objects in the macroscopic world.
Does quantum mechanics accept a stochastic support?
Foundations of Physics
12
10
1017-1037
1982
10.1007/BF01889274
Arguments are given in favor of a stochastic theory of quantum mechanics, clearly distinguishable from Brownian motion theory. A brief exposition of the phenomenological theory of stochastic quantum mechanics is presented, followed by a list of its main results and perspectives. A possible answer to the question about the origin of stochasticity is given in stochastic electrodynamics by assigning a real character to the vacuum radiation field. This theory is shown to reproduce important quantum mechanical results, some of which are presented explicitly to illustrate its potentialities. Finally the main problems and some perspectives of research within stochastic electrodynamics are discussed.
Time in relativistic and nonrelativistic quantum mechanics
International Journal of Quantum Information
7
595-602
2009
10.1142/S021974990900516X
The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The spacetime-position operator acts in the Hilbert space of functions of space and time. Dynamics, however, makes eigenstates of the time operator unphysical. This poses a problem for the standard interpretation of QM and reinforces the role of alternative interpretations such as the Bohmian one. The Bohmian interpretation, despite of being nonlocal in accordance with the Bell theorem, is shown to be relativistic covariant.
bohmian interpretation; quantum mechanics; relativity; time
Fluid Mechanics of Spin Casting of Metals
Annual Review of Fluid Mechanics
29
1
373-397
1997
10.1146/annurev.fluid.29.1.373
Casting of molten metals against a spinning wheel substrate is considered. Issues of fluid mechanics divide between steady and unsteady behavior (stability). The previous work on steady casting is hung on a framework provided by the long-puddle model of planar flow casting. Heat and fluid flow interact only through the shape of the solidification front in this case. In contrast, there is little previous work concerning stability issues. Stability is discussed in a broad-brush manner using the planar flow process for illustration. Issues range from meniscus motion and resulting ribbon texture to morphological-type instabilities of the solidification front. Fundamental and applied questions arise for both steady and unsteady behavior.
chill-block; melt spinning; planar flow; single roll
Some rock mechanics issues in petroleum engineering
Rock Mechanics in Civil and Environmental Engineering
39-44
2010
A brief discussion of some rock mechanics issues that arise in petroleum engineering is given, with an emphasis on new developments and unresolved questions. Four specific topics are addressed. The first is wellbore stability, with a focus on the use of true-triaxial failure criteria to model deviated boreholes. Next, two yet unresolved issues that arise in the modeling of fractured reservoirs are discussed, one related to the macroscopic permeability of the fracture system, and the other to flow interactions between the fractures and matrix blocks. Lastly, the equations of poroelasticity that govern the coupling between fluid flow and geomechanical processes are reviewed.
boreholes; flow; media; mogi; naturally fractured reservoirs; networks; percolation; permeability
lattice gas automata for fluid mechanics
physica A
140
326-335
1986
A lattice gas is the representation of a gas by its restriction on the nodes of a regular lattice for discrete time steps. It was recently shown by Frisch, Hasslacher and Pomeau that such very simple models lead to the incompressible Navier-Stokes equation provided the lattice has enough symmetry and the local rules for collisions between particles obey the usual conservation laws of classical mechanics. We present here recent results of numerical simulations to illustrate the power of this new approach to fluid mechanics which may give new tools for numerical studies and build a bridge between cellular automata theory and complex physical problems.
lattice gas automata
Some applications of unsaturated soil mechanics
Unsaturated Soils: Theory and Practise 2011
19-29
2011
After a brief review of a number of developments of unsaturated soil mechanics, the paper pre- sents some applications to engineering problems. The first case involves the collapse of a residual soil in Brazil triggered by a water level increase caused by the filling of a dam reservoir. The second case analyzes the effects of rainfall on a natural slope in Ancona (Italy). The final case refers to the subsidence in the re- gion of Ravenna related to the depletion of deep gas reservoirs. The ensemble of the cases described illus- trates the potential of unsaturated soil mechanics concepts for the understanding and reproduction of ob- served field behaviour.
collapse; rainfall effects; slope; subsidence; suction; unsaturated soils
A toy model for quantum mechanics
Foundations of Physics
37
10
1447-1460
2007
10.1007/s10701-007-9171-3
The toy model used by Spekkens R. Spekkens, Phys. Rev. A 75, 032110 (2007) to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.
Thesaurus of rock and soil mechanics terms
Thesaurus of rock and soil mechanics terms
1984
This thesaurus is a structured list of 'controlled' terms (or keywords) used to index the material contained in the Geomechanics Abstracts database which itself contains bibliographic references to publications pertaining to the fields of rock and soil mechanics. Included are topics such as properties of rocks and soils, mining, tunnelling, foundation engineering, and communication. Terms are arranged alphabetically with preferred ones in bold type and non-preferred terms in italics. For collections on mining and earth sciences in general. Compilers are with the Imperial College of Science and Technology, London Book Published by Pergamon Press, United States, 1984
Descriptors; ENGINEERING; TERMS & phrases; THESAURI
Dynamics-dependent symmetries in Newtonian mechanics
Physica Scripta
89
1
015101
2014
10.1088/0031-8949/89/01/015101
We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines the square roots of the kinetic and potential energies and connects solutions of the same dynamical problem (the potential is an invariant function). The other symmetry connects solutions of different dynamical problems (the potential is a scalar function). The existence of corresponding conserved quantities is examined using Noether's theorem and it is shown that the invariant-potential symmetry is correlated with energy conservation. In the Hamilton-Jacobi picture the invariant-potential transformation provides an example of a 'field-dependent' symmetry in point mechanics. It is shown that this transformation is not a symmetry of the Schrödinger equation. © 2014 The Royal Swedish Academy of Sciences.
Fermi and Bose pressures in statistical mechanics
American Journal of Physics
72
8
1082
2004
10.1119/1.1737395
I show how the pressure in Fermi and Bose systems, identified in standard discussions of quantum statistical mechanics by the use of thermodynamic analogies, can be derived directly in terms of the flux of momentum across a surface by using the quantum mechanical stress tensor. In this approach, which is analogous to classical kinetic theory, the pressure is naturally defined locally. The approach leads to a simple interpretation of the pressure in terms of the momentum flow encoded in the wave functions. The stress-tensor and thermodynamic approaches are related by an interesting application of boundary perturbation theory for quantum systems. I investigate the properties of quasi-continuous systems, the relations for Fermi and Bose pressures, shape-dependent effects and anisotropies, and the treatment of particles in external fields, and note several interesting problems for graduate courses in statistical mechanics.
Fracture mechanics aids steel casting design
Materials & Design
2
1
21-33
1980
10.1016/0261-3069(80)90028-X
Synopsis - The purpose of this paper is to demonstrate, to the designer, the value of fracture mechanics in design and material selection for steel castings. Simultaneously, it is hoped that this article illustrates the need for today's designers to increase their understanding of the significance of defects, not just in technical terms, but in terms of the economic gains which can be achieved by judicious application of modern design ideas to the assurance of quality, safety and reliability. While it has been necessary to assume some prior knowledge on the part of the reader, this has been kept to a minimum; emphasis is placed on the practical use of fracture toughness criteria for establishing safety levels for particular service applications and on the fracture mechanics approach for both founder and designer.
Electroelastic Fracture Mechanics of Piezoelectric Layered Composites
Journal of Intelligent Material Systems and Structures
16
7-8
573-582
2005
10.1177/1045389X05048329
This paper develops a theoretical electroelastic fracture mechanics for piezoelectric layered composites. A piezoelectric layer bonded between two elastic or piezoelectric materials containing a crack normal to the interfaces is considered. The ends of the crack are situated at equal distances away from the interfaces. Both analytical and simulation methods are formulated to determine the effects of applied electric field and polarization switching on the fracture mechanics parameters such as stress intensity factor, energy release rate, and energy density factor. The results for the exact (permeable) and approximate (impermeable) boundary conditions are presented in graphical form.
elasticity; energy density factor; energy release rate; finite element method; integral transforms; intensity factor; piezocomposites; polarization switching; smart; stress
Principles of statistical mechanics of random networks
Evolution
14
2002
10.1016/S0550-3213(03)00504-2
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilibrium uncorrelated networks, fat-tailed degree distributions may exist only starting from some critical average number of connections of a vertex, in a phase with a condensate of edges.
Adaptation and Self-Organizing Systems; High Energy Physics - Lattice; High Energy Physics - Theory; Mathematical Physics; Networking and Internet Architecture; Statistical Mechanics
Contact Mechanics of Laser-Textured Surfaces
Tribol. Lett.
50
1
41-48
2012
10.1007/s11249-012-0064-z
We study numerically the contact mechanics of a flat and a curved solid. Each solid bears laser-induced, periodic grooves on its rubbing surface. Our surface topographies produce a similar load and resolution dependence of the true contact area as nominally flat, but randomly rough, self-affine surfaces. However, the contact area of laser-textured solids depends on their relative ori- entation. The estimated true contact areas correlate with kinetic friction measurements.
á; contact mechanics á friction; material treatment effects
Quantum Mechanics from Focusing and Symmetry
Foundations of Physics
38
9
818-842
2008
10.1007/s10701-008-9239-8
A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak assumptions, and from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed.\n\nKeywords Bell's inequality - Born's rule - Epistemic interpretation - EPR paradox - Focusing - Symmetry
gt_cmc; gts_statfound
The molecular mechanics of eukaryotic translation
Annu Rev Biochem
73
657-704
2004
10.1146/annurev.biochem.73.030403.080419
Great advances have been made in the past three decades in understanding the molecular mechanics underlying protein synthesis in bacteria, but our understanding of the corresponding events in eukaryotic organisms is only beginning to catch up. In this review we describe the current state of our knowledge and ignorance of the molecular mechanics underlying eukaryotic translation. We discuss the mechanisms conserved across the three kingdoms of life as well as the important divergences that have taken place in the pathway.
Archaeal Proteins/biosynthesis/genetics; Codon, Initiator; Eukaryotic Cells; Eukaryotic Initiation Factors/metabolism; Fungal Proteins/biosynthesis/genetics; Models, Biological; Peptide Chain Initiation, Translational; Peptide Chain Termination, Translational; *Protein Biosynthesis; Proteins/genetics; Research Support, Non-U.S. Gov't; Research Support, U.S. Gov't, P.H.S.; RNA, Messenger/genetics/metabolism
On the Problem of Degeneracy in Quantum Mechanics
Phys.~Rev.
57
641
1940
10.1103/PhysRev.57.641
The problem of degeneracy in quantum mechanics is related to the existence\nof groups of contact transformations under which the Hamiltonian\nis invariant. The correspondence between transformations in classical\nand quantum theories is developed. The Fock-Bargmann treatment of\nthe symmetry group of the hydrogenic atom comes under this theory.\nThe symmetry group of the 2-dimensional Kepler problem is found to\nbe the 3-dimensional rotation group; that of the n-dimensional isotropic\noscillator is isomorphic to the unimodular unitary group in n dimensions.\nThe 2-dimensional anisotropic oscillator has the same symmetry as\nthe isotropic oscillator in classical mechanics, but the quantum-mechanical\nproblem presents complications which leave its symmetry group in\ndoubt.
Fracture mechanics analysis of a pipe elbow
Nuclear Engineering and Design
112
211-220
1989
10.1016/0029-5493(89)90158-1
The fracture mechanics assessment of surface flaws in many cases requires extensive numerical efforts, e.g. in performing finite element analyses for 3-dimensional structures. In this context the J-integral parameter is widely used to correlate crack initiation and early increments of the ductile tearing mode of crack growth. A practical analysis capability for the J-evaluation is given with the line-spring model. It lowers the fracture mechanics part of the structural analysis about one order of magnitude. The application of the line-spring method within the scope of the ABAQUS finite element code is described and results are compared with J-integral values obtained by means of 3-dimensional energy release rate analyses.
Strange Attractors and Chaos in Nonlinear Mechanics
ASME Journal of Applied Mechanics
50
1021-1032
1983
10.1115/1.3167185
We Review several examples of nonlinear mechanical and electrical systems and related mathematical models that display chaotic dynamics or strange attractors are reviewed. Some simple mathematical models - iterated piecewise linear mappings - are introduced to explain and illustrate the concepts of sensitive dependence on initial conditions and chaos. In particular, the role of homoclinic orbits and the horeshoe map in the generation of chaos is described, and it is indicated how the existence of such features can be detected in specific nonlinear differential equations.
strange attractors; chaos; nonlinear mechanics
Tetrahexylsexithiophene: crystal structure and molecular mechanics calculations
Macromolecular Chemistry and Physics
199
9
1973-1979
1998
10.1002/(SICI)1521-3935(19980901)199:9<1973::AID-MACP1973>3.0.CO;2-6
The synthesis, crystal structure and detailed molecular mechanics calculations, including crystal packing interactions, of tetrahexylsubstituted sexithienylene are presented. Unexpectedly the molecule, which arranges in the P-1 space group, displays no herringbone arrangement, thienylenic rings are far from coplanarity and the alkylic side chains present different conformations. Molecular mechanics fully accounts for these findings. From crystal packing computations it is derived that different arrangements are unable to lower the packing energy, due to the closeness of two alkyl chains on the same side of the thienylenic backbone, which prevents interspersion of non-parallel molecules.
Acoustics as a branch of fluid mechanics
Journal of Fluid Mechanics
106
261-298
1981
10.1017/S0022112081001602
Gives a review of six areas of current activity and importance in aeroacoustics, including (i) the generation of sound and vorticity by vorticity and sound, respectively, (ii) the basis for, and consequences of, the application of a Kutta condition in unsteady leading- and trailing-edge flows, and (iii) the suppression or amplification of broadband hydrodynamic and acoustic fields in a jet under the influence of weak discrete tone forcing. The intention is also to promote acceptance once again of acoustics as a serious branch of fluid mechanics
How Molecular Mechanics Can Measure Nanoscopic Flow
Journal of Physical Chemistry C
116
27
14694-14700
2012
Doi 10.1021/Jp3037654
Molecular mechanics translates macroscopic effects to a molecular scale, using distinct mechanical properties of a molecular structure. By this, the interaction of matter can be monitored with outstanding spatial resolution on a nanoscopic scale. We present the application of molecular Mechanics to measure shear forces due to dynamics pressures and streams at surfaces using a bionic approach. Our system monitors the deflection of a short DNA strand in response to an external molecular flow and bases on a fluorescence resonance energy transfer as a read-out. This way, quenching or temperature effects can be excluded, and the working range of the system can easily be fine-tuned to match diverse shear forces and dynamic pressures.
fluorescence; pressure; sensor
MATHEMATICA -BASED FORMULA VERIFICATION IN APPLIED MECHANICS
Proceedings of the ASME–Greek Section: First National Conference on Recent Advances in Mechanical Engineering
1-6
2001
Mathematica is a modern and powerful computer algebra system offering all types of computational facilities (symbolic, numerical and graphical) to its user in an integrated environment. Therefore, it has been repeatedly used in mechanical engineering applications. In this paper, we will show that Mathematica can also be useful for formula verification (either logical or algebraic) by employing either its own internal commands or extensions of these commands such as Maeder’s Prolog interpreter in Mathematica and, recently, Buchberger’s Theorema, based also on Mathematica. External reasoning systems (such as OTTER) can also be called from Mathe- matica. The engineering applications of this paper are ob- tained from applied mechanics and illustrate these not so well known possibilities of Mathematica related to formula verification.
applied mechanics; formula verification; logical computations; mathematica; symbolic computations
Multichannel framework for singular quantum mechanics
Annals of Physics
340
1
267-292
2014
http://dx.doi.org/10.1016/j.aop.2013.10.005
Abstract A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances.
Renormalization; Singular quantum mechanics; S-matrix; Unitarity
Communication Complexity as a Principle of Quantum Mechanics
Foundations of Physics
36
4
512-525
2006
10.1007/s10701-005-9029-5
We introduce a two-party communication complexity problem in which the probability of success by using a particular strategy allows the parties to detect with certainty whether or not some forbidden communication has taken place. We show that the probability of success is bounded by nature; any conceivable method which gives a probability of success outside these bounds is impossible. Moreover, any conceivable method to solve the problem which gives a probability success within these bounds is possible in nature. This example suggests that a suitably chosen set of communication complexity problems could be the basis of an information-theoretic axiomatization of quantum mechanics.
03; 65; bell; communication complexity; foundations; of quantum mechanics; pacs; quantum communication; quantum correlations; s inequalities; ta; tsirelson; ud
Damage mechanics : basic variables in continuum theories
International Journal of Solids and Structures
36
5
747-761
1999
10.1016/S0020-7683(98)00044-4
It is shown that any type of material damage that causes stiffness degradation in general requires description by an eighth order damage tensor but that the principle of strain equivalence permits a reduction to a tensor of order four. The actual number of independent damage parameters in such a tensor is related to the material and damage symmetry. For the isotropic case, there must be two independent damage parameters which can be expressed in terms of damage parameter with physical meaning.
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
arXiv preprint arXiv:1304.3719
27
2013
10.1142/S0217979214501793
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder's group on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schr\"odinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wave functions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" nonlocality.
anomalous diffusion; emergence; quantum mechanics; zero-point field
Chemistry, physics and fracture mechanics in search for superhard materials, and the origin of superhardness in nc-TiN/a-Si3N4 and related nanocomposites
Journal of Physics and Chemistry of Solids
68
5-6
1161-1168
2007
10.1016/j.jpcs.2007.01.013
Superhard materials (H>40 GPa) are presently subject of intense research. One distinguishes between intrinsic superhard materials, such as c-BN and diamond and extrinsic ones, such as heterostructures and nanocomposites. After a brief discussion of material's parameters that determine its strength, we focus on the superhard nanocomposites nc-MenN/a-XNm (Me=Ti, V, W, (TiAl)N,...; X=Si, B). Recent progress in the understanding of the origin of hardness enhancement in superhard nc-TiN/a-Si3N4 nanocomposites ("nc-" stands for "nanocrystalline, "a-" for "X-ray amorphous")11The term "X-ray amorphous" does not exclude the formation of a locally pseudomorph interface because even if such, 1-2 monolayer thin, interface would be perfectly grown on the TiN template it could never give rise to Bragg reflections in the three-dimensional nanocomposites with randomly oriented TiN nanocrystals. We used the formula "Si3N4" in order to emphasize that Si is covalently bonded to N only with Si 2p binding energy of 101.7??0.1 eV determined by XPS and being equal to that in Si3N4. is summarized. The optimum nanostructure with one monolayer of interfacial Si3N4 was confirmed by both experiments with the deposition of TiN/Si3N4 heterostructures by S??derberg et al., and by first principle density functional theory calculations of Hao et al. These calculations show that the de-cohesion energy of the TiN/Si3N4/TiN sandwich is enhanced as compared with bulk Si3N4. A new, non-linear constitutive materials model, that accounts for the pressure enhancement of elastic moduli and of flow stress was developed and tested by means of advanced FEM calculations. Significant deviations of the mechanical behaviour of super- and ultrahard materials from the prediction of the linear mechanics with a constant yield stress have been demonstrated. ?? 2007 Elsevier Ltd. All rights reserved.
A. Interfaces; A. Nanostructures; C. ab initio calculations; D. Mechanical properties
Thin-layer chromatography of glycosphingolipids.
Methods in enzymology
230
1988
371-389
1994
10.1016/0076-6879(94)30025-9
Thin-layer chromatography of glycosphingolipids. RL SCHNAAR, LK NEEDHAM Methods in enzymology 230, 371-389, Elsevier, 1994. Chromatographie couche mince; Thin layer chromatography; Cromatografía
Thin film thermal device applications
Thin Solid Films
50
81-98
1978
10.1016/0040-6090(78)90095-0
A number of physical properties of thin films of different materials undergo rapid changes with temperature and also on irradiation with infrared radiation. Some of these properties are exploited to yield very fast and sensitive thin film thermal and infrared photon detectors. This review briefly describes some of these devices.
Characterization of optical thin films.
Applied optics
18
12
1969-1977
1979
10.1364/AO.18.001969
Various properties of dielectric thin films are discussed in this paper: refractive index and absorption coefficient, light scattering, structure, microstructure, density, gas sorption, chemical composition, homogeneity, adhesion, hardness and mechanical stress, and environmental influences.
Optical properties of thin films
Thin Solid Films
23
1
1-65
1960
10.1088/0034-4885/23/1/301
The optical conductivity spectra were calculated in B2-TiMe (0 0 1) thin films (Me=Fe,Co,Ni) using the electronic structure obtained by means of the full potential linearized augmented plane wave (FLAPW) method. The changes of optical conductivity in bulk alloys and thin films are analyzed. The difference of the optical conductivity spectrum of the TiNi monoclinic phase from experiment is discussed.
Thin/cambered/reflexed airfoil development for micro air vehicle applications at reynolds numbers of 60,000 to 100,000
Collection of Technical Papers - 2006 Atmospheric Flight Mechanics Conference
2
1159-1164
2006
doi:10.2514/6.2006-6508
Airfoil development for micro-air vehicle applications is dominated by laminar separation bubble formation. XFOIL, a low Reynolds number airfoil analysis tool is utilized in an effort to understand and document the role camber plays in laminar separation bubble formation, size, and location. In addition, the direct effect camber has in the production of lift and drag is evaluated through assessment of the maximum coefficient of lift and maximum coefficient of lift/coefficient of drag attained by airfoils of varying camber. Camber values of 1, 2, 3,4, 5, 6, 7, 8, and 9% chord are evaluated at Reynolds numbers of 60,000, 80,000, and 100,000 for angles of attack over a range from 0 to 10 degrees. Results show a direct relationship between the camber and maximum coefficient of lift with a growing dependence on Reynolds number at higher camber values. Maximum coefficient of lift / coefficient of drag showed a peak in performance for mid to high range camber values and a low dependency on Reynolds number. Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Aircraft; Airfoil analysis tool; Airfoils; Angles of attack; Bubble formation; Camber plays; Camber values; Coefficient of drag; Coefficient of lift; Drag; Laminar flow; Laminar separation bubble formation; Lift; Reynolds number
Three-dimensional finite-element modeling of a thin-skinned fold-thrust belt wedge: Provo salient, Sevier belt, Utah
Geology
32
7
561-564
2004
10.1130/g20415.1
Three-dimensional finite-element (FE) analysis of a fold-thrust belt wedge model provides graphical and quantitative information for the strain geometry, kinematics, and mechanics of salient formation in three-dimensional space. A nonlinear, elastic-plastic FE model, using the initial basin configuration of the restored Provo salient, Utah, develops realistic deformation features (e.g., salient) in the deformed sedimentary prism. The three-dimensional fold-thrust belt wedge model shows different deformation characteristics (based on S1, γmax, and σ1 orientations and material-displacement directions) in different parts of the salient, and its behavior is closely related to the preexisting template of the predeformational basin shape. The model results indicate plane-strain deformation with symmetric finite-strain geometry in the middle of the salient and nonplane-strain deformation with nonsymmetric finite-strain geometry at the lateral boundaries. Thus, conventional two-dimensional plane-strain assumptions in fold-thrust belt analysis (e.g., in balancing cross sections) are reasonable only in the middle of the salient; however, at the lateral boundaries, the results indicate fully three dimensional deformation and suggest that restorations need to be more carefully constrained in three dimensions on the basis of detailed geologic data.
Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film - exact solution
Journal of Fluid Mechanics
126
237-250
1983
10.1017/S0022112083000130
In this investigation the creeping flow due to the motion of a liquid drop or a bubble in another immiscible fluid is examined when the interface is partially covered by a stagnant layer of surfactant. The associated boundary-value problem involves mixed boundary conditions at the interface, which lead to a set of dual series equations. An inversion of these equations yields the exact solution to the stagnant cap problem. Several useful results are obtained in closed form. Among these are the expressions for the drag force, the difference between the maximum and the minimum interfacial tensions, and the amount of adsorbed surfactant. A shifting of the centre of the internal vortex is observed.
Fracture behaviors of a functionally graded thin superconducting film with transport currents based on the strain energy density theory
Theoretical and Applied Fracture Mechanics
74
73-78
2014
10.1016/j.tafmec.2014.07.002
In this study, the strain energy density theory is used to investigate a central crack problem for a functionally graded superconducting film with the applied transport currents, where the Kim critical state model is adopted and the shear modulus is assumed to vary along the film’s width in a form of hyperbolic function. The flux and current densities, the stress intensity factors (SIFs) and energy density factors (EDFs) are all analytically obtained. Numerical results show the effects of applied transport currents, model parameters, and crack length on the EDFs and/or SIFs. Among others, in the process of descending transport current, increasing the graded parameter of shear modulus can inhibit crack propagation, and in general, the crack will propagate and grow into the field of shear modulus decreasing. Moreover, the fracture angle is independent of the applied transport currents, and the fracture angle generally increases slightly with either the increasing of material graded parameter or the increasing of crack length. This study should be useful for the application of superconducting devices.
Crack; Energy density theory; Functionally graded superconducting film; Transport currents
Model on transport phenomena and epitaxial growth of silicon thin film in SiHCl3-H-2 system under atmospheric pressure
Journal of Crystal Growth
169
1
61-72
1996
10.1016/0022-0248(96)00376-4
A transport and epitaxy model to describe silicon epitaxial film growth in a SiHCl3-H-2 system under atmospheric pressure is developed by numerical calculations and comparison with experiments. The rate of epitaxial growth is calculated by computing the transport of momentum, heat and chemical species in a reactor incorporating chemical reactions at a substrate surface described by the Eley-Rideal model. The reaction processes determining the growth rare consist of chemisorption of SiHCl3 and decomposition by H-2, rate constants of which are evaluated from the model and measured results. The state of the surface during the epitaxial growth is also discussed considering the intermediate species, elementary reactions and rate-limiting processes. The epitaxial growth rate is able to be predicted by the model in this study over wide growth conditions of the species concentrations and the temperatures.
absolute rate constants; chemical-vapor-deposition; fluid-mechanics; mathematical-model; molecular-beam; rotating-disk; si; surface-reactions; temperature-programmed desorption; thermal-diffusion
Mechanical Characterization of Thin-Film Composites using the Load-Deflection Response of Multilayer Membranes - Elastic and Fracture Properties
Mater. Res. Soc. Symp. Proc.
977
908-977
2007
This paper reports on the refinement of a mechanical model for the\nload-deflection of multilayer membranes under uniform differential\npressure and on its application to the experimental extraction of\nmaterial parameters. Going beyond previous results, the analytical\nmodel takes into account the mechanics of multilayers and elastic\nsupports covering all cases between rigidly clamped to simply supported\nstructures and enables the straightforward assessment of stress profiles\nwithin the deformed structures. A comprehensive set of long membranes\nmade of various multilayers of silicon nitride and oxide films are\nfabricated and characterized. The out-of-plane deflection profile\nunder pressure load is monitored by means of a laser profilometer.\nThe pressure is stepped up until fracture occurs. From the stress\nprofiles in the membrane at fracture, the brittle material strength\nis analyzed using Weibull statistics. The bulge setup has been fully\nautomated for the measurement of 80 membranes per wafer. This realizes,\nfor the first time, the high throughput-acquisition of mechanical\nthin film data with convincing statistical control.
Influence of p-layer on the performance of n-i-p mu c-Si:H thin film solar cells
Science China-Physics Mechanics & Astronomy
53
11
2042-2046
2010
10.1007/s11433-010-4143-6
The high pressure radio frequency plasma enhanced chemical vapor deposition (RF-PECVD) process was adopted to prepare the n-i-p microcrystalline silicon solar cells, the influence of p-type layers on the performance of the solar cells was investigated, and the optimum p layer suited to the n-i-p microcrystalline silicon solar cells was obtained. The experimental results demonstrate that the performance of the solar cells can be highly affected by the structural and optical properties of the p-layers, and the performance of solar cells can be greatly improved by optimizing p layers. We have achieved an initial active-area efficiency of 8.17% (V (oc)=0.49 V, J (sc)=24.9 mA/cm(2), FF=67%) for the mu c-Si:H single-junction n-i-p solar cells and an initial active-area efficiency of 10.93% (V (oc)=1.31 V, J (sc)=13.09 mA/cm(2), FF=64%) for the a-Si:H/mu c-Si:H tandem n-i-p solar cells.
Absolute instability of a thin visco-elastic plate in an air flow
European Journal of Mechanics a-Solids
23
6
1069-1084
2004
DOI 10.1016/j.euromechsol.2004.05.009
Motivated by aerodynamic applications, we study in the present paper the destabilization of a thin visco-elastic plate by the stress produced by a flow of air on one side or both sides of the plate parallel to the plate. The research is a follow up on our recent discovery [cf. Brevdo, L., Il'ichev, A., 2001. Cold Reg. Sci. Technol. 33, 77-89] that a floating ice layer is destabilized by wind stress, and the unstable wave packets related to the buckling mode propagate against the wind. The visco-elastic Kelvin-Voigt model is used for describing the viscous damping. The quiescent state of the plate is computed as a function of the stress applied. We use the Lifshitz-Landau thin-plate treatment for obtaining a description of the dynamics of small disturbances in a visco-elastic plate under stress in the framework of the Kirchhoff-Love model. The dispersion relation of the model is computed; it is a polynomial of wavenumber and frequency. Stability computations are performed for a great variety of values of the physical parameters, for the stress produced by both a laminar as well as a turbulent air flow. Particular attention is given to plates made from aluminum or steel. For vanishing viscosity, it is found that all the non-zero wavenumbers in the model are unstable for any non-zero value of the stress applied. A non-vanishing viscosity of plates made from aluminum or steel produces a short-wave cut-off of the unstable wavenumbers but makes practically no influence on the growth rate of the normal modes close to its maximum value. In all the cases treated, it was found that all the unstable normal modes possess negative phase speeds, and the maximum of the growing wave packet propagates against the direction of the air stress applied. In all the cases, the model is found to be absolutely unstable. The absolute instability characteristics are computed as functions of the Reynolds number based on,the distance from the leading edge of the plate. We argue that the results of the analysis suggest that the destabilization of a variety of flows having plates as solid boundaries, such as boundary layers on the surfaces of flying vehicles, channel flows, duct,flows etc., cannot be treated without taking account of the absolute instability of the plates involved. (C) 2004 Elsevier SAS. All rights reserved.
absolute instability; boundary-layer; compliant surfaces; convective instabilities; film; floating ice layer; hydrodynamic stability; inclined plane; stress; tangential stress induced by a laminar or turbulen; thin kirchhoff-love plate in an air flow
Chaos and quantum mechanics.
Annals of the New York Academy of Sciences
1045
308-32
2005
10.1196/annals.1350.026
The relationship between chaos and quantum mechanics has been somewhat uneasy--even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes--such as chaos--that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions. Finally, we have the striking prediction that time-series from measured quantum systems can be chaotic far from the classical regime, with Lyapunov exponents differing from their classical values. These predictions can be tested in next-generation experiments.
Fracture Mechanics Ch05
Fracture Mechanics
105-121
2012
10.1016/B978-0-12-385001-0.00005-5
Prediction of crack growth involves two aspects, that is, when would the crack start to grow, and in what direction. Under Mode I conditions, the crack grows in its original direction. The fracture criterion thus can be established using either KI in Irwin's stress intensity factor theory, or GI in the energy release theory including the Griffith theory. Under general mixed mode conditions, experimental observations indicate that the crack will no longer grow in its original direction and KII also plays a role in crack growth. Hence, an appropriate fracture criterion is required to establish, to predict mixed mode crack extension. As in the Mode I fracture, both energy and near-tip stress field approaches are used in mixed mode fracture studies. In the energy balance approach, a small kink from the main crack tip is analyzed to determine the energy release rate along the direction of the kink.
crack kinking; maximum energy release criterion; maximum tensile stress criterion; mixed mode fracture; stain energy density criterion
Nanofluids by quantum mechanics
Proceedings of the ASME Micro/Nanoscale Heat and Mass Transfer International Conference 2009, MNHMT2009
1
387
2010
10.1115/MNHMT2009-18014
The enhanced heat transfer of nanofluids is shown not to be caused by the increase in thermal conductivity based on the concentration of nanoparticles (NPs) given by the long-standing Hamilton and Crosser (HC) mixing rules. Instead, heat transfer is enhanced because quantum mechanics (QM) restricts the specific heat of NPs to vanish, the consequence of which is that thermal kT energy absorbed from collisions of solvent molecules cannot be conserved by an increase in temperature. Conservation may only proceed by the QED induced up-conversion of the low frequency absorbed kT energy to the EM frequency of the NP, typically in the VUV. Here EM stands for electrodynamics, QED for quantum electrodynamics, and VUV for vacuum ultraviolet. The EM confinement is quasi-bound so that the VUV radiation promptly leaks from the NPs. Classically, collisions increase the NP temperature with EM emission occurring in the far infrared (FIR) that is absorbed with little penetration at the NP surface. But the VUV is absorbed at large penetrations, thereby enhancing heat transfer in proportion to the number of NPs without increasing the nanofluid conductivity - the process called QED induced heat transfer. Nanofluid conductivity given by the HC mixing rules for NPs in solvents is still valid and need not be modified. © 2009 by ASME.
Concentration of; Enhanced heat transfer; Enhancin; Electrodynamics; Energy conservation; Heat exchan; Nanofluidics
T he Mechanics and
Materials Research
32
February
151-159
2007
The following article is based on the Outstanding Young Investigator Award presentation given by Ju Li on April 19, 2006, at the Materials Research Society Spring Meeting in San Francisco. Li received the award "for his innovative work on the atomistic and first-principles modeling of nanoindentation and ideal strength in revealing the genesis of materials deformation and fracture." Defect nucleation plays a critical role in the mechanical behavior of materials, especially if the system size is reduced to the submicron scale. At the most fundamental level, defect nucleation is controlled by bond breaking and reformation events, driven typically by mechanical strain and electronegativity differences. For these processes, atomistic and first-principles calculations are uniquely suited to provide an unprecedented level of mechanistic detail. Several connecting threads incorporating notions in continuum mechanics and explicit knowledge of the interatomic energy landscape can be identified, such as homogeneous versus heterogeneous nucleation, cleavage versus shear-faulting tendencies, chemomechanical coupling, and the fact that defects are singularities at the continuum level but regularized at the atomic scale. Examples are chosen from nanoindentation, crack-tip processes, and grain-boundary processes. In addition to the capacity of simulations to identify candidate mechanisms, the computed athermal strength, activation energy, and activation volume can be compared quantitatively with experiments to define the fundamental properties of defects in solids.
Mechanics of blood flow.
Journal of biomechanical engineering
103
May 1981
102-115
1981
The historical development of the mechanics of blood flow can be traced from ancient times, to Leonardo da Vinci and Leonhard Euler and up to the present times with increasing biological knowledge and mathematical analysis. In the last two decades, quantitative and numerical methods have steadily given more complete and precise understanding. In the arterial system wave propagation computations based on nonlinear one-dimensional modeling have given the best representation of pulse wave propagation. In the veins, the theory of unsteady flow in collapsible tubes has recently been extensively developed. In the last decade, progress has been made in describing the blood flow at junctions, through stenoses, in bends and in capillary blood vessels. The rheological behavior of individual red blood cells has been explored. A working model consists of an elastic membrane filled with viscous fluid. This model forms a basis for understanding the viscous and viscoelastic behavior of blood.
Mechanics of Earthflows
Proceedings of the International Workshop on Occurence and Mechanism of Flow-Like Landslides in Natural Slopes and Earthflills, Associazione Geotechnica Italiana
1-8
2003
Earth flows are mass movements of fine-grained soils that range from slow flows with velocities on the order of meters or less per year to rapid flows that have velocities as high as several meters per second. Slow earth flows form in deposits of fine-grained plastic clay or silt and move episodically or by sustained, relatively steady movement. Most slow earth flows move primarily by sliding on a basal shear surface, accompanied by internal deformation. Coulomb plastic-flow models may be used to describe the mechanics of slow earth flows. Most rapid earth flows form in highly sensitive clay deposits and usually progress to completion in a matter of minutes to hours by a sequence of smaller failures that spontaneously liquefy and flow out of the source area. Rapid earth flows may be modeled as non-Newtonian fluids.
coulomb-plastic flow; earth flows; non-newtonian flow; rapid earth flows; slow earth flows
Pitching mechanics, revisited.
International journal of sports physical therapy
8
5
652-60
2013
UNLABELLED: The overhead pitching motion is described as a coordinated sequence of body movements and muscular forces that have an ultimate goal of achieving high ball velocity and target accuracy. An understanding of the dynamic overhead throwing motion outlined in this clinical commentary can assist the clinician in addressing the unique injuries experienced by the pitcher. The potential biomechanical sources for injury have been studied utilizing videography and electromyographic techniques due to the rapid pace with which the pitching motion occurs. This clinical comentary will describe what is widely accepted as the six phases of the pitching motion and the relationship to the kinetic chain theory as well as outline the common mechanical faults that can lead to increased tissue stress and potential injury.\n\nLEVEL OF EVIDENCE: 5.
5; baseball; calabrese; corresponding author; dpt; gary j; level of evidence; overhead athlete; pitching mechanics; pt
Statistical mechanics of magnetohydrodynamics
Physical Review E
53
5
5200
1996
10.1103/PhysRevE.53.5200
A statistical mechanical formulation for the steady state of self-organized magnetohydrodynamic plasma is studied based on the empirical variational principle, δ(E-λH)=0, for the steady state, where E and H denote the energy and the helicity of a magnetic field. The eigenfunctions of the curl operator are shown to span the phase space of a magnetic field in a bounded system, and the invariant measure is found. The classical ensemble theory is formulated assuming the Shannon or Rényi entropy. To avoid the divergence of the expectation values at nonzero temperature, Bose-Einstein statistics is also phenomenologically treated. It is implied that the spectra of the energy, helicity, and the helicity fluctuation obey the power law for a multiply connected domain with a nonzero cohomological field. For the toroidal system, these powers are implied to be three, three, and two, respectively. The invariant measure for the incompressible flow in a bounded domain is also given.
Quantum Mechanics and Gravitation
Physics
4
1
149
2002
10.1007/BF02770283
In summer 1999 an experiment at ILL, Grenoble was conducted. So-called ultra-cold neutrons (UCN) were trapped in the vertical direction between the Fermi-potential of a smooth mirror below and the gravitational potential of the earth above Ne00, Ru00. If quantum mechanics turns out to be a sufficiently correct description of the phenomena in the regime of classical, weak gravitation, one should observe the forming of quantized bound states in the vertical direction above a mirror. Already in a simplified view, the data of the experiment provides strong evidence for the existence of such gravitationally bound quantized states. A successful quantum-mechanical description would then provide a convincing argument, that the socalled first quantization can be used for gravitation as an interaction potential, as this is widely expected. Furthermore, looking at the characteristic length scales of about 10 mikron of such bound states formed by UCN, one sees, that a complete quantum mechanical description of this experiment additionally would enable one to check for possible modifications of Newtonian gravitation on distance scales being one order of magnitude below currently available tests Ad00. The work presented here deals mainly with the development of a quantum mechanical description of the experiment.
chemical physics; nanophysics
Mechanics of competition walking.
The Journal of physiology
315
243-251
1981
1. The work done at each step to lift and accelerate the centre of mass of the body has been measured in competition walkers during locomotion from 2 to 20 km/hr. 2. Three distinct phases characterize the mechanics of walking. From 2 to 6 km/hr the vertical displacement during each step, Sv, increases to a maximum (3.5 vs. 6 cm in normal walking) due to an increase in the amplitude of the rotation over the supporting leg. 3. The transfer, R, between potential energy of vertical displacement and kinetic energy of forward motion during this rotation, reaches a maximum at 4-5 km/hr (R = 65%). From 6 to 10 km/hr R decreases more steeply than in normal walking, indicating a smaller utilization of the pendulum-like mechanism characteristic of walking. 4. Above 10 km/hr potential and kinetic energies vary during each step because both are simultaneously taken up and released by the muscles with almost no transfer between them (R = 2-10%). Above 13-14 km/hr an aerial phase (25-60 msec) takes place during the step. 5. Speeds considerably greater than in normal walking are attained thanks to a greater efficiency of doing positive work. This is made possible by a mechanism of locomotion allowing an important storage and recovery of mechanical energy by the muscles.
Discrete-Time Quantum-Mechanics
Computers & Mathematics With Applications
28
10-12
279-317
1994
This paper summarizes a research program that has been underway for\na decade. The objective is to find a fast and accurate scheme for\nsolving quantum problems which does not involve a Monte Carlo algorithm.\nWe use an alternative strategy based on the method of finite elements.\nWe are able to formulate fully consistent quantum-mechanical systems\ndirectly on a lattice in terms of operator difference equations.\nOne advantage of this discretized formulation of quantum mechanics\nis that the ambiguities associated with operator ordering are eliminated.\nFurthermore, the scheme provides an easy way in which to obtain the\nenergy levels of the theory numerically. A generalized version of\nthis discretization scheme can be applied to quantum field theory\nproblems. The difficulties normally associated with fermion doubling\nare eliminated. Also, one can incorporate local gauge invariance\nin the finite-element formulation. Results for some field theory\nmodels are summarized. In particular, we review the calculation of\nthe anomaly in two-dimensional quantum electrodynamics (the Schwinger\nmodel). Finally, we discuss nonabelian gauge theories.
Universality in cell mechanics
Soft Matter
4
9
1750
2008
10.1039/b804866e
The cytoskeleton (CSK) of the adherent living cell is arguably the most complex form of soft matter that exists in nature. It is constituted by hundreds of different proteins that interact with each other in a highly specific manner and, as a requirement for life, exists out of thermodynamic equilibrium and in a constant state of remodeling. While such structural and dynamical complexity may have conferred the cell with diverse and unpredictable mechanical properties, recent evidence indicates that the behavior of the CSK conforms to a limited set of empirical laws that appear to be simple and universal. While mechanistic understanding of such laws is still lacking, their very existence suggests that rather than being addressed solely in terms of molecular details and specific interactions, cell mechanics need to be addressed also from an integrative point of view.
Operational Axiomatic Accounting Mechanics
Accounting Review
41
3
426-442
1966
The article focuses on the development of accounting mechanics in an attitude natural to the computer environment. The task mentioned is undertaken by restructuring the accounting language. The new product is hereinafter referred to as the "notation." The most essential and conspicuous component of the notation is the root, which is a slight extension of the notion of a chart of accounts. The root establishes the hierarchies of a given accounting system but differs most strikingly from a chart of accounts in that its elements are not accounts. The concepts of an entry, journal, account, gross, net, and statement are derived within the root context and terminology; the meanings given to these words are very distinguishable from classical usage. The root and the directed tree of network analysis are equivalent; hence another body of knowledge can be brought to bear. The notation is suitable for use by engineers, mathematicians, etc., hence communication between accounting and related disciplines stands to be improved. And lastly, another view is offered of unit-value flow, aggregation, and statement generation.
ACCOUNTING; ACCOUNTS; AXIOMS; BUSINESS records; COMPUTATIONAL linguistics -- Network analysis; COMPUTER programs; DYNKIN diagrams; FINANCIAL statements; MATHEMATICAL models
Non-Newtonian Mechanics
Work
27
2001
10.1142/S0217751X02005797
The classical motion of spinning particles can be described without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincare' group; and only requiring the conservation of the linear and angular momenta we derive the zitterbewegung: namely the decomposition of the 4-velocity in the newtonian constant term p/m and in a non-newtonian time-oscillating spacelike term. Consequently, free classical particles do not obey, in general, the Principle of Inertia. Superluminal motions are also allowed, without violating Special Relativity, provided that the energy-momentum moves along the worldline of the center-of-mass. Moreover, a non-linear, non-constant relation holds between the time durations measured in different reference frames. Newtonian Mechanics is re-obtained as a particular case of the present theory: namely for spinless systems with no zitterbewegung. Introducing a Lagrangian containing also derivatives of the 4-velocity we get a new equation of the motion, actually a generalization of the Newton Law a=F/m. Requiring the rotational symmetry and the reparametrization invariance we derive the classical spin vector and the conserved scalar Hamiltonian, respectively. We derive also the classical Dirac spin and analyze the general solution of the Eulero-Lagrange equation for Dirac particles. The interesting case of spinning systems with zero intrinsic angular momentum is also studied.
Mechanics of Geomaterial Interfaces
Studies in Applied Mechanics
42
77-103
1995
10.1016/S0922-5382(06)80007-3
This chapter reviews the modeling the contact pressure between a flat but not necessarily vertical structure and level ice sheet. It describes the relevant developments in modeling the contact without drowning the reader in a wealth of details. The theoretical modeling of the structure–ice contact interface has mainly concentrated on clarifying the contact load that the edge of ice cover can carry and modeling the ice failure at or beneath the interface. These models mostly have been pragmatic in the sense that the main parameters influencing the load have been included using regression techniques. The concept of interface has; however, a larger context than only the contact and in the chapter, restriction is to the phenomena at the contact. Recently it has been realized that the process of ice failure has a bearing on the dynamic response of the structure under the contact load. Some models of contact based on the ice failure process have been developed to answer particular problems, such as the ice-induced vibrations.
Quantum mechanics of measurement
arXiv preprint quant-ph/9605002
18
1996
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement outcomes can be negative, implying that measurement can be described via unitary, entropy-conserving, interactions, while still producing randomness in a measurement device. In such a framework, quantum measurement is not accompanied by a wave-function collapse, or a quantum jump. The theory is applied to the measurement of incompatible variables, giving rise to a stronger entropic uncertainty relation than heretofore known. It is also applied to standard quantum measurement situations such as the Stern-Gerlach and double-slit experiments to illustrate how randomness, inherent in the conventional quantum probabilities, arises in a unitary framework. Finally, the present view clarifies the relationship between classical and quantum concepts.
Testing quantum mechanics
Annals of Physics
194
2
336-386
1989
10.1016/0003-4916(89)90276-5
This paper presents a general framework for introducing nonlinear corrections into ordinary quantum mechanics, that can serve as a guide to experiments that would be sensitive to such corrections. In the class of generalized theories described here, the equations that determine the time-dependence of the wave function are no longer linear, but are of Hamiltonian type. Also, wave functions that differ by a constant factor represent the same physical state and satisfy the same time-dependence equations. As a result, there is no difficulty in combining separated subsystems. Prescriptions are given for determining the states in which observables have definite values and for calculating the expectation values of observables for general states, but the calculation of probabilities requires detailed analysis of the method of measurement. A study is presented of various experimental possibilities, including the precession of spinning particles in external fields, experiments of Stern-Gerlach type, and the broadening and de-tuning of absorption lines.
Load mechanics of the wrist.
Hand clinics
13
1
109-28
1997
During the last decade, we have been studying load mechanics under a variety of conditions using pressure-sensitive film and, more recently, three-dimensional reconstructions and motion analysis. In all of these studies using pressure-sensitive film, the simulated pathologic or traumatic conditions that were tested showed that all areas in which an increase in contact area or pressure occurred, localized to one area of one joint, coincided with areas in which degenerative changes occurred in the simulated clinical situation. The areas in which there was a decrease or no change in contact area or pressure coincided with areas that were spared from degenerative changes in simulated clinical situations. More recent work has demonstrated that normal carpal kinematics during wrist flexion and extension do not have an instantaneous screw axis that is fixed in or limited to the capitate. These findings change the understanding previously based on studies suggesting that the center of rotation was fixed in the capitate. It was noted that during global wrist motion the radiolunate joint contributes more motion and flexion than the capitolunate joint, but the capitolunate joint contributes more motion and extension than the radiolunate joint. It also was demonstrated that translational motion is a normal component of carpal kinematics.
Biomechanical Phenomena; Carpal Bones; Carpal Bones: physiology; Humans; Photography; Pressure; Wrist Joint; Wrist Joint: physiology
Mechanics of Breathing
Mechanics of Breathing: New Insights from New Technologies: Second Edition
9788847056
99-120
2014
10.1007/978-88-470-5647-3
Under normal conditions, a healthy lung is fully aerated, and no part will be airless or collapsed (or de-recruited). This is essential for optimum gas exchange, i.e., oxygenation of blood and removal of carbon dioxide (CO<inf>2</inf>) from the blood. Blood flow through an airless lung causes shunt, i.e., flow of blood that is not oxygenated and cannot eliminate CO<inf>2</inf>, resulting in hypoxemia and CO<inf>2</inf> retention. De-recruitment can be seen in almost all patients during anesthesia and more so in acute lung injury (ALI) and as a complication in chronic obstructive lung disease. Airways close during a deep expiration and if lung volume is reduced by loss of respiratory muscle tone (anesthetics, sedatives, muscle relaxants), increased lung weight (edema in ALI), increased abdominal weight (obesity, abdominal edema), or increased gravitational forces (e.g., fighter pilots), alveolar gas will be adsorbed causing de-recruitment (atelectasis). Direct compression of lung may force gas out of the alveoli but may not be the most important mechanism. Reopening of the lung can be achieved by different recruitment maneuvers, balancing between the highest possible reopening and least possible damage to the lung, an issue that is not always met by full consensus. This makes lung recruitment a hot topic in research and clinic.
and Mechanics of Solids
Mathematics and Mechanics of Solids
April 2002
281-288
2011
10.1177/108128603031209
Ion containing polymers display certain spectacular mechanoelectrical phenomena when suitably composited with a conductor phase such as a metal, a conductive polymer or graphite-sometimes called ionic polymer conductor composites. When subjected to a dynamic electric field they deform dynamically (actuation), and if dynamically deformed they generate a dynamic electric field (transduction or sensing). Here, we present a description of these phenomena in the linear regime, and in steady-state conditions using the standard Onsager formulation. We describe the underlining principle of ionic polymer-metal composite actuation/sensing phenomena using linear irreversible thermodynamics. When static conditions are imposed, a simple description of the mechanoelectric effect is possible based upon two forms of transport: ion transport (with a current density J) and electro-osmotic solvent transport (with a flux, Q). The conjugate forces include the electric field, E, and the pressure gradient, -delp. We also present some estimates on the Onsager coefficients.
GTC telescope mechanics design
Proceedings of SPIE - The International Society for Optical Engineering
4004
92-103
2000
The purpose of the Gran Telescopio de CANARIAS (GTC) project is the design, construction, erection and startup of a telescope with a segmented primary mirror equivalent to a circular aperture of 10 m in diameter. The GTC project was created to satisfy the needs of Spanish astronomers for more telescope time and larger telescopes. The GTC project does more than simply increment the list of `8-10 meter class' telescopes. Its requirement for higher specifications differentiates it from other telescopes of its generation. The GTC will combine a large collecting surface with excellent image quality and suitably optimized observation in both the visible and the infrared. The Gran Telescopio de CANARIAS Project Office Telescope Group, based in the Canary Islands, together with a joint venture (UTE) of Spanish companies, are developing the telescope mechanics systems, taking into account the scientific requirements established.
Mechanics of the Pneumatic Tire
Rubber Chemistry and Technology
40
1
271-322
1967
10.5254/1.3539045
Abstract We have attempted to describe the mechanical problems of tires, from the point of view of elasticity theory, and have, in this connection, regarded research on the stresses and deformations in the casing as the primary problem of tire mechanics. Less attention was paid to factors which have to do with the behavior of tires with respect to the vehicle, because we believe that the effects of the choice of any design or structural parameters or materials, upon the behavior of tires, are not explainable in a sufficiently general manner, as long as the above problem, designated as the chief one, cannot be handled, at least numerically. How far we still have to go, in spite of many efforts, can be seen from Section III. The striking thing here is that belted tires have scarcely been investigated up to now. This may be due, in part, to the fact that the prerequisites for a theoretical investigation, reported in Section I, have been provided only imperfectly for this type of tire, up to now. Our own cont...
Respiratory mechanics in kyphoscoliosis
Monaldi Arch Chest Dis
48
1
69-79
1993
Kyphoscoliosis is a restrictive respiratory disorder in which total respiratory and lung elastances and lung resistance are increased. Specific airway conductance is increased because of greater lung elastic recoil. Corrective surgical procedures usually result in further immediate increases beyond that related to anaesthesia alone. Despite thoracic deformities, kyphoscoliotics maintain near-normal ventilation through increased central drive, and compensatory mechanisms including force-length and force-velocity properties of contracting inspiratory muscles, the Hering-Breuer reflex, inspiratory duration and airflow. The magnitude of compensation to loading in kyphoscoliotics is proportionately the same as in normal subjects. A recent study has shown that post-inspiratory muscle activity in anaesthetized kyphoscoliotics is proportionate to the magnitude of elastic recoil and intrinsic flow resistance. Expiratory decay may also be influenced by viscoelastic behaviour of thoracic tissues and the transition between their passive and active state.
Airway Resistance; Humans; Kyphosis/*physiopathology/surgery; Lung Compliance; *Respiratory Mechanics; Respiratory Muscles/physiopathology; Scoliosis/*physiopathology/surgery
Fundamentals of Quantum Mechanics
American Journal of Physics
36
8
769
1968
10.1119/1.1975141
This graduate-level text employs a formal, classical viewpoint to survey the fundamentals of quantum optics. Its coverage includes the quantum theory of partial coherence and the nature of the relations between classical and quantum theories of coherence. Students and professional physicists interested in intensity interferometry, photon counting correlations, and lasers will find this volume extremely helpful. Topics include partially coherent light, photoelectric counting distributions, dynamical determination of statistical description, and equations of motion and coherent-state representation of the electromagnetic field. Additional subjects encompass quantum theory of optical correlation phenomena, special state of radiation fields, and intensity interferometry in quantum optics. The text offers particularly complete treatments of properties of the coherent states and of the "diagonal" representations for statistical states. These methods are applied to studies of coherence, coincident counting rates, and counting distributions for a number of physically significant states, including thermal and laser-like fields.
Mechanics of Asset Forfeiture
MECHANICS OF ASSET FORFEITURE
1993
Assets can be forfeited administratively, criminally, and civilly. For example, most local forfeitures in California have been processed through the Special Investigations/Asset Removal Group and Financial Investigation (FINVEST) units of the San Diego County Integrated Narcotics Task Force. Civil forfeiture against the property itself requires an initial showing of probable cause, which is subject to rebuttal. Criminal forfeitures proceed as part of the criminal case and require proof beyond a reasonable doubt. State and Federal law provide for two types of civil forfeiture: administrative and judicial. Individuals facing the forfeiture of their property have several possible defenses at their disposal: the innocent owner defense for those unaware of the illegal activity, proportionality, and position of the innocent lienholder. Forfeiture prosecutions, like any other prosecution, must weigh the advantages versus real life considerations of police budgets, court caseload, agent caseload, attorney caseload, and minimum value assets. However, once an asset is forfeited, its proceeds are shared between agencies according to the amount of work performed on the case; the assets received by law enforcement agencies are then used to continue the war on drugs.
CALIFORNIA; Civil proceedings; Drug forfeiture; Drug law enforcement; Federal law violations; State laws
Mechanics of Crystalline Nanowires
MRS Bulletin
34
03
178-183
2009
10.1557/mrs2009.49
Nanowires are among the most exciting one-dimensional nanomaterials\nbecause of their unique properties, which result primarily from their\nchemical composition and large surface area to volume ratio. These\nproperties make them ideal building blocks for the development of\nnext generation electronics, opto-electronics, and sensor systems.\nIn this article, we focus on the unique mechanical properties of\nnanowires, which emerge from surface atoms having different electron\ndensities and fewer bonding neighbors than atoms lying within the\nnanowire bulk. In this respect, atomistic simulations have revealed\na plethora of novel surface-driven mechanical behavior and properties,\nincluding both increases and decreases in elastic stiffness, phase\ntransformations, shape memory, and pseudoelastic effects. This article\nreviews such atomistic simulations, as well as experimental data\nof these phenomena, while assessing future challenges and directions.
Teaching mechanics with maple
ASEE Annual Conference and Exposition, Conference Proceedings
2011
Classical mechanics is a disciple of theoretical physics and is one of the main constituent parts of physics. The instruction of theoretical physics courses plays an important role in the research of basic science and training physics skill sets. Most students consider that the knowledge of theoretical physics to be very abstract thus causing many difficulties in its study and understanding. Teachers can implement some teaching reform strategies to improve the quality of theoretical physics instruction in the context of classical mechanics. Such strategies may include: stimulate students' interest in learning, perfect students' cognitive structure and knowledge structure of theoretical physics; optimize the system of theoretical physics curriculum, enrich the instruction contents; apply heuristic instruction in theoretical physics teaching; establish virtual theoretical physics experiments and improve assessment and appraisal methods, promote students' all-round development. Physics is guided by simple principles, but for many topics, physics tends to be obscured in the profusion of mathematics. This paper describes some of the merits of using computer algebra in teaching mechanics. We report on our experience in teaching, during the course of several years, dynamical systems and mechanics courses to second-year engineering students by using symbolic computation. When they enter this course they have already taken one to two semesters of calculus, and during their high-school studies they must have already studied particle kinematics and dynamics. Simulation software and computer algebra systems allow students to experiment with phenomena which are too complex to calculate or too expensive to be reproduced in a laboratory, or are simply not accessible to the senses. A computer algebra system is essentially the ability to manipulate concepts, using computer expressions, which are symbolic, algebraic and not limited to numerical evaluation. A computer algebra systems can perform many of the mathematical techniques which are part and parcel of a traditional physics course. The successful use of computer algebra systems does not imply that the mathematical skills are no longer at a premium: such skills are important as ever. However, computer algebra systems may remove the need for those poorly understood mathematical techniques, which are practiced and taught simply because they serve as useful tools. The conceptual and reasoning difficulties that students have in introductory and advanced physics courses, including calculus-based honors courses, are well-documented by the physics education community. The appropriate use of computer algebra systems can therefore be an important aid in the training of better physicists and engineers. In this paper we will discuss ways in which computer algebra systems like Maple can be used by instructors and students in order to help students make these connections and to use them once they are made. Benefits that accrue to upper-class students able to make effective use of a computer algebra system provide a further rationale for introducing student to use of these systems in our courses, especially for those who plan to major in physics or other technical fields. © 2011 American Society for Engineering Education.
Plate Rheology and Mechanics
Journal of Metamorphic Geology
99 - 151
2007
http://dx.doi.org/10.1016/B978-0-444-53802-4.00112-3
Depending on loading conditions and timescale, lithosphere exhibits elastic, brittle (plastic), or viscous (ductile) properties. As can be inferred from rock mechanics data, a large part of the long-term lithospheric strength is supported in the ductile or ductile-elastic regime, while it also maintains important brittle strength. At seismic timescale(s), the entire lithosphere should respond in the elastic or brittle-elastic regime. However, rock mechanics experiments are conducted on simple rocks/minerals at simplified conditions and high strain rates 10-8-10-4s-1). These data cannot be reliably extended to geological time and spatial scales (strain rates 10-17-10-13s-1) without additional parametrization or validation based on geological timescale observations of large-scale deformation. For the oceanic lithosphere, the Goetze and Evan's brittle-elastic-ductile yield strength envelopes (YSEs) were validated by geodynamic-scale observations, such as the observations of plate flexure. For continents, the uncertainties of flexural models and of other data sources are much stronger due to the complex structure and history of continental plates. For example, in a common continental rheology model, dubbed `jelly-sandwich', the strength mainly resides in the crust and mantle, while in some alternative models the mantle is weak and the strength is limited to the upper crust. We address the problems related to lithosphere rheology and mechanics by first reviewing the rock mechanics, Te (flexure) and Ts (earthquake) data, and long-term observations such as folding or subsidence data, and then by examining the physical plausibility of various rheological models. For the latter, we review the results of thermomechanical numerical experiments aimed to test the possible tectonic implications of different rheology models. In particular, it appears that irrespective of the actual crustal strength, the models implying weak mantle are unable to explain either the persistence of mountain ranges for long periods of time or the integrity of the downgoing slab in collisional systems. Also there is certainly no single rheology model for continents: the `jelly-sandwich' is a useful first-order model with which to parametrize the long-term strength of the lithosphere. It is concluded that dry olivine rheology laws seem to well represent long-term behavior of the continental and oceanic mantle lithosphere. As to the crustal rheology, analysis of the results of thermomechanical models and of Te data based on robust variants of flexural models suggests that continental plates with Te 30-50% smaller than their theoretical mechanical thickness hm (i.e., Te=20-60km) should be characterized by a weak lower or intermediate crustal rheology enabling mechanical decoupling between the crust and the mantle. The older plates such as cratons are strong due to crust-mantle coupling. It is shown also that Ts data may reflect current intraplate stress level but cannot be decoded in terms of long-term rheology.
Derivation of the stress concentrations at holes in orthotropic plates using thermoelastic stress analysis
SEM Annual Conference Exposition on Experimental and Applied Mechanics Experimental Mechanics of High Performance Systems
10
2009
An experimental study of the stress distribution around holes in orthotropic composite laminates has been conducted using thermoelastic stress analysis (TSA). Quantitative thermoelastic studies of stress concentrations in metallic plates is a straightforward matter, all that is required is the ratio of the response from the hole and a far-field reading. For orthotropic materials the situation is more complex as the response is not simply proportional to the sum of the principal stresses. In general the thermoelastic response of an orthotropic laminate is a function of the stresses in the principal surface material directions and the associated coefficient of thermal expansion. The approach in this paper is to obtain stress factors at the hole and identify the maxima in the plot. Specimens manufactured from a variety of different laminate lay-ups (unidirectional (UD), cross-ply (CP), angle-ply (AP) and quasi-isotropic (QI)) are considered. In all these cases the principal stress directions at the hole are not coincident with the principal material directions and it is a challenging proposition to derive meaningful stress data from these configurations. To validate the approach the experimental data are compared to analytical models. To better understand the nature of the response finite element models are produced that mimic the thermoelastic response.
tj mechanical engineering machinery
Breakage mechanics — Part II : Modelling granular materials
Mechanics and Physics of solidechanics and Physics of solid
55
1298-1320
2007
10.1016/j.jmps.2006.11.004
The compression of granular materials has been traditionally modelled with the limitations of classical elasto-plasticity. The energy was implicitly assumed to dissipate from the frictional interaction of particles. However, the fact that brittle granular materials crush suggests that energy must also be dissipated from the fracturing of the grains, as in fracture mechanics. The concept of breakage as a thermomechanical internal variable was introduced in Part I [Einav, I., 2006. Breakage mechanics—Part I: theory. J. Mech. Phys. Solids 00,000–000] to describe the fracturing mechanisms. The theory allows to treat ideal theoretical materials that undergo dissipation purely from breakage with no other mechanism allowed for the energy consumption. However, as accounted for in elasto-plasticity, dissipation must also occur from the frictional rearrangement of grains. The combination of the two dissipative mechanisms of breakage and plasticity must therefore be investigated, as we do in this paper. Those two mechanisms are generally coupled, in the sense that one inevitably appears when the other develops. Plastic dissipation emerges as a by-product of breakage dissipation because after grains crush, local rearrangement must occur. This scenario may be termed an ‘active breakage mechanism’, and typifies compression deformations. In shear the plastic dissipation is dominant but breakage appears inevitably from grains abrasion. This scenario may be called a ‘passive breakage mechanism’. Based on the coupling assumption, models are developed for granular materials. In particular, we show that in compression isotropic hardening of sands may appear without involving plastic strains, i.e., independent of frictional dissipation. This interpretation of hardening is different from the one used in classical critical state soil mechanics.
breakage; dissipation; granular materials; micromechanics; plasticity
Bohmian quantum mechanics with quantum trajectories
ProQuest Dissertations and Theses
3413218
193
2010
The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors, especially, in this case, in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.
0402:Philosophy of Science; 0599:Quantum physics; Bohm, David; Bohmian quantum mechanics; Crucial experiment; Duhem-Quine thesis; History and philosophy of science; Interpretation of quantum mechanics; Nano-science and technology; Philosophy of Science; Philosophy, religion and theology; Pure sciences; Quantum physics; Quantum trajectories
A review of the mechanics of metal spinning
Journal of Materials Processing Technology
210
1
3-23
2010
10.1016/j.jmatprotec.2009.08.021
This review presents a thorough survey of academic work on the analysis and application of the mechanics of spinning. It surveys most literature published in English and the most important publications in German and Japanese languages. The review aims to provide insight into the mechanics of the process and act as a guide for researchers working on both metal spinning and other modern flexible forming processes. The review of existing work has revealed several gaps in current knowledge of spinning mechanics: the evolution of the stress state and the strain history of the workpiece in both conventional and shear spinning is not well understood, mainly due to the very long solution times that would occur in modelling the process throughout its duration with a sufficiently fine mesh to capture detailed behaviour through the workpiece thickness; the evolution of microstructure, residual stress and hence springback, has not been examined-either numerically or by experiment; the failure mechanisms of spinning - fracture and wrinkling - are only partially understood, through analogy with other processes, and as yet models of the process have not made use of contemporary damage mechanics; the design of toolpaths required to make particular parts without failure remains an art, and cannot currently be performed automatically with confidence. Studies on novel process configurations in spinning have shown that great potential for innovation in spinning exists. The process has the potential to be more flexible, to produce a wider range of shapes, and to form more challenging materials. © 2009 Elsevier B.V. All rights reserved.
Conventional spinning; Mechanics; Metal spinning; Shear spinning
Asbestos-related diseases in automobile mechanics
Annals of Occupational Hygiene
56
55-60
2012
10.1093/annhyg/mer066
Purpose: Automobile mechanics have been exposed to asbestos in the past, mainly due to the presence of chrysotile asbestos in brakes and clutches. Despite the large number of automobile mechanics, little is known about the non-malignant respiratory diseases observed in this population. The aim of this retrospective multicenter study was to analyse the frequency of pleural and parenchymal abnormalities on high-resolution computed tomography (HRCT) in a population of automobile mechanics.Methods: The study population consisted of 103 automobile mechanics with no other source of occupational exposure to asbestos, referred to three occupational health departments in the Paris area for systematic screening of asbestos-related diseases. All subjects were examined by HRCT and all images were reviewed separately by two independent readers; who in the case of disagreement discussed until they reached agreement. Multiple logistic regression models were constructed to investigate factors associated with pleural plaques.Results: Pleural plaques were observed in five cases (4.9%) and interstitial abnormalities consistent with asbestosis were observed in one case. After adjustment for age, smoking status, and a history of non-asbestos-related respiratory diseases, multiple logistic regression models showed a significant association between the duration of exposure to asbestos and pleural plaques.Conclusions: The asbestos exposure experienced by automobile mechanics may lead to pleural plaques. The low prevalence of non-malignant asbestos-related diseases, using a very sensitive diagnostic tool, is in favor of a low cumulative exposure to asbestos in this population of workers.
asbestos; automobile mechanics; brakes; high-resolution computed tomography; pleural plaques
USNCTAM perspectives on mechanics in medicine.
Journal of the Royal Society, Interface / the Royal Society
11
20140301
2014
10.1098/rsif.2014.0301
Over decades, the theoretical and applied mechanics community has developed sophisticated approaches for analysing the behaviour of complex engineering systems. Most of these approaches have targeted systems in the transportation, materials, defence and energy industries. Applying and further developing engineering approaches for understanding, predicting and modulating the response of complicated biomedical processes not only holds great promise in meeting societal needs, but also poses serious challenges. This report, prepared for the US National Committee on Theoretical and Applied Mechanics, aims to identify the most pressing challenges in biological sciences and medicine that can be tackled within the broad field of mechanics. This echoes and complements a number of national and international initiatives aiming at fostering interdisciplinary biomedical research. This report also comments on cultural/educational challenges. Specifically, this report focuses on three major thrusts in which we believe mechanics has and will continue to have a substantial impact. (i) Rationally engineering injectable nano/microdevices for imaging and therapy of disease. Within this context, we discuss nanoparticle carrier design, vascular transport and adhesion, endocytosis and tumour growth in response to therapy, as well as uncertainty quantification techniques to better connect models and experiments. (ii) Design of biomedical devices, including point-of-care diagnostic systems, model organ and multi-organ microdevices, and pulsatile ventricular assistant devices. (iii) Mechanics of cellular processes, including mechanosensing and mechanotransduction, improved characterization of cellular constitutive behaviour, and microfluidic systems for single-cell studies.
biomechanics; nanotechnology
The Quantum Mechanics of Closed Systems
Quantum
104
1992
A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system. Not every set of alternative coarse-grained histories that can be described may be consistently assigned probabilities because of quantum mechanical interference between individual histories of the set. In the quantum mechanics of closed systems, containing both observer and observed, probabilities are assigned to those sets of alternative histories for which there is negligible interference between individual histories as a consequence of the system's initial condition and dynamics. Such sets of histories are said to decohere. Typical mechanisms of decoherence that are widespread in our universe are illustrated. Copenhagen quantum mechanics is an approximation to the more general quantum framework of closed subsystems. It is appropriate when there is an approximately isolated subsystem that is a participant in a measurement situation in which (among other things) the decoherence of alternative registrations of the apparatus can be idealized as exact. Since the quantum mechanics of closed systems does not posit the existence of the quasiclassical domain of everyday experience, the domain of the approximate aplicability of classical physics must be explained. We describe how a quasiclassical domain described by averages of densities of approximately conserved quantities could be an emergent feature of an initial condition of the universe that implies the approximate classical behavior of spacetime on accessible scales.
Unsaturated Soil Mechanics in Engineering Practice
Unsaturated Soil Mechanics in Engineering Practice
2012
The definitive guide to unsaturated soil- from the world's experts on the subject. This book builds upon and substantially updates Fredlund and Rahardjo's publication, Soil Mechanics for Unsaturated Soils, the current standard in the field of unsaturated soils. It provides readers with more thorough coverage of the state of the art of unsaturated soil behavior and better reflects the manner in which practical unsaturated soil engineering problems are solved. Retaining the fundamental physics of unsaturated soil behavior presented in the earlier book, this new publication places greater emphasis on the importance of the "soil-water characteristic curve" in solving practical engineering problems, as well as the quantification of thermal and moisture boundary conditions based on the use of weather data. Topics covered include: Theory to Practice of Unsaturated Soil Mechanics. Nature and Phase Properties of Unsaturated Soil. State Variables for Unsaturated Soils. Measurement and Estimation of State Variables. Soil-Water Characteristic Curves for Unsaturated Soils. Ground Surface Moisture Flux Boundary Conditions. Theory of Water Flow through Unsaturated Soils. Solving Saturated/Unsaturated Water Flow Problems. Air Flow through Unsaturated Soils. Heat Flow Analysis for Unsaturated Soils. Shear Strength of Unsaturated Soils. Shear Strength Applications in Plastic and Limit Equilibrium. Stress-Deformation Analysis for Unsaturated Soils. Solving Stress-Deformation Problems with Unsaturated Soils. Compressibility and Pore Pressure Parameters. Consolidation and Swelling Processes in Unsaturated Soils. Unsaturated Soil Mechanics in Engineering Practice is essential reading for geotechnical engineers, civil engineers, and undergraduate- and graduate-level civil engineering students with a focus on soil mechanics. © 2012 John Wiley & Sons, Inc.
An historical perspective on cell mechanics.
Pflügers Archiv : European journal of physiology
456
1
3-12
2008
10.1007/s00424-007-0405-1
The physical properties of the protoplasm have long been of interest, and today, several intricate methods, including atomic force microscopy, have been employed in studies of cellular mechanics. However, many current concepts and experimental approaches actually have their beginnings over 300 years ago. Unfortunately, these pioneering studies have been all but forgotten. In this paper, we have reviewed some of the early literature on cellular mechanics to place modern work within an historical framework. It is clear that with current nanoscience approaches, modern experiments employing cell indentation, manipulation, particle rheology and micro- or nano-needle poking are now quantifying mechanical properties which were only qualitatively described 100 years ago. Aside from the variety of approaches our predecessors have employed to understand cellular mechanics, we feel an understanding of the past will help to propel nanoscience into the future. As nanophysiology and nanomedicine are developing, we as a community should take time to consider the early roots of these fields.
Animals; Biomechanics; Cell Biology; Cell Biology: history; Cell Physiological Phenomena; Cells; Cells: cytology; Cells: ultrastructure; Cytoplasm; Cytoplasm: physiology; History, 18th Century; History, 19th Century; History, 20th Century; History, 21st Century; Humans; Microscopy; Microscopy, Atomic Force; Microscopy: history; Microscopy: instrumentation
Statistical-Mechanics of Terrestrial Ecosystems
Ecological Modelling
63
1-4
319-323
1992
The statistical mechanics of terrestrial ecosystems are outlined. The observables are continuous functions of biotic variables and the states are measures on the phase space of these biotic variables, where coupling constants may depend on external climatic parameters. The subsystem dynamics of the biomasses tums out to be Hamiltonian and the Gibbs states, which are the equilibrium measures, seem to be realized in the measurement data of certain selection forests. On the basis of a model for the stress and thinning forces, we have derived the Fokker-Planck dynamics of ecosystems and have compared exact solutions with measurement data for beech forests, thinned from below between 1870 and 1970.
Quantum Mechanics in Phase Space
Asia Pacific Physics Newsletter
01
01
37-46
2012
10.1142/S2251158X12000069
Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.
Statistical mechanics of complex networks
Rev. Mod. Physics
74
47
2002
Complex networks describe a wide range of systems in nature and society.\nFrequently cited examples include the cell, a network of chemicals\nlinked by chemical reactions, and the Internet, a network of routers\nand computers connected by physical links. While traditionally these\nsystems have been modeled as random graphs, it is increasingly recognized\nthat the topology and evolution of real networks are governed by\nrobust organizing principles. This article reviews the recent advances\nin the field of complex networks, focusing on the statistical mechanics\nof network topology and dynamics. After reviewing the empirical data\nthat motivated the recent interest in networks, the authors discuss\nthe main models and analytical tools, covering random graphs, small-world\nand scale-free networks, the emerging theory of evolving networks,\nand the interplay between topology and the network’s robustness against\nfailures and attacks.
On the quantum mechanics of supermembranes
Nuclear Physics B
305
4
545-581
1988
10.1016/0550-3213(88)90116-2
We study the quantum-mechanical properties of a supermembrane and examine the nature of its ground state. A supersymmetric gauge theory of area-preserving transformations provides a convenient framework for this study. The supermembrane can be viewed as a limiting case of a class of models in supersymmetric quantum mechanics. Its mass does not depend on the zero modes and vanishes only if the wave function is a singlet under supersymmetry transformations of the nonzero modes. We exhibit the complexity of the supermembrane ground state and examine various truncations of these models. None of these truncations has massless states.
Currents in nonequilibrium statistical mechanics
Physical Review E
79
2
21112
2009
10.1103/PhysRevE.79.021112
Nonzero currents characterize the nonequilibrium state in stochastic dynamics (or master equation) models of natural systems. In such models there is a matrix R of transition probabilities connecting the states of the system. We show that if the strength of a transition increases, so does the current along the corresponding bond. We also address the inverse problem: given a set of observed currents, we show the extent to which the original " R " can be recovered. These considerations lead to a general discussion of time scales and substance flows.
inverse problems; statistical mechanics; stochasti
Continuum Mechanics of Electromagnetic Solids
Journal of Applied Mechanics
56
4
986
1989
10.1115/1.3176205
Along with magnetohydrodynamics in the case of fluids, piezoelectricity is the most well-known electro-magneto-mechanical coupling. Discovered by Pierre and Jacques Curie in 1880 in such crystals as sodium chlorate, tourmaline, quartz, topax, and Rochelle salt, piezoelectricity is the appearance of an electric polarization in a crystal of appropriate symmetry when the latter is subjected to a pressure (so-called direct effect) and the deformation of such a crystal when subjected to an electric field (inverse field). The inverse effect was discovered by Lippman but experimentally verified by the Curie brothers.
I.2. Mechanics of materials.
Studies in health technology and informatics
152
13-26
2010
10.1016/0160-9327(78)90104-7
Mechanics of materials is the science of forces applied on a body and response of the body in terms of deformation. Different type of loadings on bodies with different geometries or made of different material give rise to different deformations. Last but not the least, this science allows to predict the failure of a body under certain loading condition hence makes it possible to optimize the design for that particular condition.
Biocompatible Materials; Biocompatible Materials: chemistry; Biomechanics; Biomedical Engineering; Models, Biological; Models, Chemical; Physics
Fabric mechanics as a design tool
Indian Journal of Fibre & Textile Research
19
3
107-113
1994
A systematic approach to engineer a complex textile structure with the help of modern computational techniques is proposed. It is suggested that textile designers and engineers should start from first principles and then develop powerful new approaches to suit the special complexities of various textile structures in order to meet the needs of customers and manufacturers. It is also suggested that the textile engineers should accept cultural change and develop advanced software to create, manipulate and evaluate new fabric structures in order to make the fabric mechanics a valuable design tool.
Common misconceptions regarding quantum mechanics
Am. J. Phys.
64
1
31
1996
10.1119/1.18288
This paper lists 15 commonly held misconceptions concerning quantum mechanics, such as "Energy eigenstates are the only allowed states" and "The wave function is dimensionless." A few suggestions are offered to help combat these misconceptions in teaching.
Statistical mechanics of complex networks
arXiv
cond-mat.s
2001
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
cond-mat.dis-nn; cond-mat.stat-mech; cs.NI; math.MP; math-ph; nlin.AO; physics.data-an
Statistical mechanics of complex networks
Reviews of modern physics
74
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the networkís robustness against failures and attacks.
Statistical mechanics of program systems
Journal of Physics A: Mathematical and General
39
33
10355-10361
2006
10.1088/0305-4470/39/33/006
We discuss the collective behaviour of a set of\noperators and variables that constitute a program and\nthe emergence of meaningful computational properties in\nthe language of statistical mechanics. This is done by\nappropriately modifying available Monte Carlo methods\nto deal with hierarchical structures. The study\nsuggests, in analogy with simulated annealing, a method\nto automatically design programs. Reasonable solutions\ncan be found, at low temperatures, when the method is\napplied to simple toy problems such as finding an\nalgorithm that determines the roots of a function or\none that makes a nonlinear regression. Peaks in the\nspecific heat are interpreted as signalling phase\ntransitions which separate regions where different\nalgorithmic strategies are used to solve the problem.
Statistical mechanics and disordered systems
Communications of the ACM
28
4
363-373
1985
10.1145/3341.3344
Considering the nature of the problem, it is natural that numerical methods should play a major role in modern statistical mechanics. One of the most fruitful approaches has been the use of computer simulations. This approch has increased in importance in recent years with the development of powerful methods of analysis for extracting information from the data and with the continued improvement in the capacity of modern computers. Since computers are able to simulate the equilibrium propertis of the model systems, they may also prove useful for solving the hard optimization problems that arise in the engineeirng of complex systems.
Mechanics of swinging a bat
American Journal of Physics
77
1
36
2009
10.1119/1.2983146
Measurements on the swing of a baseball bat are analyzed to extract the basic mechanics of the swing. The force acting on the bat is determined from the velocity of the center of mass, and the angular velocity of the bat provides additional information on the couple exerted by the two hands. The motion of the bat was calculated for other force-couple combinations to determine their effects on the swing of the bat. It was found that a couple is needed to start the swing, and a large opposing couple is required near the end of the swing to prevent the bat rotating through an excessive angle before it impacts with the ball.
Railroad Track Mechanics and Technology
Railroad Track Mechanics and Technology
405-425
1978
10.1016/B978-0-08-021923-3.50025-5
Testing of triaxial samples of ballast where the boundary stress conditions are known provides a rapid method of doing comparative tests on ballast to highlight the relative significance of the different loading conditions in causing permanent deformation of ballast. The paper initially considers the effect of the packing condition of the ballast and the grading of the material on the permanent deformation. It then considers the effect of different stress conditions on the basic deformational properties of the ballast and concludes with examination of the synthesis of different traffic patterns, examining such factors as frequency (speed) and programme patterns (2 levels) of loading.
On the Completeness of Quantum Mechanics
Contemporary Research in the Foundations and Philosophy of Quantum Theory
1-65
1973
10.1007/BF00484961
This paper explores the program of hidden variables as a way of making simultaneous assignments of point-values to all the observables of a quantum system, and it assesses the impact on that program of recent work on "locality" by bell and wigner. it argues that although this work does not bear, essentially, on locality (but has to do rather with locality-independent algebraic constraints of an arbitrary nature) it does show that the machinery of random variables over a common phase space is idle in the hidden variables program. the paper concludes with a detailed suggestion for treating the observables as "statistical variables", in a format that completes the assignments of quantum theory neatly and locally.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
1
47-97
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society.\nFrequently cited examples include the cell, a network of chemicals\nlinked by chemical reactions, and the Internet, a network of routers\nand computers connected by physical links. While traditionally these\nsystems have been modeled as random graphs, it is increasingly recognized\nthat the topology and evolution of real networks are governed by\nrobust organizing principles. This article reviews the recent advances\nin the field of complex networks, focusing on the statistical mechanics\nof network topology and dynamics. After reviewing the empirical data\nthat motivated the recent interest in networks, the authors discuss\nthe main models and analytical tools, covering random graphs, small-world\nand scale-free networks, the emerging theory of evolving networks,\nand the interplay between topology and the network's robustness against\nfailures and attacks.
Statistical mechanics of the majority game
Journal of Physics A: Mathematical and General
36
47
14
2003
10.1088/0305-4470/36/47/002
The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfield like hamiltonian. On the basis of a replica symmetric calculations, we draw the phase diagram, which contains the analog of a retrieval phase. The number of metastable states is estimated using the annealed approximation. The results are confronted with extensive numerical simulations.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
1
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Ventricular Mechanics: Techniques and Applications.
Magnetic resonance imaging clinics of North America
23
1
7-13
2015
10.1016/j.mric.2014.08.005
Magnetic resonance assessment of regional myocardial function is a novel potentially important tool for early identification of cardiac pathology. Many cardiac magnetic resonance techniques have been developed for detection and quantification of regional strain abnormalities including steady-state free-precession CINE, tagging, displacement encoding with stimulated echoes, strain encoding imaging, and feature tracking. Potential clinical applications of magnetic resonance strain imaging include early detection of systolic dysfunction in heart failure patients with both ischemic and nonischemic etiologies.
imaging ventricular mechanics; strain magnetic resonance cardiac
Student understanding of quantum mechanics
Am. J. Phys.
69
8
885-895
2001
We investigate the difficulties of advanced undergraduate students toward the end of a full year upper-level quantum mechanics course with concepts related to quantum measurements and time development. Our analysis is based upon a test administered to 89 students from six universities and interviews with 9 students. Strikingly, most students shared the same difficulties despite variations in background, reaching styles, and textbooks. Concepts related to stationary states, eigenstates, and time dependence of expectation values were found to be particularly difficult. An analysis of written tests and interviews suggests that widespread misconceptions originate from an inability to discriminate between related concepts and a tendency to overgeneralize. (C) 2001 American Association of Physics Teachers.
Structural Engineering, Mechanics and Computation
Structural Engineering, Mechanics and Computation
393-400
2001
10.1016/B978-008043948-8/50040-0
This chapter presents a full interaction method for calculating the elastic bending stresses and shear stud forces in composite beams with shear studs at discrete points. The method implicitly recognizes the breaks in the shear connection at the steel–concrete interface. Shear transfer discontinuities are explained to lead to significant variations in direct bending stress over those predicted from the method of transformed sections. These variations are the most pronounced in deep beams supporting shallow composite slabs. Rubbing at the steel–concrete interface may explain the better than expected dynamic performance observed in long span composite beams by providing friction sites that improve damping. The method presented can be easily adapted to analyze other types of members, where one is concerned about the effects of breaks in the shear connection among the components of composite members.
Fluid mechanics and homeland security
Annu. Rev. Fluid Mech.
38
87-110
2006
Homeland security involves many applications of fluid mechanics and\noffers many opportunities for research and development. This review\nexplores a wide selection of fluids topics in counterterrorism and\nsuggests future directions. Broad topics range from preparedness\nand deterrence of impending terrorist attacks to detection, response,\nand recovery. Specific topics include aircraft hardening, blast mitigation,\nsensors and sampling, explosive detection, microfluidics and labs-on-a-chip,\nchemical plume dispersal in urban settings, and building ventilation.\nAlso discussed are vapor plumes and standoff detection, nonlethal\nweapons, airborne disease spread, personal protective equipment,\nand decontamination. Involvement in these applications requires fluid\ndynamicists to think across the traditional boundaries of the field\nand to work with related disciplines, especially chemistry, biology,\naerosol science, and atmospheric science.
AEROSOL/AIRBORNE/AIRCRAFT/aircraft hardening/APPLI
Quantum mechanics without probability amplitudes
Foundations of Physics
16
4
391-405
1986
10.1007/BF01882696
{Abstract First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by probability tables, which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The new version of the rule is surprisingly simple, especially when one considers that the notion of complex phases, so crucial in the evaluation of inner products, is entirely absent from the representation of states used here.}
Statistical Mechanics of Learning : Generalization
Engineering
1-4
2002
10.1103/PhysRevLett.89.108302
The effort to build machines that are able to learn and undertake tasks such as datamining, image processing and pattern recognition has led to the development of artificial neural networks in which learning from examples may be described and understood. The contribution to this subject made over the past decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics, and include many examples and exercises.
Statistical mechanics of hypothesis evaluation
Journal of Physics A: Mathematical and General
27
10
3355-3363
1994
Following ideas of Gull, Skilling and MacKay (1992), we develop and\nexplore a statistical-mechanics framework through which one may assign\nvalues to the parameters of a model for a 'rule' (instanced, here,\nby the noisy linear perceptron), on the basis of data instancing\nthe rule. The 'evidence' which the data offers in support of a given\nassignment, is likened to the free energy of a system with quenched\nvariables (the data): the most probable (MAP) assignments of parameters\nare those which minimize this free-energy; tracking the free-energy\nminimum may lead to 'phase transitions' in the preferred assignments.\nWe explore the extent to which the MAP assignments lead to optimal\nperformance.
On the mechanics of fretting fatigue
Wear
125
1-2
129-146
1988
10.1016/0043-1648(88)90198-6
The current state of knowledge of the prediction of fretting fatigue is reviewed and a summary given of the way fracture mechanics may be used to analyse a propagating crack. Recent experimental work on an aluminium alloy, HE15-TF, which discovered a distinct size effect (indicating that the absolute size of the contact has a marked effect on fatigue life), is reported and mechanical aspects of the problem, i.e. interfacial traction distribution, stress-state-induced and surface finish effects are discussed in depth. It is concluded that fretting fatigue is an initiation-controlled process and a tentative explanation of the size effect is proposed. pyright 1988.
Measuring the mechanics of morphogenesis
Current Opinion in Plant Biology
16
1
25-32
2013
10.1016/j.pbi.2012.11.002
The past decades have seen a rapid increase in the understanding of plant morphogenesis at the molecular-genetic level. However, the control of growth and morphogenesis by molecular and signaling networks ultimately requires the coordinated regulation of mechanical properties in individual cells. There is also increasing evidence that mechanical stresses can feedback on hormone signaling and growth, and may have a central role in developmental patterning. Thus the development of techniques to investigate the mechanical properties of plant tissue at the cellular level is key to understanding growth and morphogenesis. ?? 2012 Elsevier Ltd.
Statistical mechanics of complex networks
Review of Modern Physics
74
47-97
2002
DOI: 10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society.\nFrequently cited examples include the cell, a network of chemicals\nlinked by chemical reactions, and the Internet, a network of routers\nand computers connected by physical links. While traditionally these\nsystems have been modeled as random graphs, it is increasingly recognized\nthat the topology and evolution of real networks are governed by\nrobust organizing principles. This article reviews the recent advances\nin the field of complex networks, focusing on the statistical mechanics\nof network topology and dynamics. After reviewing the empirical data\nthat motivated the recent interest in networks, the authors discuss\nthe main models and analytical tools, covering random graphs, small-world\nand scale-free networks, the emerging theory of evolving networks,\nand the interplay between topology and the network's robustness against\nfailures and attacks.
social networks
Macroscopic systems in quantum mechanics
Physica A: Statistical Mechanics and its Applications
194
1-4
542-550
1993
10.1016/0378-4371(93)90384-G
A macroscopic system is a quantum system with numerous degrees of freedom. As a consequence the description in terms of individual levels and eigenstates is inappropriate. Rather, the relevant concepts are macrostates and macrovariables. It is shown how to construct these. It is found that on this macroscopic level the state of the system can be described as a classical ensemble. This result provides the answer to the paradoxes of quantum measurement theory. It is also shown that the evolution of the ensemble is governed by a classical master equation.
Structural Engineering, Mechanics and Computation
Structural Engineering, Mechanics and Computation
1505-1511
2001
10.1016/B978-008043948-8/50169-7
An alternative approach to the teaching of structural engineering is based on the use of computer. In this approach, emphasis is shifted to a deeper understanding of the behavior of structures for which the computer plays an important role. The introduction of suitable methodologies for the validation of computer results and the utilization of the power of computers to promote deeper learning should be essential in teaching engineering students. Intelligent use of computers can help a person achieve this goal. This chapter shows how a different approach, using computers to model real world problems, can allow a person to widely explore the design space and very quickly acquire a deeper knowledge, which has traditionally been the domain of the experienced engineer.
Mathematical Methods of Classical Mechanics
Order A Journal On The Theory Of Ordered Sets And Its Applications
60
60
xvi+508
1989
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Fracture Mechanics of Concrete Structures
Journal Of The Structural Division
108
4
1-999
1995
Material properties (heterogeneity and non-linearity) and disturbing phenomena (slow crack growth and microcracking) cause several research-workers to be pessimistic about the applicability of fracture mechanics to concrete structures. A critical review of the preceding works dealing with concrete fracture is presented. During the 1960s and 1970s it became more and more evident that notch sensitivity is not a material property but only a phenomenon dependent on the specimen and crack sizes, and that the degree of heterogeneity is only a matter of scale. A true fracture collapse can occur only with very large structures. On the other hand a real ultimate strength collapse can occur only with very small fracture specimens. Usually, with the sizes of the structures built by man and the lengths of the natural cracks, the two collapses are interacting.
Computational Mechanics in Structural Engineering
Computational Mechanics in Structural Engineering
169-178
1999
10.1016/B978-008043008-9/50051-X
This chapter discusses parallel implementations of the explicit/implicit integration algorithms for dynamic analysis of structures. The parallelism of the explicit integration is based on the domain decomposition method and use of lumped mass matrix. That of the latter implicit integration is on the block parallelization of the assembling, the triangular factorization of the equivalent stiffness matrices, and the back/forward substitutions in each Newmark step. Implementations are carried out on the clustered network systems with PVM parallel environment. The developed parallel integration algorithms are incorporated into the general purpose finite element system (PFEM), which is a general purpose serial-parallel mixed system for structural analysis. Furthermore, this chapter illustrates examples and the parallel efficiencies.
Quantum Mechanics in Phase Space
Asia Pacific Physics Newsletter
01
01
37-46
2011
10.1142/S2251158X12000069
Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.
Mechanics of multidimensional isolated horizons
Classical and Quantum Gravity
22
11
2001-2016
2005
10.1088/0264-9381/22/11/006
Recently a multidimensional generalization of Isolated Horizon framework has been proposed by Lewandowski and Pawlowski (gr-qc/0410146). Therein the geometric description was easily generalized to higher dimensions and the structure of the constraints induced by the Einstein equations was analyzed. In particular, the geometric version of the zeroth law of the black hole thermodynamics was proved. In this work we show how the IH mechanics can be formulated in a dimension--independent fashion and derive the first law of BH thermodynamics for arbitrary dimensional IH. We also propose a definition of energy for non--rotating horizons.
General Relativity and Quantum Cosmology; High Energy Physics - Theory
Computational Mechanics in Structural Engineering
Computational Mechanics in Structural Engineering
97-110
1999
10.1016/B978-008043008-9/50046-6
This chapter discusses the problem of different cases of excitations of the train-bridge system for the purpose of assessment of vehicle-running safety and serviceability. The dynamic model of a train-bridge system consists of the train model and the bridge model. Self-excitations of the system are the track irregularity and the vehicle hunting movement. The wind load and earthquake action are considered to be the main external excitations. The introduced method is to analyze serviceability, by studying the peak distribution of structural responses and transforming their first-passage probability distribution into the extreme distribution, which is more convenient for engineering purposes.
Uncertainty relations of Statistical Mechanics
Physical Review A
31
5
2265-3239
2009
Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum Mechanics. Such a complementarity is expressed as the impossibility of perform an exact simultaneous determination of the system energy and temperature by using an experimental procedure based on the thermal equilibrium with other system regarded as a measure apparatus (thermometer). In this work, we provide a simple generalization of this latter approach with the consideration of a thermodynamic situation with several control parameters.
Mixing quantum and classical mechanics
Physical Review A
56
1
162-175
1997
10.1103/PhysRevA.56.162
Quantum-classical mixing is studied by a group-theoretical approach, and a quantum-classical equation of motion is derived. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. The exact formalism is applied to coupled quantum and classical oscillators. Various approximations, such as the mean-field and the multiconfiguration mean-field approaches, which are of great utility in studying realistic multidimensional systems, are derived. Based on the formulation, a natural classification of the previously suggested quantum-classical equations of motion arises, and several problems from earlier works are resolved.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
1
47-97
2002
10.1088/1478-3967/1/3/006
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Statistical Mechanics of Complex Networks
Rev. Mod. Phys.
74
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
Determinism, Chaos and Quantum Mechanics.
Institut de Physique Theorique Universite Catholique de Louvain, Louvain-la-Neuve, Belgium. Página web disponible en: http://www. fyma. ucl. ac. be/files/Turin. pdf Acceso en julio
23
2004
After some general remarks on the notion of ”determinism”, I will discuss the precise meaning of chaos theory and the frequent misunderstandings concerning the implications of that theory. After reviewing the status of probabilistic rea- soning in classical physics, I will also briefly discuss misun- derstandings occurring in the context of quantum mechan- ics.
Statistical mechanics of complex networks
arXiv
54
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society.\nFrequently cited examples include the cell, a network of chemicals\nlinked by chemical reactions, and the Internet, a network of routers\nand computers connected by physical links. While traditionally these\nsystems have been modeled as random graphs, it is increasingly recognized\nthat the topology and evolution of real networks are governed by\nrobust organizing principles. This article reviews the recent advances\nin the field of complex networks, focusing on the statistical mechanics\nof network topology and dynamics. After reviewing the empirical data\nthat motivated the recent interest in networks, the authors discuss\nthe main models and analytical tools, covering random graphs, small-world\nand scale-free networks, the emerging theory of evolving networks,\nand the interplay between topology and the network's robustness against\nfailures and attacks.
Non-Hamiltonian equilibrium statistical mechanics.
Physical review. E, Statistical, nonlinear, and soft matter physics
67
2 Pt 1
021101
2003
10.1103/PhysRevE.67.021101
In this paper the equilibrium statistical mechanics of non-Hamiltonian systems is formulated introducing an algebraic bracket. The latter defines non-Hamiltonian equations of motion in classical phase space according to the approach introduced in Phys. Rev. E 64, 056125 (2001). The Jacobi identity is no longer satisfied by the generalized bracket and as a result the algebra of phase space functions is not time translation invariant. The presence of a nonzero phase space compressibility spoils also the time-reversal invariance of the dynamics. The general Liouville equation is rederived and the properties of statistical averages are accounted for. The features of time correlation functions and linear response theory are also discussed.
Structural Engineering, Mechanics and Computation
Structural Engineering, Mechanics and Computation
1497-1504
2001
10.1016/B978-008043948-8/50168-5
This chapter outlines a minimum core curriculum for the structural analysis teaching within a first civil engineering degree. Aspects that should assist in effective learning and promote teaching toward understanding are also discussed. Structural engineering is one of the disciplines included in the under graduate civil engineering university degree. There is a growing demand to include more environmental, managerial and economics subjects, and other humanitarian topics in the civil engineering course. There is, thus, pressure to reduce the structural engineering content of the course. Topics that are considered essential are discussed and proposals to make the learning process as time effective as possible are outlined in the chapter. The change over the years should have been away from hand-numerical expedient methods to topics that assist the understanding of structural behavior. Experience in approximate methods is necessary to check computer analyses.
Certificate Recocation: Mechanics and Meaning.
Financial Cryptography
158-164
1998
Revocation of public key certificates is controversial in every aspect: methodol- ogy, mechanics, and even meaning. This isn't so surprising, though, when considered in the context of current public key infrastructure (PKI) implementations. PKIs axe still immature; consumers, including application developers and end-users, are just beginning to understand the implications of large-scale, heterogeneous PKIs, let alone PKI subtleties such as revoca- tion. In this paper, which is the product of a panel discussion at Financial Cryptography '98, we illustrate some of the semantic meanings possible with current certificate revocation tech- nology and their impel on the process of determining trust relationships among public keys in the PKI. Further, we postulate that real-world financial applications provide analogous and appropriate models for certificate revocation.
Relationalism rehabilitated? I: Classical mechanics
British Journal for the Philosophy of Science
53
2
183-204
2002
10.1093/bjps/53.2.183
The implications for the substantivalist-relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
graph; network
The Physics of Granular Mechanics
Mechanics of Natural Solids
1-26
2012
10.1007/978-3-642-03578-4_2
The em hydrodynamic approach to a continuum mechanical description of granular behavior is reviewed and elucidated. By considering energy and momentum conservation simultaneously, the general formalism of em hydrodynamics provides a systematic method to derive the structure of constitutive relations, including all gradient terms needed for nonuniform systems. An important input to arrive at different relations (say, for Newtonian fluid, solid and granular medium) is the energy, especially the number and types of its variables. Starting from a careful examination of the physics underlying granular behavior, we identify the independent variables and suggest a simple and qualitatively appropriate expression for the granular energy. The resultant hydrodynamic theory, especially the constitutive relation, is presented and given preliminary validation.
Computational Mechanics in Structural Engineering
Computational Mechanics in Structural Engineering
361-374
1999
10.1016/B978-008043008-9/50066-1
This chapter reviews a new formulation fully coupled three-dimensional buffeting analysis of long span cable-supported bridges. The formulation is a complete finite element approach and a pseudo-excitation method. Dynamic coupling between modes of vibration, interaction between bridge deck and towers and cables, and varying wind speed and structural properties along bridge deck and towers and cables can be taken into consideration using this formulation. This chapter closes with the discussion of Tsing Ma long suspension bridge in Hong Kong, in which the new formulation is validated through a comparison with Scanlan's method, and aeroelastic effects, multi-mode effects, inter-mode effects, interaction between bridge components are investigated.
Statistical mechanics of complex networks
World Wide Web Internet And Web Information Systems
74
January
54
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Principles of Fractional Quantum Mechanics
Arxiv preprint arXiv10095533
2
31
2010
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction is described by a potential, the total energy of the particle is equal to its total kinetic plus potential energies. We derive the Schrodinger and Dirac equations as the conditions the wavefunction must satisfy at each point in order to fulfill the corresponding energy equation. In our approach quantum theory is tangible, experimentally justified and theoretically consistent. PACS numbers: 03.65.-w Keywords: Quantum principles; Quantum dynamics; Schrodinger equation; Dirac equation
Statistical mechanics of complex networks
Reviews of modern physics
74
54
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Complex networks
Quantum mechanics of superconducting nanowires
Physical Review B - Condensed Matter and Materials Physics
78
May
1-6
2008
10.1103/PhysRevB.78.014512
In a short superconducting nanowire connected to bulk superconducting leads, quantum phase slips behave as a system of linearly (as opposed to logarithmically) interacting charges. This system maps onto quantum mechanics of a particle in a periodic potential. We show that, while the state with a high density of phase slips is not a true insulator (a consequence of Josephson tunneling between the leads), for a range of parameters it behaves as such down to unobservably small temperatures. We also show that quantum phase slips give rise to multiple branches (bands) in the energy-current relation and to an interband ("exciton") mode.
Statistical mechanics of complex networks
Reviews of modern physics
74
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks
Narrow resonances is statistical mechanics
Physical Review
10
2
694
1974
10.1103/PhysRevD.10.694
behaves like a noninteracting It is shown that when the dynamics of a system is dominated by narrow-resonance system with added species of free particles, corresponding formation it to all the quantum numbers and the statistics of each of the resonances. This equivalence, widely assumed and used in practice, is established by explicitly constructing unitarity that correspond to purely resonance-dominated many-particle S matrices consistent with dynamics. These are then used in the S-matrix formulation of statistical mechanics to obtain the grand partition function, which is seen to reveal the above result. In the following paper, operational criteria are presented for determining when in general narrow resonances and loosely bound states may be treated as "elementary" particles.
Mechanics of rotating isolated horizons
Physical Review D
64
4
31
2001
10.1103/PhysRevD.64.044016
Black hole mechanics was recently extended by replacing the more commonly used event horizons in stationary space-times with isolated horizons in more general space-times (which may admit radiation arbitrarily close to black holes). However, so far the detailed analysis has been restricted to non-rotating black holes (although it incorporated arbitrary distortion, as well as electromagnetic, Yang-Mills and dilatonic charges). We now fill this gap by first introducing the notion of isolated horizon angular momentum and then extending the first law to the rotating case.
General Relativity and Quantum Cosmology
Statistical mechanics of complex networks
Reviews of modern physics
74
1-54
2002
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network’s robustness against failures and attacks.
New directions in computational mechanics
Nuclear Engineering and Design
114
2
197-210
1989
A few areas of computation mechanics are identified in which considerable progress has occurred and continued extension and refinement are anticipated. In particular, some recent results are presented of calculations performed with general purpose large-scale nonlinear finite element programs. Recent progress in the development of finite element methods for fluids is described. Examples of adaptive refinement and "SUPG" type methods are presented. The ideas emanating from finite elements in fluids are now having some impact on solids and structures. Examples of new element technology for kinematically constrained media and space-time formulations in elastodynamics are presented. © 1989.
Statistical mechanics of complex networks
World Wide Web Internet And Web Information Systems
74
1
78
2007
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Superconformal Black Hole Quantum Mechanics
Journal of High Energy Physics
8
2004
10.1088/1126-6708/2005/11/017
In recent work, the superconformal quantum mechanics describing D0 branes in the AdS2xS^2xCY3 attractor geometry of a Calabi-Yau black hole with D4 brane charges p^A has been constructed and found to contain a large degeneracy of chiral primary bound states. In this paper it is shown that the asymptotic growth of chiral primaries for N D0 branes exactly matches the Bekenstein-Hawking area law for a black hole with D4 brane charge p^A and D0 brane charge N. This large degeneracy arises from D0 branes in lowest Landau levels which tile the CY3xS^2 horizon. It is conjectured that such a multi-D0 brane CFT1 is holographically dual to IIA string theory on AdS2xS^2xCY3.
Damage Mechanics in Engineering Materials
Studies in Applied Mechanics
46
481-500
1998
10.1016/S0922-5382(98)80059-7
The present study concerns finite element predictions of carbon-fiber/epoxy-resin composite coupon delamination tests up to fracture. For these predictions, a previously-defined damage mesomodel of composite laminates is used and implemented in a tridimensional F.E. code. This F.E. software includes the interlaminar interfacial deterioration as well as the main inner layer damage mechanisms. This code is able to predict at any time and at any point the “intensities” of the different damage mechanisms up to fracture. However herein, attention is being focused on the identification and comparison of F.E. predictions with M55J/M18 carbon/epoxy experimental results obtained from the AEROSPATIALE company.
Statistical mechanics of cellular automata
Reviews of Modern Physics
55
3
601-644
1983
10.1103/RevModPhys.55.601
Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of" elementary" cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving ...
Statistical mechanics of complex networks
Rev. Mod. Phys.
74
January
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Statistical mechanics of Lame solitons
Physica Scripta
73
6
545-555
2006
10.1088/0031-8949/73/6/005
We study the exact statistical mechanics of Lame solitons using a\ntransfer matrix method. This requires a knowledge of the first forbidden\nband of the corresponding Schrodinger equation with the periodic\nLame potential. Since the latter is a quasi-exactly solvable system,\nan analytical evaluation of the partition function can be done only\nfor a few temperatures. We also study approximately the finite temperature\nthermodynamics using the ideal kink gas phenomenology. The zero-temperature\n'thermodynamics' of the soliton lattice solutions is also addressed.\nMoreover, in appropriate limits our results reduce to that of the\nsine-Gordon problem.
sine-gordon periodic potentials equation fields mo
Statistical mechanics of complex networks
Reviews of Modern Physics
74
78
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of complex networks
arXiv
cond-mat
54
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
New directions in computational mechanics
Nuclear Engineering and Design
114
2
197-210
1989
http://dx.doi.org/10.1016/0029-5493(89)90191-X
A few areas of computation mechanics are identified in which considerable progress has occurred and continued extension and refinement are anticipated. In particular, some recent results are presented of calculations performed with general purpose large-scale nonlinear finite element programs. Recent progress in the development of finite element methods for fluids is described. Examples of adaptive refinement and “SUPG” type methods are presented. The ideas emanating from finite elements in fluids are now having some impact on solids and structures. Examples of new element technology for kinematically constrained media and space-time formulations in elastodynamics are presented.
Statistical mechanics of complex networks
arXivorg
cond-mat
54
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of steiner trees
Physical Review Letters
101
2008
10.1103/PhysRevLett.101.037208
The minimum weight Steiner tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new optimization algorithm for MST and allows us to analyze the statistical mechanics properties of MST on random graphs of various types.
Statistical Mechanics of Complex Networks
Reviews of Modern Physics
74
47-97
2002
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemicalreactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized thatthe topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recentinterest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network’s robustness against failures and attacks.
Nonlinear Boundaries in Quantum Mechanics
Arxiv preprint arXiv:1106.4510
1-5
2011
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a linear boundary condition, but not both. Further analysis shows that non-linear boundaries for the ring restore gauge invariance but lead unexpectedly to eigenfunctions with a continuous eigenvalue spectrum, a discreet subset of which forms a Hilbert space with energy bands. This Hilbert space maintains the principle of superposition of eigenfunctions despite the nonlinearity. The momentum operator remains Hermitian. If physical reality requires gauge invariance, it would appear that quantum mechanics should incorporate these nonlinear boundary conditions.
Pressure distribution in an elastomer confined by a long thin-walled flexible hollow cylinder under the assumption of a hydrostatic stress state
Mechanics Research Communications
45
77-84
2012
DOI 10.1016/j.mechrescom.2012.04.003
The stress distribution in a pressurized elastomer confined by a hollow cylinder is of interest in various applications of material testing and manufacturing. A relatively accurate closed form solution for the pressure distribution inside an elastomer confined by a rigid hollow cylinder was presented by Yu et al. (2001). But in many practical applications the assumption of a rigid hollow cylinder is not appropriate, because the cylinder deformations have a significant influence on the stresses inside the elastomer. Thus in this paper a solution for an elastomer confined by a deformable hollow cylinder is derived. Both axial and radial deformations of the hollow cylinder are taken into account, while the bending stiffness of the cylinder wall is neglected, i.e. the cylinder wall is treated according to the membrane theory. The accuracy of the proposed closed form solution is verified by a parametric finite element simulation. (C) 2012 Elsevier Ltd. All rights reserved.
axisymmetry; bulk modulus; compressed elastomer method; confined elastomer; flexible hollow cylinder; hydrostatic stress state; pressure distribution; pressure loss; shear lag
A non-linear model for the dynamics of open cross-section thin-walled beams - Part II: Forced motion
International Journal of Non-Linear Mechanics
38
7
1083-1094
2003
10.1016/S0020-7462(02)00054-9
The discrete equations developed in Part I are here used to analyze the non-linear dynamics of an inextensional shear indeformable beam with given end constraints. The model takes into account the non-linear effects of warping and of torsional elongation. Non-linear 3D oscillations of a beam with a cross-section having one symmetry axis is examined. Only terms of higher magnitude are retained in the equations, which exhibit quadratic, cubic and combination resonances. A harmonic load acting in the direction of the symmetry axis and in resonance with the corresponding natural frequency, is considered. Steady-state solutions and their stability are studied; in particular the effects of non-linear warping and of torsional elongation on the response are highlighted. ?? 2002 Elsevier Science Ltd. All rights reserved.
Beams; Flexural-torsional dynamics; Non-linear resonances; Open cross-section; Warping non-linear effects
Comment on "The properties of free polymer surfaces and their influence on the glass transition temperature of thin polystyrene films" by J.S. Sharp, J.H. Teichroeb and J.A. Forrest.
The European physical journal. E, Soft matter
22
4
281-6; discussion 287-91
2007
10.1140/epje/e2007-00030-1
Sharp, Teichroeb and Forrest [J.S. Sharp, J.H. Teichroeb, J.A. Forrest, Eur. Phys. J. E 15, 473 (2004)] recently published a viscoelastic contact mechanics analysis of the embedment of gold nanospheres into a polystyrene (PS) surface. In the present comment, we investigate the viscoelastic response of the surface and conclude that the embedment experiments do not support the hypothesis of a liquid surface layer of sufficiently reduced "rheological temperature" to explain reports of very large reductions in the glass temperature of freely standing ultrathin polystyrene films. We also report some errors and discrepancies in the paper under comment that resulted in an inability to reproduce the reported calculations. We present our findings of error in a spirit of clarifying the problem of embedment of spheres into surfaces and in order that others can understand why they may not reproduce the results reported by Sharp, Teichroeb and Forrest. In the comment, we also examine the effects of the magnitude of the forces that result from the polymer surface-nanosphere particle interactions on the viscoelastic properties deduced from the embedment data and we provide a comparison of apparent surface or "rheological" temperature vs. experimental temperature that indicates further work needs to be performed to fully understand the surface embedment experiments. Finally, we comment that the nanosphere embedment measurements have potential as a powerful tool to determine surface viscoelastic properties.
Elasticity; Glass; Glass: chemistry; Gold; Gold: chemistry; Nanotubes; Polystyrenes; Polystyrenes: chemistry; Rheology; Surface Properties; Time Factors; Transition Temperature; Viscosity
Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries
Journal of Chemical Theory and Computation
10
9
3784-3790
2014
dx.doi.org/10.1021/ct500512f
Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/ MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct “approximately” optimal link orbitals for practical QM/MM calculations
Free vibration of composite plates using the finite difference method
Thin-Walled Structures
42
3
399-414
2004
10.1016/j.tws.2003.07.001
The finite difference method was used to solve differential equations of motion of free vibration of composite plates with different boundary conditions. The effects of shear deformation and rotary inertia on the natural frequencies of laminated composite plates are investigated in this paper. Four cases are studied: neglecting both shear deformation and rotary inertia, considering only rotary inertia, considering only shear deformation, and considering both. Solutions were obtained for symmetric and angle-ply laminated plates. The factors that affect natural frequencies of different composite plates, such as span-to-depth ratio, aspect ratio, angle-ply, and lamination sequence were also investigated. Results were found to agree well with exact and approximate solutions reported in literature. Shear deformation showed a considerable effect on the natural frequencies for composite plates, whereas the rotary inertia effect was found to be negligible. ?? 2003 Elsevier Ltd. All rights reserved.
Composite materials; Free vibration; Laminates; Natural frequency; Plates; Rotary inertia; Shear deformation
Analysis of multi-layered filament-wound composite pipes under internal pressure
Composite Structures
53
4
483-491
2001
10.1016/S0263-8223(01)00061-7
Composite pipes in this study are composed of multi-layered filament-wound (FW) structures. Each layer of the pipes is assumed to be anisotropy. Based on the three-dimensional (3-D) anisotropic elasticity, an exact elastic solution for stresses and deformations of the pipes under internal pressure is presented. Moreover, detailed stress and strain distributions for three given angle-ply pipe designs are investigated by using the present theory. The shear extension coupling is also considered because the lay-up angles with +ø and -ø layers cannot exist in the same radius. For cylindrical-pressure vessels with different angle-ply pipe, the ratio of applied hoop-to-axial stress in each layer is different. Even if quite a thin-walled pipe, the ratio of hoop-to-axial stress is no longer a constant of 2:1. © 2001 Published by Elsevier Science Ltd.
Anisotropic analysis; Elasticity solution; Internal pressure; Laminated composite cylindrical pipe
Characterisation of mechanical behaviour and damage analysis of 2D woven composites under bending
Composites Part B: Engineering
75
156-166
2015
10.1016/j.compositesb.2015.01.036
In this paper, flexural loading of woven carbon fabric-reinforced polymer laminates is studied using a combination of experimental material characterisation, microscopic damage analysis and numerical simulations. Mechanical behaviour of these materials was quantified by carrying out tensile and large-deflection bending tests. A substantial difference was found between the materials' tensile and flexural properties due to a size effect and stress stiffening of thin laminates. A digital image-correlation technique capable of full-field strain-measurement was used to determine in-plane shear properties of the studied materials. Optical microscopy and micro-computed tomography were employed to investigate deformation and damage mechanisms in the specimens fractured in bending. Various damage modes such as matrix cracking, delaminations, tow debonding and fibre fracture were observed in these microstructural studies. A two-dimensional finite-element (FE) model was developed to analyse the onset and propagation of inter-ply delamination and intra-ply fabric fracture as well as their coupling in the fractured specimen. The developed FE model provided a correct prediction of the material's flexural response and successfully simulated the sequence and interaction of damage modes observed experimentally.
Active control of a piezo-composite rotating beam using coupled plant dynamics
Journal of Sound and Vibration
329
14
2716-2737
2010
10.1016/j.jsv.2010.01.023
Optimal control of a thin-walled rotating beam is considered using a higher-order shear deformation theory (HSDT). The beam is pretwisted, doubly tapered, and carries a tip rotor. It comprises an orthotropic host with surface-embedded transversely isotropic piezoelectric sensor-actuator pairs. Spanwise and thicknesswise variation of the electric field applied to actuators is considered. This yields a coupled electro-mechanical system, wherein all displacement variables are coupled via the electric field. Hence, coupling between bending-transverse shear and extension-twist occurs even when the ply angle configuration has circumferentially uniform stiffness. Optimal LQR control with state feedback is used to obtain the control input, i.e., charge density (hence voltage) applied to actuators. Parametric studies involving ply-angle, rotation speeds of beam and rotor, pretwist, taper, rotor mass, and saturation constraint on actuator voltage, are performed. The HSDT yields lowest coupled natural frequencies (as compared to unshearable and first-order shear models) thus providing conservative data, useful for passive and active control designs. The present plant model, with spanwise varying electric field, yields an order-of-magnitude reduction in settling time and control voltage, and lower response, vis-a-vis the decoupled approach.
Static analysis of thick laminated shells with different boundary conditions using GDQ
Thin-Walled Structures
51
76-81
2012
10.1016/j.tws.2011.11.004
Equilibrium equations and the associated boundary conditions for doubly curved, relatively deep and thick composite shells are shown. Two First Order Shear Deformation theories (FSDTs) are used. The first one uses plate stiffness parameters for thick shells and the other includes the effect of curvature in the calculation of stiffness parameters. Equilibrium equations are put together with the equations of stress resultants to arrive at a system of seventeen first order differential equations. These equations are solved numerically with the aid of General Differential Quadrature (GDQ) method for isotropic, cross-ply, angle-ply and general lay-up cylindrical shells with six types of different boundary conditions using above mentioned theories. Results obtained using both theories are compared with the available results in literature and those obtained using a three-dimensional (3D) analysis to test the accuracy of the shell theories presented here.
Response and failure of square laminates under combined loads
Composite Structures
55
337-345
2002
10.1016/S0263-8223(01)00141-6
A non-linear finite-element method (FEM) which is based on the von Karman's assumptions, the Mindlin's plate theory and the principle of minimum total potential energy is used to study the first-play failure of thin laminated composite plates under combined loading i.e. transverse load with uni-axial compression and transverse load with in-plane shear. The mode of failure, the first failed layer number, the first failed node number and the associated maximum transverse deflection are found at different values of load combinations. Failure envelopes in the form of interaction curves are obtained for five types of laminate using the Tsai-Hill failure criterion and for (??45/0/90)2s laminate using the other failure criteria as well. ?? 2002 Elsevier Science Ltd. All rights reserved.
Combined loading; Failure envelop; First-ply failure; Mode of failure
Energy absorption and bending stiffness in CFRP laminates: The effect of 45?? plies
Thin-Walled Structures
46
7-9
860-869
2008
10.1016/j.tws.2008.01.024
The impact characteristics of cross-ply and angle-ply composite laminates were investigated, with an instrumented impact drop tester by performing gravity-assisted drop tests on [0/90]6s and [0/45/90]4s laminates. The impact energy was kept constant at 12 J for all the tests. From the dynamic responses presented here as force history, energy history and force-displacement plots, relevant characteristics such as contact time, delamination load, absorbed energy, bending stiffness, after impact deflection, etc. were obtained. The plots were non-smooth, disclosing the salient features of the composites. It was important to note that the [0/45/90]4s was more resistant to impact bending, but incurred more damage as exhibited by its higher contact time and absorbed energy. The laminates were sectioned through the impact point and magnified macro- and micro-photographs were taken to show the failure modes, which include delamination, matrix cracking, etc. ?? 2008 Elsevier Ltd. All rights reserved.
Absorbed energy; Bending stiffness; Composite laminates and impact damage; Dynamic loading
Nonlinear vibration of hybrid laminated plates resting on elastic foundations in thermal environments
APPLIED MATHEMATICAL MODELLING
1-16
2012
10.1016/j.apm.2012.02.001
This paper deals with large amplitude vibration of hybrid laminated plates containing piezoelectric layers resting on an elastic foundation in thermal environments. The motion equation of the plate that includes plate-foundation interaction is based on a higher order shear deformation plate theory and solved by a two-step perturbation technique. The thermo-piezoelectric effects are also included and the material properties of both orthotropic layers and piezoelectric layers are assumed to be temperature-dependent. The numerical illustrations concern nonlinear vibration characteristics of unsymmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electrical loading conditions. The results show that the foundation stiffness and stacking sequence have a significant effect on the nonlinear vibration characteristics of the hybrid laminated plate. The results also reveal that the temperature rise reduces the natural frequency, but it only has a small effect on the nonlinear to linear frequency ratios of the hybrid laminated plate. The results confirm that the effect of the applied voltage on the natural frequency and the nonlinear to linear frequency ratios of the hybrid laminated plate is marginal except the plate is sufficiently thin.
elastic foundation; Nonlinear Vibration; perturbation technique; temperature-dependent properties; thermo-piezoelectric effect
Postbuckling response and strength of laminates under combined in-plane loads
Composites Science and Technology
59
5
727-736
1999
http://dx.doi.org/10.1016/S0266-3538(98)00125-0
The objective of this work is to study the postbuckling behaviour and progressive failure response of thin, symmetric laminates under uniaxial compression and uniaxial compression combined with in-plane shear loads (positive and negative). First-order shear deformation theory and geometric non-linearity in the von Karman sense are used with a finite-element procedure. The 3-D Tsai-Hill criterion is used to predict failure of a lamina and the maximum stress criterion is used to predict onset of delamination at the interface of two adjacent layers. The effect of plate aspect ratio and ply lay-ups on the load deflection response is presented. Load interaction diagrams for (±45/0/90)2s, (±45)4s and (0/90)4s laminates are obtained in terms of the buckling, the first-ply and the ultimate failure loads. In addition, progressive failure response of the (±45/0/90)2s laminate is also presented to show the buckling loads, failure loads, maximum transverse displacements associated with the failure loads and failure modes and locations at various load ratios.
B. Strength; C. Buckling; C. Failure criterion; C. Finite-element analysis; C. Laminate
A closed-form solution for the internal stresses in thick composite cylinders induced by cyclical environmental conditions
Composite Structures
58
1
1-9
2002
10.1016/S0263-8223(02)00051-X
The paper presents a new semi-analytical model to assess the internal stress field in cylindrical pipes due to cyclical temperature and humidity conditions. The solution applies to both thin or thick laminated pipes composed of orthotropic plies following Fick's diffusion laws. The only restriction put on those diffusion laws is that the Arrh??nius activation energy should be ply independent. Firstly, the resulting time and space dependent moisture concentration field within the interior of the pipe wall is calculated. It is the sum of the permanent solution, due to the mean relative humidity conditions imposed on the two lateral surfaces of the pipe, and a cyclical vanishing solution. Secondly, the mechanical problem is solved leading to the full stress field solution over the pipe interior and close to the lateral surfaces. The final solution can be implemented in a friendly-user software to assess the combined effects of the pipe thickness, ply stacking sequence and transient service conditions over the internal stress field. ?? 2002 Elsevier Science Ltd. All rights reserved.
Cyclical temperature and humidity conditions; Hygrothermal stresses; Moisture concentration; Thick composite pipes
Advances in the Ritz formulation for free vibration response of doubly-curved anisotropic laminated composite shallow and deep shells
Composite Structures
101
111-128
2013
10.1016/j.compstruct.2013.01.018
The hierarchical trigonometric Ritz formulation (HTRF) developed in the framework of the Carrera unified formulation (CUF), for the first time, is extended to shell structures in order to cope with the free vibration response of doubly-curved anisotropic laminated composite shells. The HTRF is the outcome of the combination of advanced shell theories hierarchically generated via the CUF with the trigonometric Ritz method. It is based on so-called Ritz fundamental primary nuclei obtained by virtue of the principle of virtual displacements (PVD). The PVD is further used to derive the governing differential equations and natural boundary conditions. Donnell–Mushtari’s shallow shell-type equations are given as a particular condition. Several shell geometries accounting for thin and thick shallow cylindrical and spherical shells, deep cylindrical shells and hollow circular cylindrical shells, with cross-ply and angle-ply staking sequences are investigated. CUF-based refined shell models are assessed by comparison with the 3D elasticity solution. Convergence and accuracy of the presented formulation are examined. The effects of significant parameters such as stacking sequence, length-to-thickness ratio and radius-to-length ratio on the circular frequency parameters are discussed.
Advanced hierarchical shell theories; Doubly-curved anisotropic laminated shells; Free vibration; Ritz method
Design and optimization of laminated conical shells for buckling
Thin-Walled Structures
43
1
107-133
2005
10.1016/j.tws.2004.07.003
Optimum laminate configuration for the maximum buckling load of filament-wound laminated conical shells is investigated. In the case of a laminated conical shell, the thickness and the ply orientation (the design variables) are functions of the shell coordinates, influencing both the buckling load and the weight of the structure. Thus, optimization can be performed by maximization of the buckling load for a specific weight, or by minimization of the weight of the structure under the constraint of applied buckling load. Due to the complex nature of the problem a preliminary investigation is made into the characteristic behavior of the buckling load with respect to the volume as a function of the ply orientation. The exact buckling load is calculated by means of the computer code STAGS-A (Structural Analysis of General Shells [Almroth BO, Brogan FA, Meller E, Zele F, Petersen HT. Collapse analysis for shells of general shape, user's manual for STAGS-A computer code. Technical report AFFDL TR-71-8; 1973]) by adding a user written subroutine WALL, see Ref. [Goldfeld Y, Arbocz J. Buckling of laminated conical shells taking into account the variations of the stiffness coefficients. AIAA J 2004; 42(3):642–649]. The optimization problem is solved using response surface methodology.
Enhanced two-level optimization of anisotropic laminated composite plates with strength and buckling constraints
Thin-Walled Structures
47
11
1161-1167
2009
10.1016/j.tws.2009.04.008
In laminated composite design, ply orientations are often restricted to 0deg, 90deg, pm45deg. However, studies have shown that an expanded set of ply orientations may lead to more efficient structures for specific problems. In particular, 60deg plies are optimum for shear in buckling for long anisotropic composite laminated plates. A two-level optimization approach, using 0deg, 90deg, pm45deg, pm30deg, pm60deg plies, is presented. At the first level, lamination parameters and plate thicknesses are used to minimize the mass of the composite plate subject to strength and buckling constraints. At the second level, a new modified particle swarm is used to determine laminate stacking sequences. It is shown that mass savings of up to 7.2percent can be achieved and that the modified particle swarm outperforms the standard particle swarm in terms of quality of design and efficiency.
Lamination parameters; Lay-up optimization; Particle swarm
Analytical solutions for vibrations of laminated and sandwich plates using mixed theory
Composite Structures
63
3-4
361-373
2004
10.1016/S0263-8223(03)00185-5
A semi-analytical method has been presented in this paper to evaluate the natural frequencies as well as displacement and stress eigenvectors for simply supported, cross-ply laminated and sandwich plates by using higher order mixed theory. Models based on equivalent single layer as well as layerwise (LW) theories have been formulated. By assuming a non-linear variation of axial displacements through the plate thickness, the warping of the transverse cross-section has been considered. Hamilton’s principle has been employed to derive the equilibrium equations. The proposed LW model fulfills a priori the continuity of displacements as well as the transverse and the normal stress components at each interface between two adjacent layers. Results obtained by present higher order mixed theory have been found in good agreement with those obtained by three-dimensional elasticity solutions. After establishing the accuracy of present results for orthotropic plates, new results for thin and thick sandwich plates have been presented which can serve as benchmark solutions for future investigations.
Analytical solutions; Cross-ply laminates; Free vibrations; Mixed theory
Relations between Newtonian mechanics, general relativity, and quantum mechanics
American Journal of Physics
70
8
798
2002
10.1119/1.1479740
When Euclidean coordinate lengths are replaced by the metric lengths of a curved geometry within Newton’s second law of motion, the metric form of the second law can be shown to be identical to the geodesic equation of motion of general relativity. The metric coefficients are contained in the metric lengths and satisfy the field equations of general relativity. Because metric lengths are the physically measured lengths, their use makes it possible to understand general relativity directly in terms of physical quantities such as energy and momentum within a curved space–time. The metric form of the second law contains gravitational effects in exactly the same manner as occurs in relativity. Its mathematical derivation uses vectors rather than tensors, and nongravitational forces can occur in this modified second law without a tensor form. Because quantum mechanics is based on Newtonian concepts of energy and momentum, it is shown that when metric lengths replace coordinate lengths in Dirac’s wave equation, it has a covariant form under a metric transformation of the physically measured distances themselves, rather than a coordinate transformation. Metric transformations are also used to describe the Dirac equation for the gravitational central field in a Schwarzschild metric.
Mechanical Properties of Two Plain-Woven Chemical Vapor Infiltrated Silicon Carbide-Matrix Composites
Journal of the American Ceramic Society
84
5
1043-1051
2001
10.1111/j.1151-2916.2001.tb00788.x
The elastic and inelastic properties of a chemical vapor infiltrated (CVI) SiC matrix reinforced with either plain-woven carbon fibers (C/SiC) or SIC fibers (SiC/SiC) have been investigated, It has been investigated whether the mechanics of a plain weave can be described using the theory of a cross-ply laminate, because it enables a simple mechanics approach to the nonlinear mechanical behavior. The influences of interphase, fiber anisotropy, and porosity are included. The approach results in a reduction of the composite system to a fiber/matrix system with an interface. The tensile behavior is described by five damage stages. C/SiC can be modeled using one damage stage and a constant damage parameter. The tensile behavior of SiC/SiC undergoes four damage stages, Stiffness reduction due to transverse cracks in the transverse bundles is very different from cross-ply behavior. Compressive failure is initiated by interlaminar cracks between the fiber bundles. The crack path is dictated by the bundle waviness. For SiC/SiC, the compressive behavior is mostly linear to failure. C/SiC exhibits initial nonlinear behavior because of residual crack openings, Above the point where the cracks close, the compressive behavior is linear. Global compressive failure is characterized by a major crack oriented at a certain angle to the axial loading. In shear, the matrix cracks orientate in the principal tensile stress direction (i,e., 45 degrees to the fiber direction) with very high crack densities before failure, but only SiC/SiC shows significant degradation in shear modulus, Hysteresis is observed during unloading/reloading sequences and increasing permanent strain.
Finite element modelling of the progressive crushing of braided composite tubes under axial impact
International Journal of Impact Engineering
37
6
662-672
2010
10.1016/j.ijimpeng.2009.09.005
Composite tubular structures are of interest as viable energy absorbing components in vehicular front rail structures to improve crashworthiness. Desirable tools in designing such structures are models capable of simulating damage growth in composite materials. Our model (CODAM for COmposite DAMage), which is a continuum damage mechanics based model for composite materials with physically based inputs, has shown promise in predicting damage evolution and failure in composites. In this study, the model is used to simulate the damage propagation, failure morphology and energy absorption in triaxially braided composite tubes under axial compression. The model parameters are based on results from standard and specialized material testing and a crack band scaling law is used to minimize mesh sensitivity (or lack of objectivity) of the numerical results. Axial crushing of two-ply and four-ply square tubes with and without the presence of an external plug initiator are simulated in LS-DYNA. Refinements over previous attempts by the authors include the addition of a pre-defined debris wedge, a distinguishing feature in tubes displaying a splaying mode of failure, and representation of delamination using a tiebreak contact interface that allows energy absorption through the un-tying process. It is shown that the model adequately predicts the failure characteristics and energy absorption of the crushing events. Using numerical simulations, the process of damage progression is investigated in detail and energy absorptions in different damage mechanisms are presented quantitatively. ?? 2009 Elsevier Ltd. All rights reserved.
Braided; composite tubes; Damage mechanics; Energy absorption; Numerical simulation; Progressive crushing
The large deviation approach to statistical mechanics
Phys. Rep.
478
1
2009
10.1016/j.physrep.2009.05.002
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein?s theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
The large deviation approach to statistical mechanics.
Physics Reports
478
1
1-69
2009
10.1016/j.physrep.2009.05.002
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein’s theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
02.50.-r; 05.20.-y; 05.40.-a; 65.40.Gr
The large deviation approach to statistical mechanics
arXiv
cond-mat.s
2008
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
Structure and mechanics of healing myocardial infarcts.
Annual review of biomedical engineering
7
223-253
2005
10.1146/annurev.bioeng.7.060804.100453
Therapies for myocardial infarction have historically been developed by trial and error, rather than from an understanding of the structure and function of the healing infarct. With exciting new bioengineering therapies for myocardial infarction on the horizon, we have reviewed the time course of structural and mechanical changes in the healing infarct in an attempt to identify key structural determinants of mechanics at several stages of healing. Based on temporal correlation, we hypothesize that normal passive material properties dominate the mechanics during acute ischemia, edema during the subsequent necrotic phase, large collagen fiber structure during the fibrotic phase, and cross-linking of collagen during the long-term remodeling phase. We hope these hypotheses will stimulate further research on infarct mechanics, particularly studies that integrate material testing, in vivo mechanics, and quantitative structural analysis.
abstract therapies for myocardial; and function of the; by trial and error; collagen; constitutive properties; cross-linking; deformation; developed; edema; infarction have historically been; necrosis; rather than from an; scar; strain; stress; understanding of the structure; ventricular function
Finite element approximation of field dislocation mechanics
Journal of the Mechanics and Physics of Solids
53
1
143-170
2005
10.1016/j.jmps.2004.05.007
A tool for studying links between continuum plasticity and dislocation theory within a field framework is presented. A finite element implementation of the geometrically linear version of a recently proposed theory of field dislocation mechanics (J. Mech. Phys. Solids 49 (2001) 761; Proc. Roy. Soc. 459 (2003) 1343; J. Mech. Phys. Solids 52 (2004) 301) represents the main idea behind the tool. The constitutive ingredients of the theory under consideration are simply elasticity and a specification of dislocation velocity and nucleation. The set of equations to be approximated are non-standard in the context of solid mechanics applications. It comprises the standard second-order equilibrium equations, a first-order div-curl system for the elastic incompatibility, and a first-order, wave-propagative system for the evolution of dislocation density. The latter two sets of equations require special treatment as the standard Galerkin method is not adequate, and are solved utilizing a least-squares finite element strategy. The implementation is validated against analytical results of the classical elastic theory of dislocations and analytical results of the theory itself. Elastic stress fields of dislocation distributions in generally anisotropic media of finite extent, deviation from elastic response, yield-drop, and back-stress are shown to be natural consequences of the model. The development of inhomogeneity, from homogeneous initial conditions and boundary conditions corresponding to homogeneous deformation in conventional plasticity, is also demonstrated. To our knowledge, this work represents the first computational implementation of a theory of dislocation mechanics where no analytical results, singular solutions in particular, are required to formulate the implementation. In particular, a part of the work is the first finite element implementation of Kr??ner's linear elastic theory of continuously distributed dislocations in its full generality. ?? 2004 Elsevier Ltd. All rights reserved.
Dislocation mechanics; Finite elements; Internal stress; Plasticity
Nonextensive statistical mechanics: A brief introduction
Continuum Mechanics and Thermodynamics
16
3
223-235
2004
10.1007/s00161-004-0174-4
Boltzmann-Gibbs statistical mechanics is based on the entropy $S_{BG}=-k \sum_{i=1}^W p_i \ln p_i$. It enables a successful thermal approach of ubiquitous systems, such as those involving short-range interactions, markovian processes, and, generally speaking, those systems whose dynamical occupancy of phase space tends to be ergodic. For systems whose microscopic dynamics is more complex, it is natural to expect that the dynamical occupancy of phase space will have a less trivial structure, for example a (multi)fractal or hierarchical geometry. The question naturally arises whether it is possible to study such systems with concepts and methods similar to those of standard statistical mechanics. The answer appears to be {\it yes} for ubiquitous systems, but the concept of entropy needs to be adequately generalized. Some classes of such systems can be satisfactorily approached with the entropy $S_q=k\frac{1-\sum_{i=1}^W p_i^q}{q-1}$ (with $q \in \cal R$, and $S_1 =S_{BG}$). This theory is sometimes referred in the literature as {\it nonextensive statistical mechanics}. We provide here a brief introduction to the formalism, its dynamical foundations, and some illustrative applications. In addition to these, we illustrate with a few examples the concept of {\it stability} (or {\it experimental robustness}) introduced by B. Lesche in 1982 and recently revisited by S. Abe.
Entropy stability; Metastability; Nonextensive entropy; Nonextensive statistical mechanics; Nonlinear dynamics
Fracture mechanics of flanged reinforced concrete sections
Engineering Structures
29
9
2334-2343
2007
10.1016/j.engstruct.2006.11.020
This work reports on the application of fracture mechanics to study the flexural behavior of T-section reinforced concrete beams. Twelve beam specimens; nine flanged and three rectangular, were tested experimentally in a four point bending test in a displacement controlled environment. Three main parameters were considered: the ratio of the flange width to web thickness (Blb), the ratio of slab thickness to total height (t(s), h), and the ratio of the tension reinforcement steel. The beam's size was 70 x 300 x 1400 mm, the reinforcing steel's tension ratios varied between 0.48%, 0.61% and 0.73%, the values of (Blb) varied between 1, 1.5, 2, 2.5 while the values of (t(s)/h) varied between 0, 0.1, 0.15, 0.2. All the beams have a constant span/depth ratio of 4, and initial notch/depth ratio of 0.3. The concrete used had cube strength of 25 MPa at the time of testing while the reinforcing steel has a nominal yield strength of 530 MPa. Measurements included load, steel strain, concrete strain and deflection. The Fracture Mechanics algorithm proposed by Baluch was employed to analytically investigate the fracture behavior of the T-shaped reinforced concrete beams. The results obtained from the Fracture Mechanics approach were checked against the experimental results. Moreover, a finite element analysis was carried out for the same purpose. The results of both the Fracture Mechanics approach and the finite element analysis were found to be in good agreement with the experimental results. Yet, both approaches underestimate the maximum capacity of the beam. (c) 2007 Elsevier Ltd. All rights reserved.
flanged section; flexure design; fracture mechanics; reinforced concrete
Mechanics of advanced materials for lightweight structures
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
225
11
2481-2496
2011
10.1177/0954406211417068
In recent years, there have been a lot of new developments concerning the use of advanced materials for lightweight structures. Examples are long- and short-fibre-reinforced composites, sandwiches, foams, and, last but not least, nanostructures. The analysis of structures made of these materials can be performed on the basis of the Mechanics of Composites. However, stimulated by new applications, new manufacturing technologies, new material compositions, etc. a review of the Mechanics of Composites is necessary. In this article, some of the actual trends are discussed, for example developments in the application of long- and short-fibre-reinforced composites, laminates affected by multifield loadings, effective property-based analysis of foams, and the description of nanostructures within the concepts of Continuum Mechanics. The starting point of the review are the Engineering Mechanics basics on the level of the BSc program, that means the classical Strength of Materials. Extensions of Materials Strength foundations (for example, inclusion of anisotropy) are often sufficient as first improved estimates. If it is necessary, elements of Continuum Mechanics, of Material Testing or Numerical Solution Techniques can be implied. The every year increasing number of publications in the field of advanced materials for lightweight structures does not allow to give a complete overview over the state of the art. Recognizing this fact, the author will give a report only of directions related to his own research group and/or in the surrounding of his team. © Authors 2011.
Foam structures; Functionally graded structures; Laminates; Nanostructures; Sandwiches
Surface-Launched Acoustic Wave Sensors: Chemical Sensing and Thin-Film Characterization
Surface-Launched Acoustic Wave Sensors: Chemical Sensing and Thin-Film Characterization
60-63
1997
With respect to chemical applications, surface-launched acoustic wave sensors were originally developed as sensing devices for specific chemical and biological species, but more recently have been applied to the study of thin film and interfacial properties. These devices exploit the phenomenon of piezoelectricity, the instigation of mechanical motion in solids by oscillating electrical fields. This book presents the principles of design and operation of these sensors and explores their traditional and emerging applications with a focus on devices that employ acoustic waves launched and received on the same surface. Surface-Launched Acoustic Wave Sensors begins with a review of piezoelectricity and the genesis of acoustic wave devices, and the advent of chemical sensor technology. Subsequent chapters explore acoustic waves in solids and device structure, theory of acoustic wave response, and the various categories of acoustic wave device. The book describes the design of these devices and how they are applied in chemistry for the detection of species present in the gas and liquid phase, as well as the study of thin films placed on the sensor surface. Other topics covered include polymeric glass transitions, polymer properties, biosensor technology, and the development of sensor arrays. Each of the various types of device is examined with a view toward its application in chemistry in general and analytical chemistry in particular. Presenting the most up-to-date information available on this rapidly evolving technology, and supplemented with scores of helpful illustrations and tables, Surface-Launched Acoustic Wave Sensors draws information from such diverse areas of scientific investigation as acoustic wave physics, applied mathematics, chemistry, electronics, fluid mechanics, materials science, piezoelectricity, and polymer science. The material presented on these topics is both self-consistent and readable for the nonexpertallowing industrial chemists, graduate students, and undergraduates to gain a deeper understanding of these devices, their designs, and applications. This book concerns the design, operation, and application of devices capable of generating acoustic waves in the ultrasonic frequency range. The clear emphasis of the text is the study of chemical and/or biochemical systems imposed on the surface of such devices, whether operated in the gas or liquid phase, i.e., on acoustic wave chemical and biological sensors. Presenting the most up-to-date information available on this rapidly evolving technology, and supplemented with scores of helpful illustrations and tables, Surface-Launched Acoustic Wave Sensors: Reviews piezoelectricity and the genesis of acoustic wave devices as well as the advent of chemical sensor technology Explores acoustic waves in solids and device structure, theory of acoustic wave response, and the various categories of acoustic wave device Describes device design and how these devices are applied in chemistry to detect species present in the gas and liquid phase, as well as to study thin films placed on the sensor surface Covers polymeric glass transitions, polymer properties, biosensor technology, and the development of sensor arrays
Feature: Thin clients: slim security?
Network Security
2010
4
2010
10.1016/S1353-4858(10)70048-9
Thin computing has been around since early 1993, starting life as graphical workstations and X terminals. The devices have evolved, along with advancements in modern computing technologies, to become more complex, hybrid embedded devices and appliances
Nanocrystalline silicon thin film transistors
IEE Proceedings -- Circuits, Devices & Systems
150
339
2003
10.1049/ip-cds:20030573
Presents a discussion on nanocrystalline silicon thin film transistors (TFT). Fabrication issues for TFTs on plastic substrates; Characteristics of TFT; Description about nanocrystalline silicon film deposition.
CRYSTALLINE polymers; SILICON; THIN film transistors
Thin-layer chromatography of the phosphoinositides.
Journal of lipid research
9
4
532-3
1968
Thin-layer chromatography for the separation of mono-, di-, and triphosphoinositides (0.3-3 micro g total phosphorus) is described.
Animals; Brain Chemistry; Calcium; Cattle; Chromatography; Methods; Oxalates; Phosphatidylinositols; Phosphatidylinositols: analysis; Thin Layer
Mechanical properties of thin films
Metallurgical and Materials Transactions A
1989
Abstract The mechanical properties of thin films on substrates are described and studied. It is shown that very large stresses may be present in the thin films that comprise integrated circuits and magnetic disks and that these stresses can cause deformation and fracture to ...
Statistical mechanics of complex networks
Reviews of Modern Physics
74
January
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Mechanics of Masonry in Compression
Journal of Structural Engineering
111
4
857-870
1985
10.1061/(ASCE)0733-9445(1985)111:4(857)
Strength and deformation of clay-unit masonry under uniaxial con- centric compressive force were investigated. Biaxial tension-compression tests of bricks and triaxial compression tests of mortar were done to establish con- stitutive relations for each material. Mortar strengths and brick types were var- ied. Interaction effects of these two materials were examined using a theory proposed by others. A numerical model based on this theory was used to com- pute the force-deformation relationship for a stack-bond prism. Results of the analysis were compared with measured strengths and deformations of test prisms. Results of the study indicated that mechanics of clay-unit masonry in compression could be well represented with a relatively simple model, and the most significant parameter to consider was the dilatant behavior of the mortar.
Structural mechanics of bent DNA
Endeavour
20
2
61-67
1996
10.1016/0160-9327(96)10016-8
The DNA molecule is a familiar object. It is often depicted in magazines and advertisements as a double helix, with the letters of the genetic code strung along the two spiral backbones and joined together in pairs. In such pictures the molecule is usually shown as straight; yet in the chromosomes of living organisms, DNA is curved and wound up into condensed packages. This article explains what is involved in such bending of DNA in the cell. It uses the ideas of structural mechanics - a tool of engineers - to show how the various components fit together when the molecule is bent.
Mathematical Methods of Classical Mechanics
Book
60
xvi+508
1989
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Statistical mechanics of complex networks
Rev. Mod. Phys.
74
1
47
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell; a network of chemicals linked by chemical reactions; and the Internet; a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs; it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks; focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks; the authors discuss the main models and analytical tools; covering random graphs; small-world and scale-free networks; the emerging theory of evolving networks; and the interplay between topology and the network’s robustness against failures and attacks.
Tunneling in Fractional Quantum Mechanics
Delta
17
2010
We study the tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schr\"odinger equation for these potentials, we calculate the corresponding reflection and transmission coefficients. These coefficients have a very interesting behaviour. In particular, we can have zero energy tunneling when the order of the Riesz fractional derivative is different from 2. For both potentials, the zero energy limit of the transmission coefficient is given by $\mathcal{T}_0 = \cos^2{\pi/\alpha}$, where $\alpha$ is the order of the derivative ($1 < \alpha \leq 2$).
High Energy Physics - Theory; Mathematical Physics; Quantum Physics
Statistical mechanics of complex networks
Rev.Mod.Phys.
74
47-97
2001
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the eld of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
model; network; network fragility; networks; topology
Quantum mechanics and the equivalence principle
Classical and Quantum Gravity
21
11
2761-2772
2004
10.1088/0264-9381/21/11/017
A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurement is made far from the turning point of the classical trajectory. The results are then confirmed using the so-called dwell time definition of quantum tunnelling. I conclude with some remarks about the strong equivalence principle in quantum mechanics.
Statistical mechanics of complex networks
arXiv:cond-math
54
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
47-97
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Von Bekesy and cochlear mechanics
Hear Res
293
31-43
2012
10.1016/j.heares.2012.04.017
Georg Bekesy laid the foundation for cochlear mechanics, foremost by demonstrating the traveling wave that is the substrate for mammalian cochlear mechanical processing. He made mechanical measurements and physical models in order to understand that fundamental cochlear response. In this tribute to Bekesy we make a bridge between modern traveling wave observations and those of Bekesy, discuss the mechanical properties and measurements that he considered to be so important, and touch on the range of computational traveling wave models.
20th Century; 21st Century; Acoustic Stimulation; Anatomic; Animals; *Audiology/history; Biological; Cellular; Cochlea/anatomy & histology/*physiology; Computer Simulation; *Hearing; History; Humans; *Mechanotransduction; Models; Motion; Time Factors; Vibration
Statistical mechanics of tethered surfaces
Physical Review Letters
57
7
791-794
1986
10.1103/PhysRevLett.57.791
We study the statistical mechanics of two-dimensional surfaces of fixed connectivity embedded in d dimensions, as exemplified by hard spheres tethered together by strings into a triangular net. Without self-avoidance, entropy generates elastic interactions at large distances, and the radius of gyration RG increases as (lnL)1/2, where L is the linear size of the uncrumpled surface. With self-avoidance RG grows as Lν, with ν=4/(d+2) as obtained from a Flory theory and in good agreement with our Monte Carlo results for d=3.
Quantum mechanics: A new chapter?
arXiv:1209.1029
2012
We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Gr\"ossing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely due to the quantized interactions leading to a discrete set of transferred momenta. A separate experimental confirmation of this interpretation for double-slit interferometry of photons has been given by the group of Steinberg.
Higher-order supersymmetric quantum mechanics
AIP Conference Proceedings
236-273
2004
10.1063/1.1853203
We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order SUSY transformations are used to derive in a simple way the higher-order case. The second order technique is addressed directly, and through this approach unexpected possibilities for designing spectra are uncovered. The formalism is applied to the harmonic oscillator: the corresponding H-SUSY partner Hamiltonians are ruled by polynomial Heisenberg algebras which allow a straight construction of the coherent states.
High Energy Physics - Theory; Mathematical Physics; Quantum Physics
Statistical mechanics of complex networks
World Wide Web Internet And Web Information Systems
74
January
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
{Coexistent effects in quantum mechanics}
International Journal of Theoretical Physics
2
2
147-155
1969
10.1007/BF00669562
{Effects are defined in this paper as observable changes in the state of a macrosystem, which are caused by interaction with a microsystem. These effects are the starting point of Ludwig's axiomatic foundation of quantum theory. In this theory the concept of commensurability is developed by considering effects which can be caused together, by one single microsystem. Such effects are called coexistent. It is shown that in ordinary quantum mechanics the formal definition of coexistence and the corresponding postulates given by Ludwig are consistent with the dynamics of interaction processes leading to effects.}
Mechanics and thermodynamics of propulsion
Journal of the Franklin Institute
280
5
454-455
1965
10.1016/0016-0032(65)90539-9
The present volume proceeds under the principle that a few fundamental physical principles can with suitable application furnish students of mechanical and aeronautical engineering with an understanding of all aspects of aircraft and spacecraft propulsion. This methodology can further yield usefully quantitative assessments of performance, and indicate prospects for further improvement. Attention is given to the jet propulsion principle, the mechanics and thermodynamics of fluid flow, the thermodynamics of aircraft gas turbine engines, axial compressors and turbines, centrifugal compressors, chemical propellant rocket engine operation and performance, turbomachinery for liquid propellant rockets, and electrical rocket propulsion.
Boltzmann's approach to statistical mechanics
Chance in Physics: Foundations and Perspectives
2001
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identification of the state of a physical system with a probability distribution on its phase space, of its thermodynamic entropy with the Gibbs entropy of , and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics – are thoroughly misguided.
Mechanics and imaging of the macrocirculation
Magnetic Resonance in Medicine
14
2
179-186
1990
10.1002/mrm.1910140204
Abstract 10.1002/mrm.1910140204.abs The mechanics of the macrocirculation are examined as a basis for imaging blood flow within the system. The macrocirculation is denned as that part of the circulation in which inertial forces are not negligible compared to viscous forces and as such in human subjects comprises the heart and large blood vessels. Because the flow in the system is so complicated, understanding is built up piecemeal by considering various relatively well-characterized flows which can be seen as approximations to the actual flow. © 1990 Academic Press, Inc.
Statistical mechanics of complex networks
Rev.Mod.Phys.
74
47-97
2001
Complex networks describe a wide range of systems in nature and society, much quoted examplesincluding the cell, a network of chemicals linked by chemical reactions, or the Internet, a networkof routers and computers connected by physical links. While traditionally these systems weremodeled as random graphs, it is increasingly recognized that the topology and evolution of realnetworks is governed by robust organizing principles. Here we review the recent advances in theeld of complex networks, focusing on the statistical mechanics of network topology and dynamics.After reviewing the empirical data that motivated the recent interest in networks, we discuss themain models and analytical tools, covering random graphs, small-world and scale-free networks, aswell as the interplay between topology and the network's robustness against failures and attacks.
curso; dynamics; evolution; model; network; network fragility; networks; review; topology
Research directions in computational mechanics
Computer Methods in Applied Mechanics and Engineering
192
7-8
913-922
2003
10.1016/S0045-7825(02)00616-3
This article is derived from a report prepared by the US National\nCommittee on Theoretical and Applied previous termMechanics.next\nterm It is part of that committee's agenda to develop position papers\non previous termresearch directions innext term various areas of\nprevious termmechanics.next term This is the most recent work devoted\nto previous termcomputational mechanics.next term The report was\nauthored by a subcommittee consisting of Tinsley Oden (Chair), Ted\nBelytschko, Ivo Babuška and Thomas Hughes. It also incorporates\nsuggestions made by the USNCTAM at large.
Error
Statistical mechanics of complex networks
Reviews of modern physics
74
1
47
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society.\nFrequently cited examples include the cell, a network of chemicals\nlinked by chemical reactions, and the Internet, a network of routers\nand computers connected by physical links. While traditionally these\nsystems have been modeled as random graphs, it is increasingly recognized\nthat the topology and evolution of real networks are governed by\nrobust organizing principles. This article reviews the recent advances\nin the field of complex networks, focusing on the statistical mechanics\nof network topology and dynamics. After reviewing the empirical data\nthat motivated the recent interest in networks, the authors discuss\nthe main models and analytical tools, covering random graphs, small-world\nand scale-free networks, the emerging theory of evolving networks,\nand the interplay between topology and the network's robustness against\nfailures and attacks.
Inverse Problems in Engineering Mechanics
Inverse Problems in Engineering Mechanics
477-484
1998
10.1016/B978-008043319-6/50054-6
Discrete wavelets transform is widely used for the wave and image analysis. Particularly, the data compression ability is a useful tool for the image data analysis. On the other hand, discrete wavelets analysis can be applied to the linear systems, because wavelet transform is one of the linear transformations in linear space. In this chapter, an inverse approach employing the discrete wavelets transform is proposed. An optimal sensor position can be decided by means of the correlative analysis for the wavelets solution of ill-posed system equations. The method is applied to an estimation of the high-frequency current distributions on a film conductor. Intensive experimental verification shows the validity of the method.
Mixing quantum and classical mechanics
Phys. Rev. A
56
1
162-175
1997
10.1103/PhysRevA.56.162
Quantum-classical mixing is studied by a group-theoretical approach,\nand a quantum-classical equation of motion is derived. The quantum-classical\nbracket entering the equation preserves the Lie algebra structure\nof quantum and classical mechanics, and, therefore, leads to a natural\ndescription of interaction between quantum and classical degrees\nof freedom. The exact formalism is applied to coupled quantum and\nclassical oscillators. Various approximations, such as the mean-field\nand the multiconfiguration mean-field approaches, which are of great\nutility in studying realistic multidimensional systems, are derived.\nBased on the formulation, a natural classification of the previously\nsuggested quantum-classical equations of motion arises, and several\nproblems from earlier works are resolved.
Quantum Mechanics of the Doubled Torus
Journal of High Energy Physics
2006
062
31
2006
10.1088/1126-6708/2006/10/062
We investigate the quantum mechanics of the doubled torus system, introduced by Hull [1] to describe T-folds in a more geometric way. Classically, this system consists of a world-sheet Lagrangian together with some constraints, which reduce the number of degrees of freedom to the correct physical number. We consider this system from the point of view of constrained Hamiltonian dynamics. In this case the constraints are second class, and we can quantize on the constrained surface using Dirac brackets. We perform the quantization for a simple T-fold background and compare to results for the conventional non-doubled torus system. Finally, we formulate a consistent supersymmetric version of the doubled torus system, including supersymmetric constraints.
Mixing quantum and classical mechanics
Physical Review A
56
1
162-175
1997
10.1103/PhysRevA.56.162
Quantum-classical mixing is studied by a group-theoretical approach, and a quantum-classical equation of motion is derived. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. The exact formalism is applied to coupled quantum and classical oscillators. Various approximations, such as the mean-field and the multiconfiguration mean-field approaches, which are of great utility in studying realistic multidimensional systems, are derived. Based on the formulation, a natural classification of the previously suggested quantum-classical equations of motion arises, and several problems from earlier works are resolved.
String theory modifies quantum mechanics
Phys. Lett. B
293
1-2
37-48
1992
10.1016/0370-2693(92)91478-R
We argue that the light particles in string theory obey an effective quantum mechanics modified by the inclusion of a quantum-gravitational friction term, induced by unavoidable couplings to unobserved massive string states in the space-time foam. This term is related to the W-symmetries that couple light particles to massive solitonic string states in black hole backgrounds, and has a formal similarity to simple models of environmental quantum friction. It increases apparent entropy, and may induce the wave functions of macroscopic systems to collapse.
BLACK-HOLES; BOSONIC SIGMA-MODELS; BREAKING; CENTRAL CHARGE ACTION; EQUATIONS; GRAVITY; RENORMALIZATION-GROUP; S-MATRIX; SYSTEMS; ZAMOLODCHIKOV C-THEOREM
Quantum Mechanics in Phase Space
Physics
1-15
2011
Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.
History of Physics; Quantum Physics
Relational Holism and Quantum Mechanics
The British Journal for the Philosophy of Science
37
1
71-81
1986
One can give a strong sense to the idea that a relation does not 'reduce' to non-relational properties by saying that a relation does not supervene upon the non-relational properties of its relata. That there are such inherent relations I call the doctrine of relational holism, a doctrine which seems to conflict with traditional ideas about physicalism. At least parts of classical physics seem to be free of relational holism, but quantum mechanics, on at least some interpretations, incorporates the doctrine in an all pervasive way.
Basic mechanics: Learning by teaching
Proceedings - Frontiers in Education Conference
3
2003
Two distinct teaching styles were adopted for a Basic Mechanics course designed for technology students. The statics section of the course was taught conventionally using lectures and tutorials, whereas the dynamics part was delivered using the concept of "learning by teaching". This paper concentrates on the responses, learning outcomes, and strategies adopted by the students on the dynamics section of the course. Using the postulate "What I hear, I forget; What I see, I remember; What I do, I understand" the students, working in small groups were asked to learn agreed topics within the dynamics part of the course and then teach these to other groups of students within their year. The feedback has generally been positive with 82% of the students saying they enjoyed the course. Some of the teaching resources produced by the students are of a very high standard.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
78
2007
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
1
47
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
Mechanics of a turning snow ski
International Journal of Mechanical Sciences
36
5
421-429
1994
10.1016/0020-7403(94)90045-0
Modelling the turning motion of snow skis is simulated via a single-ski representation followed by numerically solving the associated differential equations of motion. The forces applied to the ski are assumed to be gravity, the longitudinal friction occurring between the ski and snow, and a skidding force (snow resistance force) corresponding to a system centripetal force and making curvilinear motion possible. The skidding force is calculated via a water jet analogy. Our model quantitatively shows that a ski's side-cut, i.e. its midlength taper, remarkably effects the radius of curvature of a ski trail made when skiing down a ski slope.
Equations of motion; Friction; Loads (forces); Mathematical models; Mechanics; Numerical analysis; Skidding; Snow; Sporting goods; Surfaces
Statistical mechanics of complex networks
Rev. Mod. Phys
74
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Quantum mechanics: A new chapter?
arXiv
8
2012
We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Gr\"ossing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely due to the quantized interactions leading to a discrete set of transferred momenta. A separate experimental confirmation of this interpretation for double-slit interferometry of photons has been given by the group of Steinberg.
Fluid Mechanics–Foam Flotation Interactions
Separation Science and Technology
15
5
1213-1227
1980
10.1080/01496398008066967
Foam flotation methods have been used for years for ore concentration and show considerable promise for the removal of a variety of pollutants from wastewaters. However, scant attention has been given to the critical interaction in these processes of surface chemistry and fluid mechanics. A numerical model of an air bubble with an attached floc particle rising in a Stokes flow regime through a liquid pool at the bottom of a batch foam flotation column was developed. This model computed the viscous forces acting to separate the bubble and particle, and these forces were compared with those given by previous investigators. This research demonstrates that, while previous methods have correctly estimated the magnitudes of the viscous forces, they have failed to correctly estimate the directions.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
47-97
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
method; network
Game Mechanics for Cooperative Games
ZON Digital Games 2008
72-80
2008
10.1523/JNEUROSCI.1920-10.2010
In this paper, we approach the subject of Cooperative Video Games and their Design. We start out by examining Cooperative Game Mechanics - these include common Design Patterns used currently in Cooperative Video Games and how the challenge archetypes are currently used in Cooperative Video Games. We then proceed to examine our experience in designing a cooperative two player video game using the previously mentioned patterns and challenges, and we present some preliminary evaluation data of the game.
Statistical mechanics of complex networks
other
74
1
47-97
2002
10.1088/1478-3967/1/3/006
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
Complexity; Introduction; Network
Lecture Notes in Quantum Mechanics
Quantum
quant-ph
September
267
2006
arXiv:quant-ph/0605180v4
These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory; Entanglement; Quantum computation; Wigner-Weyl formalism; The adiabatic picture; Berry phase; Linear response theory; Kubo formula; Modern approach to scattering theory with mesoscopic orientation; Theory of the resolvent and the Green function; Gauge and Galilei Symmetries; Motion in magnetic field; Quantum Hall effect; Quantization of the electromagnetic field; Fock space formalism.
Mixing quantum and classical mechanics
Physical Review A
56
1
162-175
1997
10.1103/PhysRevA.56.162
Quantum-classical mixing is studied by a group-theoretical approach, and a quantum-classical equation of motion is derived. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. The exact formalism is applied to coupled quantum and classical oscillators. Various approximations, such as the mean-field and the multiconfiguration mean-field approaches, which are of great utility in studying realistic multidimensional systems, are derived. Based on the formulation, a natural classification of the previously suggested quantum-classical equations of motion arises, and several problems from earlier works are resolved.
Structural Engineering, Mechanics and Computation
Structural Engineering, Mechanics and Computation
779-786
2001
10.1016/B978-008043948-8/50085-0
Photoelastic and finite element methods are used to investigate the effect of loss of support on behavior of multi-storey cracked frames subjected to vertical and horizontal loads taking into consideration the soil–structure interaction effect. The effect of loss of support location, crack presence, loading, and soil type is investigated. In the finite element method the soil medium is represented by four node quadrilateral linear strain elements and the frame is represented by beam elements and fracture elements. In the photoelastic method, the flexible material represents the soil, and the Alardit CT-200 simulates the frame and its foundation. The internal forces in frames and internal stresses and strains in soil are obtained using the finite element and photoelastic methods. A parametric study to investigate the effect of loss of support on the behavior of multi-storey cracked frames is carried out.
Light Quanta and Wave Mechanics
Physical Review
31
5
895-899
1928
10.1103/PhysRev.31.895
Light quanta are treated by wave mechanics by analogy with electrons. It is shown that their wave equation is the ordinary optical wave equation. Heisenberg's principle of indeterminateness becomes a description of diffraction. In problems in which localization of quanta is found experimentally, wave packets are to be set up; these are applied to the experiments of Bothe and Geiger, and of Compton. The paths of quanta coincide with the rays of geometrical optics, with a deviation of the error in geometrical optics; by the principle of indeterminateness, more accurate laws for the paths are neither necessary nor possible.
Statistical mechanics of complex networks
Rev. Mod. Phys.
74
54
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Biofluid mechanics of the pulmonary system
Annals of Biomedical Engineering
33
12 SPEC. ISS.
1681-1688
2005
10.1007/s10439-005-8758-0
Presents an overview of leading areas of discovery in bio-fluid mechanics related to the pulmonary system, with particular reference to the airways. Areas briefly reviewed include airway gas dynamics, impedance studies, collapsible-tube studies, and airway liquid studies. Emphasis is placed on promising further directions, such as analysis of interacting fluid-mechanical or fluid-structure phenomena, multi-scale modeling across widely varying length and time scales, and integration of advanced simulations into respiratory investigation and pulmonary medicine.
Airway flow; Airway lining liquid; Artificial ventilation; Fluid structure interaction; Lung disease
Advances in Mathematical Fluid Mechanics
Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday
83-104
2010
10.1007/978-3-642-04068-9
In this paper we present a comparative numerical study of non-Newtonian shear-thinning and viscoelastic blood flow models through an idealized stenosis. Three-dimensional numerical simulations are performed using a finite volume semidiscretization in space, on structured grids, and a multistage Runge-Kutta scheme for time integration, to investigate the influence of combined effects of inertia, viscosity and viscoelasticity in this particular geometry. This work lays the foundation for future applications to pulsatile flows in stenosed vessels using constitutive models capturing the rheological response of blood, under relevant physiological conditions. © 2010 Springer-Verlag Berlin Heidelberg.
Blood rheology; Non-Newtonian fluids; Numerical simulations; Stenosis
Molecular Mechanics Studies of Cellulases
Glycosyl Hydrolases for Biomass Conversion
112-130
2000
10.1021/bk-2001-0769.ch007
Molecular Mechanics (MM) simulations are ideally suited for studying the properties of aqueous solutions of biological molecules, which are difficult to probe experimentally. To date, there have been relatively few MM calculations of cellulases, although there are a number of questions which could perhaps be answered with modeling studies. Several examples of MM calculations of cellulase systems are given to illustrate the potential applications in understanding and modifying cellulase activity. These include the calculation of the change in substrate binding affinity for the Tyr240Phe point mutant of the E1 cellulase from Acidothermus cellulolyticus, and the calculation of the potential of mean force for the binding of a glucose molecule to methane, as a model for the sidechain of alanine.
Statistical mechanics of complex networks
Reviews of modern physics
54
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
78
2007
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of complex network.
Reviews of Modern Physics
74
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Shape Optimization in Fluid Mechanics
Annual Review of Fluid Mechanics
36
1
255-279
2004
10.1146/annurev.fluid.36.050802.121926
This paper is a short and nonexhaustive survey of some recent devel- opments in optimal shape design (OSD) for fluids. OSD is an interesting field both mathematically and for industrial applications. Existence, sensitivity, and compati- bility of discretizations are important theoretical issues. Efficient algorithmic imple- mentations with low complexity are also critical. In this paper we discuss topological optimization, algorithmic differentiation, gradient smoothers, Computer Aided Design (CAD)-free platforms and shock differentiation; all these are applied to a multicriterion optimization for a supersonic business jet
Fluid mechanics and homeland security
Annu. Rev. Fluid Mech.
38
1
87-110
2006
10.1146/annurev.fluid.38.050304.092111
Homeland security involves many applications of fluid mechanics and offers many opportunities for research and development. This review explores a wide selection of fluids topics in counterterrorism and suggests future directions. Broad topics range from preparedness and deterrence of impending terrorist attacks to detection, response, and recovery. Specific topics include aircraft hardening, blast mitigation, sensors and sampling, explosive detection, microfluidics and labs-on-a-chip, chemical plume dispersal in urban settings, and building ventilation. Also discussed are vapor plumes and standoff detection, nonlethal weapons, airborne disease spread, personal protective equipment, and decontamination. Involvement in these applications requires fluid dynamicists to think across the traditional boundaries of the field and to work with related disciplines, especially chemistry, biology, aerosol science, and atmospheric science.
Quantum Mechanics of Consecutive Measurements
eprint arXiv:0911.1142
3
5
2009
I analyze consecutive projective measurements in quantum mechanics in terms of quantum information theory and a no-collapse picture of measurement. I show that the entropy of all detectors that consecutively measured a quantum state is given by the entropy of the last measurement, while the amount of information that any of the consecutive measurements has about the quantum state is equal to the entropy of the preparation, that is, the first measurement of the pure state. Because the entropy of consecutive measurements cannot decrease, the entropy of the last detector tends to its maximum irrespective of the preparation. The formalism leads to a succinct description of the quantum Zeno and anti-Zeno effects.
Quantum Physics
Mixing quantum and classical mechanics
Physical Review A
56
1
162
1997
10.1103/PhysRevA.56.162
Quantum-classical mixing is studied by a group-theoretical approach, and a quantum-classical equation of motion is derived. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. The exact formalism is applied to coupled quantum and classical oscillators. Various approximations, such as the mean-field and the multiconfiguration mean-field approaches, which are of great utility in studying realistic multidimensional systems, are derived. Based on the formulation, a natural classification of the previously suggested quantum-classical equations of motion arises, and several problems from earlier works are resolved.
Parametric investigation of joint mechanics
ACI Structural Journal
90
December
61-71
1993
The influence of design variables such as axial load, amount of transverse reinforcement, concrete strength, presence of transverse beams, and bond demand on the strength and behavior of beam-column joints is investigated. Observations are drawn from a database of 86 beam-column joint tests compiled from published literature, and from the results of a simple mechanical model developed using equilibrium, kinematic, and material considerations. The study provides a detailed description of the parametric dependence of joint behavior, and underscores diversity in experimental techniques used in various countries. It is concluded that this factor is largely responsible for the differences in the empirical interpretations of observed joint behavior that have been proposed by U.S., New Zealand, and Japanese investigators to explain joint mechanics.
structural journal
Geomeric phases in Quantum Mechanics
arXiv
1
31
2009
Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase rotation, to SU(2) phase rotation and to holonomic quantum computation (HQC). The connections in Schrodinger equations are treated by two alternative approaches. Implementation of HQC is demonstrated by the use of 'dark states' including detailed calculations with the connections, for implementing the quantum gates. 'Anyons' are related to the symmetries of the wave functions,in a two-dimensional space, and the use of this concept is demonstrated by analyzing an example taken from the field of Quantum Hall effects.
Student understanding of quantum mechanics
American Journal of Physics
69
8
885
2001
10.1119/1.1365404
We investigate the difficulties of advanced undergraduate students toward the end of a full year upper-level quantum mechanics course with concepts related to quantum measurements and time development. Our analysis is based upon a test administered to 89 students from six universities and interviews with 9 students. Strikingly, most students shared the same difficulties despite variations in background, teaching styles, and textbooks. Concepts related to stationary states, eigenstates, and time dependence of expectation values were found to be particularly difficult. An analysis of written tests and interviews suggests that widespread misconceptions originate from an inability to discriminate between related concepts and a tendency to overgeneralize.
Structural Engineering, Mechanics and Computation
Structural Engineering, Mechanics and Computation
1147-1154
2001
10.1016/B978-008043948-8/50128-4
This chapter is concerned with simultaneous layout structural optimization of trusses using genetic algorithms (GAs). The inclusion of shape and topology variables in addition to size variables makes the optimization problem highly complex. This is because the number of design variables is increased and a simultaneous treatment of design variables of different types requires working on quite complicated design spaces. In the view of the computational efficiency of the GA, an adaptive 3-phase search approach is proposed to be used in conjunction with the GA. Several examples from the literature are solved and compared with the solution algorithm. Besides, optimum designs with respect to only size, and both size and shape design variables are also obtained for the example problems to examine the effects of considering different variables on the optimum solution.
Statistical mechanics of complex networks
REVIEWS OF MODERN PHYSICS
74
January
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
78
2007
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of complex networks
Review of Modern Physics
74
January
47-97
2002
http://dx.doi.org/10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
MECHANICS OF MANUFACTURING IN SPACE.
Proceedings of the U.S. National Congress of Applied Mechanics
305-308
1986
Establishment of a Space Station Program, which will provide a permanent manned presence, large facilities and a good deal of electrical power, makes manufacturing in space even more attractive. This program is emphasizing space manufacturing, satellite servicing, space transportation for higher energy earth orbits and planetary missions, construction of large structures and vehicles and terrestrial and astronomical observations. The development of automation and robotics for the Space Station is receiving special emphasis. This evolution of working in space is discussed and extrapolated into the future, considering a potential lunar base for mining, manufacturing and science and a manned Mars mission. These projects will involve an increasing need to construct, assemble, manufacture and automate operations in space.
Statistical mechanics of complex networks
World Wide Web Internet And Web Information Systems
74
1
47-97
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the networks robustness against failures and attacks.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
47
2002
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of complex networks
Rev. Mod. Phys.
74
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
Quantum mechanics and classical trajectories
New York
606
7
8
2010
The classical limit hbar->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr"odinger equation. In this paper I elaborate on an idea of M. Reuter to represent wave functions by parallel sections of a flat vector bundle over phase space, using the connection of Fedosov's construction of deformation quantization. This generalizes the ordinary Schr"odinger representation, and allows naturally for a description of quantum states in terms of a curve plus a wave function. Hamilton's equation arises in this context as a condition on the curve, ensuring the dynamics to split into a classical and a quantum part.
Mechanics of Ultra-Strength Materials
MRS Bulletin
34
03
167-172
2009
http://dx.doi.org/10.1557/mrs2009.47
ABSTRACT Recent experiments on nanoscale materials, including nanowires, nanopillars, nanoparticles, nanolayers, and nanocrystals, have revealed a host of “ultra-strength” phenomena, defined by stresses in the material generally rising up to a significant fraction of the ideal strength—the highest achievable strength of a defect-free crystal. This article presents an overview of the strength-controlling deformation mechanisms and related mechanics models in ultra-strength nanoscale materials. The critical role of the activation volume is highlighted in understanding the deformation mechanisms, as well as the size, temperature, and strain rate dependence of ultra strength.
Intrinsic decoherence in quantum mechanics
Physical Review A
44
9
5401-5406
1991
10.1103/PhysRevA.44.5401
A model for intrinsic decoherence in quantum mechanics is proposed, based on a simple modification of unitary Schrödinger evolution. On sufficiently small time scales the system evolves by a random sequence of unitary phase changes generated by the Hamiltonian. The Schrödinger equation is obtained to zeroth order in the expansion parameter. Higher-order corrections lead to a loss of coherence in the energy basis. The rate of coherence loss becomes very large as the energy scale of the system is increased. The expansion parameter determines an uncertainty in the time step on very short times scales. A number of testable consequences are derived including anomalous dispersion of a free particle, decay of oscillatory systems, destruction of interference-fringe visibility, and a phase shift of interference fringes.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
1
47-97
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
Mechanics of Materials and Structures
Journal of Mechanics of Materials and Structures
4
February
2009
This study deals with the modelling of the thermomechanical phenomena due to friction effects during granular flow. A two-dimensional model using the discrete element method (DEM) and taking into account the contact detection and heat transfers between grains has been developed. Through this study, we have modelled the heat transfer by conductance and the energy dissipation by friction into a granular medium. This modelling enables better understanding of the phenomena at the contact point between grains as well as the energy dissipation by friction of a great number of grains in motion. The validity of the proposed model has been studied by considering some numerical simulations in quasistatic and dynamic regimes.
Multiscale Methods in Computational Mechanics
Applied and Computational Mechanics
55
215-231
2011
10.1007/978-90-481-9809-2
We describe various spatial and temporal multiscale approaches for composite materials and structures. Spatial multiscale approaches are grouped into two categories: information-passing and concurrent. In the concurrent multiscale methods in space multiple scales are simultaneously resolved, whereas in the information-passing schemes, the fine scale is modeled and its gross response is infused into the continuum scale. The issue of appropri- ate scale selection is discussed. Among the temporal multiscale application we describe block cycle and temporal homogenization approaches with application to fatigue life prediction of composites.
composites; concurrent; homogenization; information-passing; multiscale
Soil Mechanics and Foundation Engineering
Soil Mechanics and Foundation Engineering
365
June
576
1969
10.1098/rsta.2007.0009
We study in this Letter the neutrinoless double beta decay nuclear matrix elements (NMEs) in the framework of the interacting shell model. We analyze them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NMEs predicted by different nuclear models. In addition, it gives back the protagonist role in this process to the pairing interaction, the one which is responsible for the very existence of double beta decay emitters. We show that low seniority approximations, comparable to those implicit in the quasiparticle RPA in a spherical basis, tend to overestimate the NMEs in several decays.
Statistical mechanics of complex networks
Reviews of modern physics
74
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks. CONTENTS
Statistical mechanics of complex networks
Reviews Of Modern Physics
74
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
Information Theory and Statistical Mechanics
Physical Review
106
4
620-630
1957
10.1103/PhysRev.106.620
2010 JSM Proceedings - Papers presented at Joint Statistical Meetings - Vancouver, British Columbia, July 31 – August 5, 2010 and other ASA-sponsored conferences
Morlet wavelets in quantum mechanics
arXiv preprint arXiv:1001.0250
1-17
2010
10.12743/quanta.v1i1.5
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the use of plane wave or δ function decomposition. Morlet wavelets are particularly well-suited for this work: as Gaussians, they have a simple analytic form and they work well with Feynman path integrals. To take full advantage of Morlet wavelets we need an explicit form for the inverse Morlet transform and a manifestly covariant form for the four-dimensional Morlet wavelet. We supply both here.
Von Békésy and cochlear mechanics
Hearing Research
293
1-2
31-43
2012
10.1016/j.heares.2012.04.017
Georg Békésy laid the foundation for cochlear mechanics, foremost by demonstrating the traveling wave that is the substrate for mammalian cochlear mechanical processing. He made mechanical measurements and physical models in order to understand that fundamental cochlear response. In this tribute to B??k??sy we make a bridge between modern traveling wave observations and those of B??k??sy, discuss the mechanical properties and measurements that he considered to be so important, and touch on the range of computational traveling wave models. ?? 2012 Elsevier B.V..
Fluid mechanics of the aortic valve.
J. Fluid Mech.
35
4
721-735
1969
The closure mechanism of the human aortic valve is investigated experimentally with a rigid-walled model placed in a pulsatile water-tunnel. It is shown that the valve is controlled by a fluid feed-back system incorporating a stagnation point at the downstream end of each sinus and a trapped vortex within it, and that threequarters of the valve’s closure is accomplished during forward flow, requiring only very little reversed flow to seal it. The experiments are complemented by solutions of the inviscid-flow equations, based on a Hill spherical vortex model.
Aortic Valve; Aortic Valve: physiology; Biological; Models; Pressure
Statistical mechanics of complex networks
Reviews of Modern Physics
74
January
47-07
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Celestial Mechanics on a Microscopic Scale
Science
253
42-48
1991
10.1126/science.253.5015.42
Classical and semiclassical methods are unrivaled in providing an intuitive and computationally tractable approach to the study of atomic, molecular, and nuclear dynamics. An important advantage of such methods is their ability to uncover in a single picture underlying structures that may be hard to extract from the profusion of data supplied by detailed quantum calculations. Modern trends in semiclassical mechanics are described, particularly the combination of group theoretical methods with techniques of nonlinear dynamics. Application is made to intramolecular energy transfer and to the electronic structure of atomic Rydberg states in external electric and magnetic fields.
Time, quantum mechanics, and decoherence
Synthese
102
2
235-266
1995
10.1007/BF01089802
The relational approach to tense holds that ``the now'', ``passage'', and ``becoming''are to be understood in terms of relations between events. The debate over the adequacy of this framework is illustrated by a comparative study of the sense in which physical theories, (in)deterministic and (non)relativistic, can lend expression to the metaphysics at issue. The objective is not to settle the matter, but to clarify the nature of this metaphysics and to establish that the same issues are at stake in the relational approach to value-definiteness and probability in quantum mechanics. They concern the existence of a unique present, respectively actuality, and a notion of identity over time that cannot be paraphrased in terms of relations.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
1
47-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks
On the completeness of quantum mechanics and the interpretation of the state vector
Journal of Physics: Conference Series
442
1
012002
2013
10.1088/1742-6596/442/1/012002
Recently, it has been argued that quantum mechanics is complete, and that quantum states vectors are necessarily in one-to-one correspondence with the elements of reality, under the assumptions that quantum theory is correct and that measurement settings can be freely chosen. In this work, we argue that the adopted form of the free choice assumption is stronger than needed. In our perspective, there are hidden assumptions underlying these results, which limit their range of validity. We support our argument by a model for the bipartite two-level system, reproducing quantum mechanics, in which the free will assumption is respected, and different quantum states can be connected to the same state of reality.
Optical interpretation of special relativity and quantum mechanics
Foundations of Physics
2000
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to a light ray and can be derived from a mechanical equivalent of Fermat's principle. The similarities between light propagation and mechanics are then extended to quantum mechanics, showing that relativistic quantum mechanics can be derived from a wave equation in modified space-time. Non-relativistic results, such as de Broglie's wavelength, Schroedinger equation and uncertainty principle are shown to be direct consequences of the theory and it is argued that relativistic conclusions are also possible.
General Physics; Optics
Modelling of fretting fatigue in a fracture-mechanics framework
Tribology International
39
10
1220-1226
2006
10.1016/j.triboint.2006.02.029
The use of fracture mechanics as an alternative to (Cauchy) stress-based fatigue criteria is illustrated in this paper, using the "crack analogue" concept to deal with crack initiation in a fracture mechanics framework. A very simple model, based entirely on independently derived parameters, is shown to be able to capture the qualitative effects of the normal and tangential loads of fretting-fatigue performance. The accuracy of the total life predictions is also satisfactory. Examples of how to account for residual stresses and size effect with such a model are discussed. (c) 2006 Elsevier Ltd. All rights reserved.
crack analogue; crack propagation; fracture mechanics; fretting fatigue; modelling; ti-6al4v
Comprehensive evaluation of animated instructional software for mechanics of materials
Proceedings - Frontiers in Education Conference, FIE
3
S3B-6-S3B-11
2004
10.1109/FIE.2004.1408753
During the past three years, the Basic Engineering Department at the University of Missouri Rolla has been developing a second-generation suite of instructional software called MecMovies for the Mechanics of Materials course. In the Fall 2003 semester, MecMovies was integrated into assignments throughout the entire semester for one of the six UMR Mechanics of Materials sections. This paper presents a comparison of student performance in the experimental section with student performance in five control sections along with discussion of student qualitative ratings and comments. © 2004 IEEE.
Animation; Internet; Problem solving; Statistical; Assessments; Instructional software; Mechanics of; Computer software
An introduction to the mechanics of morphogenesis for plant biologists
Trends in Plant Science
15
6
353-360
2010
10.1016/j.tplants.2010.04.002
Plants are under tremendous mechanical forces generated by turgor pressure. How do these forces mediate growth and development? In order to answer this question, it is necessary to understand the mechanics of growth and morphogenesis. In this 'mathless' tutorial, the concepts of strain, mechanical stress and buckling are reviewed and illustrated with recent work on leaf shape, on leaf vasculature, and on organogenesis at the shoot apical meristem. ?? 2010 Elsevier Ltd. All rights reserved.
An overview of the transactional interpretation of quantum mechanics
International Journal of Theoretical Physics
27
2
227-236
1988
10.1007/BF00670751
It is now nearly a year since my paper[1] appeared describing the transactional interpretation of quantum mechanics (TI). That review article contained a detailed discussion of the interpretations and interpretational problems of quantum mechanics. For the present discussion, therefore, I will present only a brief summary of the transactional interpretation and will address some of the points and questions raised concerning the transactional interpretation and its relation to the Copenhagen interpretation (CI).
Of pendulums, polymers, and robots: Computational mechanics with constraints
American Journal of Physics
81
7
537-544
2013
10.1119/1.4803533
The motion of point masses under the influence of a potential can be computed by simple methods. However, if the trajectories are restricted by mechanical constraints such as strings, rails, crankshafts, and molecular bonds, special numerical techniques must be invoked. The need for efficient computational strategies is particularly pressing for molecular simulations, where large systems of compound molecules are tracked. The best strategy is the use of Cartesian coordinates in combination with constraint forces in the Lagrange formulation. This approach has led to the extremely successful SHAKE and RATTLE algorithms. The same ideas may be profitably applied in very different fields such as robotics, mechanics, and geometry, and the study of chaos in simple systems.
A New Look At The Path Integral Of Quantum Mechanics
1009.6032
2010
The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct explanation of the relationship of the A-model to quantum mechanics; such a relationship has been explored from several points of view in the last few years. These phenomena have an analog for Chern-Simons gauge theory in three dimensions: integration cycles in the path integral of this theory can be derived from N=4 super Yang-Mills theory in four dimensions. Hence, under certain conditions, a Chern-Simons path integral in three dimensions is equivalent to an N=4 path integral in four dimensions.
The physical principles of quantum mechanics. A critical review
The European Physical Journal Plus
127
1
12
2012
10.1140/epjp/i2012-12012-4
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.
Momentum flow as an alternative perspective in elementary mechanics
American Journal of Physics
48
5
365-369
1980
10.1119/1.12106
Through a series of sample problems and solutions, the case is made that the notion of force as momentum flow can serve as the basis for vastly expanding the importance of Newton’s third law, ’’action and reaction,’’ as experienced by students in elementary mechanics courses. The reasons this potential has been neglected seem more ’’cultural’’ than pedagogical. The final section raises some particular issues concerning the advisability of actually teaching elementary mechanics from this alternative point of view.
Contexts, Systems and Modalities: a new ontology for quantum mechanics
Arxiv Preprints
1
1-7
2014
10.1007/s10701-015-9952-z
The purpose of this article is to present standard quantum mechanics from an ontological point of view called physical realism: it states that the goal of physics is to study entities of the natural world, existing independently from any particular observer’s perception, and obeying universal and intelligible rules. Though the compatibility of physical realism and quantum mechanics has been much debated, we claim here that both are perfectly compatible, provided that what is meant by physical properties is – slightly but profoundly – modified: contrary to the ordinary, classical ontology, physical properties must be attributed jointly to the system, and to the context in which it is embedded. This intrinsically bipartite nature of physical reality sheds new light on counter- intuitive features of quantum mechanics such as non-locality or the quantum-classical boundary
Contact mechanics with adhesion: Interfacial separation and contact area
arXiv.org
cond-mat.s
4
46004
2008
10.1209/0295-5075/84/46004
We study the adhesive contact between elastic solids with randomly rough, self affine fractal surfaces. We present molecular dynamics (MD) simulation results for the interfacial stress distribution and the wall-wall separation. We compare the MD results for the relative contact area and the average interfacial separation, with the prediction of the contact mechanics theory of Persson. We find good agreement between theory and the simulation results. We apply the theory to the system studied by Benz et al. involving polymer in contact with polymer, but in this case the adhesion gives only a small modification of the interfacial separation as a function of the squeezing pressure.
The Metaphysics of Time Reversal: Hutchison on Classical Mechanics
British Journal for the Philosophy of Science
46
3
331-340
1995
In a series of recent papers Keith Hutchison challenges the conventional reasoning underlying the claim that classical mechanics is time reversal invariant. By what right do we exclude irreversible dissipative forces like friction when we make this claim? he asks. Short of a defensible criterion we do run the risk of merely having stipulated classical mechanics reversible. Is there a good criterion? Hutchison thinks not, but in this essay I propose a defensible criterion and defend it from objections. Classical mechanics is claimed to be reversible for good reason.
Time; Temporal Asymmetry
Celestial mechanics, from high-school to Newton's Principia
Moon
11
2003
A high-school exercise is used to get an insight into planetary motion.
How transferable are hydrogen parameters in molecular mechanics calculations?
Journal of Computational Chemistry
13
8
971-978
1992
10.1002/jcc.540130807
Interactions of water with various methyl hydrogens were studied using ab initio quantum mechanics and molecular mechanics. our goal was to determine the effect of electronegative substituents on the nonbonded interactions of hydrogens. We found that methyl hydrogens are indeed very much affected by substituents and that standard van der Waals parameters used for these hydrogens in molecular mechanics do not reproduce these effects. Adjusted van der Waals parameters are presented that reproduce the ab initio values, and their use is discussed, as well as a general approach to van der Waals parameters on all types of hydrogens.
The analysis of fracture and damage mechanics on the wellbore stability
Fracture and Damage Mechanics V, Pts 1 and 2
324-325
25-28
2006
In this paper, the conception of natural fracture stress in rocks is given according to mesomechanics analysis. The quantitative analysis about wellbore collapse and stratum fracture is made and the density range of drilling fluid is determined. The result is the same as the conclusion which was given by the traditional Mohr-Coulomb criterion in petroleum engineering. The new method of combining mesomechanics with fracture mechanics is used to study the wellbore stability in petroleum engineering, which can reveal the nature of the rock deformation mechanism and provide theoretical reference to design of the drilling engineering.
meso-fracture mechanics; natural failure stress; wellbore instability
Meso-Mechanics and Meso-Structures: A Matter of Scale
Journal of Thermoplastic Composite Materials
11
5
478-490
1998
10.1177/089270579801100507
Meso-mechanics and meso-structures are described in terms of the scales at which they are observed and formulated. Select composite examples are presented to illustrate that meso-mechanics and/or meso-structures are meaningful only when they refer to a specific scale in a hierarchical scale observation/simulation. These examples include different types of composite unit cells, woven fabric unit cells, and progressive fracture as a composite enhanced infrastructure made from reinforced concrete. The results from the select examples indicate that meso-mechanics and meso-structures are elusive terms and depend mainly on the investigators' knowledge and available information.
Faults Monitoring and Diagnosis of Air Compressor from Vibration Mechanics
Applied Mechanics and Materials
164
334-337
2012
10.4028/www.scientific.net/AMM.164.334
This paper introduces vibration analysis, state monitoring, faults diagnosis, system compose, test scheme and measure point disposal of air compressor. This uses CDMS to do. Analyzing the mechanics vibration parameters in time domain and frequency chart in frequency domain. According to the results of information dispose finding out faults reasons and position, educing diagnosis conclusion, the motor-side bearings 3628 has more serious pitting and peeling off, recommended replacement, the horizontal chute and vertical chute of the air compressor has wear, exists insufficient lubrication. Lubrication management and monitoring should be strengthened. © (2012) Trans Tech Publications.
Air compressor; Faults diagnosis; State monitoring; Vibration analysis; Vibration mechanics
A Crack-damage mechanics model for composite laminate
Engineering Fracture Mechanics
21
5
1019-1029
1985
10.1016/0013-7944(85)90007-4
A crack-damage mechanics model for fiber-reinforced composite laminate is proposed based on the basic theory of continuum damage mechanics. The model considered includes a central through short crack and material damage in the vicinity of the crack tip. The quantitative relation between the crack size and the equivalent crack damage is derived. The expression of the crack energy release rate G associated with the damage energy release rate Y is also obtained. Also, a method for evaluation of the crack energy release rate of fiberreinforced composite laminate has been presented.
Autologous blood instillation alters respiratory mechanics in horses
Equine veterinary journal
27
1
46-50
1995
10.1111/j.2042-3306.1995.tb03031.x
To investigate physiological consequences of autologous blood instillation in the lungs of healthy horses, respiratory mechanics and bronchial response to histamine were studied in 8 Thoroughbreds before and after introducing autologous blood (n = 5) and sterile saline solution (n = 3) into their lungs. Blood instillation resulted in a decrease in dynamic compliance (Cdyn) and increased respiratory resistance (R). Bronchial sensitivity and reactivity were unchanged after blood introduction. There were no significant changes in pulmonary mechanics or bronchial response after saline instillation.
Administration, Topical; Animals; Blood Transfusion, Autologous; Bronchial Provocation Tests/veterinary; Female; Hemorrhage/physiopathology/*veterinary; Histamine/diagnostic use; Horse Diseases/*physiopathology; Horses; Lung Diseases/physiopathology/*veterinary; Male; Physical Exertion/*physiology; Respiratory Mechanics/*physiology
BEM-FEM coupling for 3D fracture mechanics applications
Computational Mechanics
2003
10.1007/s00466-003-0510-8
Attention is here focused on the implementation of a coupled BEM-FEM procedure employing the BE method for the modelling of the near-crack region and the FEM for the far-field, where no singularities in the stress field are expected to arise. The symmetric variational version of the BE method is utilized, allowing to obtain a final linear system endowed with a symmetric matrix. With respect to 3D linear elastic fracture mechanics, the code developed is used to evaluate stress intensity factors for some benchmarks and simulate fracture propagation.
BEM; Coupling; FEM; Fracture mechanics
Unstructured grid finite-element methods for fluid mechanics
Reports on Progress in Physics
61
6
569
1998
The development of unstructured grid-based, finite-element methods for the simulation of fluid flows
Contact mechanics and lubrication hydrodynamics of chemical mechanical polishing
Journal of the Electrochemical Society
146
4
1523-1528
1999
10.1149/1.1391798
A preliminary model for the contact mechanics and fluid mechanics of the chemical mechanical polishing process is presented. Only the basic equations of elastic contact surface mechanics and hydrodynamic lubrication are required. Although the model is highly idealized, no ad hoc assumptions or adjustable parameters are required. Some new experimental results are presented, reinforcing the counterintuitive experimental determination of suction fluid pressure below the pad. The model correctly predicts the magnitude of the suction pressure and the effect of load, speed and roughness. (C) 1999 The Electrochemical Society. S0013-4651(98)04-081-6. All rights reserved.
Applications of fluid mechanics in hydrology and environmental engineering
Recent Advances in Fluid Mechanics
29-40
2004
Fluid mechanics constitutes the scientific foundation of hydrology and environmental engineering and has been the basis of a multitude of approaches and models that have proliferated during the past half a century. This foundation also serves as a connection between seeming disparate models. This paper provides a discussion of preliminary fluid mechanics concepts and their application to hydrology and environmental engineering. Extending the discussion further, it may be possible to develop a unified approaches in hydrology and environmental engineering.
channel flow routing; diffusion wave theory; dynamic wave theory; kinematic wave theory; overland flow; streamflow hydrograph; subsurface flow; unsaturated flow; watershed
The fluid mechanics of cancer and its therapy
Annual Review of Fluid Mechanics
45
325-355
2013
10.1146/annurev-fluid-120710-101102
Fluid mechanics is involved in the growth, progression, metastasis, and therapy of cancer. Blood vessels transport oxygen and nutrients to cancerous tissues, provide a route for metastasizing cancer cells to distant organs, and deliver drugs to tumors. The irregular and leaky tumor vasculature is responsible for increased interstitial pressure in the tumor microenvironment, whereas multiscale flow-structure interaction processes control tumor growth, metastasis, and nanoparticle-mediated drug delivery. We outline these flow-mediated processes, along with related experimental and computational methods for the diagnosis, predictive modeling, and therapy of cancer. Expected final online publication date for the Annual Review of Fluid Mechanics Volume 45 is December 17, 2012. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
angiogenesis; blood flow; nanoparticles; tumor
The ZX-calculus is complete for stabilizer quantum mechanics
New Journal of Physics
093021
26
2013
10.1088/1367-2630/16/9/093021
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer quantum mechanics, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.
Non-Newtonian Fluids: Fluid Mechanics, Mixing and Heat Transfer
London: Pergamon Press.
1960
Reviewed in J. Sci. Ind. Research (India) 19A, 572(1960). [on SciFinder (R)]
Multiple-time states and multiple-time measurements in quantum mechanics
Physical Review A
79
5
052110
2009
10.1103/PhysRevA.79.052110
We discuss experimental situations that consist of multiple preparation and measurement stages. This leads us to an alternative approach to quantum mechanics. In particular, we introduce the idea of multitime quantum states which are the appropriate tools for describing these experimental situations. We also describe multitime measurements and discuss their relation to multitime states. A consequence of our formalism is to put states and operators on an equal footing. Finally we discuss the implications of our approach to quantum mechanics for the problem of the flow of time.
Application of fracture mechanics to soils: An overview
Geotechnical Special Publication No.43. Symposium, ASCE National Convention
1-20
1994
A review of the origin of fissures in clays as well as their classification based upon size, geometry, roughness, intensity and spacing is presented. An overview of research work conducted to analyze the effect of fissures on the strength and failure characteristics of clays is introduced. The work reviewed includes the use of the Mohr-Coulomb failure criterion and Linear Elastic Fracture Mechanics (LEFM) theory to predict the way fissured clays fail in the field. The propagation mechanics of a shear band in a simulated clay slope is studied using a laboratory experiment and LEFM theory. The propagation mechanics of the shear band in the experiment was predicted very well by LEFM theory. This demonstrates the usefulness of this theory for understanding and solving geotechnical engineering problems.
From mechanics to thermodynamics—analysis of selected examples
European Journal of Physics
34
2
345-357
2013
10.1088/0143-0807/34/2/345
We present and discuss a selection of classical mechanics and thermodynamics problems. The discussion is based on the use of the impulse–momentum equation simultaneously with the centre-of-mass (pseudo-work) equation or the first law of thermodynamics, depending on the nature of the problem. Thermodynamical aspects of classical mechanics, namely problems involving non-conservative forces or variation of mechanical energy are discussed in different reference frames, in connection with the use of one or other of the energy equations, and also compliance with the principle of relativity.
On the mechanics of integrin clustering during cell-substrate adhesion
Acta Mechanica Solida Sinica
25
5
467-472
2012
10.1016/S0894-9166(12)60041-X
Recent numerical simulations have indicated that integrin clustering during cellsubstrate adhesion can be driven by the presence of a repulsive layer between the cell membrane and the substrate (Paszek et al., PLoS Comput Biol 5:12, 2009). Here we present a simple mechanics model of this phenomenon in which the attraction between integrins is mediated by the long-range elastic deformation of the membrane and the repulsive layer. We obtain analytical solutions to the problem by employing the small deformation theory of an infinitely extended plate resting on an elastic foundation. ?? 2012 The Chinese Society of Theoretical and Applied Mechanics.
attractive interaction; cell-substrate adhesion; integrin clustering; mechanics model
Scalable, inquiry-based, multimodal modules for Engineering Mechanics curriculum
2008 38th Annual Frontiers in Education Conference
T3A-14-T3A-15
2008
10.1109/FIE.2008.4720336
Students struggle to conceptualize Engineering Mechanics fundamentals because they cannot successfully visualize or intuitively comprehend the effects of external loads on mechanisms. Traditionally, Engineering Mechanics courses have been primarily lecture-based with little experimentation. The authors contend that through the use of scalable, inquiry-based, mutimodal modules, lower-division engineering students can more effectively interpret Engineering Mechanics concepts. An emphasis should be placed on engendering properly conceived intuition and critical thinking, and contextualizing concepts and fundamentals before and in parallel to developing Calculus-based skills. The authors hypothesize that by utilizing simple, inquiry-based exercises, instructors can better diminish misconceptions and improve concept mastery. This paper presents plans for implementation and assessment of scalable, inquirybased, multimodal modules for Statics and Dynamics. © 2008 IEEE.
Statistical mechanics and large-scale velocity fluctuations of turbulence
Physics of Fluids
23
November
1-7
2011
10.1063/1.3667268
Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these fluctuations are additive and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for a canonical ensemble in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, which is confirmed by experiments of a variety of turbulent flows. Thus, through the large-scale fluctuations, turbulence is related to the statistical mechanics.
Fracture mechanics investigations on high-temperature gas-cooled reactor materials
Nuclear Technology
66
2
371-379
1984
The prototype nuclear process heat plant and the high-temperature gas-cooled reactor need materials that can withstand temperatures up to 1223K (950C). An elaboration of fracture mechanics concepts that holds for the complete temperature regime must consider all possible phenomena like creep damage and precipitation during exposure, etc. In tests on the Inconel-617, Hastelloy-X, and Nimonic-86 alloys with respect to fatigue crack growth, creep crack growth, and toughness (J integral R curves) up to 1273K (1000C), the first creep crack growth results were obtained in helium to compare with the air results. It was shown that pure fatigue crack growth behavior can be described by linear elastic fracture mechanics up to 1273K
chromium alloys; cracks; creep; fission reactor materials; fracture mechanics; fracture toughness; iron alloys; molybdenum; nickel alloys
Analysis of Random Anisotropic Damage Mechanics Problems of Rock Mass
Rock Mechanics and Rock Engineering
23
91-112
1990
10.1007/BF01043306
A probabilistic analysis method of random anisotropic damage mechanics problems is proposed in parts I and II. In part I, based on the measured character- istics of random crack distribution on the surface of a rock specimen, a probabilistic distribution law of damage variables for rock mass is presented as a Beta distribution by using the Monte-Carlo statistical simulation method. In part II, statistical esti- mation of a damage state and properties of random damaged rock mass are evaluated by Rosenblueth's point estimate method. Combining with the F. E. method, rock mechanics problem for random damaged state have been analyzed.
8 - Fracture mechanics characterization of polymer composites for aerospace applications
Polymer Composites in the Aerospace Industry
191-230
2015
http://dx.doi.org/10.1016/B978-0-85709-523-7.00008-6
Abstract Fibre-reinforced polymer-matrix composites find increasing use in high-performance aerospace structures and elements due to their light weight and the related high specific strength and stiffness. Over the last 20–30 years, fracture mechanics test method development for these materials has yielded several standards, and additional standard procedures are in preparation. The current status of standardization and development is briefly reviewed, and the applicability of fracture mechanics data for composites design and other uses in aerospace is discussed. Major issues are laminate layup, fatigue behaviour and service conditions. These are illustrated by selected data from the fracture mechanics literature.
Aerospace applications; Delamination resistance tests; Fibre-reinforced polymer-matrix composites; Fracture toughness; Test methodology
T -stress effects on crack kinking in Finite Fracture Mechanics
Engineering Fracture Mechanics
132
169-176
2014
10.1016/j.engfracmech.2014.10.011
Finite Fracture Mechanics (FFM) is a coupled criterion, based on the contemporaneous fulfilment of the energy balance and a proper stress requirement. When dealing with mixed-mode brittle fracture of cracked elements, T-stress affects both the conditions. In the present work, the problem is investigated as the mode mixity varies. Results are provided in terms of the critical stress intensity factors and the critical kinking angle, by referring to two different definitions of dimensionless T-stress, depending on which mode (I or II) dominates. This novel approach is validated by a comparison with PMMA experimental data available in the Literature.
alberto; alberto carpinteri; alberto sapora; brittle materials; carpinteri; cornetti; crack kinking; email address; failure analysis; finite fracture mechanics; it; pietro; pietro cornetti; polito; preprint submitted to engineering; sapora; t -stress
Meso-mechanics and meso-structure -- a matter of scale
Journal of Thermoplastic Composite Materials
11
5
478-490
1998
Meso-mechanics and meso-structures are described in terms of the scales at which they are observed and formulated. Select composite examples are presented to illustrate that meso-mechanics and/or meso-structures are meaningful only when they refer to a specific scale in a hierarchical scale observation/simulation. These examples include different types of composite unit cells, woven fabric unit cells, and progressive fracture as a composite enhanced infrastructure made from reinforced concrete. The results from the select examples indicate that meso-mechanics and meso-structures are elusive terms and depend mainly on the investigators' knowledge and available information.
Patents on video game mechanics to strangle innovation, fun
Ars Technica
2008
As the gaming industry grows more competitive, patenting broad ideas and game …
Influences of Dysfunctional Respiratory Mechanics on Orofacial Pain
Dental Clinics Of North America
41
2
211-227
1997
This article reviewed the anatomic issues of respiration and the active and passive mechanics of the thorax as related to dysfunctional breathing. Influences from respiratory dysfunction on forward head posture and temporomandibular dysfunction were offered. Discussion of inspiratory and expiratory muscle responsibilities, effects of diaphragmatic dystonia and abdominal weakness, and results of improper coordination and timing of respiratory muscle should all give the dentist and physical therapist an appreciation of the need for careful observation and appropriate treatment with the patient experiencing TMD and dysfunctional respiratory mechanics. Summaries of hyperinflation relationships and treatment considerations should help in the management of TMD.
Proof of the ergodic theorem and the H-theorem in quantum mechanics
The European Physical Journal H
41
2010
10.1140/epjh/e2010-00008-5
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without "assumptions of disorder"), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity.
Can We Consider Quantum Mechanics to Be a Description of Reality?
Rethinking Scientific Change and Theory Comparison
209-217
2008
10.1007/978-1-4020-6279-7_14
The paper deals with the status of Quantum Mechanics as a description of reality when quantum formalism is supplemented with the decoherence mechanism. The reasons why it is often argued that Quantum Mechanics provides nothing more than a description of the appearance of reality are examined. Then, through a comparison with Relativistic Mechanics, it is showed that, were the very notion of reality not questionable, it would be possible to support the idea that it provides a description of this reality and not only of its appearance.
Decoherence; Description; Quantum Physics; Realism; Reality
Geotechnical engineering beyond soil mechanics: a case study
Canadian Geotechnical Journal
25
4
637-661
1988
10.1139/t88-076
Geotechnical engineering embraces soil mechanics, rock mechanics, and engineering geology. In practice it employs a wide variety of techniques ranging from site mapping and characterization to advanced theoretical analysis and performance monitoring. This paper draws on the development of the Alberta Oil Sands as a case study to illustrate the breadth of application of geotechnical engineering in large-scale resource developments. Detailed discussions are presented on geotechnical contributions to surface mining and slope stability, waste handling and tailings dam construction, and in situ recovery processes.
Alberta;Athabasca Oil Sands;Canada;dams;engineerin; case study; dams; engineering geology; liquefaction; mining; monitoring; oil sands; organic residues; pore pressure; pressure; sedimentary rocks; seepage; shear strength; slope stability; soil mechanics; surface mining; tailings; waste disposal
Mechanics of Composite Materials: Past, Present and Future
Nasa Technical Memorandum
11
Compendex
3-14
1984
Composite mechanics disciplines are presented and described at their various levels of sophistication and attendant scales of application. Correlation with experimental data is used as the prime discriminator between alternative methods and level of sophistication. Major emphasis is placed on: (1) where composite mechanics has been; (2) what it has accomplished; (3) where it is headed, based on present research activities; and (4) at the risk of being presumptuous, where it should be headed. The discussion is developed using selected, but typical examples of each composite mechanics discipline identifying degree of success, with respect to correlation with experimental data, and problems remaining. The discussion is centered about fiber/resin composites drawn mainly from the author's research activities/experience spanning two decades at Lewis.
Process mechanics of low plasticity burnishing of nitinol alloy
Journal of Materials Engineering and Performance
21
12
2607-2617
2012
10.1007/s11665-012-0313-1
Nitinol alloys have received considerable attention in biomedical and aerospace applications. Surface integrity of Nitinol devices by various manufacturing processes is crucial for their functionality. Low plasticity burnishing (LPB) is very promising to modify surface integrity due to its unique capability to adjust material properties down to the deep subsurface on the order of a few millimeters. Burnishing mechanics is essential to understand its effect on surface properties. The depth and width of burnished surface materials are characterized. A three-dimensional finite element simulation has been developed to incorporate the superelastic mechanical behavior of Nitinol. The simulation predictions are validated with the experimental results. The contact stresses, residual stresses, and strain profiles are investigated to better understand burnishing mechanics.
Burnishing; Finite element analysis; Medical device; Nitinol; Process mechanics
Dynamic models of ARDS lung mechanics for optimal patient ventilation.
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference
2
861-4
2004
10.1109/IEMBS.2004.1403294
Mechanical ventilation is often used to treat patients with acute respiratory distress syndrome (ARDS). However, the optimal setting is still controversial, and physicians often rely on experience and intuition. The purpose of this research is to develop a model of the essential lung mechanics to help determining the optimal ventilator setting in clinical situations. The model is a compilation of physiologically based mechanics parameters, which are adjustable to represent patient specific conditions. Further investigation improvements are required, however it shows good initial for eventual clinical use.
--ards; lung mechanics; lung model
Science and the Mechanics' Institutes, 1820-1850: the Case of Sheffield
Annals of Science
451-474
1975
10.1080/00033797500200391
This paper points out that the provincial mechanics' institutes of England in their early years were as much the product of a general and pervasive scientific culture as they were of a particular educational movement. To this extent the institutes can be interpreted within the context of wider social and economic changes. The bulk of the paper relates to the Mechanics' Institute at Sheffield in the period 1832–50, but through this and other material it is argued that this case study deserves general consideration.
Many-body quantum mechanics as a symplectic dynamical system
Physical Review A
22
6
2362-2373
1980
10.1103/PhysRevA.22.2362
An approach is formulated to the problem of obtaining approximate solutions to many-body quantum mechanics. The starting point is the representation of quantum mechanics as Hamiltonian mechanics on a symplectic manifold (phase space). It is shown that Dirac's variation of an action integral provides a natural mechanism for constraining the dynamics to symplectic submanifolds and gives rise to a hierarchy of approximate many-body theories of which Hartree-Fock, random-phase approximation, time-dependent Hartree-Fock, and the double commutator equations of motion formalism are special cases.
Group-theoretical foundations of classical mechanics: The Lagrangian gauge problem
Communications in Mathematical Physics
12
1
64-79
1969
10.1007/BF01646436
This paper is devoted to the study of the classical, single and free particle...
An axiomatic formulation of the Montevideo interpretation of quantum mechanics
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
42
4
256-263
2011
10.1016/j.shpsb.2011.10.002
We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects. Unlike in ordinary quantum mechanics, classical time only plays the role of an unobservable parameter. The formulation eliminates any privileged role of the measurement process giving an objective definition of when an event occurs in a system.
Decoherence; Interpretation of quantum mechanics; Measurement problem
Molecular mechanics studies of acyl halides: II. Vibrational spectra
Journal of Computational Chemistry
19
12
1387-1401
1998
http://dx.doi.org/10.1002/(SICI)1096-987X(199809)19:12<1387::AID-JCC6>3.0.CO;2-E
A newly developed acyl halide mol. mechanics (MM3) force field can accurately calc. mol. geometry, usually to within exptl. error. The new force field can also calc. vibrational frequencies. The acyl halides studied were formyl halides, acetyl halides, propionyl halides, n-butyryl halides, 2-methylpropionyl halides, and 2,2-dimethylpropionyl halides. The rms deviation for vibrational frequencies was 28 cm-1
4-atoms; acyl halide mol mechanics vibrational frequency; FIELD; Force Field; FORCE-FIELD; FREQUENCIES; FREQUENCY; GEOMETRY; HFCO; IR acyl halide mol mechanics; MOLECULAR-STRUCTURE; SPECTRA; Spectrum; structure; VIBRATIONAL FREQUENCIES; VIBRATIONAL-SPECTRA; VIBRATIONAL-SPECTRUM
Statistical mechanics of low-density parity-check codes
Journal of Physics A: Mathematical and General
37
6
R1-R43
2004
10.1088/0305-4470/37/6/R01
We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay–Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multi-spin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.
Prediction of progressive failure in multidirectional composite laminated panels
International Journal of Solids and Structures
44
2648-2676
2007
10.1016/j.ijsolstr.2006.08.010
A mechanism-based progressive failure analyses (PFA) approach is developed for fiber reinforced composite laminates. Each ply of the laminate is modeled as a nonlinear elastic degrading lamina in a state of plane stress according to Schapery theory (ST). In this theory, each lamina degrades as characterized through laboratory scale experiments. In the fiber direction, elastic behavior prevails, however, in the present work, the phenomenon of fiber microbuckling, which is responsible for the sudden degradation of the axial lamina properties under compression, is explicitly accounted for by allowing the fiber rotation at a material point to be a variable in the problem. The latter is motivated by experimental and numerical simulations that show that local fiber rotations in conjunction with a continuously degrading matrix are responsible for the onset of fiber microbuckling leading to kink banding. These features are built into a user defined material subroutine that is implemented through the commercial finite element (FE) software ABAQUS in conjunction with classical lamination theory (CLT) that considers a laminate as a collection of perfectly bonded lamina (Herakovich, C.T., 1998. Mechanics of Fibrous Composites. Wiley, New York). The present model, thus, disbands the notion of a fixed compressive strength, and instead uses the mechanics of the failure process to provide the in situ compression strength of a material point in a lamina, the latter being dictated strongly by the current local stress state, the current state of the lamina transverse material properties and the local fiber rotation. The inputs to the present work are laboratory scale, coupon level test data that provide information on the lamina transverse property degradation (i.e. appropriate, measured, strain-stress relations of the lamina transverse properties), the elastic lamina orthotropic properties, the ultimate tensile strength of the lamina in the fiber direction, the stacking sequence of the laminate and the geometry of the structural panel. The validity of the approach advocated is demonstrated through numerical simulations of the response of two composite structural panels that are loaded to complete failure. A flat, 24-ply unstiffened panel with a cutout subjected to in-plane shear loading, and a double notched 70-ply unstiffened stitched panel subjected to axial compression are selected for study. The predictions of the simulations are compared against experimental data. Good agreement between the present PFA and the experimental data are reported. © 2006 Elsevier Ltd. All rights reserved.
{F}requency response analysis of laminated composite beams
Mechanics of Composite Materials
30
5
484-492
1995
10.1007/BF00616777
Fibre composite materials are widely used in structural applications requiring high stiffness-to-weight and strength-toweight ratios and a high damping. The significance of damping to the dynamic performance of structures is broadly recognized. Passive damping is an essential dynamic parameter for vibration and sound control, fatigue endurance, and impact resistance. Because of the increased need for highly damped structures, significant progress has been recently achieved in the analysis of damping of composites. Recent works on the damping mechanics of composite laminates [1-4] and structures [5-8] have shown that composite damping is anisotropic, highly tailorable, and depends on an array of micromechanical, laminate, and structural parameters, including constituent material properties, fibre volume ratios, ply angles, ply thicknesses, ply stacking sequence, temperature, moisture, and existing damage.\nAlthough several solutions for composite damping in laminated beams have been derived previously [9, 10], these solutions were generally limited to relatively simple geometries and loading situations. For composites with complex geometries and loading situations. For composites with complex geometries and loading situations, such solutions are generally impractical. The finite element method, however, is well suited to such problems, because of its capability to deal with complex geometries and complicated loading situations. Some authors [8] have used the triangular plane finite element for calculation of laminated composite beams by the finite element method which leads to increase of the storage requirements and computing time.\nIn this paper, an integrated finite element method is developed for calculation of damping modeling by uniting the laminate and structural damping theories. Damping in the system is represented by using the complex stiffness approach which derives from the elastic-viscoelastic correspondence principle. Since the dynamic moduli and loss factors of viscoelastic materials depend to a significant extent on frequency, the frequency-dependent model is examined.\nAs can be seen from many publications [11-13] on laminated composite beams, it is the usual practice that relations between the generalized forces and strains are obtained by simply ignoring the terms associated with strains in the y-direction. However, it is more widespread to ignore the stresses in the y-direction than the strains [14], as the constitutive relation for isotropic beams could be derived by ignoring the stresses, but not the strains, from the three-dimensional elasticity relations. In this paper, the modeling of laminated composite beams has been considered by a systematic reduction of the constitutive relations of a three-dimensional anisotropic body.
Statistical inference in quantum mechanics
Reports on Mathematical Physics
17
2
265-274
1980
Statistical inference is discussed in the context of a C*-algebra. No restrictions are placed on the a priori state and the partial measurement state is required to satisfy an absolute continuity condition. This permits the treatment of unbounded "Radon-Nikodym" derivatives within the theory. Relations between statistical inference, conditioning and entropy are presented. Finally, a discussion of the measuring process is given.
the Scandal of Quantum Mechanics
American Journal of Physics
76
11
989
2008
10.1119/1.2967702
pilot wave theory, hiden variable theory, de Broglie Bohm theory, macroscopic states are combination of an enormous number of quantum mechanical eigenstates, between which interference cancels, for macroscopic apparatus, microscopic event triggers a macroscopically visible transition from metastable state into the stable states.
Cell division: Biochemically controlled mechanics
Current Biology
11
737-740
2001
10.1016/S0960-9822(01)00434-1
Technical advances are providing new insights into the mechanical properties of cells. Now, by combining genetic and biochemical studies with high-resolution mechanical measurements from atomic force microscopy, the biochemical bases of mechanical processes such as cytokinesis should be discernible.
Mechanics of applying nitrogen fertilizer
Nitrogen in crop production
475-491; 1
1982
Recent developments in application equipment are described under the following headings: high-pressure liquids (anhydrous NH3, cold NH3, high-pressure NH3, dual application); low-pressure liquids; nonpressure solution (N solutions and clear liquids, injection into irrigation water); suspensions; granular N and mixed fertilizers; and aerial application
irrigation; nitrogen; WATER
Statistical mechanics of colored objects
Physics Letters B
478
1-3
161-171
2000
10.1016/S0370-2693(00)00257-4
A microscopic model of deconfined matter based on color interactions between semi-classical quarks is studied. A hadronization mechanism is imposed to examine the properties and the disassembly of a thermalized quark plasma and to investigate the possible existence of a phase transition from quark matter to hadron matter.
Nuclear Theory
Information, quantum mechanics, and gravity
Foundations of Physics
35
1
131-154
2005
10.1007/s10701-004-1928-3
This is a basically expository article, with some new observations, tracing con- nections of the quantum potential to Fisher information, to K¨ ahler geometry of the projective Hilbert space of a quantum system, and to the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter. KEY
quantum potential; schr odinger; weyl geometry
Research trends in ice mechanics
International Journal of Solids and Structures
37
1-2
131-153
2000
10.1016/S0020-7683(99)00084-0
In sea ice geophysics, the formulation and implementation of a continuum anisotropic ice dynamics model is required in order to increase the spatial resolution of the Polar Ice Prediction System (PIPS) used by the National/ Naval Ice Center to provide sea-ice analyses, forecasts, outlooks and ship-routing recommendations within the marginal ice zone of Arctic and Antarctic seas. Currently, too little is known about the formation of leads in the Arctic, a situation that should rapidly improve via automated ice-tracking SAR algorithms. Many questions remain concerning the influences of inhomogeneities (thermal cracks, ridges, thickness variability, and rubble) on wave propagation, constitutive behavior and overall ice strength at various scales. Floe scale ice models appear to offer the means to bridge the scales between geophysical and structural applications by being able to accurately model the mechanics of ridging, rafting and leading. At the scale of ice forces on structures and ships, a diverse range of creep-brittle failure modes awaits incorporation into ice force models. Knowledge concerning the multiaxial compressive failure of freshwater and saline ice is now available. The constitutive modeling of sea ice lags well behind that for freshwater ice. The important issues of scale effects and inhomogeneities on tensile strength at lab- to structural-scale are discussed, as are the links between various scales.
Breakup; Compressive; Floe scale; Fracture; Geophysical scale; Grain boundary sliding; Ice dynamics; Ice forces; Ice mechanics; Ice-structure interaction; Leads; Multiaxial; Rafting; Ridges; Ships; Structural scale; Tensile; Waves
How to teach Quantum Mechanics
European Journal of Physics
25
6
7
2004
10.1088/0143-0807/25/6/008
In the spirit and style of John S. Bell's well known paper on How to Teach Special Relativity it is argued, that a ``Bohmian pedagogy''provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
January
48-94
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Statistical mechanics of complex networks
Reviews of modern physics
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems ...
Dynamical symmetries in classical mechanics
European Journal of Physics
33
1
73-83
2011
10.1088/0143-0807/33/1/006
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that symmetry.
Arrival time in quantum mechanics
quant-ph/9704010
1997
doi:10.1103/PhysRevA.56.3425
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a spatial point.
Statistical mechanics approach to econophysics
Encyclopedia of Complexity and System …
24
2007
This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.
Catalysis: the mechanics of metathesis.
Nature chemistry
2
7
524-525
2010
10.1038/nchem.710
Olefin metathesis is a flexible and efficient method for making carbon–carbon bonds and has found widespread application in academia and industry. Now, a detailed mechanistic study looking at key catalytic intermediates offers new insight into this reaction, and may prove useful in the development of more active and selective catalysts.
Soil mechanics in pavement engineering
Géotechnique
46
3
383-426
1996
10.1680/geot.1996.46.3.383
Application of soil mechanics principles to the design of pavement foundations, the design of complete pavements and to their structural evaluation `in-service' has lagged some way behind knowledge accumulated through research. Present design methods are generally empirical and often based on use of the California Bearing Ratio test, which was abandoned in California some ®fty years ago. The soil mechanics problem is one of understanding how soils and granular materials respond to repeated loading and applying this knowledge to pavement design with the aid of appropriate theoretical analysis and an understanding of failure mechanisms. Non-linear stress-strain characteristics are a particular feature of the problem and have to be catered for in design and evaluation. Various `tools' are available to assist the pavement engineer. These include theoretical analysis, laboratory testing apparatus, ®eld testing and full-scale trials with appropriate instrumentation. The resilient and permanent strain response of clays and granular materials is reviewed in the context of the requirements for design. The essentially empirical UK Highways Agency method of design and its evolution are discussed in the light of current soil mechanics knowledge. By contrast, the development of mechanistically based approaches is outlined, together with suggestions for the implementation of present knowledge in a practical method of design for pavement foundations. Parallels are drawn between road and rail track design and developments relating to the latter are also reviewed. A forward look suggests that further research to improve understanding of the effective stress state below pavements and the application of recent theoretical work on partially saturated soils could form the basis for improved pavement engineering in the future.
clays; deformation; design; eld instrumentation; loading; pavements and roads; repeated
Cavitation Erosion and Fluid Mechanics
Sulzer Technical Review [English ed.]
68
3
7
1986
The "Pilatus" high-velocity cavitation facility simulates cavitation in the form of an attached cavity by means of a step venturi. Extensive erosion tests with resistant steel specimens and soft substitute materials establish the influence of flow velocity and average cavity length on the loss of material. The erosion model yields the correlation between eroded material and the determinant flow and operating parameters.
FRACTURE-MECHANICS FOR PIEZOELECTRIC CERAMICS
Journal of the Mechanics and Physics of Solids
40
4
739-765
1992
WE STUDY cracks either in piezoelectrics, or on interfaces between piezoelectrics and other materials such as metal electrodes or polymers matrices. The projected applications include ferroelectric actuators operating statically or cyclically, over the major portion of the samples, in the linear regime of the constitutive curve, but the elevated field around defects causes the materials to undergo hyteresis locally. The fracture mechanics viewpoint is adopted-that is, except for a region localized at the crack tip, the materials are taken to be linearly pieozelectric. The problem thus breaks into two subproblems: (i) determining the macroscopic field regarding the crack tip as a physically structureless point, and (ii) considering the hysteresis and other irreversible processes near the crack tip at a relevant microscopic level. The first subproblem, which prompts a phenomenological fracture theory, receives a thorough investigation in this paper. Griffith's energy accounting is extended to include energy change due to both deformation and polarization. Four modes of square root singularities are identified at the tip of a crack in a homogeneous piezoelectic. A new type of singularity is discovered around interface crack tips. Specifically, the singularities in general form two pairs: r-1/2 +/- i-epsilon and r-1/2 +/- kappa, where epsilon and kappa are real numbers depending on the constitutive constants. Also solved is a class of boundary value problems involving many cracks on the interface between half-spaces. Fracture mechanics are established for ferroelectric ceramics under small-scale hysteresis conditions, which facilitates the experiment study of fracture resistance and fatigue crack growth under combined mechanical and electrical loading. Both poled and unpoled ferroelectric ceramics are discussed.
The Scope of Quantum Mechanics
The British Journal for the Philosophy of Science
9
34
133-134
1958
Whyte responds to a statement made by l rosenfeld in his review of david bohm's "causality and chance in modern physics". he asserts that "exact science can never correctly define the limitations to the validity of its most comprehensive or advanced expressions, and individual scientists never know the boundaries of their own knowledge." (staff)
Organic mechanics
Financial Times
2009
Science and finance. As better ways are sought to explain and even predict martket behaviour, attention is swinging towards the links that sustaiun ecosystems, write Clive Cookson, Gillian Tett and Chris Cook "Some were becoming concerned about systemic risk before the financial crisis erupted. The Bank of England started experimenting about five years ago with computer models of the banking system as an ecological network. The US National Academy of Sciences and the Federal Reserve Bank of New York launched a joint study in 2006 that brought together 100 experts to explore parallels between systemic risk in the financial sector and various fields of science and technology, from ecology to engineering. But the financial storm had set in by the time its conclusions were published" (Kambhu et al 2007) (...)"The crude forms of the “efficient market hypothesis” developed in the 1970s began to refashion the banking world in the 1990s, by which time the academic branch of economics was moving towards more subtle forms of behavioural finance. Similarly, the forms of classical physics that have driven financial engineering have long been superseded by more complex theories, such as refinements of relativity and quantum theory" ... Changing the hypothesis: why ‘adaptive’ trumps ‘efficient’ (...)"Hence the move to look at branches of science beyond physics – and at biology in particular. Professor Andrew Lo of MIT has developed the adaptive market hypothesis, attempting to introduce the principles of evolution – competition, adaptation and natural selection – to his financial models. Prof Lo believes that some of the features of human behaviour – such as loss aversion, overconfidence, overreaction and other behavioural biases – that are underappreciated by simpler models are, in fact, rational. These aspects of human behaviour, while not conforming to the caricature of homo economicus, may be optimal strategies for human behaviour that have been honed by millennia of evolutionary pressure. Indeed, he takes this evolutionary process seriously: he is fond of pointing out to his audiences that they have both “mammalian” and “reptilian” brains that can be employed at different moments. Prof Lo believes that prices reflect not just information in the market place, but also deep-seated and slowly evolved human biases. We can apply this change of view in irrational economic behaviour (Nicholas Taleb in Black Swan, Richard Thaler in Nude...) to debate in Ancient Economy bettween Moses Finley and the others as Keith Hopkins ? (...)"The crude forms of the “efficient market hypothesis” developed in the 1970s began to refashion the banking world in the 1990s, by which time the academic branch of economics was moving towards more subtle forms of behavioural finance. Similarly, the forms of classical physics that have driven financial engineering have long been superseded by more complex theories, such as refinements of relativity and quantum theory"
Evolutionary Economy; Management as Science
Mesoporous silicon oxynitride thin films.
Chemical communications (Cambridge, England)
8
900-2
2006
10.1039/b513854j
Highly-ordered, pore-modified with amine groups, and glass-like mesoporous silicon oxynitride thin films were prepared by heat treatment of as-synthesized mesoporous silica thin films in a flowing ammonia environment at high temperatures.
Thin film transistors including indolocarbazoles.
U.S. Pat. Appl. Publ.
US20060125009A1
15 pp.
2006
This invention describes a thin film transistor composed of a semiconductor layer including an optionally substituted indolocarbazole. [on SciFinder(R)]
org thin film transistor indolocarbazole
Discrete mechanics, “time machines” and hybrid systems
EPJ Web of Conferences
58
01013
2013
10.1051/epjconf/20135801013
Modifying the discrete mechanics proposed by T.D. Lee, we construct a class of discrete classical Hamiltonian systems, in which time is one of the dynamical variables. This includes a toy model of time machines which can travel forward and backward in time and which differ from models based on closed timelike curves (CTCs). In the continuum limit, we explore the interaction between such time reversing machines and quantum mechanical objects, employing a recent description of quantum-classical hybrids.
Integrable supersymmetric fluid mechanics from superstrings
Phys. Lett. A
284
4-5
146-151
2001
10.1016/S0375-9601(01)00305-X
Following the construction of a model for the planar supersymmetric Chaplygin gas, supersymmetric fluid mechanics in (1 + 1) dimensions is obtained from the light-cone parametrized Nambu-Goto superstring in (2 + 1) dimensions. The lineal model is completely integrable and can be formulated neatly using Riemann coordinates. Infinite towers of conserved charges and supercharges are exhibited. They form irreducible representations of a dynamical (hidden) SO(2, 1) symmetry group. © 2001 Elsevier Science B.V.
Lattice Boltzmann equation for relativistic quantum mechanics
Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences
360
1792
429-436
2002
DOI 10.1098/rsta.2001.0937
Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.
lattice boltzmann equation; nonlinear interactions; relativistic quantum mechanics; schrodinger-equation
Friction force: from mechanics to thermodynamics
Eur. J. Phys.
31
1159-1175
2010
10.1088/0143-0807/31/5/017
We study some mechanical problems in which a friction force is acting on the system. Using the fundamental concepts of state, time evolution and energy conservation we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws of thermodynamics and then apply them to investigate time evolution and heat transfer of some significant examples.
Mechanics reform: a report from the trenches
Proceedings - Frontiers in Education Conference
2
12c5-7 - 12c5-12
1999
A new project for the enhancement of undergraduate engineering courses via the use of interactive learning and computers in the classroom is being developed at Penn State University. This project involves the introduction of teamwork, projects, simulation, visualization, and experiment in a course traditionally containing none of these. This paper will describe the Interactive Mechanics/Dynamics concept, our efforts to implement it, and some of the issues we have had to overcome during its implementation.
Financial Time Series and Statistical Mechanics
Evolution
x
16
2001
A few characteristic exponents describing power law behaviors of roughness, coherence and persistence in stochastic time series are compared to each other. Relevant techniques for analyzing such time series are recalled in order to distinguish how the various exponents are measured, and what basic differences exist between each one. Financial time series, like the JPY/DEM and USD/DEM exchange rates are used for illustration, but mathematical ones, like (fractional or not) Brownian walks can be used also as indicated.
Statistical Mechanics
Uniaxial testing in rock mechanics laboratories
Engineering Geology
4
3
179-285
1970
10.1016/0013-7952(70)90034-7
Laboratory testing of rock specimens in uniaxial tension and compression is reviewed in detail, with the aim of selecting equipment, procedures and tolerances as a basis for test standardization. Major topics of the review include composition, condition and preparation of test materials, theoretical background of deformation and fracture in rocks, detailed mechanics of uniaxial laboratory tests, and practical test procedures.
The mechanics of individuality in nature
Foundations of Physics
1
4
395-408
1971
10.1007/BF00708587
Abstract Evidence is presented to support the hypothesis that there is a set of basically similar phenomena or characteristics of physics, biology, and sociology. Six of these are identified. Five of them are usually associated with quantum mechanics. They are the existence of eigenstates, transform domains, bosons and fermions, particles and antiparticles, and complementarity. The sixth, namely alternation of generation, is usually associated with biology. The hypothesis leads to some new points of view and interpretations in biology, sociology, and physics.
Mechanics of biomaterials : vascular graft prosthesis
Application of Engineering Mechanics in Medicine
May
1-25
2005
This paper focuses on blood compatible and hemodynamic materials to be used on vascular graft prostheses. We will discuss how blood interacts with vessels under normal conditions and the use of artificial vessels. We shall present the properties of different biomaterials used for manufacturing vascular graft prostheses.
Biocompatible biomaterials; Nylon; Polyurethane Elastomer.; PTFE; Teflon; vascular grafts
Quantum Monte Carlo Methods in Statistical Mechanics
ArXiv
11
2000
This paper deals with the optimization of trial states for the computation of dominant eigenvalues of operators and very large matrices. In addition to preliminary results for the energy spectrum of van der Waals clusters, we review results of the application of this method to the computation of relaxation times of independent relaxation modes at the Ising critical point in two dimensions.
Chemical Physics; Computational Physics; Statistical Mechanics
Limitations on Cloning in Classical Mechanics
Journal of Mathematical Physics
53
1
11
2010
10.1063/1.3676295
In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, more inclusive definition of cloning, we give examples of classical cloning processes. We also prove that a cloning machine must be at least as complicated as the object it is supposed to clone.
Max Born's Statistical Interpretation of Quantum Mechanics.
Science (New York, N.Y.)
218
4578
1193-8
1982
10.1126/science.218.4578.1193
In the summer of 1926, a statistical element was introduced for the first time in the fundamental laws of physics in two papers by Born. After a brief account of Born's earlier involvements with quantum physics, including his bringing the new mechanics to the United States, the motivation for and contents of Born's two papers are discussed. The reaction of his colleagues is described.
Ab initio vs molecular mechanics thermochemistry: Homocubanes
Journal of Chemical Information and Computer Sciences
44
903-906
2004
10.1021/ci0300285
The standard enthalpies of formation and strain energies for a series of homocubanes have been investigated by high-level ab initio G3(MP2)/B3LYP method. The relative stabilities of isomers are discussed. The comparison is made between the results of ab initio and molecular mechanics methods with the aim of assessing their performances. The usefulness of high-level calculations for generating thermochemical databases of relatively large molecules (e.g. C(11)H(14)) was also demonstrated.
Energy Mental Models: Mechanics through Electromagnetism
AIP Conference Proceedings 720
81-84
2004
10.1063/1.1807259
We investigated students’ mental models for energy, and changes in these models in going from mechanics to electromagnetism contexts. We interviewed students in a two‐semester calculus‐based physics course. Our research design included semi‐structured interviews with demonstration. Based on our findings in the interviews we are developing a first version of an ‘Energy Mental Model Inventory.’
The information interpretation of quantum mechanics
Arxiv Preprints
i
7
2000
In the information interpretation of quantum mechanics, information is the most fundamental, basic entity. Every quantized system is associated with a definite discrete amount of information (cf. Zeilinger). This information content remains constant at all times and is permutated one-to-one throughout the system evolution. What is interpreted as measurement is a particular type of information transfer over a fictitious interface. The concept of a many-to-one state reduction is not a fundamental one but results from the practical impossibility to reconstruct the original state after the measurement.
A mechanical model for teaching quantum mechanics
Am. J. Phys.
46
242-243
1978
10.1119/1.11132
The wave function Ψin quantum mechanics is a rather abstract quantity\nwith which the physics student often has trouble. It is instructionally\nadvantageous therefore, to have a mechanical model which can be described\nboth by the quantum-mechanical formalism and also by derivations\nfrom ''first principles.'' It is shown that a particle traveling\nin a helical path gives rise to such a model.
Solutions of wave equations: bound states; quantum
Shot peening mechanics: experimental and theoretical analysis
Mechanics of Materials
19
2-3
251-260
1995
10.1016/0167-6636(94)00036-G
Shot peening is a process of cold-working the surface of structural or machine parts by involving multiple and progressively repeated impact. Interaction between shot and target is discussed and the sequence of events during the loading and unloading cycles which lead to plasticity and residual stress development are examined. Statistical and dynamical aspects of single impact are considered and a number of theoretical expressions for the parameters of the process are presented. The theoretical expressions compare well with experiments.
Particle Path Formulation of Quantum Mechanics
Quantum
19
1996
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle paths are shown to impart wave like behaviour to a particle in motion and to imply various other assumptions and conjectures attributed to the formalism of Quantum Mechanics. The Klein-Gordon and other similar equations are derived by incorporating these properties in the path-integral formalism.
Quantum Physics
Reduced-order controllers for fluid mechanics applications
Manipulation and Control of Jets in Crossflow
439
119-138
2003
Controller complexity is a crucial parameter for control in engineering applications. Controllers with a large number of states are of no practical interest because of the amount of hardware and computer power necessary to compute a real-time control law. Consequently, it is crucial to reduce the order of the controller. This summary provides a background on some techniques useful for deriving reduced-order controllers for fluid mechanics applications, setting the stage for the specific topics described later in this text.
flow-control; mems; model; nonlinear feedback-control; point; semiinfinite plate
A Relativistic Version of Nelson's Stochastic Mechanics
Europhysics Letters (EPL)
13
1
13-17
1990
10.1209/0295-5075/13/1/003
Markov diffusions corresponding to solutions of the Klein-Gordon equation are introduced in a\r similar way as in Nelson's stochastic mechanics. A relativistic version of the Nelson-Newton law for\r Markov diffusions is established. Stochastic generalizations of the proper time and of the\r relativistic action functional are proposed and a stochastic version of the relativistic principle\r of least action is stated. The formalism can be regarded as a quantization procedure leading from\r classical special relativity to the Klein-Gordon equation.
Open string theory as dissipative quantum mechanics
Nuclear Physics B
329
1
117-138
1990
10.1016/0550-3213(90)90060-Q
We argue that vacuum configuration of open strings correspond to Caldeira-Leggett models of dissipative quantum mechanics (DQM) evaluated at a delocalization critical point. This connection reveals that critical DQM can be expected to manifest reparametrization invariance (inherited from the conformal invariance of string theory) rather than just scale invariance. This connection should open up new ways of constructing analytic and approximate solutions of open string theory (in particular, topological solitons such as monopoles and instantons).
From molecular models to continuum mechanics
Arch. Ration. Mech. Anal.
164
4
341-381
2002
Summary: We present here a limiting process allowing us to write some continuum mechanics models as a natural asymptotic of molecular models. The approach is based on the hypothesis that the macroscopic displacement is equal to the microscopic one. We carry out the corresponding calculations in the case of two-body energies, including higher-order terms, and also in the case of Thomas-Fermi type models.
Simulating mechanics to study emergence in games
Association for the Advancement of Artificial Intelligence
7
2011
This paper presents the latest version of the Machinations framework. This framework uses diagrams to represent the flow of tangible and abstract resources through a game. This flow represents the mechanics that make up a game’s interbal economy and has a large impact on the emergent gameplay of most simulation games, strategy games and board games. This paper shows how Machinations diagrams can be used simulate and balance games before they are built.
emergence; game design; gameplay; videogames
Reconstruction of Quantum Mechanics with Information Operators
Arxiv Preprints
2008
We reconstruct quantum mechanics by introducing ”information operators” and excluding the concept of wave functions. Multiple information operators simultaneously describe a single system and continuously develop in time even in the process of a measurement. We also introduce the concept of condensation for a system with many degrees of freedom in a rather general meaning. In terms of the multiplicity of description and the condensation, we explain quantum phenomena including measurements without the collapse of the wave function.
Geometric mechanics of many-body systems
Journal of Computational and Applied Mathematics
140
403-422
2002
10.1016/S0377-0427(01)00400-9
Geometric mechanics for many-body systems is first reviewed, and then applied to jointed cylinders with twist-free condition in order to obtain equations of motion under vanishing total angular momentum condition. The resultant equations are integrated numerically to set the system to turn a somersault. ?? 2002 Elsevier Science B.V. All rights reserved.
Many-body system; Non-holonomic constraints; Total angular momentum
Mechanics of delaminations in laminate composite structures
Mechanics of Composite Materials
37
5-6
367-380
2001
10.1023/A:1014210527476
A survey of the literature and state of the art of the mechanical aspects of delaminations in laminate composite structures is presented. Surface and internal delaminations of various origin, shape, and location are discussed. The origination, stability, and postcritical behavior of delaminations under quasi-static, cyclic, and dynamic loads are analyzed. Some problems for further investigations are discussed.
Delaminations; Fatigue; Fracture; Laminate composites; Load-carrying capacity; Plates; Shells; Stability
Statistical mechanics of protein-like heteropolymers.
Proc Natl Acad Sci USA
96
9
4904-7
1999
A strategy is outlined for obtaining the free energy of a typical designed heteropolymer. The design procedure considers the probability that the target conformation is occupied in comparison with all the other conformations that could house the given sequence. Numerical calculations on lattice heteropolymer models are presented to illustrate the key physical principles.
Animals; Humans; Models, Molecular; Models, Statistical; Polymers; Polymers: chemistry; Protein Conformation; Proteins; Proteins: chemistry
Statistical mechanics of two-dimensional foams
Europhysics Letters
90
6
60002
2010
10.1209/0295-5075/90/60002
The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable the total cell curvature is introduced, which plays the role of energy in conventional statistical thermodynamics. The probability distribution of the number of sides for a cell of given area is derived. This expression allows to correlate the distribution of sides ("topological disorder") to the distribution of sizes ("geometrical disorder") in a foam. The model predictions agree well with available experimental data.
Brownian Motion and Nonequilibrium Statistical Mechanics.
Science (New York, N.Y.)
233
4761
330-334
1986
10.1126/science.233.4761.330
This article is a personal reflection of the branch of nonequilibrium statistical mechanics called the linear response theory that has as its heart the fluctuation-dissipation thereom, which states that irreversible processes ip nonequilibrium are necessarily related to thermal fluctuations in equilibrium. Its origi lies in the Einstein relation for the diffusion constant and the mobility of a Brownian particle. The short history of the fluctuation-dissipation theorem is described. Then the linear response theory is brifly summarized and the meaning of stochastization is considered. The Langevin equation approach and its extensions are reviewed.
Mechanics of soft-solid-liquid-crystal interfaces
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
72
October 2004
2005
10.1103/PhysRevE.72.011706
The interfacial mechanics of soft elastic solids and nematic liquid crystals is presented. The theory can be applied to interfaces involving gels, elastomers, biomaterials, and thermotropic nematic liquid crystals. A model of anisotropic elastic interfaces is formulated and used to derive two fundamental capillary quantities: (i) interfacial torques on the nematic orientation, and (ii) capillary pressure. The couplings between soft-solid deformation and liquid-crystal anisotropic interfacial tension is shown to lead to strain-induced anchoring transitions, and strain-induced morphological instabilities.
Inequivalence of ensembles in statistical mechanics
Stochastic Analysis and Applications
1095
14
2000
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that all these ensembles may not yield the same results even in the thermodynamic limit except at high temperatures. An investigation of the coupling between systems suggest that the state of thermodynamic equilibrium is a special case of statistical equilibrium. As a byproduct of this analysis we have obtained a general form for probability density function in an interval.
Decoherence, measurement and interpretation of quantum mechanics
Arxiv Preprints
2
2
9
2009
According to our modal-Hamiltonian interpretation (MHI) of quantum mechanics, the Hamiltonian of the closed system defines the set of its definite-valued observables. This definition seems to be incompatible with the pointer basis selected by the environment-induced decoherence (EID) of the open system. In this paper we argue that decoherence can be understood from a closed system perspective which (i) shows that the incompatibility between MHI and EID is only apparent, and (ii) solves certain conceptual challenges that the EID program still has to face.
In silico modeling of airway mechanics
Drug Discovery Today: Disease Models
4
3
125-129
2007
10.1016/j.ddmod.2007.12.002
Modeling of airway wall mechanics has recently led to major new insights about the complex behavior of airways during asthma attacks. These advances transformed the concept of airway interdependence from local static relationships to parallel and serial dynamic interactions that describe the behavior of airways embedded in the bronchial tree. A recent study demonstrated that several paradoxical experimental results could be explained with an advanced model that allows the exploration of promising new therapeutic approaches.
Landau Problem in Noncommutative Quantum Mechanics
Chinese Physics C
32
2
8
2008
10.1088/1674-1137/32/2/003
The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schr$\ddot{o}$dinger equations on noncommutative(NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as well as the corresponding eigenfunctions and eigenvalues.
High Energy Physics - Theory; Mathematical Physics
On the fracture mechanics of piezoelectric solids
International Journal of Solids and Structures
29
21
2613-2622
1992
10.1016/0020-7683(92)90225-I
A fracture mechanics analysis is developed within the realm of two-dimensional linear piezoelectricity. The asymptotic expressions for the electromechanical fields in the vicinity of the crack are deduced, and their behavior is illustrated through several examples. The modelling of the electric field's effects on crack arrest and crack skewing constitutes one of the important features of this article.
Bridging the scales with statistical damage mechanics
ICF XI - 11th International Conference on Fracture
2005
Many engineering solid materials, such as polycrystal ceramics, metals, and alloys, have random homogeneous microstructure. In structural applications micro-cracks nucleate, propagate and cluster, which leads to heterogeneous microstructure and structural failure. Krajcinovic and Rinaldi (K&R) [1] consider the homogeneous to heterogeneous phase transition, including the failure, using the tools of statistical mechanics and fractal geometry. A lattice model is used to reproduce the damage process in quasi-brittle material up to the threshold of failure
Quantum mechanics, environmental fluctuations and Wigner function
Rendiconti del Seminario della Facoltà di Scienze dell'Università di Cagliari
2002
Quantum mechanics of classically chaotic systems show drastic changes when they are coupled to environment. A kicked harmonic oscillator is linearly coupled to a heat bath via its position. It is found that the effects of the bath is to suppress the quantum effect of ballistic motion shown by the uncoupled kicked oscillator. In the asymptotic time regime ballistic dynamics is destroyed and quantum-classical correspondence is restored. The Wigner distribution picture of the dynamics is adopted.
FIS/01 Fisica sperimentale
Measurement and Classical Regime in Quantum Mechanics
PhilSci Archive
1-56
2011
In this article, I shall focus on two of the main problems raising interpretational issues in quantum mechanics, namely the notorious measurement problem and the equally important but not quite as widely discussed problem of the classical regime. The two problems are distinct, but they are both intimately related to some of the issues arising from entanglement and density operators. The article will aim to be fairly non-technical in language, but modern in out- look and covering the chosen topics in more depth than most introductory treatments.
The Fracture Mechanics of Carbon Fibre Laminates
Journal of Composite Materials
8
130-141
1974
Critical stress intensity factors and fracture surface energies have beer. measured for a series of 0°/90° carbon fibre reinforced epoxide and carbon fibre reinforced glass composites. The fracture surface energies have been measured by three separate techniques, one of which depends on the applicability of the Griffith-Irwin criterion and the others of which do not. A comparison of these energies and of the dependence of critical stress intensity factors on crack length therefore provides information about the applicability of linear elastic fracture mechanics to carbon fibre com posites.
Hydrogen Bonds In Molecular Mechanics Force Fields
Advances in Protein Chemistry
72
105-119
2005
10.1016/S0065-3233(05)72004-0
This chapter reviews formulation and parametrization of molecular mechanics force fields with special attention to technical and inherent problems. Most striking among the shortcomings is the inadequacy of the simple point charge description as a means to describe energy and forces of interactions between polar molecules and between polar groups in macromolecules, including hydrogen bonds. The current state of efforts to improve the description of polar interactions is discussed.
Entanglement entropy and the simulation of quantum mechanics
J. Phys. A: Math. Theor.
40
25
6689-6696
2007
10.1088/1751-8113/40/25/S13
The relation between entanglement entropy and the computational difficulty\nof classically simulating quantum mechanics is briefly reviewed.\nMatrix product states are proven to provide an efficient representation\nof one-dimensional quantum systems. Further applications of the techniques\nbased on matrix product states, some of their spin-off and their\nrecent generalizations to scale invariant theories and higher dimension\nsystems are also discussed.
spin chains; MPS
Necessary and sufficient postulates of quantum mechanics
Theoretical and Mathematical Physics
142
3
431-446
2005
10.1007/s11232-005-0034-9
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the Hilbert space and linear operators are only secondary structures of the theory, while the primary structures are the elements of a noncommutative algebra (observables) and the functionals on this algebra, associated with the results of a single observation.
Quantum gravity, shadow states, and quantum mechanics
Classical and Quantum Gravity
20
6
35
2002
10.1088/0264-9381/20/6/302
A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle. Maxwell fields will be discussed in the second paper of this series which further develops the program and provides details.
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Quantum Physics
The Ithaca Interpretation of Quantum Mechanics
Pramana
51
5
21
1996
10.1007/BF02827447
I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)
Quantum Mechanics as an Exotic Probability Theory
Maximum Entropy and Bayesian Methods
237-244
1996
Recent results suggest that quantum mechanical phenomena may be interpreted as a failure of standard probability theory and may be described by a Bayesian complex probability theory.
about real physical systems; a position to make; bayesian; by adding extra assumptions; complex probability theory; one is also in; predictions; probability theory than proving; quantum mechanics; theorems in a partic-; there is more to; to the standard; ular mathematical system
Mandibular Mechanics in Varanus niloticus (Reptilia: Lacertilia)
Herpetologica
35
2
158-163
1979
During postembryonic ontogeny, Varanus niloticus shows the formation of a crushing dentition correlated with changes in mandibular mechanics. Postembryonic changes of the feeding apparatus of V. niloticus might be correlated with an adaptational shift from an insectivorous to a molluscivorous diet. Proportional changes of the lower jaw result in a slower yet stronger bite. The adaptational shift, involving quantitative and qualitative modifications of a complex of funcionally correlated characters, results from differential growth during ontogeny.
Anatomy; Biomechanics; Dentition; Lacertilia; Reptilia
Axisymmetric benchmark solutions in fracture mechanics
Engineering Fracture Mechanics
102
348-357
2013
10.1016/j.engfracmech.2013.01.010
The paper presents benchmark solutions for problems involving axisymmetric cracks in infinite and semi-infinite elastic domains. The solutions are obtained by means of three algorithms: an axisymmetric displacement discontinuity method, an axisymmetric finite element method, and a full three-dimensional displacement discontinuity method. The benchmark examples include computation of the crack path for the near-surface propagation of a bowl-shaped crack. ?? 2013 Elsevier Ltd.
Axisymmetric crack; Computation; Crack propagation; Stress intensity factors
Conventions in relativity theory and quantum mechanics
Foundations of Physics
32
4
27
2001
http://dx.doi.org/10.1.1.16.6577
The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.
Supersymmetry in quantum mechanics with point interactions
Physics Letters B
562
3-4
358-364
2003
10.1016/S0370-2693(03)00575-6
We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N=2 supersymmetric models on a circle with two point interactions as well as a superpotential. A hidden su(2) structure inherent in the system plays a crucial role to construct the N=2 supercharges. Spontaneous breaking of supersymmetry due to point interactions and an extension to higher N-extended supersymmetry are also discussed.
Retarded learning: rigorous results from statistical mechanics
Physical Review Letters
86
10
2174-2177
2001
10.1103/PhysRevLett.86.2174
We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the scaled critical number of examples below which learning of the direction is impossible. The asymptotic tightness of the bounds suggests an asymptotically optimal method for learning nonsmooth distributions.
Simple new axioms for quantum mechanics
International journal of theoretical physics
37
1
343–348
1998
10.1023/A:1026631221235
The space of pure states of any physical system,classical or quantum, is identified as a Poisson spacewith a transition probability. These two structures areconnected through unitarity. Classical and quantum mechanics are each characterized by asimple axiom on the transition probability p. Unitaritythen determines the Poisson bracket of quantum mechanicsup to a multiplicative constant (identified with Planck's constant).
Non-Life Insurance Pricing : Statistical Mechanics Viewpoint
Environment
10
2003
10.1142/S0129183105007005
We consider the insurance company as a physical system which is immersed in its environment (the financial market). The insurer company interacts with the market by exchanging the money through the payments for loss claims and receiving the premium. Here in the equilibrium state we obtain the premium by using the canonical ensemble theory, and compare it with the it Esscher principle, the actuaristic well known formula for premium calculation. We simulate the case of automobile insurance for quantitative comparison.
pricing securities; statistical mechanics
Quantum Mechanics in the Light of Quantum Cosmology
Proceedings of the 3rd International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, Japan, 1989
321-343
1990
% % Records from refdb (journal lrr) created at 2007-01-17T07:16:29 % % note: the URLs in this bibtex database may contain characters which will be % interpreted incorrectly by tex, unless used as argument of a \url command (or % an
Some fundamental issues of damage mechanics
Mechanics of Materials
21
3
217-230
1995
10.1016/0167-6636(95)00010-0
The present paper focuses on the discussion of a set of rational criteria for the selection of the damage parameter. The paper considers scalar, second-, fourth-, and six-order tensor representations of damage and evaluates the accuracy with which they approximate exact, micromechanical solutions. Considerations of geometrical, stiffness and failure criteria favor the selection of effective stiffness as being the most appropriate choice for the damage parameter. © 1995.
Brittle failure; Characteristic lengths; Damage; Damage parameter; Effective continuum models; Elastic percolation; Microcracks
Hamilton–Jacobi mechanics from pseudo-supersymmetry
Classical and Quantum Gravity
25
4
045017
2008
10.1088/0264-9381/25/4/045017
For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is the `BPS' condition for preservation of 1/2 pseudo-supersymmetry. The examples of the relativistic and non-relativistic particle, in a general potential, are worked through in detail, and used to discuss the relation to cosmology and to supersymmetric quantum mechanics.
Multi - Instanton Contributions in Quantum Mechanics. 2.
Nucl.Phys.
B218
2
333-348
1983
We present a simplified derivation for the expression of the contribution of multi-instanton configurations in quantum mechanics in the semiclassical limit. We show that the expression one obtains is valid not only for the ground state energy but also for all excited states. We illustrate our method on a few new examples. We conjecture a relation between the various perturbative expansions of these multi-instanton contributions.
Twist and Untwist Mechanics of the Left Ventricle
Heart Failure Clinics
4
3
315-324
2008
10.1016/j.hfc.2008.03.001
The counterdirectional rotation of the left ventricle apex with respect to the base is referred to as left ventricular twist or torsion. This review provides a theoretic basis for understanding the physiologic sequence of left ventricular twist during a cardiac cycle. Variations in left ventricular twist encountered in different experimental and clinical situations are discussed. © 2008 Elsevier Inc. All rights reserved.
Lattice Boltzmann equation for relativistic quantum mechanics.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
360
1792
429-36
2002
10.1098/rsta.2001.0937
Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.
Colloids; Colloids: chemistry; Computer Simulation; Crystallization; Crystallization: methods; Diffusion; Kinetics; Mechanics; Models, Biological; Models, Chemical; Models, Statistical; Particle Size; Quantum Theory; Rheology; Rheology: methods
Invariant variational principle for Hamiltonian mechanics
Journal of Physics A: Mathematical and Theoretical
41
23
17
2007
10.1088/1751-8113/41/23/235210
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure omega without any need to choose some 1-form gamma, such that omega= d gamma, which is not unique and does not even generally exist in a global sense.
Some Recent Asymptotic Results in Fluid Mechanics
Analysis and Simulation of Fluid Dynamics
1-13
2007
The general equations of fluid mechanics are the law of mass conservation,\nthe Navier-Stokes equation, the law of energy conservation and the\nlaws of thermodynamics. These equations are merely written in this\ngenerality. Instead, one often prefers simplified forms. To obtain\nreduced systems, the easiest route is to introduce dimensionless\nnumbers which quantify the importance of various physical processes.\nMany recent works are devoted to the study of the classical solutions\nwhen such a dimensionless number goes to zero. A few results in this\nfield are here reviewed.
Shot peening mechanics: experimental and theoretical analysis
Mechanics of Materials
19
2-3
251-260
1995
http://dx.doi.org/10.1016/0167-6636(94)00036-G
Shot peening is a process of cold-working the surface of structural or machine parts by involving multiple and progressively repeated impact. Interaction between shot and target is discussed and the sequence of events during the loading and unloading cycles which lead to plasticity and residual stress development are examined. Statistical and dynamical aspects of single impact are considered and a number of theoretical expressions for the parameters of the process are presented. The theoretical expressions compare well with experiments. © 1995.
Application of fracture mechanics to cementitious composites
NATO ASI Series E : Applied Sciences
94
1985
The volume contains 25 papers presented at the meeting. The papers are grouped under general topics that include advances in nonlinear fracture mechanics, experimental observations of fracture processes in cement composites, numerical modeling of fracture, experimental methods of determining fracture parameters, damage and continuum modeling, strain-rate and dynamic effects on crack propagation, stress corrosion, time and temperature effects on fracture, and implications for concrete structures.
Vinculin, cell mechanics, and tumor cell invasion
Cell Biology International
n/a–n/a
2013
10.1002/cbin.10064
The focal adhesion protein, vinculin, is important for transmitting mechanical forces and orchestrating mechanical signaling events. Deregulation of vinculin results in altered cell adhesion, contractility, motility, and growth, all of which are important processes in cancer metastasis. This review summarizes recent reports on the role of vinculin in cellular force generation and signaling, and discusses implications of vinculin's function for promoting cancer cell migration in 3D environments.
The mechanics of z-fiber reinforcement
Composite Structures
36
1-2
23-32
1996
10.1016/S0263-8223(96)00053-0
The practice of z-fiber reinforcement increase the laminates, through-the-thickness joints and structural is being examined for its ability to strength of advanced interfaces. and the structure this technology is obtaining an understanding the z-fiber reinforcement Crucial to the development of the interaction Specific issues that were addressed composite between of paper reports the results of an analysis effort that studied the mechanics of this interaction. in which it is embedded. This in these analyses include thermal loadings, crack initiation, crack growth and load transfer.
The canonical connection in quantum mechanics
Journal of Mathematical Physics
37
2
625-636
1996
10.1063/1.531432
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry's phase, can also be found in systems which have slow variables taking values in such a coset space.
Hierarchical modeling in the mechanics of materials.
International Journal of Solids and Structures
37
1--2
379-389
2000
Many problems in the mechanics of materials involve the operation of either multiple spatial or temporal scales simultaneously. As a result, an important thrust of recent work in this area has been the development of methods allowing for the consideration of multiple scales simultaneously. In this paper, we examine hierarchical approaches to modeling problems of this kind with special reference to the way in which information can be fed from one scale to the next in models of plasticity.
Basic Mechanics of the Metal-Cutting Process
Journal of Applied Mech
11
168-175
1944
Mathematical analysis of geometry and mechanics of metal cutting process, covering two common types of geometry which occur in cutting; that of straight edged cutting tool moving relative to work piece in direction perpendicular to its cutting edge, termed "orthogonal cutting," and similar cutting tool so set that cutting edge is oblique to direction of relative motion of tool and work, termed "oblique cutting".
Mixing and irreversibility in classical mechanics
Physics
12
2005
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems in the basis of the approach to the analysis of dynamics of nonequilibrium systems is used. The problem of "coarse-grain" of the phase space in this method is eliminated. The formula, which expresses the entropy through the work of forces between systems, is submitted. The essential link between thermodynamics and classical mechanics was found.
Second order supersymmetry transformations in quantum mechanics
Topics in Mathematical Physics, General Relativity and Cosmology in Honor of Jerzy Plebanski
167-175
2006
We propose a natural classification scheme of the second order\nsupersymmetry transformations in quantum mechanics. The possibilities\nof manipulating spectra offered by those transformations are also\nexplored. In particular, it is shown that the difficulty of modifying\nthe excited state levels can be now overcome, therefore enlarging the\npossibilities offered by the standard first order treatment. The\nresults are illustrated taking as the initial system the standard\nharmonic oscillator.
Time-development operator method in quantum mechanics
American Journal of Physics
69
508
2001
10.1119/1.1326079
We discuss the time-development operator method in quantum mechanics. The equivalence of this method and the usual method of expansion in terms of energy eigenfunctions discussed in textbooks is pointed out. As examples of cases of time-dependent Hamiltonians, we discuss the time development of a Gaussian wave packet for a charged particle subject to a time-dependent electric field using an operator differential equation. We also consider a spin in a time-dependent magnetic field through a time-development operator.
Hydrogen bonds in molecular mechanics force fields.
Advances in protein chemistry
72
105-19
2005
10.1016/S0065-3233(05)72004-0
This chapter reviews formulation and parametrization of molecular mechanics force fields with special attention to technical and inherent problems. Most striking among the shortcomings is the inadequacy of the simple point charge description as a means to describe energy and forces of interactions between polar molecules and between polar groups in macromolecules, including hydrogen bonds. The current state of efforts to improve the description of polar interactions is discussed.
Quantum Mechanics in Nonintertial Reference Frames
Annals of Physics
260
1
27-49
1997
10.1006/aphy.1997.5720
The Galilean covariance of nonrelativistic quantum mechanics is generalized to acceleration transformations. Projective representations of the group of acceleration transformations are constructed and the resulting unitary operators are shown to implement arbitrary accelerations. These unitary operators are used to modify the time-dependent Schrödinger equation and produce the quantum mechanical analog of fictitious forces. The relationship of accelerating systems to gravitational forces is discussed, as well as the effects of accelerations on the internal structure of quantum mechanical systems.
The molecular mechanics of eukaryotic translation.
Annu.Rev.Biochem.
73
657-704
2004
Great advances have been made in understanding the molecular mechanisc underlying protein sysntesis in bacteria in the past three decades, but our understanding of the correspoinding events in eukaryotic organisms is only beginning to catch up. In this review we describe the current state of our knowledge and ignorance of the molecular mechanics underling eukaryotic translation. We discuss the mechanisms conserved across the three kingdoms of lifs as well as the important divergences that have taken place in the pathway.
bacteria; EUKARYOTIC TRANSLATION; MECHANISM; MECHANISMS; PATHWAY; protein; Review; translation
The Smith chart and quantum mechanics
American Journal of Physics
61
4
310
1993
10.1119/1.17262
The Schrödinger equation and the equation describing the behavior of voltage on a transmission line are both linear second‐order equations, which may be solved by convenient matrix methods. By drawing analogies between these two problems, it is shown that a method used for antenna impedance matching based on the Smith chart corresponds in quantum mechanics to a simple conformal transformation of the logarithmic derivative of the wave function. One thereby can arrive at an elementary derivation of the Wentzel–Kramers–Brillouin quantization condition.
Magnetic resonance imaging and ventricular mechanics.
Phil. Trans. Roy. Soc. London A
359
1783
1263-1276
2001
Methods for cardiac geometry and motion reconstruction from multi-planar tagged magnetic resonance images (MRI) have been developed and refined over the last decade. This paper firstly provides an overview of a finite-element reconstruction method, including variants for interactive three-dimensional reconstruction. The second part of this paper discusses recent applications of MRI and ventricular modelling in the study of electrical-mechanical coupling.
Cardiac Mechanics; Image Processing; Magnetic Resonance Imaging
Hyperconfluent third-order supersymmetric quantum mechanics
Arxiv preprint
9
2011
The hyperconfluent third-order supersymmetric quantum mechanics, in which all the factorization energies tend to a common value, is analyzed. It will be shown that the final potential as well can be achieved by applying consecutively a confluent second-order and a first-order SUSY transformations, both with the same factorization energy. The technique will be applied to the free particle and the Coulomb potential.
High Energy Physics - Theory; Mathematical Physics; Quantum Physics
Preparation of States in Open Quantum Mechanics
Open Systems & Information Dynamics
18
03
253-260
2011
10.1142/S1230161211000170
We study preparation of states for open quantum mechanics. For non-Markovian systems that are initially correlated with the environment, the affects of the preparation procedure are nontrivial. This is due to the indirect affects on the state of the environment induced via the correlations with the system and the act of preparation on the system. We give three concrete examples of preparation procedure to elucidate our claims.
Pleural effusion complicates monitoring of respiratory mechanics*
Critical Care Medicine
39
10
2294-2299
2011
10.1097/CCM.0b013e3182227bb5
Although pleural effusion reduces respiratory system compliance by restricting the lungs, the effusion volume is partially accommodated by chest wall expansion. The implications for these opposing volume changes on airway pressure monitoring in ventilated patients with pleural effusion are unreported. We investigated the interactions among pleural effusion, positive end-expiratory pressure, and indices of respiratory mechanics in a swine model.
Anomalous commutator algebra for conformal quantum mechanics
Physical Review D
67
1-11
2003
10.1103/PhysRevD.67.045018
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry breaking, which is explicitly displayed at the level of the generators of the SO(2,1) conformal group. Correspondingly, the associated breakdown of the conservation of the dilation and special conformal charges is derived.
Classical Information and Interpretation of Quantum Mechanics
English
1
1-20
2010
This work is a discussion on the concept of information. We define here classical information as an abstraction that is able to be copied. We consider the connection between the process of copying information in quantum systems and the emergence of the so-called classical realism. The problem of interpretation of quantum mechanics in this context is discussed as well.
Entanglement entropy and the simulation of Quantum Mechanics
Matrix
July
9
2006
10.1088/1751-8113/40/25/S13
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum systems. Further applications of the techniques based on matrix product states, some of their spin-off and their recent generalizations to scale invariant theories and higher dimensions systems are also discussed.
High Energy Physics - Theory; Other Condensed Matter; Quantum Physics
Finite element methods in fracture mechanics
Finite Element Methods in Engineering Proceedings of the Fifth International Conference in Australia on Finite Element Methods
31
1
1
1989
Finite-element methodology specific to the analysis of fracture mechanics problems is reviewed. Primary emphasis is on the important algorithmic developments which have enhanced the numerical modeling of fracture processes. Methodologies to address elastostatic problems in two and three dimensions, elastodynamic problems, elastoplastic problems, special considerations for three-dimensional nonlinear problems, and the modeling of stable crack growth are reviewed. In addition, the future needs of the fracture community are discussed and open questions are identified.
Relational reality in relativistic quantum mechanics
Physics Letters A
294
3-4
129-133
2002
10.1016/S0375-9601(02)00043-9
Up to now it has been impossible to find a realistic interpretation for the reduction process in relativistic quantum mechanics. The basic problem is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allows us to introduce a covariant notion for the collapse of quantum states.
General Relativity and Quantum Cosmology; Quantum Physics
Scattering in PT-symmetric quantum mechanics
Annals of Physics
322
2
41
2006
10.1016/j.aop.2006.05.011
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with hermiticity, T invariance and PT invariance.
An exact solution for the statics and dynamics of laminated thick plates with orthotropic layers
International Journal of Solids and Structures
26
7
655-662
1990
10.1016/0020-7683(90)90036-U
In this study, the three-dimensional state equation for the jth ply of a laminated thick orthotropic plate is established in the local coordinate system according to the knowledge which has been introduced in the paper by Sundara Raja Iyengar and Pandya (1983, Fiber Sci. Technol.18, 19–36). Because all the physical quantities appearing in the state equation are just the compatible quantities of the interfaces, it is extremly convenient to develop the state equation of the whole plate. Furthermore, the number of unknowns included in the final equations has no relationship with that of the plies of the plate. Exact solutions are presented for the statics and dynamics of a three-ply orthotropic thick plates with simply supported edges. Numerical results are obtained and compared with those of Srinivas and Rao (1970, Int. J. Solids Structures6, 1463–1481) and thin plate theory.
Active shape and vibration control for piezoelectric bonded composite structures using various geometric nonlinearities
Composite Structures
122
239-249
2015
10.1016/j.compstruct.2014.11.031
This paper deals with simulations of the static and dynamic response, including shape and vibration control, for piezoelectric bonded smart structures using various geometrically nonlinear shell theories based on the first-order shear deformation (FOSD) hypothesis. The nonlinear theories include refined von Kármán nonlinear shell theory (RVK5), moderate rotation shell theory (MRT5), fully geometrically nonlinear shell theory with moderate rotations (LRT5), and fully geometrically nonlinear shell theory with large rotations (LRT56). The structures simulated are mainly comprised of cross-ply or angle-ply laminated thin-walled master structures bonded with isotropic piezoelectric layers or patches that are considered as actuators. Nonlinear finite element (FE) models are constructed for shape and vibration control of structures undergoing large displacements and rotations. Various plates and shells are validated by comparison with those reported in the literature, and then simulated for the current shape and vibration control. A widely used negative proportional velocity feedback control is adopted for the active vibration control. From the simulations, it can be concluded that large rotation theory should be considered for structures undergoing deformations beyond the range of moderate rotations. Additionally, the results show that by applying an appropriate voltage, a desired shape can be achieved, as well as the vibration can be significantly suppressed.
Large rotations; Piezoelectric; Shape control; Smart structures; Vibration control
A micromechanics-based analysis for tailoring glass-fiber-reinforced thermoplastic laminates with near-zero coefficients of thermal expansion
Composites Science and Technology
60
9
1851-1861
2000
http://dx.doi.org/10.1016/S0266-3538(00)00073-7
This paper presents an attempt at tailoring fiber composite laminates with near-zero coefficients of thermal expansion (CTEs) in one particular in-plane direction by using conventional low-cost glass fibers. Specifically, laminates of symmetric and balanced ±θ angle-ply lay-ups in a glass/polypropylene system have been examined. An absolute strain-measurement technique utilizing a scanning laser extensometer has been applied to experimental determination of the ply-angle dependence of the laminate in-plane thermal expansion behavior in the range from room temperature to 120°C at a heating/cooling rate of 0.5°C/min. A preliminary analysis based on the classical thin-laminate theory predicts near-zero CTE values at θ of around 30° but experimentally, a laminate with θ≈30° shows an average CTE value of about −8×10−6/K. To evaluate this discrepancy in a quantitative manner, a refined analysis based on a well-accepted ‘mean-field’ micromechanics formulation has been developed, taking into account a possible inelastic effect caused by creep of the matrix material. A set of closed-form expressions for the laminate effective in-plane CTEs is obtained, and experimental data are thereby reasonably assessed.
A. Glass fibres; A. Polymer-matrix composites (PMCs); B. Thermomechanical properties; C. Anisotropy; C. Laminates
A mixed variational formulation for interlaminar stresses in thickness-tapered composite laminates
International Journal of Solids and Structures
33
16
2377-2399
1996
10.1016/0020-7683(95)00158-1
Stress fields in laminated plates containing an abrupt thickness taper are determined following Pagano's methodology of using the Hellinger-Reissner functional with the stress components approximated within layers by expressions explicit in the thickness coordinate [Pagano, N. J. (1978). Stress fields in composite laminates. Int. J. Solids Structures 14, 385–400; Pagano, N. J. (1983). Axisymmetric stress fields in involute bodies of revolution. In Advances in Aerospace Structures, Materials and Dynamics; A Symposium on Composites, AD-06, (eds U. Yuceoglu, R. L. Sierakowski and D. A. Glasgow) ASME, NY, pp. 57–64]. The Euler equations from the variational principle area set of variable coefficient, differential-algebraic equations (DAEs) in the longitudinal coordinate. Difficulties with the number of differential equations and boundary conditions are resolved. Solution of the system is by higher-order one-step finite difference scheme. Numerical ill-conditioning encountered when modeling layers that are thin relative to other layers in a model was remedied by choosing stress shape functions and displacement weighting functions that are different than those used by Pagano. The example problems discussed are dropped-ply laminates (laminates with terminated internal plies), that are subjected to in-plane compression or shear under the assumption that the response is adequately modeled by generalized plane deformation elasticity.
Analysis of composite ENF specimen using higher order beam theories
Thin-Walled Structures
46
6
676-688
2008
10.1016/j.tws.2007.11.004
Mathematical modelling, for the stress analysis of symmetric composite end notch flexure (ENF) specimen, has been presented using classical beam theory, first, second, and third order shear deformation beam theories to determine the strain energy release rate (SERR) for symmetric composites under mode II interlaminar fracture. In the present formulation, appropriate matching conditions have been applied at the crack tip and these matching conditions at the crack tip have been derived by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Compliance method has been used to calculate the SERR. Beam models under plane stress and plane strain conditions agree with each other with good performance to analyze the unidirectional and cross-ply composite ENF specimens, whereas for multidirectional composite ENF specimen, only the beam model under plane strain condition appears to be applicable with moderate performance. Third order shear deformation beam model of ENF specimen has been found to be better than other beam models in determining the SERR for unidirectional, cross-ply and multidirectional composites under mode II interlaminar fracture. ?? 2007 Elsevier Ltd. All rights reserved.
Composite laminates; Delamination; End notch flexure specimen; Interlaminar fracture; Shear deformation beam theories; Strain energy release rate
Optimum design of composite laminated plates via a multi-objective function
International journal of mechanical sciences
37
3
317-326
1995
This paper deals with the optimum design of composite laminated plates under stiffness and gauge constraints. A multi-objective function which combines the plate weight and the strain onergy stored in the plate by weighting parameters is introduced. This objective function is minimized while satisfying constraints such as the structural deformation and the limits on design variables. Both ply orientation angles and ply thicknesses of the composite plate are used as the design variables. The stiffness analysis is performed by the finite element method in which a triangu- lar element is used that is suitable for the analysis of thin to thick plates and includes the transverse shear effects. Analyses of the derivatives of the objective function and the constraint functions with respect to the design variables is performed analytically. The mathematical programming method called the constrained variable metric is used to solve this optimum problem. An example is provided for the optimal design of a rectangular laminated plate.
Active damping of laminated cylindrical shells conveying fluid using 1–3 piezoelectric composites
Composite Structures
98
261-271
2013
http://dx.doi.org/10.1016/j.compstruct.2012.09.051
In this paper, the performance of the active constrained layer damping (ACLD) treatment for active control of thin laminated cylindrical shells conveying fluid has been investigated. The constraining layer of the ACLD treatment has been considered to be made of vertically or obliquely reinforced 1–3 piezoelectric composite (PZC) materials. A three-dimensional finite element model has been developed for the laminated shells integrated with the patches of ACLD treatment to describe the coupled hydroelastic behavior of the shells. Velocity feedback control law has been implemented to activate the patches. Symmetric and antisymmetric cross-ply and antisymmetric angle-ply shells have been considered for evaluating the numerical results. Emphasis has also been placed on investigating the effect of the variation of the piezoelectric fiber orientation angle in the PZC constraining layer on the performance of the patches.
Active damping; Conveying fluid; Piezoelectric composite; Smart structures
Nonlinear response of laminated cylindrical panels
Thin-Walled Structures
39
6
519-533
2001
10.1016/S0263-8231(01)00010-6
The geometric nonlinear responses of laminated composite cylindrical panels subjected to (i) axial compression and (ii) central concentrated load are investigated in this work. The parameters considered are: number of layers, symmetric/antisymmetric laminate constructions, cross-ply/angle-ply fibre orientation, boundary conditions and central angle of panel. An eight-node degenerated layered shell element with an efficient explicit through-thickness integration scheme is employed. It has been observed that the cylindrical panels under axial compression exhibit stable post-buckling paths and the number of layers in the laminate for a given total thickness has considerable influence on the load-deflection behaviour. The strength of shallow panels with longitudinal edges hinged, curved edges free and subjected to a central concentrated load is controlled by the limit point load, whereas for deep panels with other parameters remaining the same, the strength is controlled by the bifurcation load. The boundary conditions have significant influence on the load-carrying capacity. The panels with longitudinal edges hinged and curved edges free should be avoided in construction, as they undergo either limit point or bifurcation failure at very low load levels compared with other edge conditions. ?? 2001 Elsevier Science Ltd.
Bifurication load; Degenerated shell element; Explicit through-thickness integration; Geometric nonlinear; Limit point
Active structural-acoustic control of laminated cylindrical panels using smart damping treatment
International Journal of Mechanical Sciences
49
9
1001-1017
2007
10.1016/j.ijmecsci.2007.02.001
In this paper, the performance of active constrained layer damping (ACLD) treatment for active structural-acoustic control of a vibrating thin laminated cylindrical panel has been investigated. The constraining layer of the ACLD treatment has been considered to be made of piezoelectric fiber-reinforced composite (PFRC) material. A finite element model has been developed for the laminated panels integrated with the patches of ACLD treatment to describe the coupled structural-acoustic behavior of the panels enclosing an acoustic cavity. Both velocity and pressure rate feedback controls have been implemented to activate the patches. Symmetric and antisymmetric cross-ply and antisymmetric angle-ply panels have been considered for evaluating the numerical results. Emphasis has also been placed on investigating the effect of the piezoelectric fiber orientation in the PFRC layer and the shallowness angle of the cylindrical panels on the performance of the patches. ?? 2007 Elsevier Ltd. All rights reserved.
Acoustic; Active; Constrained layer damping; Piezoelectric composites; Structural
Simulating the progressive crushing of fabric reinforced composite structures
Composite Structures
76
1-2
130-137
2006
10.1016/j.compstruct.2006.06.019
Simulating the crush response of a glass fabric reinforced thin-walled laminated structural component has been undertaken using the finite element modelling method. The finite element model was developed and analyzed using the PAM-CRASH analysis tool, employing a modified bi-phase material model to describe the behaviour of the elementary ply. The material model treats the orthotropic ply as a quasi-homogeneous layer that includes progressive damage to model material fracture. Description of the material behaviour is accomplished based upon experimentally recorded stress-strain data for both tensile and compressive cases of loading. Simulation results for the demonstrator's crush response are compared to experimentally recorded data and the predicted deformation states and failure patterns show good resemblance to the experimental data. The initial load response is also well predicted by the simulation and refinement of the material characterisation process is proposed to improve the models accuracy over the full range of crushing. © 2006 Elsevier Ltd. All rights reserved.
Finite element modelling; Material characterisation; Progressive damage
Influence of fabric structure and thickness on the ballistic impact behavior of Ultrahigh molecular weight polyethylene composite laminate
Materials & Design
54
315-322
2014
10.1016/j.matdes.2013.08.074
This paper presents the influence of fabric structure and thickness on the ballistic impact behavior of Ultrahigh molecular weight polyethylene (UHMWPE) composite laminate. UHMWPE composite laminates, reinforced by three kinds of fabric structures, unidirectional prepreg, 2D plain-woven and 3D single-ply orthogonal woven fabrics, were fabricated via hot pressing curing process. Through a series of standard ballistic tests, we demonstrated that unidirectional composite laminates exhibit higher ballistic impact velocity and absorbed energy capacity compared to others. A bi-linear relationship was found between the ballistic limit velocity and specimen thickness. Furthermore, the dominant failure mechanisms of unidirectional composite laminates were identified to be plugging and hole friction for thin laminates, whereas delamination, fiber tension and bulging for thick ones.
Ballistic behavior; Composite laminates; Single-ply 3D orthogonal woven fabric; Ultrahigh molecular weight polyethylene
Linear and non-linear failure analysis of composite laminates with transverse shear
Composites Science and Technology
44
227-255
1992
10.1016/0266-3538(92)90015-U
A finite element computational procedure has been developed to find\nlinear and non-linear (von Kármán) first-ply failure loads of composite\nlaminates subjected to in-plane and transverse loads. The finite\nelement model is based on first-order shear deformation theory and\nseveral phenomenological failure criteria. Linear and non-linear\nfirst-ply failure loads are computed for a uniformly distributed\ntransverse load, a concentrated transverse load acting at the centre\nof the plate, and a uniformly distributed in-plane edge load for\nsimply supported and clamped boundary conditions. It is found that\nthe failure loads predicted by various failure criteria differ from\none another by a maximum of 35% in the case of linearloads and 50%\nin the case on non-linear loads; the failure locations differ from\neach other in a random way. Furthermore, it is demonstrated that\nthe difference between the linear and non-linear failure loads is\nlarge in the case of transversely loaded simply supported laminates\nand thin plates. The difference is found to be quite small in the\ncase of in-plane (tensile) loading and thick laminates.
composite laminate
Large deformation analysis of moderately thick laminated plates on nonlinear elastic foundations by DQM
Composite Structures
80
4
569-579
2007
10.1016/j.compstruct.2006.07.004
In this paper, the nonlinear behavior of symmetric and antisymmetric cross ply, thin to moderately thick, elastic rectangular laminated plates resting on nonlinear elastic foundations are studied using differential quadrature method (DQM). The first-order shear deformation theory (FSDT) in conjunction with the Green’s strain and von Karman hypothesis are assumed for modeling the nonlinear behavior. Elastic foundation is modeled as shear deformable with cubic nonlinearity. The differential quadrature (DQ) discretized form of the governing equations with the various types of boundary conditions are derived. The Newton–Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Comparisons are made and the convergence studies are performed to show the accuracy of the results even with a few number of grid points. The effects of thickness-to-length ratio, aspect ratio, number of plies, fiber orientation and staking sequence on the nonlinear behavior of cross ply laminated plates with different boundary conditions resting on elastic foundations are studied.
Differential quadrature method; Elastic foundations; Laminated plates; Large deformation
Investigation of the effect of shell plan-form dimensions on mode-shapes of the laminated composite cylindrical shallow shells using SDSST and FEM
Steel and Composite Structures
12
4
303-324
2012
This paper presents the mode-shape analysis of the cross-ply laminated composite cylindrical shallow shells. First, the kinematic relations of strains and deformation are given. Then, using Hamilton's principle, governing differential equations are developed for a general curved shell. Finally, the stress-strain relation for the laminated, cross-ply composite shells are obtained. By using some simplifications and assuming Fourier series as a displacement field, the governed differential equations are solved by the matrix algebra for shallow shells. Employing the computer algebra system called MATHEMATICA; a computer program has been prepared for the solution. The results obtained by this solution are compared with the results obtained by (ANSYS and SAP2000) programs, in order to verify the accuracy and reliability of the solution presented.
anisotropy; finite element method (fem); free-vibration; shell theory; structural composites; thin; vibration
A new approach to teaching and learning mechanics
Faculty of Sciences, Freudenthal Institute
FIsme Scientific Library 54
320
2007
In this thesis a research project is described that took place from 2000 until 2004 in the Centre for Science and Mathematics Education in Utrecht. It involves a didactical research into the teaching and learning of an introduction to mechanics for fourth grade pre-university level students (Dutch: 4 VWO). Many people consider mechanics as an important part of physics, well worth teaching and learning, but also as a topic in which many difficulties in learning and understanding surface. The aims of the research are to contribute to a further understanding of these difficulties and to point in the direction of possible solutions.
mechanics; physics; science
Fluid mechanics from the beginning to the third millennium
International Journal of Engineering Education
14
3
177-185
1998
Although the christening of the discipline is a relatively recent undertaking, fluid mechanics goes back to the time of archaic Homo sapiens. The art of fluids in motion was born when quite empirically, unceremoniously and without a hint of what either a fluid or mechanics is, the resourceful inhabitants of the planet Earth discovered that a streamlined object travels farther as compared to a blunt one. Great changes took place during the first half of this century in both the teaching and research of the discipline, and it appears that the subject is set for another upheaval as we approach the third millennium. This paper discusses those past and future evolutions of fluid mechanics.
The Born Rule in Quantum and Classical Mechanics
Physical Review A
73
5
5
2006
10.1103/PhysRevA.73.052109
Considerable effort has been devoted to deriving the Born rule (e.g. that psi(x) 2 dx is the probability of finding a system, described by psi, between x and x + dx) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of it classical mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.
Hamiltonian and physical Hilbert space in polymer quantum mechanics
Classical and Quantum Gravity
24
6
1495-1511
2007
10.1088/0264-9381/24/6/008
In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schrodinger quantum mechanics. The kinematical cornerstone of our framework is the so-called polymer representation of the Heisenberg-Weyl (HW) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schrodinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.
Studies in elastic fracture mechanics based on the material force method
International Journal for Numerical Methods in Engineering
58
12
1817-1835
2003
10.1002/nme.834
The object of this work is to discuss a further improvement of the material force method for nonlinear hyperelastostatic fracture mechanics. We investigate the accuracy of the material force method within a 'modified boundary layer'-formulation using a Ramberg-Osgood material type for the sake of comparison. The proposed improvement leads to a reliable and very accurate method to compute the vectorial J-integral in fracture mechanics. Copyright (C) 2003 John Wiley Sons, Ltd.
Fracture mechanics; J-integral; Material force method; Ramberg-Osgood material law; T-stress
The Contextual Character of Modal Interpretations of Quantum Mechanics
Annalen der Physik
1925
21
2007
In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum mechanics.
Quantum Physics
On the Density Matrix of Nonequilibrium Steady-State Statistical Mechanics
Journal of the Physical Society of Japan
71
8
1795-1797
2002
10.1143/JPSJ.71.1795
This paper derives a density matrix of the steady-state statistical mechanics compatible with the steady-state thermodynamics proposed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf 130}, 29 (1998)]. To this end, we adopt three plausible basic assumptions for uniform steady states: (i) equivalence between any two subsystems of the total, (ii) statistical independence between any two subsystems, and (iii) additivity of energy. With a suitable definition of energy, it is then shown that uniform steady states driven by mechanical forces may be described by the Gibbs distribution.
10; 1143; 1795; 71; constructing thermodynamics and statistical; density matrix; doi; far from equilibrium is; jpsj; mechanics; steady-state statistical mechanics; steady-state thermodynamics; undoubtedly a major goal; yet to be
A plasticity framework for (linear elastic) fracture mechanics
Journal of the Mechanics and Physics of Solids
56
2092-2116
2008
10.1016/j.jmps.2007.10.011
An incremental description of (linear elastic) fracture mechanics is presented which shows a perfect analogy with the plasticity theory. After comparing (in terms of angle of propagation, of safe-equilibrium domains, and of energy dissipation) several criteria for crack propagation, the formulation of a generic criterion stemming from the associated plasticity theory is presented and its feature discussed. The analogy between plasticity and quasi-static crack growth leads also to a new algorithm for crack propagation for an arbitrary number of cracks in multi-connected materials, which is driven by the increment of external actions. Stability of crack path under mode I loading is finally analyzed. ?? 2007 Elsevier Ltd. All rights reserved.
Crack propagation criteria and algorithms; Fracture mechanics; Mode I crack path stability; Plasticity; Quasi-static crack growth
Statistical mechanics and hydrodynamics of lattice gas automata: An overview
Physica D: Nonlinear Phenomena
47
1-2
3-8
1991
10.1016/0167-2789(91)90272-B
Some of the issues raised by recent work on lattice gas automata are reviewed.
a Continuum-Damage-Mechanics Model of Hydraulic Fracturing
Journal of Petroleum Technology
45
3
198-205
1993
This work introduces a relatively new branch of fracture mechanics, continuum damage mechanics (CDM), as an extension to current hydraulic-fracture-propagation models. The new approach attempts to resolve inconsistencies evident in current model applications. The fluid-flow-constrained tip-propagation boundary condition of the Perkins-Kern-Nordgren (PKN) model is replaced by a new one derived from continuum damage mechanics. This paper demonstrates how ''abnormally high treating pressures'' can be interpreted by identifying a combined parameter responsible for fracture-propagation retardation. Model results are given in a form suitable for computer representation to allow easy application in treating pressure interpretation and designing fracture treatments.
Statistical mechanics of colloids and Boltzmann’s definition of the entropy
American Journal of Physics
74
3
187
2006
10.1119/1.2174962
The Boltzmannentropy as traditionally presented in statistical mechanicstextbooks is only a special case and not Boltzmann's fundamental definition. The difference becomes important when the traditional expression for the entropy is applied to colloids, for which it makes incorrect predictions. Boltzmann's original definition of the entropy in terms of the probabilities of states of composite systems leads to consistent and correct statistical mechanics and thermodynamics.
The Lyapunov characteristic exponents - Applications to celestial mechanics
Celestial Mechanics
34
95-115
1984
10.1007/BF01235793
Liapunov characteristic exponent (LCEs) are introduced discussed in terms of the divergence of nearby orbits and the spectral properties of a linear operator. A simple example of a periodic orbit is explored and then generalized, and theoretical results of LCEs are presented with a special emphasis on Hamiltonian systems. The connection between Kolmogorov entropy and LCEs is given via Pesin's formula. Numerical techniques to compute LCEs are described, with special emphasis on the work of Benettin et al. (1980), and computations of LCEs in the context of celestial mechanics are reviewed.
Shape optimization under fatigue using continuum damage mechanics
Computer-Aided Design
34
12
929-938
2002
http://dx.doi.org/10.1016/S0010-4485(01)00147-6
An introduction and overview of the developments in shape optimization for fatigue problems is given, beginning with the main ideas in the field of static shape optimization. The use of numerical tools together with the incorporation of non-linear material properties in the continuum mechanics design has led to new possibilities for the analysis of fatigue behaviour in mechanical engineering structures. Based on publications by Lemaitre and Chaboche, the material behaviour is described by defining different partial differential equation systems on micro-scale and meso-scale. From this an optimal algorithm results for the shape optimization of mechanical engineering structures using continuum damage mechanics. Our numerical and experimental tests show a significant increase of lifetime in comparison to classical shapes.
Continuum damage mechanics; Fatigue model; Shape optimization
An Introduction to Fluid Mechanics and Transport Phenomena
An Introduction to Fluid Mechanics and Transport Phenomena
86
173-183
2008
10.1007/978-1-4020-8537-6_10
This book presents the foundations of fluid mechanics and transport phenomena in a concise way. It is suitable as an introduction to the subject as it contains many examples, proposed problems and a chapter for self-evaluation. The solutions to all problems are displayed in the corresponding appendix.\n\nThe content is divided into four parts: fundamentals, conservation principles, dimensional analysis and transport phenomena at interfaces. The transport phenomena of momentum, heat and mass are presented from a rigorous fluid mechanics point of view, and they are explained using a unified, systematic approach, including the analogies between the various transport phenomena.
Limit analysis of plane problems in soil mechanics
Journal of Soil Mechanics and Foundations Division
96
4
1311-1334
1970
A computer method is developed for failure analysis of plane problems in soil mechanics. It is assumed that the soil obeys the Mohr-Coulomb failure criterion and that all stresses vary linearly within each element of a triangular mesh which spans the zone under investigation. An optimal statically admissible stress field corresponding to a lower bound solution is isolated by the method of linear programming. The method has been applied to several bearing capacity and earth pressure problems.
Computation; Computer programming; Earth pressure; Limit design; Load bearing capacity; Plasticity; Soil mechanics
Polymer melt processing : foundations in fluid mechanics and heat transfer
Cambridge series in chemical engineering
x, 250 p., [2] p. of plates
2008
10.1017/CBO9780511813177
Most of the shaping in the manufacture of polymeric objects is carried out in the melt state, as it is a substantial part of the physical property development. Melt processing involves an interplay between fluid mechanics and heat transfer in rheologically complex liquids, and taken as a whole it is a nice example of the importance of coupled transport processes. This book is on the underlying foundations of polymer melt processing, which can be derived from relatively straightforward ideas in fluid mechanics and heat transfer; the level is that of an advanced undergraduate or beginning graduate course, and the material can serve as the text for a course in polymer processing or for a second course in transport processes.
Fluid mechanics.; Heat Transmission.; Polymer melting.
Overview of computational structural mechanics in the Department of Defense
Computational Fluid and Solid Mechanics 2003, Vols 1 and 2, Proceedings
313-315
2003
10.1016/B978-008044046-0.50078-6
Computational Structural Mechanics (CSM) is extremely important to the Department of Defense (DoD). Different classes of problems are addressed by each of the armed services and the Defense Threat Reduction Agency (DTRA). This paper gives an overview of some of the types of problems that face the DoD (focused primarily on the Army) and the codes that are used to meet these challenges. More details on how these codes are used are presented in subsequent papers in this session.
computational fluid dynamics; computational structural mechanics; coupled codes; discrete particle methods; finite element analysis; finite volume analysis; high performance computing
Geotechnical engineering beyond soil mechanics: a case study
Canadian Geotechnical Journal
25
4
637-661
1988
Geotechnical engineering embraces soil mechanics, rock mechanics, and engineering geology. In practice it employs a wide variety of techniques ranging from site mapping and characterization to advanced theoretical analysis and performance monitoring. This paper draws on the development of the Alberta Oil Sands as a case study to illustrate the breadth of application of geotechnical engineering in large-scale resource developments. Detailed discussions are presented on geotechnical contributions to surface mining and slope stability, waste handling and tailings dam construction, and in situ recovery processes.
case study; dams; engineering geology; liquefaction; mining; monitoring; oil sands; organic residues; pore pressure; pressure; sedimentary rocks; seepage; shear strength; slope stability; soil mechanics; surface mining; tailings; waste disposal
A slippery slope: resolving cognitive conflict in mechanics
Teaching Mathematics and its Applications
30
4
216-221
2011
10.1093/teamat/hrr015
This article considers the role of socio-cognitive conflict in addressing students' mechanics preconceptions. A discussion problem was posed to sixth-form students taking an introductory mechanics unit. The problem involved a child choosing either to slide down a smooth slide or to jump off the top. Students were invited to predict which route would be quicker. Their experience suggested that jumping would be faster, but they struggled to use their knowledge of mechanics to explain why sliding (in the absence of friction) would be slower. The resolution of the cognitive conflict between their reasoning about the physical situation and their everyday experience led to a better understanding of resolved forces and how they affect acceleration.
Flight mechanics and echolocation in trawling insectivorous bats
Bat Research News
31
3
42
1990
Dep. Zool., Univ. Bristol, Woodland Rd., Bristol BS8 1UG, England.
behavior; echolocation; feeding; flight; foods; morphology
A Quasi-Newtonian Approach to Bohmian Mechanics I: Quantum Potential
Annales de la Fondation Louis de …
3
2009
In a previous paper, we obtained the functional form of quantum potential by a quasi-Newtonian approach and without appealing to the wave function. We also described briefly the characteristics of this approach to the Bohmian mechanics. In this article, we consider the quantization problem and we show that the 'eigenvalue postulate' is a natural consequence of continuity condition and there is no need for postulating that the spectrum of energy and angular momentum are eigenvalues of their relevant operators. In other words, the Bohmian mechanics predicts the 'eigenvalue postulate'.
2009; bohmian mechanics; broglie; hamilton-jacobi; la fondation louis de; published in annales de; quantum potential; variational principle
Use of Latex-Free Elastic Bandage to Simulate Flap Mechanics
Dermatologic Surgery
36
1
113-114
2010
DOI 10.1111/j.1524-4725.2009.01362.x
The authors have indicated no significant interest with commercial supporters.
model; skills
Application of damage mechanics to numerical fracture simulation
Acta Technica CSAV (Ceskoslovensk Akademie Ved)
34
5
579-598
1989
This paper reviews recent attempts to develop a consistent theory of damage mechanics convenient for numerical simulation of fracture process in metals. The purpose is to introduce microstructural descriptions of damage into the continuum constitutive relations as internal state variables. The microstructural damage descriptions are based on dynamic and static experiments performed under carefully controlled conditions for broad spectrum of structural materials. The resulting constitutive relations describe the nucleation, growth and coalescence of the microscopic voids and cracks. The link between damage and fracture mechanics is discussed. The damage mechanics concept reviewed here will be used to describe spalling in metals, fast crack propagation in steels and simple uniaxial tensile tests in a series of subsequent publications.
A multiscale Molecular Dynamics approach to Contact Mechanics
Simulation
13
2005
10.1140/epje/e2006-00004-9
The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without adhesion. The calculations are compared with analytical contact mechanics models based on continuum mechanics.
Soft Condensed Matter
Arrow of time in rigged Hilbert space quantum mechanics
International Journal of Theoretical Physics
43
7-8
1675-1687
2004
10.1023/B:IJTP.0000048813.60909.8c
Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is initially discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.
Arrow of time; Irreversibility; Quantum mechanics; Rigged Hilbert space
Review of basic quantum mechanics: dynamic behavior of quantum systems
Interaction of Radiation and matter: semiclassical theory
12-25
2000
To this point our review, we have been concerned with describing the states of a system at one instant of time. The complete dynamical theory must describe, of course, connections between different instants of time. "When one makes an observation on the dynamical system, the state of the system gets changed in an unpredictable way, but in between observations causality applies, in quantum mechanics as in classical mechanics, and the system is governed by equations of motion which make the state at one time determined the state at a later time." Thus, it is only the disturbance caused by the interaction of a system with a measuring device that makes the system’s behavior cease to be strictly causal.
quantum mechanics; quantum systems
Conceptual inconsistencies in finite-dimensional quantum and classical mechanics
Physical Review A - Atomic, Molecular, and Optical Physics
88
1
1-5
2013
10.1103/PhysRevA.88.012116
Utilizing operational dynamic modeling [ D. I. Bondar et al. Phys. Rev. Lett. 109 190403 (2012)], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities are also revealed, including the nonexistence of the free particle and ambiguity in defining potential forces. Non-Hermitian mechanics is shown to have the same problems. This work compromises a popular belief that finite-dimensional mechanics is a straightforward discretization of the corresponding infinite-dimensional formulation.
An application of symmetry groups to nonlocal continuum mechanics
Computers & Mathematics with Applications
55
9
1923-1942
2008
10.1016/j.camwa.2007.07.006
In this Study the symmetry group properties of the one-dimensional elastodynamics problem in nonlocal continuum mechanics is discussed by using an approach developed for symmetry group analysis of integro-differential equations with general form. This approach is based on the modification of the invariance criterion of the differential equations, which include nonlocal variables and integro-differential operators. Lie point symmetries of the nonlocal elasticity equation are obtained based on solving nonlocal determining equations by using a new approach. The symmetry groups for different types of kernel function and the free term including the classical linear elasticity case are presented. (C) 2007 Elsevier Ltd. All rights reserved.
classification; integro-differential equations; lie symmetry groups; nonlocal continuum mechanics; point symmetries
Relativistic Quantum and Classical Mechanics in the Hilbert Space
Studies In History and Philosophy of Science Part B Studies In History and Philosophy of Modern Physics
38
1
170-180
2011
We present a formulation of relativistic classical and quantum mechanics in the Hilbert space with a linkage through the Ehrenfest quantization. We start with the covariant form of the Lorentz force and consistently derive the Dirac equation along its classical counterpart as a classical spinorial equation. This equation fills a missing link between relativistic quantum and classical mechanics and takes the role of the Koopmann-von Neumann equation in the relativistic regime.
classical; quantum mechanics; relativistic; zeno supertasks
Fracture Mechanics Characterization of Polymer Composites for Aerospace Applications
Polymer Composites in the Aerospace Industry
191-230
2015
10.1016/B978-0-85709-523-7.00008-6
Fibre-reinforced polymer-matrix composites find increasing use in high-performance aerospace structures and elements due to their light weight and the related high specific strength and stiffness. Over the last 20–30years, fracture mechanics test method development for these materials has yielded several standards, and additional standard procedures are in preparation. The current status of standardization and development is briefly reviewed, and the applicability of fracture mechanics data for composites design and other uses in aerospace is discussed. Major issues are laminate layup, fatigue behaviour and service conditions. These are illustrated by selected data from the fracture mechanics literature.
Aerospace applications; Delamination resistance tests; Fibre-reinforced polymer-matrix composites; Fracture toughness; Test methodology
Critical state soil mechanics and the behaviour of real soils
Recent Developments in Soil and Pavement Mechanics
41-80
1997
Critical State Soil Mechanics comprises concepts which are extremely powerful for understanding, analysing and predicting soil behaviour. However, most soils present characteristics which are not taken into account by this approach. These are in particular anisotropy, development of plastic strains below the state boundary surface, viscosity, structure and partial saturation. The paper summarizes the in fluence of these factors on soil behaviour and examines how it could be included into an Extended Critical State Soil Mechanics framework. Difficulties associated with the determination of critical state and the implications of localization are also discussed.
Statistical mechanics of the glass transition as revealed by a Voronoi tesselation
Physical Review E
75
050404
2007
10.1103/PhysRevE.75.050404
The statistical mechanics of simple glass forming systems in two dimensions is worked out. The glass disorder is encoded via a Voronoi tesselation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, T(g) and T(c) , the first associated with jamming and the second associated with crystallization at very low temperatures.
Degenerated mechanics in a homogeneous continuum: Potentials for spin and twist
Acta Geophysica Polonica
53
3
219-230
2005
In this paper we extend our considerations on the spin and twist motions in a homogenous continuum. Refering to our former results, we define the degenerated mechanics as that in which the displacement motions vanish while rotation motions, as the independent elastic fields, do exist. This is exactly the opposite case to the classic ideal elastic continuum in which only displacement motions are taken into account, while any independent rotation motions are excluded because of a lack of the appriopriate constitutive laws supporting the existence of an elastic response due to the rotational deformations of bonds in a lattice network. We propose a system of potentials which would help us to understand the waves and geometrical features of degenerated mechanics and its Riemannian geometry.
Degenerated mechanics; Riemannian geometry; Rotation rigidity modulus; Spin and bend-twist motion
Asymptotic adaptive methods for multi-scale problems in fluid mechanics
Journal of Engineering Mathematics
39
1-4
261-343
2001
10.1023/A:1004844002437
We report on the results of a three-year research effort aimed at investigating and exploiting the role of physically motivated asymptotic analysis in the design of numerical methods for singular limit problems in fluid mechanics. Such problems naturally arise, among others, in combustion, magneto-hydrodynamics, and geophysical fluid mechanics. Typically, they are characterized by multiple-space and/or -time scales and by the disturbing fact that standard computational techniques fail entirely, are unacceptably expensive, or both. The challenge here is to construct numerical methods which are robust, uniformly accurate, and efficient through different asymptotic regimes and over a wide range of relevant applications
Asymptotic analysis; Asymptotics-based numerical methods; Fluid mechanics; Singular limit regimes
Colby College Molecular Mechanics Exercises MOE (Molecular Operating Environment) Tutorial
Structure
October
2006
MOE is a molecular modeling program, which is specifically designed
Mechanics of Debonding and Delamination in Composites - Asymptotic Studies
Composites Engineering
5
10-11
1299-1315
1995
The purpose of this paper is to discuss fracture mechanics basis for the analysis of debonding and delamination in composites. Linear elastic interfacial fracture mechanics theories are reviewed, with emphasis on the modelling and characterization of stress and deformation fields near the edges of debonding and delamination. Relations between stress intensity factors and crack-tip strain energy release rate are presented for a variety of cases. Effects of crack growth, material anisotropy, and crack surface contact and friction are considered in detail. Explicit expressions are given for many important results. Implications of the interfacial fracture mechanics theories to the analysis of delamination and debonding in composite materials are discussed.
anisotropic; bimaterials; energy-release rates; fracture; frictionless contact; growing interface cracks; media; shear; singularities; stationary; tip fields
Guide for Verification and Validation in Computational Solid Mechanics
Society
September
1-15
2006
10.1007/s00366-007-0072-z
The American Society of Mechanical Engineers (ASME) Standards Committee on Verification and Validation in Computational Solid Mechanics (PTC 60/V&V 10) approved their first document (Guide) in July 2006. The Guide has been submitted to ASME publications and to the American National Standards Institute (ANSI) for public review. It is hoped the Guide will be published in early 2007.
Solid Mechanics; Validation
Review of Springer Handbook of Experimental Fluid Mechanics
AIAA Journal
46
2653-2655
2008
10.2514/1.38773
This Handbook consolidates authoritative and state-of-the-art information from the large number of disciplines used in experimental fluid mechanics into a readable desk reference book. It comprises four parts covering Experiments in Fluid Mechanics, Measurement of Primary Quantities, Specific Experimental Environments and Techniques, and Analyses and Post-Processing of Data. The Springer Handbook of Experimental Fluid Mechanics has been prepared for physicists and engineers in research and development in universities, industry and in governmental research institutions or national laboratories. Both experimental methodology and techniques are covered fundamentally and for a wide range of application fields. A generous use of citations directs the reader to additional material on each subject.
Contributions of Archimedes on mechanics and design of mechanisms
Mechanism and Machine Theory
72
86-93
2014
10.1016/j.mechmachtheory.2013.10.005
Relevant contributions are ascribed to Archimedes as related to early developments in mechanics with application to mechanism design with a modern vision. Archimedes developed theoretical advances that were motivated by and applied to practical problems with an enthusiastic behaviour and with a modern spirit that can be summarized in his motto ‘Give me a place to stand and I will move the earth’. In this paper his contribution to mechanics is discussed as related to his results in designing and successfully operating mechanisms.
Archimedes; History of Mechanical Engineering; History of mechanics; Mechanism design
Statistical mechanics of quantum-classical systems with holonomic constraints.
The Journal of chemical physics
124
2
024110
2006
10.1063/1.2159477
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained systems arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear-response function of constrained quantum-classical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.
Vibration of carbon nanotubes studied using nonlocal continuum mechanics
Smart Materials and Structures
15
2
659-666
2006
10.1088/0964-1726/15/2/050
A nonlocal continuum mechanics model is developed and applied to study the vibration of both single-walled nanotubes (SWNTs) and double-walled nanotubes (DWNTs) via elastic beam theories. The small-scale effects on vibration characteristics of carbon nanotubes are explicitly derived through a complete mechanics analysis. A qualitative validation study shows that the results based on nonlocal continuum mechanics are in agreement with the published experimental reports in this field. Numerical simulations are conducted to quantitatively show the small-scale effect on vibrations of both SWNTs and DWNTs with different lengths and diameters.
On the geometric character of stress in continuum mechanics
Zeitschrift fur Angewandte Mathematik und Physik
58
843-856
2007
10.1007/s00033-007-6141-8
Abstract. This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other fundamental laws of continuum mechanics may be neatly rewritten in terms of this geometric stress. A geometrically attractive and covariant derivation of the balance laws from the principle of energy balance in terms of this stress is presented.
Continuum mechanics; Differential forms; Elasticity; Stress tensor
CERAMIC-TO-METAL BONDING FROM A FRACTURE MECHANICS PERSPECTIVE.
Fracture Mechanics of Ceramics
8
225-238
1986
Preliminary experiments on SiC and Mo beams illustrate the typical fracture mode of ceramic/metal attachments. A finite element model of the experiment confirms the presence of a stress singularity at the bond edge. A fracture mechanics approach is proposed to predict joint feasibility and strength. The approach is illustrated on two simple geometries: plane strain rectangular sections bonded along one edge and butt-to-butt axisymmetric cylinders. A parametric study of these examples provides design guidelines on adherend geometry and elastic properties. The results can also be presented under the form of compatibility maps.
ADHESIVE ENERGY RELEASE; CERAMIC-TO-METAL BONDING; CERAMIC MATERIALS; FRACTURE MECHANICS; MATHEMATICAL TECHNIQUES - Fini
Enhancing an Advanced Engineering Mechanics Course Using MATLAB and Simulink
International Journal of Engineering Education
1-18
2005
An advanced engineering mechanics course teaches students to analyze and model a variety of dynamical systems using Newtonian and Lagrangian mechanics approaches. The modeling task typically produces nonlinear differential equations that are best solved numerically. In order to prepare students to competently solve these systems numerically, the students must master a suitable programming environment. This mastery is achieved incrementally throughout the semester. This paper describes a successful approach to developing the necessary programming skills, culminating in a course project in which the students model a complex dynamical system and produce a graphical animation allowing visualization of dynamical behavior. The paper also describes typical course projects that have been successfully completed by advanced undergraduate and beginning graduate students.
engineering mechanics; matlab; simulink
Nonequilibrium statistical mechanics of swarms of driven particles
Physica A: Statistical Mechanics and its Applications
314
1-4
92-96
2002
10.1002/cplx.10090
We consider here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion. New solutions for the stationary distribution of swarms with linear attraction are given in mean field approximation. These solutions represent: (i) a coherently moving swarm fluctuating around its center and, (ii) a swarm rotating around its center at rest. 2002 Elsevier Science B.V. All rights reserved.
Approximation theory; Brownian movement; Elementary particles; Free energy; High energy physics; Quantum theory; Statistical mechanics
The Mechanics of Fiber Reinforcement of Cement Matrices
ACI Special Publication
44
1-28
1974
10.14359/17884
The various factors which influence the fiber reinforcement of cement\nmatrices are briefly discussed.
Geotechnical engineering beyond soil mechanics; a case study
Canadian Geotechnical Journal = Revue Canadienne de Geotechnique
25
4
637-661
1988
Geotechnical engineering embraces soil mechanics, rock mechanics, and engineering geology. In practice it employs a wide variety of techniques ranging from site mapping and characterization to advanced theoretical analysis and performance monitoring. This paper draws on the development of the Alberta Oil Sands as a case study to illustrate the breadth of application of geotechnical engineering in large-scale resource developments. Detailed discussions are presented on geotechnical contributions to surface mining and slope stability, waste handling and tailings dam construction, and in situ recovery processes.--Modified journal abstract.
Alberta; Athabasca Oil Sands; Canada; dams; engineering geology; liquefaction; mining; monitoring; oil sands; organic residues; pore; pressure; sedimentary rocks; seepage; shear strength; slope; soil mechanics; stability; surface mining; tailings; waste disposal; Western Canada
Unsaturated soil mechanics in earth and rockfill dam engineering
Unsaturated Soils Advances in GeoEngineering Proceedings of the 1st European Conference on Unsaturated Soils EUNSAT 2008
3-32
2008
doi:10.1201/9780203884430.sec1\n10.1201/9780203884430.sec1
The paper examines a few relevant aspects of the design and performance of earth and rockfill dams. It covers the behaviour of compacted soil and rockfill, the generation of pore pressures and deformations during construction, the seepage phenomena during the operation of the dam, the important case of drawdown and a case history of a dam failure at the end of impoundment. It is argued that unsaturated soil mechanics offers today theories, experimental procedures and computational tools which provide a definite advantage over classical design methods. It offers also a new insight into field observations. © 2008 Taylor & Francis Group, London.
dams;rock mechanics;soil mechanics;soils;
A new fracture mechanics theory for orthotropic materials like wood
Engineering Fracture Mechanics
74
5
771-781
2007
10.1016/j.engfracmech.2006.06.015
A new fracture mechanics theory is derived based on a new orthotropic–isotropic transformation of the Airy stress function, making the derivation of the Wu-“mixed mode I–II” fracture criterion possible, based on the failure criterion of a flat elliptic crack. As a result of this derivation, the right fracture energy and theoretical relation between mode I and II stress intensities and energy release rates are obtained.
Energy release rate; Flat elliptic crack; Fracture energy; Linear elastic fracture mechanics; Mixed mode I–II fracture criterion; Orthotropic–isotropic Airy stress-function transfo
Asbestos exposures of mechanics performing clutch service on motor vehicles.
Journal of occupational and environmental hygiene
5
3
148-156
2008
10.1080/15459620701853227
A study was conducted to assess historical asbestos exposures of mechanics performing clutch service on motor vehicles. For most of the 20th century, friction components used in brakes and manual transmission clutches contained approximately 25-60% chrysotile asbestos. Since the late 1960s, asbestos exposure assessment studies conducted on mechanics performing brake service have frequently reported levels below the current OSHA permissible exposure limit (PEL) of 0.1 fiber/cc (flcc). Although there is a robust asbestos exposure data set for mechanics performing brake service, there are almost no data for mechanics removing and replacing clutches in manual transmission vehicles. Personal and area airborne asbestos samples were collected during the removal of asbestos-containing clutches from 15 manual transmissions obtained from salvage facilities by an experienced mechanic. Clutch plates and debris were analyzed for asbestos using EPA and ISO published analytical methods. More than 100 personal and area air samples were collected and analyzed for asbestos fibers using NIOSH methods 7400 and 7402. A separate study involved a telephone survey of 16 automotive mechanics who began work prior to 1975. The mechanics were asked about the duration, frequency, and methods used to perform clutch service. Wear debris in the bell housing surrounding clutches had an average of 0.1% chrysotile asbestos by weight, a value consistent with similar reports of brake debris. Asbestos air sampling data collected averaged 0.047 flcc. Mechanics participating in the telephone survey indicated that clutch service was performed infrequently, the entire clutch assembly was normally replaced, and there was no need to otherwise handle the asbestos-containing clutch plates. These mechanics also confirmed that wet methods were most frequently used to clean debris from the bell housing. Combining the asbestos exposure that occurred when mechanics performed clutch service, along with the duration and frequency of this task, the incremental contribution of this task to mechanics' 8-hr time-weighted average (TWA) asbestos exposures was 0.0016 flcc. Using the range of data inputs that were obtained, the authors calculated a range of TWA exposures of 3.75 x 10(-5) flcc to 0.03 flcc. The mean value of 0.0016 flcc is below background levels of asbestos that have been reported in garages during this time and below the current OSHA PEL of 0.1 flcc.
Nonlinear solid mechanics: A continuum approach for engineering
Work
First Edit
455
2000
10.1023/A:1020843529530
Nonlinear Solid Mechanics a Continuum Approach for Engineering Gerhard A. Holzapfel Graz University of Technology, Austria With a modern, comprehensive approach directed towards computational mechanics, this book covers a unique combination of subjects at present unavailable in any other text. It includes vital information on 'variational principles' constituting the cornerstone of the finite element method. In fact this is the only method by which Nonlinear Solid Mechanics is utilized in engineering practice. The book opens with a fundamental chapter on vectors and tensors. The following chapters are based on nonlinear continuum mechanics - an inevitable prerequisite for computational mechanicians. In addition, continuum field theory (applied to a representative sample of hyperelastic materials currently used in nonlinear computations such as incompressible and compressible materials) is presented, as are transversely isotropic materials, composite materials, viscoelastic materials and hyperelastic materials with isotropic damage. Another central chapter is devoted to the thermodynamics of materials, covering both finite thermoelasticity and finite thermoviscoelasticity. Also included are: an up-to-date list of almost 300 references and a comprehensive index useful examples and exercises for the student selected topics of statistical and continuum thermodynamics. Furthermore, the principle of virtual work (in both the material and spatial descriptions) is compared with two and three-field variational principles particularly designed to capture kinematic constraints such as incompressibility. All of the features combined result in an essential text for final year undergraduates, postgraduates and researchers in mechanical, civil and aerospace engineering and applied maths and physics.
Mechanical properties of thin confined polymer films close to the glass transition in the linear regime of deformation: theory and simulations.
The European physical journal. E, Soft matter
35
7
61
2012
10.1140/epje/i2012-12061-6
Over the past twenty years experiments performed on thin polymer films deposited on substrates have shown that the glass transition temperature T(g) can either decrease or increase depending on the strength of the interactions. Over the same period, experiments have also demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. A model for the dynamics of non-polar polymers, based on percolation of slow subunits, has been proposed and developed over the past ten years. It proposes a unified mechanism regarding these two features. By extending this model, we have developed a 3D model, solved by numerical simulations, in order to describe and calculate the mechanical properties of polymers close to the glass transition in the linear regime of deformation, with a spatial resolution corresponding to the subunit size. We focus on the case of polymers confined between two substrates with non-negligible interactions between the polymer and the substrates, a situation which may be compared to filled elastomers. We calculate the evolution of the elastic modulus as a function of temperature, for different film thicknesses and polymer-substrate interactions. In particular, this allows to calculate the corresponding increase of glass transition temperature, up to 20 K in the considered situations. Moreover, between the bulk T(g) and T(g) + 50 K the modulus of the confined layers is found to decrease very slowly in some cases, with moduli more than ten times larger than that of the pure matrix at temperatures up to T(g) + 50 K. This is consistent with what is observed in reinforced elastomers. This slow decrease of the modulus is accompanied by huge fluctuations of the stress at the scale of a few tens of nanometers that may even be negative as compared to the solicitation, in a way that may be analogous to mechanical heterogeneities observed recently in molecular dynamics simulations. As a consequence, confinement may result not only in an increase of the glass transition temperature, but in a huge broadening of the glass transition.
Quasi-steady spreading of A thin ridge of fluid with temperature-dependent surface tension on A heated or cooled substrate
Quarterly Journal of Mechanics and Applied Mathematics
62
4
365-402
2009
10.1093/qjmam/hbp014
We investigate theoretically the problem of the quasi-steady spreading or contraction of a thin two-dimensional sessile or pendent ridge of viscous fluid with temperature-dependent surface tension on a planar horizontal substrate that is uniformly heated or cooled relative to the atmosphere. We derive an implicit solution of the leading-order thin-film equation for the free-surface profile of the ridge and use this to examine the quasi-steady evolution of the ridge, the dynamics of the moving contact lines being modelled by a 'Tanner law' relating the velocity of the contact line to the contact angle; in particular, we obtain a complete description of the possible forms that the evolution may take. In both the case of a (sessile or pendent) ridge on a heated substrate and the case of a pendent ridge on a cooled substrate when gravitational effects are relatively weak, there is one stable final state to which the ridge may evolve. In the case of a pendent ridge on a cooled substrate when gravitational effects are stronger, there may be one or two stable final states; moreover, the contact angles may vary non-monotonically with time during the evolution to one of these states. In the case of a pendent ridge on a cooled substrate when gravitational effects are even stronger, there may be up to three stable final states with qualitatively different solutions; moreover, the ridge may evolve via an intermediate state from which quasi-steady motion cannot persist, and so there will be a transient non-quasi-steady adjustment (in which the contact angles change rapidly, with the positions of the contact lines unaffected), after which quasi-steady motion is resumed. Lastly, we consider the behaviour of the ridge in the asymptotic limits of strong heating or cooling of the substrate and of strong or weak gravitational effects.
Quantum Mechanics of Black Holes
Physics
52
1994
These lectures give a pedagogical review of dilaton gravity, Hawking radiation, the black hole information problem, and black hole pair creation. (Lectures presented at the 1994 Trieste Summer School in High Energy Physics and Cosmology)
General Relativity and Quantum Cosmology; High Energy Physics - Theory
Bell inequalities and quantum mechanics
American Journal of Physics
70
3
276
2002
10.1119/1.1427311
We employ an arrangement of polarization analyzer loops to derive several simple Bell inequalities\nand then discuss the violation of one of them in light of quantum and classical interpretations of the\ndata recorded.
STATISTICAL-MECHANICS OF HETEROPOLYMER FOLDING
Physica A
185
1-4
98-103
1992
We investigate by Monte Carlo simulation the thermodynamic behavior of a linear heteropolymer in which the interaction between different monomers contains a quenched random component. We show the existence, along with the usual coil and globule ones, of a new phase, the folded phase, characterized by long relaxation times and by the existence of few stable states.
Fractal fluctuations in quantum mechanics
Journal of Modern Optics
49
12
2027-2037
2002
10.1103/PhysRevE.65.015203
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with scattering processes in the presence of strong dynamical localization, thus explaining recent numerical observations of fractality in the latter class of systems. [Journal Article; In English; United States]
Quantum Mechanics of Neutrino Oscillations
Arxiv: hep-ph/0105319
3
1-11
2001
Subtle problems in the theory of neutrino oscillations in vacuum are discussed. It is shown that Lorentz invariance implies that in general flavor neutrinos in oscillation experiments are superpositions of massive neutrinos with different energies and different momenta. It is argued that a wave packet description of massive neutrinos is necessary in order to understand the physics of neutrino oscillations.
High Energy Physics - Phenomenology
Specific mechanics for abutment uprighting.
Australian dental journal
25
5
273-8
1980
General practitioners can use adjunctive orthodontics in preparation for complex comprehensive dental restorative procedures. Two orthodontic educators from opposite sides of the world explain and illustrate the biomechanics of controlled abutment uprighting. Solutions to the common mechanical and clinical problems are discussed.
Biomechanical Phenomena; Dental Abutments; Denture; Fixed; Humans; Orthodontic Appliances; Partial; Tooth Movement; Tooth Movement: methods
Quantum mechanics in curved space
American Journal of Physics
54
827
1986
10.1119/1.14423
The quantum mechanical wave equation for a particle in a Schwarzschild metric is derived using general relativity in the linearized approximation. The significance of the various terms in the effective Hamiltonian is discussed and shown to be associated with the post‐Newtonian terms for the corresponding classical motion.
Fracture mechanics for piezoelectric ceramics
Journal of the Mechanics and Physics of Solids
40
4
739-765
1992
We Study cracks either in piezoelectrics, or on interfaces between piezoelectrics and other materials such as metal electrodes or polymer matrices. The projected applications include ferroelectric actuators operating statically or cyclically, over the major portion of the samples, in the linear regime of the constitutive curve, but the elevated field around defects causes the materials to undergo hysteresis locally. The fracture mechanics viewpoint is adopted--that is, except for a region localized at the crack tip, the materials are taken to be linearly piezoelectric. The problem thus breaks into two subproblems: (i) determining the macroscopic field regarding the crack tip as a physically structureless point, and (ii) considering the hysteresis and other irreversible processes near the crack tip at a relevant microscopic level. The first Subproblem, which prompts a phenomenological fracture theory, receives a thorough investigation in this paper. Griffith's energy accounting is extended to include energy change due to both deformation and polarization. Four modes of square root singularities are identified at the tip of a crack in a homogeneous piezoelectric. A new type of singularity is discovered around interface crack tips. Specifically, the singularities in general form two pairs: r1/2±i[epsilon]and r1/2±i[epsilon], where [epsilon]. and k are real numbers depending on the constitutive constants. Also solved is a class of boundary value problems involving many cracks on the interface between half-spaces. Fracture mechanics are established for ferroelectric ceramics under smallscale hysteresis conditions, which facilitates the experimental study of fracture resistance and fatigue crack growth under combined mechanical and electrical loading. Both poled and unpoled fcrroelectrie ceramics are discussed.
Quantum mechanics with uniform forces
American Journal of Physics
78
12
1361
2010
10.1119/1.3481703
For a nonrelativistic particle acted on by a spatially uniform but possibly time-dependent force, or for a harmonic oscillator also subject to such a uniform force, the wave function differs from that without the force only by a spatial displacement and a phase factor. The shifts in position and phase are simply derived from a solution of the classical equations of motion.
Quantum mechanics of chaotic billiards
Physica D: Nonlinear Phenomena
131
1-4
10
1998
10.1016/S0167-2789(99)00002-0
We study the quantum behaviour of chaotic billiards which exhibit classically diffusive behaviour. In particular we consider the stadium billiard and discuss how the interplay between quantum localization and the rich structure of the classical phase space influences the quantum dynamics. The analysis of this model leads to new insight in the understanding of quantum properties of classically chaotic systems.
Geometric integrators and nonholonomic mechanics
Journal of Mathematical Physics
45
3
22
2002
10.1063/1.1644325
A geometric derivation of nonholonomic integrators is developed. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems. The theoretical methodology and the integrators obtained are, in general, different from the previously obtained.
Quantum mechanics as a statistical theory
Mathematical Proceedings of the Cambridge Philosophical Society
45
01
99-124
1949
10.1017/S0305004100000487
An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the distribution functions of the complete set of dynamical variables specifying a mechanical system (phase-space distributions), which are fundamental in any form of statistical dynamics, are expressed in terms of the wave vectors of quantum theory. This is shown to be equivalent to specifying a theory of functions of non-commuting operators, and may hence be considered as an interpretation of quantum kinematics. In the second part, the laws governing the transformation with time of these phase-space distributions are derived from the equations of motion of quantum dynamics and found to be of the required form for a dynamical stochastic process. It is shown that these phase-space transformation equations can be used as an alternative to the Schr&246;dinger equation in the solution of quantum mechanical problems, such as the evolution with time of wave packets, collision problems and the calculation of transition probabilities in perturbed systems; an approximation method is derived for this purpose. The third part, quantum statistics, deals with the phase-space distribution of members of large assemblies, with a view to applications of quantum mechanics to kinetic theories of matter. Finally, the limitations of the theory, its uniqueness and the possibilities of experimental verification are discussed.
The development of quantum mechanics
Journal of the American Chemical Society
126
20
6224-5
1933
10.1021/ja049281r
Free-energy perturbation (FEP) is considered the most accurate computational method for calculating relative solvation and binding free-energy differences. Despite some success in applying FEP methods to both drug design and lead optimization, FEP calculations are rarely used in the pharmaceutical industry. One factor limiting the use of FEP is its low throughput, which is attributed in part to the dependence of conventional methods on the user's ability to develop accurate molecular mechanics (MM) force field parameters for individual drug candidates and the time required to complete the process. In an attempt to find an FEP method that could eventually be automated, we developed a method that uses quantum mechanics (QM) for treating the solute, MM for treating the solute surroundings, and the FEP method for computing free-energy differences. The thread technique was used in all transformations and proved to be essential for the successful completion of the calculations. Relative solvation free energies for 10 structurally diverse molecular pairs were calculated, and the results were in close agreement with both the calculated results generated by conventional FEP methods and the experimentally derived values. While considerably more CPU demanding than conventional FEP methods, this method (QM/MM-based FEP) alleviates the need for development of molecule-specific MM force field parameters and therefore may enable future automation of FEP-based calculations. Moreover, calculation accuracy should be improved over conventional methods, especially for calculations reliant on MM parameters derived in the absence of experimental data.
Fracture mechanics for piezoelectric ceramics
Journal of the Mechanics and Physics of Solids
40
4
739-765
1992
10.1016/0022-5096(92)90002-J
We Study cracks either in piezoelectrics, or on interfaces between piezoelectrics and other materials such as metal electrodes or polymer matrices. The projected applications include ferroelectric actuators operating statically or cyclically, over the major portion of the samples, in the linear regime of the constitutive curve, but the elevated field around defects causes the materials to undergo hysteresis locally. The fracture mechanics viewpoint is adopted—that is, except for a region localized at the crack tip, the materials are taken to be linearly piezoelectric. The problem thus breaks into two subproblems: (i) determining the macroscopic field regarding the crack tip as a physically structureless point, and (ii) considering the hysteresis and other irreversible processes near the crack tip at a relevant microscopic level. The first Subproblem, which prompts a phenomenological fracture theory, receives a thorough investigation in this paper. Griffith's energy accounting is extended to include energy change due to both deformation and polarization. Four modes of square root singularities are identified at the tip of a crack in a homogeneous piezoelectric. A new type of singularity is discovered around interface crack tips. Specifically, the singularities in general form two pairs: r12±iϵand r12±iϵ, where ϵ. and k are real numbers depending on the constitutive constants. Also solved is a class of boundary value problems involving many cracks on the interface between half-spaces. Fracture mechanics are established for ferroelectric ceramics under smallscale hysteresis conditions, which facilitates the experimental study of fracture resistance and fatigue crack growth under combined mechanical and electrical loading. Both poled and unpoled fcrroelectrie ceramics are discussed.
Statistical mechanics of complex networks
Reviews of modern physics
74
47
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers
Statistical Mechanics of Heteropolymer Folding
Physica A
185
98-103
1992
10.1016/0378-4371(92)90442-S
We investigate by Monte Carlo simulation the thermodynamic behavior of a linear heteropolymer in which the interaction between different monomers contains a quenched random component. We show the existence, along with the usual coil and globule ones, of a new phase, the folded phase, characterized by long relaxation times and by the existence of few stable states.
Noether's theorem in generalized mechanics
Journal of Physics A: Mathematical, Nuclear and General
6
3
299-305
1973
Noether's theorem in the calculus of variations is extended to the\ncase of a lagrangian density containing higher order derivatives.\nIt is then demonstrated how some recently given results of generalized\nmechanics can be seen as consequences of conservation equations resulting\nfrom the extended version of Noether's theorem.
Optimal measurements in quantum mechanics
Physics Letters, Section A: General, Atomic and Solid State Physics
346
1-3
77-86
2005
10.1016/j.physleta.2005.08.003
Four common optimality criteria for measurements are formulated using relations in the set of observables, and their connections are clarified. As case studies, 1-0 observables, localization observables, and photon counting observables are considered. ?? 2005 Elsevier B.V. All rights reserved.
Coarse-graining; Fuzzy observables; Imprecision; Optimality criteria; Quantum measurements; State determination; State distinction
On Fractional Order Quantum Mechanics
International Journal of Nonlinear Science
8
4
469–472
2009
It is argued that fractional order (FO) calculus is more suitable to describe fractal sys- tems. Motivated by the fractal space time theory some fractional generalizations of Scrodinger and Klein-Gordon equations are given. Fractional order calculus naturally includes nonlocality which is a known property of quantum systems.
fractal space time; fractional calculus
New directions in rock mechanics — report on a forum sponsored by the American Rock Mechanics Association
International Journal of Rock Mechanics and Mining Sciences
37
4
683-698
2000
10.1016/S1365-1609(00)00014-9
The American Rock Mechanics Association (ARMA) and the ARMA Foundation sponsored a forum on New Directions for US Rock Mechanics which was held at the Asilomar Conference Center in Pacific Grove, California, USA, during 18–20 October 1998. The goal of the Forum was to focus on: (1) a strategic vision for the future of rock mechanics in the United States; (2) the identification and delineation of critical issues facing the rock mechanics community; (3) the role of research in addressing these issues; and (4) critical areas of research in each of the topic areas addressed at the forum including examples of specific research initiatives. To a large degree, rock mechanics has been used successfully to model and predict the behavior of fractured rock masses for building large structures. However, improvements on present success, and future advances in modeling and construction, are predicated on better characterization of fractured rock masses. This will require increasing emphasis on non-linear and discontinuity-based models to reflect the mechanisms at work in fractured rock masses. For example, relevant characterization schemes, as well as field, laboratory, and logging techniques have yet to be developed for weak rock conditions and for all but the simplest fluid flow conditions. This report summarizes two days of discussion held during the Forum. It was the sense of the Forum participants that fundamental improvements in in situ rock mass characterization is of the utmost importance. Every session emphasized that obtaining valid information from large volumes of rock is the prerequisite for the effective and improved practice of rock mechanics. Research and application of remote imaging and non-destructive evaluation of the subsurface should provide a source of economically realizable data from large volumes of rock. This area should be a primary goal of future research. Associated with the question of site characterization is the degree of uncertainty associated with the data, and with the chosen interpretive model. Forum participants also recommended conducting research to find implementations of stochastic techniques, which would allow uncertainty to be dealt with in a rational manner.
Background Independent Quantum Mechanics and Gravity
Matrix
9
2003
10.1103/PhysRevD.68.061501
We argue that the demand of background independence in a quantum theory of gravity calls for an extension of standard geometric quantum mechanics. We discuss a possible kinematical and dynamical generalization of the latter by way of a quantum covariance of the state space. Specifically, we apply our scheme to the problem of a background independent formulation of Matrix Theory.
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Quantum Physics
From classical to quantum mechanics through optics
European Journal of Physics
31
1
171-192
2010
10.1088/0143-0807/31/1/016
In this paper we revise the main aspects of the Hamiltonian analogy: the fact that optical paths are completely analogous to mechanical trajectories. We follow Schr\"{o}dinger's original idea and go beyond this analogy by changing over from the Hamilton's principal function $S$ to the wave function $\Psi$. We thus travel from classical to quantum mechanics through optics.
Can quantum mechanics help distributed computing?
ACM SIGACT News
39
3
67
2008
10.1145/1412700.1412717
We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of quantum information significantly reduces the need for communication. The main focus of the survey is on communication complexity but we also address other distributed tasks.
Hierarchical modeling in the mechanics of materials
International Journal of Solids and Structures
37
1-2
379-389
2000
10.1016/S0020-7683(99)00095-5
Many problems in the mechanics of materials involve the operation of either multiple spatial or temporal scales simultaneously. As a result, an important thrust of recent work in this area has been the development of methods allowing for the consideration of multiple scales simultaneously. In this paper, we examine hierarchical approaches to modeling problems of this kind with special reference to the way in which information can be fed from one scale to the next in models of plasticity.
Shape Invariant Potentials in “Discrete Quantum Mechanics”
Journal of Nonlinear Mathematical Physics
12
507-521
2005
Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of describing the equilibrium positions of Ruijsenaars-Schneider type systems, which are "discrete" counterparts of Calogero and Sutherland systems, the celebrated exactly solvable multi-particle dynamics. Deformed Hermite and Laguerre polynomials are the typical examples of the eigenfunctions of the above shape invariant discrete quantum mechanical systems.
On the fluid mechanics of bilabial plosives
Speech Communication
22
2-3
155-172
1997
10.1016/S0167-6393(97)00015-0
In this paper we present a review of some fluid mechanical phenomena involved in bilabial plosive sound production. As a basis for further discussion, firstly an in vivo experimental set-up is described. The order of magnitude of some important geometrical and fluid dynamical quantities is presented. Different theoretical flow models are then discussed and evaluated using in vitro measurements on a replica of the lips and using numerical simulations.
Statistical mechanics approach to the phase unwrapping problem
Physica A: Statistical Mechanics and its Applications
276
3
3-4
2000
The use of Mean-Field theory to unwrap principal phase patterns has been recently proposed. In this paper we generalize the Mean-Field approach to process phase patterns with arbitrary degree of undersampling. The phase unwrapping problem is formulated as that of finding the ground state of a locally constrained, finite size, spin-L Ising model under a non-uniform magnetic field. The optimization problem is solved by the Mean-Field Annealing technique. Synthetic experiments show the effectiveness of the proposed algorithm.
An introductory mechanics laboratory at UICC
American Journal of Physics
41
12
1319-1327
1973
10.1119/1.1987565
Discusses the use of a modified air table to conduct laboratory experiments which eschews research-oriented lab experience and concentrates on concepts learned in classroom. Includes a description of apparatus construction, sample instruction sheets, and a list of laboratory concepts with their relationships to classroom materials.
College Science; Instructional Materials; Laboratory Equipment; Laboratory Experiments; Laboratory Procedures; Mechanics (Physics); Physics; Science Activities; Science Education; Scientific Concepts
Hydrogen bonds in molecular mechanics force fields
Peptide Solvation and H-Bonds
72
105-119
2006
10.1016/S0065-3233(05)72004-0
This chapter reviews formulation and parametrization of molecular mechanics force fields with special attention to technical and inherent problems. Most striking among the shortcomings is the inadequacy of the simple point charge description as a means to describe energy and forces of interactions between polar molecules and between polar groups in macromolecules, including hydrogen bonds. The current state of efforts to improve the description of polar interactions is discussed.
amides; backbone; carboxylic-acids; crystals; dynamics; liquid water; peptides; potential functions; proteins; simulations
Several constants arising in statistical mechanics
Annals of Combinatorics
3
2-4
323-335
1999
10.1007/BF01608791
This is a brief survey of certain constants associated with random lattice models, including self-avoiding walks, polyominoes, the Lenz-Ising model, monomers and dimers, ice models, hard squares and hexagons, and percolation models.
A foundational principle for quantum mechanics
Foundations of Physics
29
4
631–643
1999
10.1023/A:1018820410908
In contrast to the theories of relativity, quantum mechanics is not yet based on a generally accepted conceptual foundation. It is proposed here that the missing principle may be identified through the observation that all knowledge in physics has to be expressed in propositions and
The Disconnect Between Quantum Mechanics and Gravity
arXiv preprint arXiv:1011.3719
1-12
2010
There is a serious disconnect between quantum theory and gravity. It occurs at the level of the very foundations of quantum theory, and is far deeper than just the matter of trying to quantize a non-linear theory. We shall examine some of the physical reasons for this disconnect and show how it manifests itself at the beginning, at the level of the equivalence principle.
Cell mechanics: filaminA leads the way.
Current biology : CB
16
9
R326-7
2006
10.1016/j.cub.2006.03.075
Actin filaments are thought to be the major structural components of most eukaryotic cells, but reconstituted actin networks have yet to account for the remarkable strength exhibited by cellular networks. A new study has found that reconstituted networks that include the cross-linker filaminA can replicate many of the mechanical properties of cells if they are stressed prior to mechanical measurement.
Biomechanics; Contractile Proteins; Contractile Proteins: physiology; Microfilament Proteins; Microfilament Proteins: physiology; Microfilaments; Microfilaments: physiology; Stress, Mechanical
Statistical mechanics of random two-player games
Physical Review E
61
3
16
1999
10.1103/PhysRevE.61.2327
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate quantities such as the number of equilibrium points, the expected payoff, and the fraction of strategies played with non-zero probability as a function of the correlation between the payoff matrices of both players and compare the results with numerical simulations.
Graph reconstruction and quantum statistical mechanics
Journal of Geometry and Physics
2013
10.1016/j.geomphys.2013.03.021
We study how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator algebras reconstruct only topological information, but the statistical mechanical point of view allows for complete reconstruction of multigraphs with minimal degree three. ?? 2013 Elsevier B.V.
Graph; Graph C *-algebra; Graph reconstruction; Quantum statistical mechanics
Black hole thermodynamics and statistical mechanics
Physics of Black Holes
89–123
2009
10.1007/978-3-540-88460-6_3
We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also, through a statistical mechanical description, cast light on some of the deep prob- lems of quantizing gravity. In these lectures, I review whatwe currently knowabout black hole thermodynamics and statistical mechanics, suggest a rather speculative “universal” characterization of the underlying states, and describe some key open questions.
Quantum mechanics of fractional-spin particles
Physical Review Letters
49
14
957-959
1982
10.1103/PhysRevLett.49.957
Composites formed from charged particles and vortices in (2+1)-dimensional models, or flux tubes in three-dimensional models, can have any (fractional) angular momentum. The statistics of these objects, like their spin, interpolates continuously between the usual boson and fermion cases. How this works for two-particle quantum mechanics is discussed here.
Particle-hole technique in classical statistical mechanics
Molecular Physics
56
6
1307-1311
1985
10.1080/00268978500103071
For calcns. on classical fluids, a relation between the potential-distribution theory (expressed in terms of particle and hole distributions) and the Percus-Yevick (PY) approxn. was formulated by using rigorous inequalities, which were used to extend the PY approxn. to include triplet and higher-order many-body correlations.
378; body; classical; correlation; distribution; fluid; hole; many; mechanics; particle; Percus; potential; statistical; theory; Yevick
A quantitative test of Gibbs' statistical mechanics
Physics Letters A
207
1-2
42-46
1995
doi: 10.1016/0375-9601(95)00640-O
Tsallis' generalized statistical mechanics (GSM) is used in order to provide us with a test on the validity of the Gibbs-Boltzmann statistics, which constitutes a particular instance of the GSM, attained when the Tsallis parameter q equals unity. From both cosmic background data and the experimental value of the Stefan-Boltzmann constant, global and local bounds upon q are established.
_cleaned_10012013; hardcopyluding
Coherently enhanced measurements in classical mechanics
Quantum Measurements and Quantum Metrology
2
1
44-49
2014
10.2478/qmetro-2014-0003
We show that the recently discovered quantum-enhanced measurement protocol of coherent averaging that is capable of achieving Heisenberg-limited sensitivity without using entanglement, has a classical analogue. The classical protocol uses N harmonic oscillators coupled to a central oscillator and one measures the signal from the latter. We propose an application to the measurement of very weak interactions, and, in particular, a novel route to measuring the gravitational constant with enhanced precision.
Classical statistical mechanics approach to multipartite entanglement
Journal of Physics A: Mathematical and Theoretical
43
22
225303
2010
10.1088/1751-8113/43/22/225303
We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.
Quantum gravity, shadow states, and quantum mechanics
arXiv
gr-qc
2002
A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle. Maxwell fields will be discussed in the second paper of this series which further develops the program and provides details.
gr-qc; hep-th; quant-ph
Meshfree Methods in Computational Stochastic Mechanics
Recent Development inReliability-BasedCivil Engineering
11
187-211
2005
This chapter provides an exposition of stochastic meshfree methods that involves deter- ministic meshfree formulation, spectral representation of random fields, multivariate function decomposition, statistical moment analysis, and reliability analysis. Numer- ical results indicate that stochastic meshfree methods, employed in conjunction with dimension-reduction and decomposition methods, yield accurate and computationally efficient estimates of statistical moments and reliability. Although significant strides have been made, breakthrough research on enhancing speed and robustness of meshfree methods is essential for their successful implementation into stochastic mechanics.
Why Should we Interpret Quantum Mechanics?
Foundations of Physics
34
10
1453-1466
2004
10.1023/B:FOOP.0000044100.95918.b2
The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this epistemic view of states appears to solve foundational problems of quantum mechanics only at the price of being essentially incomplete.
Optical flow estimation in experimental fluid mechanics
Seventh International Symposium on Signal Processing and Its Applications, Vol 1, Proceedings
633-636
2003
We present in this paper a novel approach dedicated to the measurement of velocity in fluid experimental flows. Such information, which is fundamental for specialists, is usually computed by correlation methods on a special kind of images (named PIV). We present here a motion estimation technique which is based on an optical-flow extension. Results are presented on an experimental flow and are compared to those computed with standard methods of the fluid mechanics community.
Entanglement, superselection rules and supersymmetric quantum mechanics
Physics Letters A
378
34
2501-2504
2014
10.1016/j.physleta.2014.07.002
In this paper we show that the energy eigenstates of supersymmetric quantum mechanics (SUSYQM) with non-definite “fermion” number are entangled states. They are “physical states” of the model provided that observables with odd number of spin variables are allowed in the theory like it happens in the Jaynes–Cummings model. Those states generalize the so-called “spin-spring” states of the Jaynes–Cummings model which have played an important role in the study of entanglement.
Quantum Monte Carlo Methods in Statistical Mechanics
ArXiv
11
2000
This paper deals with the optimization of trial states for the computation of dominant eigenvalues of operators and very large matrices. In addition to preliminary results for the energy spectrum of van der Waals clusters, we review results of the application of this method to the computation of relaxation times of independent relaxation modes at the Ising critical point in two dimensions.
chemical physics; computational physics; statistical mechanics
An Introductory Course on Quantum Mechanics
arXiv preprint arXiv:1007.4184
204
2010
This is a very gentle introductory course on quantum mechanics aimed at the first years of the undergraduate level. The basic concepts are introduced, with many applications and illustrations. Contains 12 short chapters of equal length, ideal for a one term course. The license allows reuse of figures and text under the Attribution-Noncommercial-ShareAlike conditions.
{S}tatistical mechanics of a multilayered neural network
Phys. Rev. Lett.
65
18
2312-2315
1990
10.1103/PhysRevLett.65.2312
Statistical mechanics is applied to estimate the maximal information\ncapacity per synapse (?c) of a multilayered feedforward neural network,\nfunctioning as a parity machine. For a large number of hidden units,\nK, the replica-symmetric solution overestimates dramatically the\ncapacity, ?c?K2. However, a one-step replica-symmetry breaking gives\n?c?lnK/ln2, which coincides with a theoretical upper bound. It is\nsuggested that this asymptotic behavior is exact. Results for finite\nK are also discussed.
feed forward network;parity machine;hidden units;r
IToMM-TCRoboticsAnnouncement: Workshop on Robot Mechanics
Secretary
July
1-6
2001
After 30 years of research into the mechanics of robotic systems, this workshop will provide a summing up of the state of the art of modeling and design techniques which can be applied to a large variety of robotic systems. The aim is to obtain a synthesis, from a mechanical viewpoint, of existing solutions, methods and associated tools, and to identify open problems. This workshop will also consider specific problems from recent applications to areas such as surgery and micro-manipulation.
On the algebraic structure of quantum mechanics
Communications in Mathematical Physics
285
262-285
1967
10.1007/BF01646019
We present a reformulation of the axiomatic basis of quantum mechanics with particular reference to the manner in which the usual algebraic structures arise from certain natural physical requirements. Care is taken to distinguish between features of physical significance and those introduced for mathematical convenience. Our conclusion is that the usual algebraic structures cannot be significantly generalised without conflicting with our current experimental picture of processes occurring at the quantum level.
Quantum mechanics in terms of discrete beables
Physical Review A
48
3
1808-1818
1993
10.1103/PhysRevA.48.1808
An interpretation of quantum mechanics in terms of classical concepts, ‘‘beables,’’ due to de Broglie, Bohm, and Bell (BBB) is generalized and further developed. By assuming that all physical quantities take discrete values on sufficiently small scales, we can use this interpretation to give trajectories for all possible quantities, including the position of a particle, its spin, etc. When applied to position, it is shown that, in the continuum limit, this interpretation reduces to the causal one of Bohm. As an illustration, the BBB trajectories are computed explicitly in two simple models.
Wigner and Husimi Functions in Quantum Mechanics
Journal of the Physical Society of Japan
55
3
762-779
1986
10.1143/JPSJ.55.762
The quantum dynamics in Husimi representation is studied for the commutationrelation, time development of distribution function and eigen distribution {function.In} the integrable system, the Husimi eigen distribution function is confined almost onthe classical torus and can be approximated by Gaussian distribution with thevariance {(A4,)'} -h/2 around the torus, Further, considering the correspondence bet-ween quantum and classical mechanics, the Husimi distribution function is a betterrepresentation than the Wigner distribution function, because coarse graining is usual-ly involved in observational process.
Representation
The molecular mechanics of eukaryotic translation
Annual review of biochemistry
73
1
657–704
2004
Great advances have been made in understanding the molecular mechanisc underlying protein sysntesis in bacteria in the past three decades, but our understanding of the correspoinding events in eukaryotic organisms is only beginning to catch up. In this review we describe the current state of our knowledge and ignorance of the molecular mechanics underling eukaryotic translation. We discuss the mechanisms conserved across the three kingdoms of lifs as well as the important divergences that have taken place in the pathway.
Prediction of training performance for diesel mechanics
Swiss Journal of Psychology
62
4
233-240
2003
10.1024/1421-0185.62.4.233
The new systems of electronic fuel injection have changed the content of the job of diesel automotive mechanic. In this article we analyse the predictive value and the adverse impact of a trainability test based on a diesel mechanic minicourse. The minicourse AC had null adverse impact and was significantly related to training performance in the complete 300 hour auto mechanics course. Results are discussed and one promising alternative based on the dynamic assessment notion is suggested
Five-dimensional N=4 supersymmetric mechanics
Arxiv preprint
hep-th
2010
We perform an $su(2)$ Hamiltonian reduction in the bosonic sector of the $su(2)$-invariant action for two free $(4,4,0)$ supermultiplets. As a result, we get the five dimensional \Nf supersymmetric mechanics describing the motion of an isospin carrying particle interacting with a Yang monopole. Some possible generalizations of the action to the cases of systems with a more general bosonic action constructed with the help of the ordinary and twisted \Nf hypermultiplets are considered.
Nano Electro Mechanics of Semiconducting Carbon Nanotube
Journal of Applied Mechanics
69
4
451
2002
10.1115/1.1469003
The effect of a flattening distortion on the electronic properties of a semiconducting carbon nanotube is investigated through first-principles calculations. As a function of the mechanical deformation, electronic bandgap is reduced leading to a semiconductor-metal transition. However, further deformation reopens the bandgap and induces a metal-semiconductor transition. The semiconductormetal transitions take place as a result of curvature-induced hybridization effects, and this finding can be applied to develop novel nano electro mechanical systems.
Application of laser techniques in fluid mechanics
3rd Iberoamerican Optics Meeting and 6th Latin American Meeting on Optics, Lasers, and Their Applications
3572
271-281
1999
Optical methods are used to study the following problems in Fluid Mechanics: a) Propagation of solitary waves in water channels, b) Thermoconvective flow of petroleum-in-water emulsions; c) Flow distribution in combustion chambers; d) Propagation of blood in human veins.
blood flow; combustion analysis; petroleum emulsions; solitons
The mechanics of muscle function in locomotion.
Journal of biomechanics
3
431-451
1970
10.1016/0021-9290(70)90016-3
An engineering analysis has been developed which enables the forces transmitted by the joints of the lower limb to be calculated from experimental data. This paper describes a further extension of the analysis to investigate the mechanics of muscle action in locomotion. The resuits describe the relation of muscle tension to length and velocity and the function of muscle in the production and absorption of energy.
Flow equation for supersymmetric quantum mechanics
Journal of High Energy Physics
2009
03
028-028
2009
10.1088/1126-6708/2009/03/028
We study supersymmetric quantum mechanics with the functional RG formulated in terms of an exact and manifestly off-shell supersymmetric flow equation for the effective action. We solve the flow equation nonperturbatively in a systematic super-covariant derivative expansion and concentrate on systems with unbroken supersymmetry. Already at next-to-leading order, the energy of the first excited state for convex potentials is accurately determined within a 1% error for a wide range of couplings including deeply nonperturbative regimes.
The first law of black brane mechanics
Classical and Quantum Gravity
18
23
5269-5286
2001
10.1088/0264-9381/18/23/320
We obtain ADM and Komar surface integrals for the energy density, tension and angular momentum density of stationary p-brane solutions of Einstein’s equations. We use them to derive a Smarr-type formula for the energy den- sity and thence a first law of black brane mechanics. The intensive variable conjugate to the worldspace p-volume is an ‘effective’ tension that equals the ADM tension for uncharged branes, but vanishes for isotropic boost-invariant charged branes
From Classical to Quantum Mechanics through Optics
0909.3258
2009
doi:10.1088/0143-0807/31/1/016
In this paper we revise the main aspects of the Hamiltonian analogy: the fact that optical paths are completely analogous to mechanical trajectories. We follow Schr\"{o}dinger's original idea and go beyond this analogy by changing over from the Hamilton's principal function $S$ to the wave function $\Psi$. We thus travel from classical to quantum mechanics through optics.
Lie groups and mechanics: an introduction
arXiv
17
2004
10.2991/jnmp.2004.11.4.5
The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and in a third section we apply these methods for the diffeomorphism group of the circle with two particular examples: the Burger equation and the Camassa-Holm equation.
Commission 7: Celestial Mechanics and Dynamical Astronomy
Transactions of the International Astronomical Union, Series B
27
120-122
2010
The meeting began at 11:00 am with a brief address by outgoing president Burns highlighting the most relevant advances in Celestial Mechanics that occurred in the last 3 years.
Comment on momentum in stochastic mechanics
Journal of Mathematical Physics
27
6
1549
1986
10.1063/1.527065
Stochastic mechanics is a probabilistic description of quantum systems in terms of stochastic differential equations. Davidson [M. Davidson, Lett. Math. Phys. 5, 523 (1981)] and de Falco, De Martino, and De Siena [D. de Falco, S. De Martino, and S. De Siena, Lett. Nuovo Cimento 3 6, 457 (1983)] have introduced momentum variables into this scheme. In this paper a discussion of this attempt is presented and some difficulties concerning the physical interpretation are pointed out.
Statistical mechanics of two-dimensional coulomb systems
Physica A: Statistical Mechanics and its Applications
119
441-454
1983
10.1016/0378-4371(83)90102-4
We report the results of molecular dynamics calculations of the two-dimensional one-component plasma with logarithmic interactions between the particles. A solid-fluid transition is observed for Γ = q2kT ≈ 135. The hysteresis observed on traversing the transition region indicates that the transition is first order. The velocity autocorrelation function shows marked oscillations in the strong coupling region, with a frequency, almost independent of Γ, close to the plasma frequency.
Many-Worlds Interpretation of Quantum Mechanics
Stanford Encyclopedia of Philosophy
1-19
2002
The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.
Issues in the statistical mechanics of steady sedimentation
Advances in Physics
50
3
297-341
2001
10.1080/00018730121347
A critical review is presented of recent experimental and theoretical work on the steady sedimentation of particulate suspensions in viscous fluids. The point of view is that of a practitioner of non-equilibrium statistical physics rather than classical fluid mechanics.
III European Conference on Computational Mechanics
III European Conference on Computational Mechanics
755 - 755
2006
10.1007/1-4020-5370-3
This paper discusses the finite element development of a numerical model of 3D elements for Cabril dam, based on the main\n fundamental parameters of the dynamic response of the dam, obtained on several experimental results on ambient vibration tests\n campaigns. These experimental results are used to calibrate the numerical model of 3D finite elements considering two hypothesis\n to simulate the hydrodynamic water pressure: i) first assuming that the is properly simulated through associated water masses,\n in accordance with Westergaard’s formula, and ii) second considering water finite elements.
Masonry Arches: Historical Rules and Modern Mechanics
International Journal of Architectural Heritage
1
2
165-189
2007
10.1080/15583050701312926
Ancient structures have been designed according to semiempirical rules based on a few simplified mechanical principles; nevertheless, their structural performance is rather good in the majority of cases. In this article, the ancient rules for masonry bridges and arches, derived from some historic manuals, are analyzed on the basis of modern mechanics. Some issues on the material mechanical characteristics and on the structural response of masonry arches allow a better understanding of the structural performance and response of old arch structures.
Micro-bead mechanics with actin filaments
Physical Review E
57
2
2091-2094
1998
10.1103/PhysRevE.57.2091
Many experiments have been performed using microscopic beads to probe the small-scale mechanics of actin solutions. We calculate the minimum bead size needed to measure a valid macroscopic response function. We find that the quasi-static response is characterized by an anomalous scaling as a function of the size of the probing particles.
Concepts of coarse graining in quantum mechanics
International Journal of Theoretical Physics
32
12
2261-2269
1993
10.1007/BF00672998
Various procedures of coarse graining in quantum mechanics and their relationships are reviewed. A recently developed notion of relative coarse graining is described which is based on a certain type of classical embedding of quantum states. The ensuing structure of the set of quantum observables is studied. As an application of the new concept an operational classical limit procedure is sketched out.
Chromosome segregation: spindle mechanics come to life.
Current biology : CB
21
18
R688-90
2011
10.1016/j.cub.2011.08.008
Chromosome segregation is a mechanical process, and the spindle generates, and is subject to, mechanical force. A recent study probes how the mechanical architecture of the spindle allows it to maintain mechanical integrity despite these forces.
Animals; Biomechanical Phenomena; Chromosome Segregation; Elasticity; Microtubules; Microtubules: physiology; Spindle Apparatus; Spindle Apparatus: chemistry; Spindle Apparatus: physiology; Xenopus laevis; Xenopus Proteins; Xenopus Proteins: metabolism; Xenopus Proteins: physiology
A time-symmetric formulation of quantum mechanics
Physics Today
63
11
27-32
2010
10.1063/1.3518209
Quantum mechanics allows one to independently select both the initial and final states of a single system. Such pre- and postselection reveals novel effects that challenge our ideas about what time is and how it flows.
On the Unavoidability of the Interpretations of Quantum Mechanics
arXiv preprint arXiv:1211.3883
1-9
2012
10.1119/1.4824797
Recently, the presence in the literature (also recent) of voluminous discussions about the interpretation of quantum mechanics has been labelled as scandalous. We claim that a weak point of the debate which hosted such a conclusion is a lack of a definition of the term "interpretation". In the present note, we would "like to make precise" that meaning and to show how such a clarification is necessary in order to avoid misunderstandings.
A Toy Model for Quantum Mechanics
Foundations of Physics
37
10
1447-1460
2007
10.1007/s10701-007-9171-3
The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.
Quantum Physics
Contact mechanics of wedge and cone indenters
International Journal of Mechanical Sciences
37
3
261-275
1995
10.1016/0020-7403(94)00066-S
Several aspects of the mechanics of indentation of a half-space by an elastic indenter which is either conical or wedge-shaped are addressed. These include elucidation of the contact law, the state of stress induced when the indenter is either pressed normally or sliding with Coulomb friction, the strength of the contact, and the influence of shearing forces less than those necessary to cause sliding, including those induced by elastic mismatch.
Time and Ensemble Averages in Bohmian Mechanics
Physica Scripta
69
2
81-83
2004
10.1238/Physica.Regular.069a00081
We show that in the framework of one-dimensional Bohmian Quantum Mechanics[1], for a particle subject to a potential undergoing a weak adiabatic change, the time averages of the particle's positions typically differ markedly from the ensemble averages. We Apply this result to the case where the weak perturbing potential is the back-action of a measuring device (i.e. a protective measurement). It is shown that under these conditions, most trajectories never cross the position measured (as already shown for a particular example in [3]).
Combinatorial Entropy and the Statistical Mechanics of Polydispersity
Physical Review Letters
80
1369-1372
1998
10.1103/PhysRevLett.80.1369
A new method to treat statistical mechanics in a polydisperse system is described, applicable when the nonideal part of the free energy depends only on a few moments of a size distribution. A simple entropic contribution to the free energy is identified from combinatorial considerations. Although approximate in the general case, the method obtains the exact spinodal curve, critical points, cloud curve, and shadow curve. Polydisperse flory-huggins theory is treated as an example.
Strange Lagrangian systems and statistical mechanics
Journal of Physics A: Mathematical and Theoretical
46
26
265002
2013
10.1088/1751-8113/46/26/265002
We consider the canonical ensemble of $N$ particles admitting a strange Hamiltonian description. Each of the particles obeys a set of Newtonian equation of motion, which can also be described by the standard canonical Hamiltonian mechanics. However, the thermodynamics corresponding to the strange description and canonical description differ drastically from each other. In other words, the strange description and the standard canonical description are inequivalent on the level of thermodynamics.
Some comments on Boltzmann-Gibbs statistical mechanics
Chaos, Solitons & Fractals
6
539-559
1995
10.1016/0960-0779(95)80062-L
A nonexhaustive review is presented of the limits of the impressive and vastly known success of Boltzmann-Gibbs statistics and normal thermodynamics. These limits naturally open the door for the research of generalized formalisms that could enlarge the domain of validity of standard statistical mechanics and thermodynamics. A possible such generalization (recently proposed by the author) is commented along this perspective.
Coherent states in noncommutative quantum mechanics
Journal of Mathematical Physics
50
4
043505
2009
10.1063/1.3105926
Gazeau-Klauder coherent states in noncommutative quantum mechanics are\nconsidered. We find that these states share similar properties to those of\nordinary canonical coherent states in the sense that they saturate the related\nposition uncertainty relation, obey a Poisson distribution and possess a flat\ngeometry. Using the natural isometry between the quantum Hilbert space of\nHilbert Schmidt operators and the tensor product of the classical configuration\nspace and its dual, we reveal the inherent vector feature of these states.
Microprobing the Mechanics of Complex Interconnect Structures
Electronic Components and Technology Conference (ECTC), 2010 Proceedings 60th
1303-1308
2010
10.1109/IITC.2010.5510731
Packaging advanced silicon devices has become increasingly challenging because the effects of stresses exerted on interconnect structures during package assembly and operation are not well understood. In this study, a microprobe metrology system is used to assess the mechanics of these interconnect structures. This allows for a better understanding of the robustness of an interconnect design and the stresses that can be tolerated before damage initiation.
Bader's interatomic surface and Bohmian mechanics
Europhysics Letters
57
January
8
2002
10.1209/epl/i2002-00535-4
A Thomas-Fermi statistical analysis of Bader's interatomic surface developed in a previous work (L.Delle Site, Phys.Lett.A 286 61-64 (2001)) is here extended by considering exchange effects and electron density's inhomogeneity at basic level via Thomas-Fermi-Dirac-Weizsacker model. The results obtained show interesting connections with bohmian mechanics and lead to a statistical interpretation of the chemical properties of condensed systems at atomistic level.
Atoms; Definition; Laplacian; Molecules; Quantum Potential Equivalent; Trajectories
Sensitivity filtering from a continuum mechanics perspective
Structural and Multidisciplinary Optimization
46
4
471-475
2012
10.1007/s00158-012-0814-4
In topology optimization filtering is a popular ap- proach for preventing numerical instabilities. This short note shows that the well-known sensitivity filtering technique, that prevents checkerboards and ensures mesh-independent designs in density-based topology optimization, is equiva- lent to minimizing compliance for nonlocal elasticity prob- lems known from continuum mechanics. Hence, the note resolves the long-standing quest for finding an explanation and physical motivation for the sensitivity filter
Filtering; Regularization; Topology optimization
A Toy Model for Quantum Mechanics
Foundations of Physics
37
10
1447-1460
2007
10.1007/s10701-007-9171-3
The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.
Quantum Physics
Fermionic coordinates and supersymmetry in quantum mechanics
Nuclear Physics B
196
3
509-531
1982
10.1016/0550-3213(82)90505-3
We describe the quantum mechanics of particles with fermionic degrees of freedom, both in the Schrödinger wave function and Feynman path integral formalism. In particular we derive an exact expression for fermionic path integrals in (0 + 1) dimensions. Under suitable circumstances the theories we consider can exhibit supersymmetry. As an application we analyze in detail how the spontaneous breaking of supersymmetry, occurring in certain models recently discussed by Witten, can be derived as an instanton effect in the path integral formalism.
Optimal prediction of stiff oscillatory mechanics.
Proceedings of the National Academy of Sciences of the United States of America
97
12
6253-7
2000
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations that are easier to solve numerically. We demonstrate by examples that optimal prediction can reduce the amount of computation needed to obtain a solution by several orders of magnitude.
Optical flow estimation in experimental fluid mechanics
Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings.
1
2003
10.1109/ISSPA.2003.1224783
In this paper, we present in this paper a novel approach dedicated to the measurement of velocity in fluid experimental flows. Such information, which is fundamental for specialists, is usually computed by correlation methods on a special kind of images (named PIV). We present here a motion estimation technique which is based on an optical-flow extension. Results are presented on an experimental flow and are compared to those computed with standard methods of the fluid mechanics community.
Geometric phase in PT-symmetric quantum mechanics
Physical Review A - Atomic, Molecular, and Optical Physics
82
1
1-4
2010
10.1103/PhysRevA.82.012103
Unitary evolution in PT-symmetric quantum mechanics with a time-dependent metric is found to yield a new class of adiabatic processes. As an explicit example, a Berry-like phase associated with a PT-symmetric two-level system is derived and interpreted as the flux of a fictitious monopole with a tunable charge plus a singular string component with non-trivial phase contributions. The Hermitian analog of our results is also discussed.
Mechanics of cytogels I: Oscillations in Physarum
Cell Motility
4
6
469-503
1984
10.1002/cm.970040606
The contractility of actomyosin gels is the basis for a variety of cellular motility phenomena. We present here a mechanical analysis of contractile gels. By making certain hypotheses on the chemical regulation of cytogel contraction we formulate a model for the rhythmic contractions of plasmodia in the slime mold Physarum polycephalum which is in accord with a number of experimental observations.
actomyosin; cytogel; mechanics; oscillations; physarum
Quantum mechanics of the 1∕x2 potential
American Journal of Physics
74
2
109-117
2006
doi: 10.1119/1.2165248
In quantum mechanics a localized attractive potential typically supports a (possibly infinite) set of bound states, characterized by a discrete spectrum of allowed energies, together with a continuum of scattering states, characterized (in one dimension) by an energy-dependent phase shift. The 1 ∕ x 2 potential on 0 < x < ∞ confounds all of our intuitions and expectations. Resolving its paradoxes requires sophisticated theoretical machinery: regularization, renormalization, anomalous symmetry-breaking, and self-adjoint extensions. Our goal is to introduce the essential ideas at a level accessible to advanced undergraduates.
qm
Quantum mechanics and the social sciences: After hermeneutics
Science & Education
4
127-136
1995
10.1007/BF00486580
Quantum mechanics is interpreted, in the spirit of\nNiels Bohr and Werner Heisenberg, as about physical\nobjects in so far as these are revealed by and within\nthe local, social, and historical process of\nmeasurement. An analysis of the hermeneutical aspect of\nquantum mechanical measurement reveals close analogues\nwith the hermeneutical social/historical sciences. The\nhermeneutical analysis of science requires the move\nfrom the epistemological attitude to an ontological\none.
US research in ice mechanics: 1987–1990
Cold Regions Science and Technology
20
3
231-246
1992
10.1016/0165-232X(92)90031-O
This compilation of US ice mechanics investigations over 1987–1990 focuses on efforts that support the development of our understanding of sea ice interaction. Both ice-structure and ice-ice interaction studies have been included in hopes that insights from one area will complement developments in the other. The work discussed in the area of ice-structure interaction was intentionally limited to lateral movement of the ice against a vertical structure. It is these results that can be most easily extended to ice-ice interaction events.
Subjective and objective probabilities in quantum mechanics
Physical Review A
1-6
2005
10.1103/PhysRevA.71.052107
We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.
Applications of statistical mechanics to finance
Physica A: Statistical Mechanics and its Applications
274
216-221
1999
doi: DOI: 10.1016/S0378-4371(99)00395-7
We discuss some apparently "universal" aspects observed in the empirical analysis of stock price dynamics in financial markets. Specifically we consider (i) the empirical behavior of the return probability density function and (ii) the content of economic information in financial time series. (C) 1999 Elsevier Science B.V. All rights reserved.
econophysics
Problems with the mechanics of industrial robot grippers
Mechanism and Machine Theory
18
4
295-299
1983
10.1016/0094-114X(83)90122-2
The present paper deals with the definition and formalization of the principal problems of gripper mechanics, summarizing the methods of solving these problems and the practical results obtained by the authors in recent years. The starting point is a detailed classification of quality and quantity requirements for the gripper and the schemes of certain elements of the gripper.
Rank-ordering protein-ligand binding affinity by a quantum mechanics/molecular mechanics/Poisson-Boltzmann-surface area model
Journal of Chemical Physics
126
26101
2007
10.1063/1.2423029
The authors describe a quantum mechanics/molecular mechanics/Poisson-Boltzmann-surface area model for rank-ordering protein-ligand binding affinity in aqueous solution. Unlike many classical continuum electrostatics calculations in which the protein and ligand are treated as a uniform dielectric, this model uses quantum mechanics to explicitly describe the electronic polarization of the ligand by its environment. In solving the Poisson-Boltzmann equation, the authors use the quantum mechanical charge density directly rather than the common point-charge approximation. The authors show that useful results can be obtained by using experimental structure, by choosing a protein dielectric constant that is smaller than that typically used in classical electrostatics calculations, and by performing the calculations in a manner that can improve the odds of cancellation of errors.
electrostatics; Protein-ligandInteractions; QuantumMechanics
Fatigue life prediction: A Continuum Damage Mechanics and Fracture Mechanics approach
Materials & Design
35
220-224
2012
10.1016/j.matdes.2011.09.049
Continuum Damage Mechanics (CDM) approach is used to predict crack initiation life and Fracture Mechanics approach predicts crack growth life. Strain controlled fatigue life of a ferrous alloy, EN 19 steel, has been determined using CDM and Fracture Mechanics approach. By combining these two approaches, life could be predicted with damage value in the material. All inputs required for the models have been determined by conducting monotonic, cyclic and fracture tests. Predicted life is also compared by conducting strain controlled fatigue tests. Predicted life in the strain amplitude range of 0.3–0.7% (fatigue life range of 102–105), compares well with the experimental results. All tests have been conducted at specimen level, stress ratio of −1 and at room temperature. The variation of crack initiation and crack propagation life with strain amplitude shows that maximum life is consumed by crack growth process at higher strain amplitude and at lower strain amplitudes, maximum life is spent for crack initiation process.
Fatigue life prediction : A Continuum Damage Mechanics and Fracture Mechanics approach
Materials and Design
35
220-224
2012
10.1016/j.matdes.2011.09.049
Continuum Damage Mechanics (CDM) approach is used to predict crack initiation life and Fracture Mechanics approach predicts crack growth life. Strain controlled fatigue life of a ferrous alloy, EN 19 steel, has been determined using CDM and Fracture Mechanics approach. By combining these two approaches, life could be predicted with damage value in the material. All inputs required for the models have been determined by conducting monotonic, cyclic and fracture tests. Predicted life is also compared by con- ducting strain controlled fatigue tests. Predicted life in the strain amplitude range of 0.3–0.7% (fatigue life range of 102–105), compares well with the experimental results. All tests have been conducted at spec- imen level, stress ratio of 1 and at room temperature. The variation of crack initiation and crack prop- agation life with strain amplitude shows that maximum life is consumed by crack growth process at higher strain amplitude and at lower strain amplitudes, maximum life is spent for crack initiation process.
Ultrafast Quantum Mechanics/Molecular Mechanics Monte Carlo simulations using generalized multipole polarizabilities
Chemical Physics Letters
530
1-9
2012
10.1016/j.cplett.2012.01.008
A fast and accurate Quantum Mechanics/Molecular Mechanics method is described for thermodynamic simulation of solutes (or active sites in flexible molecules) in polar environments. The solute is described quantum mechanically and is held fixed during averaging over solvent configurations, which are described by Molecular Mechanics. Quantum calculations during simulation are replaced by the evaluation of the response of the solute to the long range electric field of the solvent, using precalculated generalized electric moments and polarizabilities. This results in huge decrease of computational time without affecting the accuracy of the QM/MM results. Implementation in a Monte Carlo program accelerated the simulations of guanine and the phenylalanine dipeptide in TIP3P water by over four orders of magnitude. Polarizability is essential for accuracy. Its inclusion decreases the average signed energy error and its standard deviation from 5.69 to 0.003 and 1.22 to 0.013kcal/mol, respectively, for the dipeptide. Hyperpolarizability contributions are insignificant.
Nanotube mechanics - Recent progress in shell buckling mechanics and quantum electromechanical coupling
Composites Science and Technology
66
1141-1150
2006
10.1016/j.compscitech.2005.10.018
In this article, we present recent progress in selected areas of carbon nanotube mechanics. First, we present the authors' experimental work on shell buckling mechanics of multi-walled carbon nanotubes using nanoindentation. A comparison with existing elastic theories showed that the shell theories under-predict the buckling loads by as much as 50%. We then present an investigation of electromechanical coupling in carbon nanotubes by focusing on phonon frequency shifts as a result of charge injection. Raman spectroscopic measurements of the electromechanical couplings under varied but controlled charge injection conditions are analyzed, and the close agreement between the model results and the measured Raman peak shifts suggests that geometrical changes of charged carbon nanotubes previously observed or speculated in different experiments can indeed originate from the simple quantum effects described herein. ?? 2005 Elsevier Ltd. All rights reserved.
A. Carbon nanotube; B. Electromechanical coupling; C. Shell buckling; D. Nanoindentation; D. Uniaxial compression
Protein/ligand binding free energies calculated with quantum mechanics/molecular mechanics.
The journal of physical chemistry. B
109
20
10474-83
2005
10.1021/jp044185y
The calculation of binding affinities for flexible ligands has hitherto required the availability of reliable molecular mechanics parameters for the ligands, a restriction that can in principle be lifted by using a mixed quantum mechanics/molecular mechanics (QM/MM) representation in which the ligand is treated quantum mechanically. The feasibility of this approach is evaluated here, combining QM/MM with the Poisson-Boltzmann/surface area model of continuum solvation and testing the method on a set of 47 benzamidine derivatives binding to trypsin. The experimental range of the absolute binding energy (DeltaG = -3.9 to -7.6 kcal/mol) is reproduced well, with a root-mean-square (RMS) error of 1.2 kcal/mol. When QM/MM is applied without reoptimization to the very different ligands of FK506 binding protein the RMS error is only 0.7 kcal/mol. The results show that QM/MM is a promising new avenue for automated docking and scoring of flexible ligands. Suggestions are made for further improvements in accuracy.
Ligands; Models, Molecular; Protein Binding; Quantum Theory
Relating the Quantum Mechanics of Discrete Systems to Standard Canonical Quantum Mechanics
Foundations of Physics
44
4
406-425
2014
10.1007/s10701-014-9788-y
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible mappings from the position operators q_i and their quantum canonical operators p_i of a canonical theory, onto the discrete, commuting operators Q_i and P_i. In this paper we are particularly interested in harmonic oscillators. In the discrete system, these turn into deterministic models, which is our motivation for this study. We regard the procedure worked out here as a "canonical formalism" for discrete dynamics, and as a stepping stone to handling discrete deterministic systems in a quantum formalism.
Canonical formalisms; Deterministic quantum mechanics; Edge states; Elliptic theta function; Twisted boundary conditions; Unitary mappings
Thin client
CRN
103-104
2000
Mergers and acquisitions have become commonplace in recent years. At the same time, a growing number of companies have begun turning to ASPs to host their critical software. These are two very different trends, but they have one thing in common - both are playing key roles in moving thin clients further into the mainstream as desktop devices. Take Community First Bankshares Inc., for example. The bank is relying on thin-client technology to streamline computing operations in the wake of a surge in growth. The bank's thin-client strategy has been the glue holding the rapidly growing business together, said Bob Thompson, the bank's senior vice president of information systems.
Insights into the mechanism and inhibition of fatty acid amide hydrolase from quantum mechanics/molecular mechanics (QM/MM) modelling.
Biochemical Society transactions
37
Pt 2
363-7
2009
10.1042/BST0370363
FAAH (fatty acid amide hydrolase) is a promising target for the treatment of several central nervous system and peripheral disorders. Combined QM/MM (quantum mechanics/molecular mechanics) calculations have elucidated the role of its unusual catalytic triad in the hydrolysis of oleamide and oleoylmethyl ester substrates, and have identified the productive inhibitor-binding orientation for the carbamoylating compound URB524. These are potentially crucial insights for designing new covalent inhibitors of this drug target.
Amidohydrolases; Amidohydrolases: antagonists & inhibitors; Amidohydrolases: metabolism; Biphenyl Compounds; Biphenyl Compounds: pharmacology; Carbamates; Carbamates: pharmacology; Catalysis; Computer Simulation; Esters; Esters: chemistry; Hydrolysis; Models, Chemical; Oleic Acids; Oleic Acids: chemistry; Quantum Theory
Quantum Mechanics in symmetry language
arXiv
22
2013
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its $L2$ integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.
Pure State Quantum Statistical Mechanics
1003.5058
2010
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement and uncertainty relations. No additional randomness is added by hand and no assumptions about a priori probabilities are made, instead measure concentration results are used to justify the methods of Statistical Physics. The approach explains the applicability of the microcanonical and canonical ensemble and the tendency to equilibrate in a natural way. This work contains a pedagogical review of the existing literature and some new results. The most important of which are: i) A measure theoretic justification for the microcanonical ensemble. ii) Bounds on the subsystem equilibration time. iii) A proof that a generic weak interaction causes decoherence in the energy eigenbasis. iv) A proof of a quantum H-Theorem. v) New estimates of the average effective dimension for initial product states and states from the mean energy ensemble. vi) A proof that time and ensemble averages of observables are typically close to each other. vii) A bound on the fluctuations of the purity of a system coupled to a bath.
Quantum mechanics in phase space
Reports on Mathematical Physics
19
3
361-381
1984
10.1016/0034-4877(84)90008-9
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita’s theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp”( - h) is defined as a tempered distribution. We show that h is in the domain of a generalized Weyl map and define Exp’( - h) as a tempered distribution provided h satisfies a certain semi-boundedness condition. The condition given is linear in h; it coincides with usual boundedness from below if h depends only on one canonical variable. Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations of the twisted structure is added.
Fluid Mechanics and Homeland Security
Annual Review of Fluid Mechanics
38
1
87-110
2006
10.1146/annurev.fluid.38.050304.092111
Homeland security involves many applications of fluid mechanics and offers many opportunities for research and development. This review explores a wide selection of fluids topics in counterterrorism and suggests future directions. Broad topics range from preparedness and deterrence of impending terrorist attacks to detection, response, and recovery. Specific topics include aircraft hardening, blast mitigation, sensors and sampling, explosive detection, microfluidics and labs-on-a-chip, chemical plume dispersal in urban settings, and building ventilation. Also discussed are vapor plumes and standoff detection, nonlethal weapons, airborne disease spread, personal protective equipment, and decontamination. Involvement in these applications requires fluid dynamicists to think across the traditional boundaries of the field and to work with related disciplines, especially chemistry, biology, aerosol science, and atmospheric science.
counterterrorism; explosions; microfluidics; plumes; ventilation
Statistical mechanics of complex networks
arXiv
54
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Adaptation and Self-Organizing Systems; Data Analysis; Disordered Systems and Neural Networks; Mathematical Physics; Networking and Internet Architecture; Statistical Mechanics; Statistics and Probability
Laser Velocimetry in Fluid Mechanics
Laser Velocimetry in Fluid Mechanics
2013
10.1002/9781118569610
In fluid mechanics, velocity measurement is fundamental in order to improve the behavior knowledge of the flow. Velocity maps help us to understand the mean flow structure and its fluctuations, in order to further validate codes. Laser velocimetry is an optical technique for velocity measurements; it is based on light scattering by tiny particles assumed to follow the flow, which allows the local fluid flow velocity and its fluctuations to be determined. It is a widely used non-intrusive technique to measure velocities in fluid flows, either locally or in a map. This book presents the various techniques of laser velocimetry, as well as their specific qualities: local measurements or in plane maps, mean or instantaneous values, 3D measurements. Flow seeding with particles is described with currently used products, as well as the appropriate aerosol generators. Post-processing of data allows us to extract synthetic information from measurements and to perform comparisons with results issued from CFD codes. The principles and characteristics of the different available techniques, all based on the scattering of light by tiny particles embedded in the flow, are described in detail; showing how they deliver different information, either locally or in a map, mean values and turbulence characteristics.
Mathematical Methods of Quantum Mechanics
Physics Today
25
56
1972
10.1063/1.3070894
This manuscript provides a self-contained introduction to math- ematical methods in quantum mechanics (spectral theory) with applications to Schrödinger operators. The first part covers mathematical foundations of quantum mechanics from self-adjointness, the spectral theorem, quantum dynamics (including Stones and the RAGE theorem) to perturbation theory for self-adjoint operators. The second part starts with a detailed study of the free Schrödinger op- erator respectively position, momentum and angular momentum operators. Then we developWeyl-Titchmarsh theory for Sturm-Liouville operators and apply it to spherically symmetric problems, in particular to the hydrogen atom. Next we investigate self-adjointness of atomic Schrödinger operators and their essential spectrum, in particular the HVZ theorem. Finally we have a look at scattering theory and prove asymptotic completeness in the short range case.
Statistical mechanics of complex networks
Rev. Mod. Phys.
74
January
47
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Photoelastic tomography as hybrid mechanics
EPJ Web of Conferences
6
32009, 8
2010
10.1051/epjconf/20100632009
Photoelastic tomography is a non-destructive method of 3D stress analysis. It permits determination of normal stress distribution in an arbitrary section of a 3D test object. In case of axial symmetry also the shear stress distribution can be determined directly from the measurement data. To determine also the other stress components one can use equations of the theory of elasticity. Such a combined application of experimental measurements and numerical handling of the equations of the theory of elasticity is named hybrid mechanics. It is shown that if stresses are due to external loads, the hybrid mechanics algorithm is based on the equations of equilibrium and compatibility. In the case of the measurement of the residual stress in glass the compatibility equation can not be applied. In this case a new relationship of axisymmetric thermoelasticity, the generalized sum rule can be applied.
Quantum mechanics and precision measurements
Physica Scripta
T59
T59
26-28
1995
10.1088/0031-8949/1995/T59/002
The accuracies of measurements of almost all fundamental physical constants have increased by\r factors of about 10 000 during the past 60 years. Although some of the improvements are due to\r greater care, most are due to new techniques based on quantum mechanics. Although the Heisenberg\r Uncertainty Principle often limits measurement accuracies, in many cases the validity of quantum\r mechanics makes possible the vastly improved measurement accuracies. Seven quantum features that\r have a profound influence on the science of measurements are: (1) Existence of discrete quantum\r states of energy. (2) Energy conservation in transitions between two states. (3) Electromagnetic\r radiation of frequency v is quantized with energy hv per quantum. (4) The identity principle. (5)\r The Heisenberg Uncertainty Principle. (6) Addition of probability amplitudes (not probabilities).\r (7) Wave and coherent phase phenomena. Of these seven quantum features, only the Heisenberg\r Uncertainty Principle limits the accuracy of measurements, and its affect is often negligibly small.\r The other six features make possible much more accurate measurements of quantum systems than with\r almost all classical systems. These effects are discussed and illustrated.
Numerical methods in rock mechanics
International Journal of Rock Mechanics and Mining Sciences
2002
10.1016/S1365-1609(02)00065-5
The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures built on and in rock masses, and hence for supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating couplings between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized. Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference list, ‘significant’ references are asterisked and ‘very significant’ references are doubly asterisked.
Consistent interpretations of quantum mechanics
Reviews of Modern Physics
64
2
339-382
1992
10.1103/RevModPhys.64.339
Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.
Handbook of Computational Fluid Mechanics
Handbook of Computational Fluid Mechanics
1-23
1996
10.1016/B978-012553010-1/50002-5
This book discusses the computational fluid mechanics. In this book, many sophisticated notions and methods of numerical analysis and engineering are invoked. Introducing these notions is beyond the scope of this chapter; nor is this chapter written to give basic ideas to a neophyte. Instead, this chapter is intended for the reader who already has some knowledge of the topic. It briefly reviews existing mathematical presumptions for a typical sample of numerical. A few standard references are also mentioned that will help the reader to investigate further. The chapter is restricted to linear scalar partial differential equations and concentrates on approximation questions. The chapter reviews the basic features of several numerical methodologies. It also discusses the answers they propose to the problem of spatial instability. This is illustrated using a model problem of advection-diffusion, and basic ideas and properties of spatially stable advective schemes are especially addressed. It focuses on basic principles and doesn't describe some of new advective schemes involving low transverse numerical diffusion. Little emphasis has also been laid on the important role of the hyperbolic analysis of flow models, leading to flux splitting and fluctuation splitting.
Statistical mechanics of complex networks
Arxiv preprint arXiv:0704.3702
78
2007
The science of complex networks is a new interdisciplinary branch of science which has arisen recently on the interface of physics, biology, social and computer sciences, and others. Its main goal is to discover general laws governing the creation and growth as well as processes taking place on networks, like e.g. the Internet, transportation or neural networks. It turned out that most real-world networks cannot be simply reduced to a compound of some individual components. Fortunately, the statistical mechanics, being one of pillars of modern physics, provides us with a very powerful set of tools and methods for describing and understanding these systems. In this thesis, we would like to present a consistent approach to complex networks based on statistical mechanics, with the central role played by the concept of statistical ensemble of networks. We show how to construct such a theory and present some practical problems where it can be applied. Among them, we pay attention to the problem of finite-size corrections and the dynamics of a simple model of mass transport on networks.
Nine formulations of quantum mechanics
American Journal of Physics
70
3
288
2002
10.1119/1.1445404
Nine formulations of nonrelativistic quantum mechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton–Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.
Statistical mechanics of complex networks
Reviews of Modern Physics
74
47-97
2002
10.1103/revmodphys.74.47
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.
Statistical mechanics of complex networks
Topology
2001
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Adaptation and Self-Organizing Systems; Data Analysis; Disordered Systems and Neural Networks; Mathematical Physics; Networking and Internet Architecture; Statistical Mechanics; Statistics and Probability
Variational Principles in Continuum Mechanics
Proceedings of the Royal Society of London. Series A
305
1
1968
Variational principles for problems in fluid dynamics, plasma dynamics and elasticity are discussed in the context of the general problem of finding a variational principle for a given system of equations. In continuum mechanics, the difficulties arise when the Eulerian description is used; the extension of Hamilton's principle is straightforward in the Lagrangian description. It is found that the solution to these difficulties is to represent the Eulerian velocity v by expressions of the type v = nablaχ + λnablaμ introduced by Clebsch (1859) for the case of isentropic fluid flow. The relation with Hamilton's principle is elucidated following work by Lin (1963). It is also shown that the potential representation of electromagnetic fields and the variational principle for Maxwell's equations can be fitted into the same overall scheme. The equations for water waves, waves in rotating and stratified fluids, Rossby waves, and plasma waves are given particular attention since the need for variational formulations of these equations has arisen in recent work on wave propagation (Whitham 1967). The idea of solving some of the equations by 'potential representations' (such as the Clebsch representation in continuum mechanics and the scalar and vector potentials in electromagnetism), and then finding a variational principle for the remaining equations, seems to be the crucial one for the general problem. An analogy with Pfaff's problem in differential forms is given to support this idea.
Quantum mechanics: Myths and facts
Foundations of Physics
37
1563-1611
2006
10.1007/s10701-007-9176-y
A common understanding of quantum mechanics (QM) among students and practical\nusers is often plagued by a number of "myths", that is, widely accepted claims\non which there is not really a general consensus among experts in foundations\nof QM. These myths include wave-particle duality, time-energy uncertainty\nrelation, fundamental randomness, the absence of measurement-independent\nreality, locality of QM, nonlocality of QM, the existence of well-defined\nrelativistic QM, the claims that quantum field theory (QFT) solves the problems\nof relativistic QM or that QFT is a theory of particles, as well as myths on\nblack-hole entropy. The fact is that the existence of various theoretical and\ninterpretational ambiguities underlying these myths does not yet allow us to\naccept them as proven facts. I review the main arguments and counterarguments\nlying behind these myths and conclude that QM is still a\nnot-yet-completely-understood theory open to further fundamental research.
General Relativity and Quantum Cosmology; High Energy Physics - Theory; Physics Education; Quantum Physics
Statistical mechanics of complex networks
Reviews of modern physics
74
1
54
2002
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Adaptation and Self-Organizing Systems; Data Analysis; Disordered Systems and Neural Networks; Mathematical Physics; Networking and Internet Architecture; Statistical Mechanics; Statistics and Probability
Statistical mechanics of complex networks
Statistical mechanics of complex networks
74
January
48-97
2002
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network’s robustness against failures and attacks.
Statistical mechanics and the ontological interpretation
Foundations of Physics
26
6
823-846
1996
10.1007/BF02058636
To complete our ontological interpretation of quantum theory we have to conclude a treatment of quantum statistical mechanics. The basic concepts in the ontological approach are the particle and the wave function. The density matrix cannot play a fundamental role here. Therefore quantum statistical mechanics will require a further statistical distribution over wave functions in addition to the distribution of particles that have a specified wave function. Ultimately the wave function of the universe will he required, but we show that if the universe in not in thermodynamic equilibrium then it can he treated in terms of weakly interacting large scale constituents that are very nearly independent of each other. In this way we obtain the same results as those of the usual approach within the framework of the ontological interpretation.
Cytoskeletal Mechanics Models and Measurements
Engineering
244
2006
10.1016/S0065-2156(08)70305-3
The purpose of this book is to present a full spectrum of views on current approaches to modeling cell mechanics. In part, this diversity of opinions stems from the different backgrounds of those who have contributed to the field. The authors of this book come from the biophysics, bioengineering, and physical chemistry communities, and each joins the discussion with their own unique perspective on biological systems. Consequently, the approaches range from finite element methods as commonly used in continuum mechanics, to models of the cytoskeleton as a cross-linked polymer network, to models of glassy materials and gels. Studies reflect both the static, instantaneous nature of the structure as well as its dynamic nature due to polymerization and the full array of biological processes. It is unlikely that a single, unifying approach will evolve from this diversity, in part because of the complexity of the phenomena underlying the mechanical properties of the cell. It is our hope, however, that a better appreciation of the various perspectives will lead to a more highly coordinated approach to these essential problems, and might facilitate discussions among those with differing views.
Information {Theory} and {Statistical} {Mechanics}
Phys. Rev.
106
4
620-630
1957
10.1103/PhysRev.106.620
Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available.
Speculative parallel asynchronous contact mechanics
ACM Transactions on …
31
1
2012
10.1145/2366145.2366170
We extend the Asynchronous Contact Mechanics algorithm [Har- mon et al. 2009] and improve its performance by two orders of mag- nitude, using only optimizations that do not compromise ACM’s three guarantees of safety, progress, and correctness. The key to this speedup is replacing ACM’s timid, forward-looking mechanism for detecting collisions—locating and rescheduling separating plane kinetic data structures—with an optimistic speculative method in- spired by Mirtich’s rigid body TimeWarp algorithm [2000]. Time warp allows us to perform collision detection over a windowof time containingmany ofACM’s asynchronous trajectory changes; in this way we cull away large intervals as being collision free. Moreover, by replacing force processing intermingled with KDS rescheduling by windows of pure processing followed by collision detection, we transform an algorithm that is very difficult to parallelize into one that is embarrassingly parallel
collision; contact; parallelization; simulation
Statistical Mechanics of Complex Networks
Reviews of Modern Physics
74
78
2001
10.1103/RevModPhys.74.47
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
Applications of Mathematics; book; Mathematical and Computational Physics; scale-free-networks; Statistical Mechanics of Complex Networks; Theoretical